Research ArticleInternet of Vehicles for E-Health Applications inView of EMI on Medical Sensors

Di Lin1 Xuanli Wu2 Fabrice Labeau3 and Athanasios Vasilakos45

1School of Information and Software Engineering University of Electronic Science and Technology of China Chengdu 610054 China2Communication Technology Research Center Harbin Institute of Technology Harbin 150000 China3Department of Electrical and Computer Engineering McGill University Montreal QC Canada H3A 0G44Department of Computer and Telecommunications Engineering University of Western Macedonia Greece5Lulea University of Technology 193187 Lulea Sweden

Correspondence should be addressed to Di Lin dilin2mailmcgillca

Received 4 December 2014 Revised 17 February 2015 Accepted 19 February 2015

Academic Editor Banshi D Gupta

Copyright copy 2015 Di Lin et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Wireless technologies are pervasive to support ubiquitous healthcare applications However RF transmission in wireless technolo-gies can lead to electromagnetic interference (EMI) onmedical sensors under a healthcare scenario and a high level of EMImay leadto a critical malfunction of medical sensors In view of EMI tomedical sensors we propose a joint power and rate control algorithmunder game theoretic framework to schedule data transmission at each of wireless sensors The objective of such a game is tomaximize the utility of each wireless user subject to the EMI constraints for medical sensorsWe show that the proposed game has auniqueNash equilibrium and our joint power and rate control algorithmwould converge to theNash equilibriumNumerical resultsillustrate that the proposed algorithm can achieve robust performance against the variations of mobile hospital environments

1 Introduction

Recent developments in cellular networks (eg UniversalMobile Telecommunication System UMTS Network) haveenabled the innovative application of E-health anytime andanywhere However RF transmission can result in electro-magnetic interference (EMI) to all of medical sensors anda high level of interference can even cause malfunction ofmedical sensors and potentially injure patients [1 2] Thusthe control of interference (eg through a joint power andrate control) is a critical issue to E-health and should beaddressed under the environment of mobile hospital whichis defined as Internet of vehicles for E-health applications inthis paper So throughout this paper we alternatively use theterms of mobile hospital and Internet of vehicles for E-healthapplications

Soomro and Cavalcanti in [3] address the possibilitiesof using wireless technologies in a medical environmentZhou et al in [4] present the scheduling of heterogeneousdata over body sensor networks Rodrigues et al in [5]present the data visualization for body sensor networks

However the potential EMI problem is not discussed in theseworks Phunchongharn et al in [1 2] present the issue ofEMI under the scenario of a wireless local area network(WLAN) for E-health applications within a hospital but thetechnology of WLAN is not applicable to our scenario inwhich a mobile hospital covers a large-scaled area (eg acity or a town) Thus the model and the power controlalgorithms in [1 2] cannot be directly used in a mobilehospital environment in which our work is interested Jointpower and rate control algorithms for wireless networks arefirstly addressed in [6] However these algorithms allocatepower and rate according to the channel conditions of usersand do not take the potential EMI impact into account Insuch a scenario a wireless user who stays close to a medicalsensor could be allowed to transmit data at a high level ofpower if only the userrsquos communication channel is in goodcondition However the RF transmission at a high level ofpower would influence the operation of medical sensorsSuch an improper power allocation by these algorithms maylead to the malfunction of EMI-sensitive medical sensors sothe aforementioned algorithms cannot be employed under

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 315948 10 pageshttpdxdoiorg1011552015315948

2 Journal of Sensors

the scenario of mobile hospitalThe importance of schedulingwireless transmission under a mobile hospital scenario as wellas the lack of efficient algorithms for transmission schedulingmotivates us to investigate how wireless users can adjusttheir power and data rate to achieve certain goals such asmaximizing the level of their utility while ensuring the minimalamount of EMI on medical sensors over Internet of vehicles forE-health applications

In this paper we address the problem of dynamicallyscheduling wireless transmission for wireless usersrsquo networksunder a mobile hospital environment The objectives of thispaper are to (i) maximize certain goals (eg utility of a game)of each user and (ii) protect themedical sensors fromharmfulinterference In this paper we propose a game of power andrate control in a mobile hospital environment and address arobust joint power and rate control algorithmwhich is shownto converge to the Nash equilibrium of game To the best ofour knowledge this is the first work which presents the jointpower and rate control algorithms under a wireless network forE-health applicationsTheprimary contributions of this paperare (i) addressing the framework of data transmission overInternet of vehicles for E-health applications (ii) establishinga game model of joint power and rate control to minimizethe amount of EMI onmedical sensors (iii) proposing a jointpower and rate control algorithm which can converge to theNash equilibrium of the proposed game

2 Related Work of EMI on Medical Sensors

Theearliest research on EMI in hospital environmentsmainlyfocuses on the immunity of medical equipment to mobilephones Tan and Hinberg in [7] firstly propose that sometypes of medical equipments such as ventilators infusionpumps and ECG monitors are quite sensitive to the EMIfrom cellular phones Then an EMI susceptibility test iscarried out by the Medicines and Healthcare Products Reg-ulatory Agency (MHRA) of UK [8] this test includes testingthe EMI of mobile phones and personal communication net-works The test results show that external pacemakers anes-thesia machines respirators and defibrillators are also sus-ceptible to EMI Trigano et al in [9] and Calcagnini et al in[10] study the EMI ofGSMmobile phones on pacemakers andinfusion pumps respectivelyTheir results show that infusionpumps and pacemakers are inhibited due to the EMI of GSMmobile phonesWith the implementation of 3Gmobile phonesystems in the United States Japan Hong Kong and so forththe research of EMI effects on medical equipments in the3G band has appeared [11 12] In 2007 the InternationalElectrotechnical Committee (IEC) publishes the EN60601-1-2 standard and the immunity levels are recommendedas 3Vm and 10Vm for life-supporting equipment (egblood pressure monitors and infusion pumps) and non-life-supporting equipment (eg defibrillators) respectivelyIn view of the advances of electromagnetic compatibility(EMC) technologies some hospitals in Singapore and theUKrelax the EMI restriction recommended in the EN60601-1-2standard and mobile phones are allowed to be used in someareas of hospitals [13] Tang et al in [14] discuss the EMI testin view of the recently developed EMCofmedical equipment

and the test takes into account the EMI of GSM900 PCS1800and 3G mobile communication systems The testing resultsshow that ECGmonitors radiographic systems audio evokedpotential systems and ultrasonic fetal heart detectors aresensitive to EMI [14] Based on the previous literature it canbe concluded that the medical equipment sensitive to cellularphones includes fetal monitors infusion pumps syringepumps ECG monitors external pacemakers respiratorsanesthesia machines and defibrillators [15]

The other research topics focus on the EMI from deviceswithin a wireless local area network (WLAN) which usuallyworks at the frequency band around 24GHzThis frequencyband is different from the frequency band which mobilephones work at and the amount of EMI on a medicalequipment is related to frequency bands Given these reasonsthe research on EMI in the scenario of wireless healthcaremonitoring starts Krishnamoorthy et al in [16] measurethe EMI on medical equipment from patient and doctordevices which work around the 24GHZ frequency bandsthe measurement is undertaken in two hospitals The resultsshow that the maximal EMI record is 0552Vm whichis within the acceptable EMI range recommended by theEN60601-1-2 standard However the measurement in [16]has not considered the QoS of data transmitted by patientdevices and healthcare staff devices The policy on mobilephone utilization such as turning off mobile phone cannotbe applicable for patient devices and healthcare staff devicesin a wireless healthcare monitoring system [17] In wirelesshealthcare monitoring systems healthcare staff and patientsshould employ wireless devices for data transmission andcommunication and the restriction on transmit power mayreduce the quality of service (QoS) of data transmissionwhich may increase the risk of medical data loss Thereforea contradiction between transmit power restriction and QoSrequirements exists in wireless healthcare monitoring sys-tems In addition when multiple patient devices and health-care staff devices transmit data simultaneously the aggre-gated signals at medical equipment would cause a higherlevel of EMI to medical equipment including life-supportingequipment (eg blood pressure monitors and infusionpumps) and non-life-supporting equipment (eg defibrilla-tors) [1] Phunchongharn et al in [1] discuss the EMI inhospital environments in view of the QoS of patient devicesand healthcare staff devices The conclusion is that EMI onmost medical equipment is within the unacceptable range ifthe transmit power of a WLAN device is larger than 10mW

All the abovementioned researches do not consider thevehicular scenarios for healthcare applications which areinteresting to this paper and thus the medical sensors inthe test may not be vehicle-mounted and wearable medicalsensors In Section 31 we address a detailed experimentwhich includes the test of EMI impact on types of vehicle-mounted and wearable medical sensors

3 Game Model

A typical mobile hospital environment is composed of vehi-cles for E-health applications and these vehicles are mountedwith a fewmedical sensors which can help doctors tomonitor

Journal of Sensors 3

the condition of patients (see Figure 2) On the vehicle for E-health applications doctors healthcare staff and the relativesof patients may use mobile phones due to these two issues(1) doctors and nurses must report the conditions of patientsover phone to the staff in a hospital or in a medical centerto arrange the medical actions which will be taken at thearrival of patients (2) Patients or their relatives need tocontact their family members over mobile phone about thechange of clinical situations as well as important informationHowever the use of mobile phones may lead to EMI impacton nearbymedical sensors [18] EMI refers to the disturbanceof electrical circuits due to electromagnetic induction orelectromagnetic radiationwhich are emitted from an externalsource [19] The disturbance may cause the degradation ofcircuitrsquos performance and the degradation can lead to a totalloss of data

In the following we first present the implementation ofmedical data collection and transmission Then we addressan experiment to show the effects of EMI onmedical sensorsAlso we address the model of EMI impact in this paperas a constraint of outrage-optimization problem which isdetailed in Section 31

31 Implementation of Data Collection and Transmission Thetransmission of data is composed of two layers one layer isfrom sensors to a mobile phone via personal area networks(with the technologies of Bluetooth or Zigbee) within avehicle and the other layer is from a mobile phone on avehicle to the medical center via wide area network (WANeg 3G or 4G networks)The latter layer of data transmissioncan be implemented as regular communicators (eg MSNor Tencent QQ) So we focus on the implementation of theformer layer the data transmission from sensors to a mobilephone Specifically we implement the data collection andtransmission by designing an integrated circuit (IC) whichcan be embedded into a regular mobile phone

By and large the IC (its architecture is shown in Figure 1)is composed of six components namely the microcontrolunit (MCU) the communication module the display mod-ule the data acquisition module the network interface andthe power supply module The data acquisition module ismodified from an off-the-shelf compact module that runsdata acquisition algorithms and this module consists ofa gas-pump unit and a gas pressure sensor The cellularcommunication module takes charge of transmitting theacquired data to a remote data server via wireless networksThe core component of this module is a Subscriber IdentityModel (SIM300C) which enables the data to access bothGSM andGPRS communication networks As the core of ourpatient device MCU would store and run communicationprotocols and control signal processing programs In the ICthe controller we used is MSP430 from Texas Instrumentswhich is widely used for ultra low power applications Inaddition a power supply module offers a stable power supplyto the patient device The display module controls the screenthat shows all the information to the user The interface isresponsible for interaction between a mobile phone and theother phones or computers Specifically an interface could be

Display moduleCommunicationmodule

MCU

moduleBP acquisitionInterface

Power supply module

Figure 1 Architecture of an IC for data collection and transmission

EMI to medical sensors

Mobile station

Ultrasonographysensor

Holter

Ultrasonographysensor

Blood pressure sensor

Blood pressure sensor

Holter

Medical data transmission EMI impact

Vehicle for E-health

Vehicle for E-health

Hospital

Reporting patient condition (talking over phone)

Figure 2 The figure illustrates the Internet of vehicles for E-healthapplications

used either to transfer medical data from sensors to a mobilephone or to debug programs running on the mobile phone

32 Experiment of Testing EMI Effects In this experimentwe test the EMI impact on 50 types of vehicle-mounted andwearable medical sensors from the cellular phones operatedby China Mobile China Unicom China Telecom Thesecellular phones are with the technologies of GSM-9001800CDMA2000 and TD-LTE and their average transmit poweris 08W

4 Journal of Sensors

The test is carried out in an anechoic chamber in order toexclude EMI impact from the other sources of RF emissionsuch as from telecommunication systemsThe test proceduresare detailed as follows (a) tabletop sensors are placed ona table 80 cm above the floor and floor-standing sensorsare placed on the floor Both the tabletop sensors andthe floor sensors are vacillated to simulate the vacillationduring the moving of a vehicle (b) one investigator whooperates a mobile phone controls the maximal power output(08W) while another investigator monitors the workingstatus of medical sensors (c) the mobile phone is graduallybrought closer to the medical sensor If the degradation ofperformance of sensors occurs themobile phone is turned offto check if the performance degradation ceases which showswhether the degradation is reversible or irreversible (d) theEMI impact on medical sensors reversible or irreversibleas well as the distance between medical sensors and mobilephones at the degradation of performance is recorded

Test result shows that EMI from cellular phones causesthe performance degradation of 68 of medical sensorswithin a 2m distance away from the cellular phones Typicaldegradation in the test includes (a) artifact in images ofultrasound sensors (b) noise on biomedical signals such aselectrocardiograph (ECG) and electroencephalogram (EEG)(c) sensor malfunction in infusion pumps syringe pumpsand ventilators (d) change of operating mode of externalpacemakers such as from aynchronized to fixed rate Thisresult is in line with [1 2]

Most of the problems of performance degradation aredue to the component parasitics and it represents the strayreactive elements which have been found in every compo-nent whether a passive or active component Capacitors haveseries inductance which can lead to a series resonant circuitWound inductors have interwinding capacitance which canlead to a parallel resonant circuit These circuits resonate atthe frequencies from 5MHz to 1000MHz Besides the issue ofcomponent parasitics the other issues which may lead to theperformance degradation of medical sensors include groundimpedance poor cable shielding and stray internal couplingpaths [20ndash23]

33 Mobile Hospital Environment A typical mobile hospi-tal environment consists of both life-supporting and non-life-supporting medical sensors either wearable or vehicle-mounted sensors The medical data which are collected bymedical sensors are required to be sent to the doctors whoare staying in a hospital to make the plan of taking actionson the patient once the vehicle arrives at the hospital Alsothe medical staff on the vehicle need to report the conditionof patients over phone to doctors and the use of mobilephone may lead to EMI on medical sensors nearby The life-supporting medical sensors contain electronic componentswhich are sensitive to EMI so they are more sensitive tothe impact of EMI than non-life-supporting sensors Life-supporting medical sensors include wearable pacemakersand non-life-supporting medical sensors include blood pres-sure sensors and Holter for ECG monitoring

Both the abovementioned life-support sensors and non-life-support sensors may have different requirements on

the transmit power of a wireless user to ensure that theuserrsquos RF transmission causes an acceptable level of EMI onmedical sensors The maximal potential transmit power ofeach wireless user should satisfy all of these requirements Tothe best of our knowledge Phunchongharn et al in [1] firstlyaddress how to model the EMI effects on medical sensorsand calculate the maximal potential transmit power of awireless user subject to the EMI constraints Mathematicallythe constraints on transmit power of a wireless user can beshown in (1) for life-support medical sensors and non-life-support medical sensors respectively [1]

sum119894isin119866

1205831radic119875119894

119863119894(119901)

le 119864NLS (119901) for 119901 isin 1198721

sum119894isin119866

1205832radic119875119894

119863119894(119902)

le 119864LS (119902) for 119902 isin 1198722

(1)

where 119864NLS(119901) and 119864LS(119902) are the acceptable EMI levelsfor non-life-support sensor 119901 and life-support sensor 119902respectively 119875

119894is transmit power of wireless user 119894119863

119894(119901) and

119863119894(119902) are the distances between the transmitter of user 119894 and

non-life-support sensor 119901 or life-support sensor 119902 1205831and 120583

2

are constant and their values suggested by IEC 60601-1-2 are7 and 23 respectively [1]119866 represents the set of wireless usersin the Internet of vehicles119872

1represents the set of non-life-

support sensors while 1198722represents the set of life-support

sensorsLet

119860 =

(((((((((((

(

1205831

1198631 (1)

sdot sdot sdot1205831

119863119899 (1)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1205831

1198631(1198981)sdot sdot sdot

1205831

119863119899(1198981)

1205832

1198631 (1)

sdot sdot sdot1205832

119863119899 (1)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1205832

1198631(1198982)sdot sdot sdot

1205832

119863119899(1198982)

)))))))))))

)

(2)

and 119909119894= radic119875119894 we can represent (1) as

119860119883 le 119861 (3)

where1198981is the cardinality of119872

11198982is the cardinality of119872

2

119883 = [1199091 119909

1198981+1198982

]119879 119861 = [119864NLS(1) sdot sdot sdot 119864NLS(1198981) 119864LS(1) sdot sdot sdot

119864LS(1198982)]119879

Remark 1 When the number of rows of 119860 is equal to 119899 thatis1198981+1198982= 119899 then we can obtain the unique solution119883 =

119860minus1119861

Remark 2 When the number of rows of 119860 is less than 119899 thatis1198981+1198982lt 119899 then the linear equation is underdetermined

We select the optimal one from infinite solutions subject tothe maximization of sum

119894isin119866119875119894

Journal of Sensors 5

Remark 3 When the number of rows of 119860 is larger than119899 that is 119898

1+ 1198982

gt 119899 then the linear equation isoverdetermined We relax the constraints of (1) with the bestapproximation that is min

119883|119860119883 minus 119861| So119883 = (119860119879119860)

minus1119860119879119861

Remark 4 Given the set of wireless users 119866 the maximaltransmit power of any wireless user 119894 (denoted as 119875

119894(119866)) can

ensure that all of medical sensors are free from EMI effectswhen 119898

1+ 1198982le 119899 (see Remarks 1 and 2) and also ensure

that the total amount of EMI onmedical sensors isminimizedwhen 119898

1+ 1198982gt 119899 (see Remark 3) since under the latter

scenario the power allocation can ensure min119883|119860119883 minus 119861|

Definition 5 The maximal potential transmit power of user119894 (ie 119875

119894(119866)) to minimize the total amount of EMI on

medical sensors as obtained from Remark 4 is defined asthe maximal effective transmit power (METP) The METP(ie 119875

119894(119866) for user 119894) will be employed to establish the game

model in Section 32 (see Theorem 11) as well as to developthe joint power and rate control algorithm in Section 32 (seeRemark 8)

34 The Game Model In this section considering a cellularnetwork in which wireless users are randomly distributedin the coverage area we address a noncooperative jointtransmit power and rate control game In this game weemploy a commonly used utility which is proposed in [24]and can be characterized as a logarithmic function of powerand rate with a squared pricing item By and large threecommon requirements in wireless communications motivatethe proposal of utility in [24]

(i) Eachwireless user aims to achieve higher level of signalto interference plus noise ratio (SINR) which is defined as

SINR119894=

119875119894ℎ119894119894119877119894

sum119895 =119894119875119895ℎ119895119894+ 119873119894

(4)

where 119875119894and 119877

119894denote the transmit power and data rate

of user 119894 respectively ℎ119895119894

denotes the channel conditionbetween users 119894 and 119895119873

119894denotes the additive white Gaussian

noise(ii) Each wireless user aims to achieve a higher data rate(iii)When the interference level is high eachwireless user

is inclined to increase its power level or decrease its data rateThe proposed utility in [24] can exactly meet the three

common requirements in the wireless communication net-works Mathematically it can be presented as

119894(119875119894 119877119894) = log (120573

1119875119894+ 1205732119877119894) minus

120582

2(1205731

1205732

1198752

119894+1205732

1205731

1198772

119894) (5)

where 120582 is the pricing factor 1205731and 120573

2are adjustable

parametersThe game with utility of (5) can be modeled as

max0le119875119894le119875119894(119866)

119894(119875119894 119877119894) 119894 = 1 2 119873 (6)

where 119875119894(119866) is METP which is defined in Definition 5

Theorem 6 There exists a unique Nash equilibrium in thegame of (6) when 119875

119894(119866) = infin and at the Nash equilibrium

(119875lowast119894 119877lowast119894) the following equations hold

119875lowast

119894= radic

1

2

1205732

1205731120582 119877

lowast

119894= radic

1

2

1205731

1205732120582 (7)

Proof We show that the utility is a jointly concave functionof 119875119894and 119877

119894by calculating its second derivatives that is

1205972119894

1205971198752119894

= minus12057321

(1205731119875119894+ 1205732119877119894)2minus 120582

1205731

1205732

1205972119894

1205971198772119894

= minus1205732

2

(1205731119875119894+ 1205732119877119894)2minus 120582

1205732

1205731

1205972119894

120597119877119894120597119875119894

= minus12057311205732

(1205731119875119894+ 1205732119877119894)2

(8)

It is obvious that 12059721198941205971198752119894

le 0 12059721198941205971198772119894

le 0(12059721198941205971198752

119894)(12059721198941205971198772

119894) minus (1205972119894120597119877119894120597119875119894)2ge 0 are strict inequal-

itiesThus the utility is a strictly concave function on (119875119894 119877119894)

Also the utility is continuous on (119875119894 119877119894) Since the strategy

space of (119875119894 119877119894) is a compact convex and nonempty subset

of two-dimensional Euclidean space of real numbers fromTheorem 12 in [25] the proof of a unique Nash equilibriumof (6) follows

Recall the first derivative of 119906119894with respect to (119875

119894 119877119894) and

write120597119894

120597119875119894

= 0 997888rarr1205732

1205731119875119894+ 1205732119877119894

minus 120582119875119894= 0

120597119894

120597119877119894

= 0 997888rarr1205731

1205731119875119894+ 1205732119877119894

minus 120582119877119894= 0

(9)

We can conclude that the Nash equilibrium (119875lowast119894 119877lowast119894)

satisfies (7)

Remark 7 Theorem 6 indicates the iterative algorithm forupdating (119875

119894 119877119894) [24]

(119875119899+1

119894 119877119899+1

119894) = (IP (119875119899

119894 119877119899

119894) IR (119875119899

119894 119877119899

119894))

IP (119875119899119894 119877119899

119894) = radic

1

2

1205732

1205731120582

IR (119875119899119894 119877119899

119894) = radic

1

2

1205731

1205732120582

(10)

where 119899 denotes the 119899th iteration

The iterative power and rate updating algorithmproposedin [24] does not take into account the METP (119875

119894(119866) =

infin) thus the Nash equilibrium (119875lowast119894 119877lowast119894) could reach above

METP which would cause harmful EMI to medical sensorsIn the following we propose a novel iterative power and rateupdating algorithm to ensure that the proposed algorithmconverges to a fixed point below METP

6 Journal of Sensors

Remark 8 Theorem 6 indicates when 119875119894lt 119875119894(119866) that is the

transmit power of user 119894 is lower than its METP we have119877119894= radic(12)(120573

11205732120582) from (9) when 119875

119894= 119875119894(119866) that is

the transmit power of user 119894 reaches its METP we have 119877119894=

(minus1205731120582119875119894(119866) + radic(120573

1120582119875119894(119866))2+ 412057311205732120582)2120573

2120582 from (9)

35 Joint Power and Control AlgorithmRemark 9 In view of Remark 8 we propose the followingiterative algorithm for updating (119875

119894 119877119894)

(119875119899+1

119894 119877119899+1

119894) = (UP

(119875119899

119894 119877119899

119894) UR

(119875119899

119894 119877119899

119894))

UP(119875119899

119894 119877119899

119894) =

radic1

2

1205732

1205731120582 if 119875119899

119894le 119875119894 (119866)

119875119894 (119866) if 119875119899

119894gt 119875119894 (119866)

UR(119875119899

119894 119877119899

119894) =

radic1

2

1205731

1205732120582

if 119875119899119894le 119875119894 (119866)

minus1205731120582119875119894 (119866) + radic(1205731120582119875119894 (119866))

2

+ 412057311205732120582

21205732120582

if 119875119899119894gt 119875119894 (119866)

(11)

where 119899 denotes the 119899th iteration 119875119894(119866) is defined as

Definition 5

Algorithm in Remark 9 indicates that we force the trans-mit power to be 119875

119894(119866) when 119875119899

119894reaches above 119875

119894(119866) in order

to ensure the minimal amount of EMI on medical sensors

Lemma 10 (Brouwerrsquos Fixed Point Theorem) Let 119878 sube 119877119899 becompact and convex and 119865 119878 rarr 119878 a continuous functionThere exists a 119904 isin 119878 such that 119904 = 119865(119904)

Proof Refer to [26]

Theorem 11 The function UP(119875119899119894 119877119899119894) has a fixed point that

is there exists a power vector Plowast = [1198751 1198752 119875

119872] such that

Plowast = UP(Plowast)

Proof Since the functionUP(119875119899119894 119877119899119894) is a continuous function

of 119875119894 by Brouwerrsquos Fixed Point Theorem in Lemma 10

showing the existence of a fixed point is equal to showing theexistence of a compact and convex set 119878 such that UP 119878 rarr119878 In the following we fabricate such a set

When 119875119899119894le 119875119894(119866) UP(119875119899

119894 119877119899119894) = radic(12)(120573

21205731120582) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 ge 119892119894= radic(12)(119873

1198941205721120582ℎ119894119894)

Let 119892 = min119894119892119894 119897119895

= max119894(ℎ1198951198942120572119894120582ℎ119894119894) and

119897 = max(max119894119892119894max119894119897119894) We have UP(119875119899

119894 119877119899119894) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 le 119892 = radic119872119897 Then we

fabricate the set 119878 = 119892 le 119875119894le max119892 119875119866

119894 such that

UP 119878 rarr 119878 The proof follows

Theorem 11 indicates that a fixed point of UP(119875119899119894 119877119899119894)

always exists In the following we show that its fixed pointis unique and converges to the Nash equilibrium of game (6)

Definition 12 A function 119865(x) is defined as a standardfunction if it satisfies the following three conditions for allx ge 0 (1) positivity 119865(x) ge 0 (2) monotonicity if x1015840 ge xthen 119865(x1015840) ge 119865(x) (3) scalability for all 120575 gt 1 120575119865(x) gt119865(120575x)

Lemma 13 If a standard function has a fixed point then thefixed point is unique Also the standard function will globallyconverge to this unique fixed point

Proof Refer to [26]

Theorem 14 The joint power and rate control algorithm willalways converge to the unique Nash equilibrium of (6)

Proof By [26] if a standard function has a fixed point thenthe fixed point is unique We can easily show thatUP(119875119899

119894 119877119899119894)

is a standard function By Theorem 11 and Lemma 13 thefixed point of UP(119875119899

119894 119877119899119894) is unique

By [26] a standard function globally converges to itsunique fixed point Thus the standard function UP(119875119899

119894 119877119899119894)

will globally converge to its unique fixed point which isalso the Nash equilibrium of game by Remark 8 At theNash equilibrium the data rate and power need to meetthe relationship of (9) (see Theorem 6) and the algorithmin (10) exactly guarantees this relationship between datarate and power Thus the joint power and rate controlalgorithm always converges to the unique Nash equilibriumof game

4 Simulation and Discussion

We gather the data on Internet of vehicles from [27] in whicha connection of network represents a transmit-receive pair ofwireless users In the simulation the vehicle network contains50 nodes and each node has a probability of 01 using themobile phone Please note that in cities when an ambulanceis close to densely populated areas it is possible that 50terminals have EMI impact on medical devices at the sametime The average distance between terminals is 8 metersEach terminal ismovingwith an arbitrary direction at a speedof 10ms (36 kmh) We clarify the characteristics of channelmodels in Section 31 Also we normalize the level of EMI 119864LSor 119864NLS (see (1)) to unity and perform about 100000 Matlab-based experiments to present the results

41 Characteristics of Channel Models We select the com-monly used set of empirical channel models which is speci-fied in ITU-R recommendation M1225 [28] for simulationITU-R M1225 model is applicable for the test scenarios inurban and suburban areas outside the high rise core wherethe buildings are of nearly uniform height [28]

119871 = 40 (1 minus 4 times 10minus3Δℎ) log119877

minus 18 logΔℎ + 21 log119891 + 80(12)

Journal of Sensors 7

Table 1 Parameters of propagationmodels in ITU-R recommenda-tion M1225 [28]

Tap Relative delay (ns) Average power (dB) Doppler spectrum1 0 00 Rayleigh2 310 minus10 Rayleigh3 710 minus90 Rayleigh4 1090 minus100 Rayleigh5 1730 minus150 Rayleigh6 2510 minus200 Rayleigh

where 119877 [km] represents the distance between base stationandmobile station119891 [MHz] represents the carrier frequencyℎ [119898] represents the base station antenna height which ismeasured from the average rooftop level

Each terrestrial test environment can be modelled as achannel impulse response model based on a tapped-delayline The model is characterized by the number of taps thetime delay relative to the first tap the average power relativeto the strongest tap and the Doppler spectrum of each tapA majority of time-delay spreads are relatively small while afew ldquoworst caserdquo multipath characteristics cause much largerdelay spreads Table 1 identifies the propagation model foreach of 6 vehicular test cases In all of these test caseswe consider the strength and relative time delay of signalcomponents as well as Doppler shift and assume that eachof 6 vehicular test cases occurs with the same probabilitySpecifically the primary parameters to characterize each ofpropagation models include

(i) time delay-spread its structure and its statisticalvariability (eg probability distribution of time delayspread)

(ii) multipath fading characteristics (eg Doppler spec-trum Rician versus Rayleigh) for the envelope ofchannels

42 Proposed Algorithm across Networks In this section wecompare the convergence rate of our algorithm (11) under thescenarios of different random networks For simplicity weset 1205731= 1205732= 05 and investigate the convergence rate for

different networksIt is observed from Figure 3 that the algorithm of

(11) under the networks with highly concentrated trans-mitreceive nodes (eg Exponential network) quickly con-verges to the fixed point (with the Intel Core i7-2760QMprocessor the running time of each iteration is around000014 s so the total time of running the algorithm with6000 iterations is 084 s Given that the ambulance is movingat a speed of 10ms the algorithm is feasible when thechannel conditions are assumed to be invariant within adistance of 84m In a fast-varying mobile environment wecan use a more powerful processor to run the algorithm toensure its feasibility) while the algorithmunder the networkswithout highly concentrated transmitreceive nodes (egErdos-Renyi network) converges to the fixed point at a lowrate Indeed the algorithm under the exponential network

0 2 4 6 8 10 12 14 16 18 2005

055

06

065

07

075

08

085

09

Util

ity

Number of iterations (times103)

Figure 3 The figure illustrates the rate of convergence to the fixedpoint of our algorithm under different random networks Blueline with ldquoΔrdquo represents exponential network red line with ldquolowastrdquorepresents preferential attachment (scale-free) network dark linewith ldquoordquo represents Erdos-Renyi network

reaches the fixed point after 7000 iterations while its conver-gence appears after 12000 iterations under the Erdos-Renyinetwork

Another result observed from Figure 3 is that higher util-ity can be achieved by exponential network in which wirelessusers have only a single or few transmitreceive pairs thanby Erdos-Renyi network in which users have multiple trans-mitreceive pairs This is because a user establishs transmit-receive pairs with most of the other users in Erdos-Renyinetwork and thus one data transmission is easily influencedby the interference from the other transmissions However inthe exponential network the users establish transmit-receivepairs with only a single or few other users and they sufferlittle interference from the other transmissions

43 Impact of EMI We first address the advantages of jointpower and rate control to the increase of utility acrosswirelessusers For the comparison of utility between using joint powerand rate control as well as using power or rate control onlywe employ the strategy of power control (proposed in [1] bysetting 119877

119894as a constant) as well as rate control (by setting

119875119894as a constant) as a benchmark Figure 4 implies that the

joint power and rate control can gain a higher average utilitythan only using the control of power or the control of rateshowing the benefits of using joint power and rate control toincrease the utility Also the value of average utility dependson the ratio of 120573

1(1205731+ 1205732) and at the Nash equilibrium of

the game we have 119877119894(119877119894+ 119875119894) = 1205731(1205731+ 1205732) (see Theorem

6) It is also observed from Figure 4 that the value of utilityis symmetric with one peak at 120573

1= 1205732 this is because at

the Nash equilibrium the utility within the strategy spacecan be denoted as log(radic2120573

11205732120582) minus12058222 (by substituting (12)

into (6)) which is symmetric at the peak of 1205731= 1205732when

119875119894le 119875119894(119866)

In the following we address the benefits of using the pro-posed algorithm to the decrease of EMI on medical sensors

8 Journal of Sensors

0 01 02 03 04 05 06 07 08 09 1055

06

065

07

075

08

085

09

095

Util

ity

1205731(1205731 + 1205732)

Figure 4 The figure shows the impact of power and rate control on the utility Blue line with ldquoΔrdquo denotes power control only red line withldquolowastrdquo denotes rate control only dark line with ldquoordquo denotes joint power and rate control

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]Proposed algorithm

1205731(1205731 + 1205732)

EN

LS

(a)

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]

Proposed algorithm

1205731(1205731 + 1205732)

ELS

(b)

Figure 5The figure shows EMI caused by RF transmission using our algorithm versus algorithm in [24] the left shows the EMI on non-life-support sensors while the right shows the EMI on life-support sensors Blue and dashed line represents using algorithm in [24] dark andsolid line represents using our algorithm Line with ldquoΔrdquo represents the case of119898

1+ 1198982gt 119899 line with ldquoordquo represents the case of119898

1+ 1198982le 119899

Figure 5 shows the comparison of EMI on medical sensorscaused by RF transmission between using our proposed algo-rithm (Remark 9) and using the algorithm proposed in [24](Remark 7) Figure 5 implies that our proposed algorithm(EMI level below 01) can dramatically reduce the amount ofEMI on medical sensors compared to the algorithm in [24](EMI level up to 08) Also our algorithm can ensure thatmedical sensors are free from EMI when 119898

1+ 1198982le 119899 and

can ensure the minimal amount of EMI when 1198981+ 1198982gt 119899

To put it another way whenwe need to consider the EMI on alarge number ofmedical sensors (119898

1+1198982gt 119899) our algorithm

can minimize the amount of EMI on medical sensors thoughit cannot keep medical sensors free from EMI as under thescenario of a small number of medical sensors (119898

1+ 1198982le

119899)

5 Conclusions

We addressed a noncooperative game to maximize the utilityof wireless users by controlling their transmit power andrate under a mobile hospital scenario We proposed thejoint power and rate control algorithm and showed thatthe algorithm would globally converge to a unique Nashequilibrium of game Some of the key inferences drawn areas follows

(i) Proposed joint power and rate control algorithmcould dramatically improve the utility of wirelessusers and reduce the amount of EMI on medicalsensors compared to current algorithm in [24] whichis the most widely used power and rate controlalgorithm under nonmedical settings

Journal of Sensors 9

(ii) Under the networks with users who have highlyconcentrated transmitreceive pairs the power andrate control algorithm can converge to the fixed pointat a higher rate than under the networks in whichtransmitreceive pairs are evenly distributed amongwireless users

(iii) Networks with users who have highly concentratedtransmitreceive pairs can achieve a higher utilitythan the networks in which transmitreceive pairs areevenly distributed among wireless users

We are extending our results to the settings in whichwireless users can be of different prioritiesWewould also liketo extendour results to a dynamic setting that is the structureof Internet of vehicles is dynamically changing over time

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by National NaturalScience Foundation of China (no 61301100) and partiallysupported by a Grant from the National High TechnologyResearch and Development Program of China (863 Programno 2012AA02A614)

References

[1] P Phunchongharn D Niyato E Hossain and S CamorlingaldquoAn EMI-aware prioritized wireless access scheme for e-Healthapplications in hospital environmentsrdquo IEEE Transactions onInformation Technology in Biomedicine vol 14 no 5 pp 1247ndash1258 2010

[2] P Phunchongharn E Hossain and S Camorlinga ldquoElec-tromagnetic interference-aware transmission scheduling andpower control for dynamic wireless access in hospital envi-ronmentsrdquo IEEE Transactions on Information Technology inBiomedicine vol 15 no 6 pp 890ndash899 2011

[3] A Soomro and D Cavalcanti ldquoOpportunities and challengesin using WPAN and WLAN technologies in medical environ-mentsrdquo IEEE Communications Magazine vol 45 no 2 pp 114ndash122 2007

[4] L Zhou J Chen B Zhen I de la Torre and SMisra ldquoOn asyn-chronous flow scheduling for wireless body sensor networksrdquoin Proceedings of the 15th IEEE International Conference on e-Health Networking Applications amp Services (Healthcom rsquo13) pp366ndash370 Lisbon Portugal October 2013

[5] J J P C Rodrigues O R E Pereira and P A C S NevesldquoBiofeedback data visualization for body sensor networksrdquoJournal of Network and Computer Applications vol 34 no 1 pp151ndash158 2011

[6] M Hayajneh and C T Abdallah ldquoDistributed joint rate andpower control game-theoretic algorithms for wireless datardquoIEEE Communications Letters vol 8 no 8 pp 511ndash513 2004

[7] K-S Tan and I Hinberg ldquoRadiofrequency susceptibility testson medical equipmentrdquo in Proceedings of the 16th AnnualInternational Conference of the IEEE Engineering in Medicine

and Biology Society Engineering Advances New Opportunitiesfor Biomedical Engineers vol 2 pp 998ndash999 November 1994

[8] ldquoElectromagnetic compatibility of medical devices with mobilecommunicationsrdquo Medical Devices Bulletin DB9702 MedicalDevices Agency London UK 1997

[9] A J Trigano A AzoulayM Rochdi andA Campillo ldquoElectro-magnetic interference of external pacemakers by walkie-talkiesand digital cellular phones experimental studyrdquo Pacing andClinical Electrophysiology vol 22 no 4 pp 588ndash593 1999

[10] G Calcagnini P Bartolini M Floris et al ldquoElectromagneticinterference to infusion pumps from GSM mobile phonesrdquo inProceedings of the 26th Annual International Conference of theIEEE Engineering in Medicine and Biology Society (EMBC rsquo04)vol 2 pp 3515ndash3518 September 2004

[11] Y Chu and A Ganz ldquoA mobile teletrauma system using 3Gnetworksrdquo IEEE Transactions on Information Technology inBiomedicine vol 8 no 4 pp 456ndash462 2004

[12] E A V Navarro J R Mas J F Navajas and C P AlcegaldquoPerformance of a 3G-based mobile telemedicine systemrdquo inProceedings of the 3rd IEEE Consumer Communications andNetworking Conference (CCNC rsquo06) vol 2 pp 1023ndash1027January 2006

[13] E-Health Insider DH to lift hospital mobile phone ban 2007httpwwwe-health-insidercomnewsitemcfmID=2542

[14] C-K Tang K-H Chan L-C Fung and S-W Leung ldquoElectro-magnetic interference immunity testing of medical equipmentto second- and third-generationmobile phonesrdquo IEEE Transac-tions on Electromagnetic Compatibility vol 51 no 3 pp 659ndash664 2009

[15] M Ardavan K Schmitt and C W Trueman ldquoA preliminaryassessment of EMI control policies in hospitalsrdquo in Proceedingsof the 14th International Symposium on Antenna Technology andApplied Electromagnetics and the American ElectromagneticsConference (ANTEMAMEREM rsquo10) pp 1ndash6 July 2010

[16] S Krishnamoorthy J H Reed C R Anderson P M Robertand S Srikanteswara ldquoCharacterization of the 24GHz ISMband electromagnetic interference in a hospital environmentrdquoin Proceedings of the 25th Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society pp 3245ndash3248 September 2003

[17] D Witters and S Seidman ldquoEMC and wireless healthcarerdquo inProceedings of the Asia-Pacific Symposium on ElectromagneticCompatibility 2010

[18] S GMyerson ldquoMobile phones in hospitals are not as hazardousas believed and should be allowed at least in non-clinical areasrdquoThe British Medical Journal vol 326 no 7387 pp 460ndash4612003

[19] F Fiori Integrated Circuit Susceptibility to Conducted RF Inter-ference Compliance Engineering 2014

[20] W D Kimmel and D D Gerke Ten Common EMI Problems inMedical Electronics Medical Electronics Design 2005

[21] G Acampora D J Cook P Rashidi and A V Vasilakos ldquoAsurvey on ambient intelligence in healthcarerdquo Proceedings of theIEEE vol 101 no 12 pp 2470ndash2494 2013

[22] D He C Chen S Chan J Bu and A V Vasilakos ldquoReTrustattack-resistant and lightweight trust management for medicalsensor networksrdquo IEEE Transactions on Information Technologyin Biomedicine vol 16 no 4 pp 623ndash632 2012

[23] N Xiong A V Vasilakos L T Yang et al ldquoComparativeanalysis of quality of service and memory usage for adaptivefailure detectors in healthcare systemsrdquo IEEE Journal on SelectedAreas in Communications vol 27 no 4 pp 495ndash509 2009

10 Journal of Sensors

[24] M R Javan and A R Sharafat ldquoEfficient and distributed SINR-Based joint resource allocation and base station assignment inwireless CDMA networksrdquo IEEE Transactions on Communica-tions vol 59 no 12 pp 3388ndash3399 2011

[25] S Tadelis GameTheory Princeton University Press 2013[26] I Benedetti S Bolognini andAMartellotti ldquoMultivalued fixed

point theoremswithout strong compactness via a generalizationof midpoint convexityrdquo Fixed Point Theory vol 15 no 1 pp 3ndash22 2014

[27] J Leskovec K J LangADasgupta andMWMahoney ldquoCom-munity structure in large networks natural cluster sizes and theabsence of large well-defined clustersrdquo Internet Mathematicsvol 6 no 1 pp 29ndash123 2009

[28] ITU-R Recommendation M1225 Guidelines for Evaluation ofRadio Transmission Technologies for IMT-2000 1997

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RoboticsJournal of

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Active and Passive Electronic Components

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

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Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

2 Journal of Sensors

the scenario of mobile hospitalThe importance of schedulingwireless transmission under a mobile hospital scenario as wellas the lack of efficient algorithms for transmission schedulingmotivates us to investigate how wireless users can adjusttheir power and data rate to achieve certain goals such asmaximizing the level of their utility while ensuring the minimalamount of EMI on medical sensors over Internet of vehicles forE-health applications

In this paper we address the problem of dynamicallyscheduling wireless transmission for wireless usersrsquo networksunder a mobile hospital environment The objectives of thispaper are to (i) maximize certain goals (eg utility of a game)of each user and (ii) protect themedical sensors fromharmfulinterference In this paper we propose a game of power andrate control in a mobile hospital environment and address arobust joint power and rate control algorithmwhich is shownto converge to the Nash equilibrium of game To the best ofour knowledge this is the first work which presents the jointpower and rate control algorithms under a wireless network forE-health applicationsTheprimary contributions of this paperare (i) addressing the framework of data transmission overInternet of vehicles for E-health applications (ii) establishinga game model of joint power and rate control to minimizethe amount of EMI onmedical sensors (iii) proposing a jointpower and rate control algorithm which can converge to theNash equilibrium of the proposed game

2 Related Work of EMI on Medical Sensors

Theearliest research on EMI in hospital environmentsmainlyfocuses on the immunity of medical equipment to mobilephones Tan and Hinberg in [7] firstly propose that sometypes of medical equipments such as ventilators infusionpumps and ECG monitors are quite sensitive to the EMIfrom cellular phones Then an EMI susceptibility test iscarried out by the Medicines and Healthcare Products Reg-ulatory Agency (MHRA) of UK [8] this test includes testingthe EMI of mobile phones and personal communication net-works The test results show that external pacemakers anes-thesia machines respirators and defibrillators are also sus-ceptible to EMI Trigano et al in [9] and Calcagnini et al in[10] study the EMI ofGSMmobile phones on pacemakers andinfusion pumps respectivelyTheir results show that infusionpumps and pacemakers are inhibited due to the EMI of GSMmobile phonesWith the implementation of 3Gmobile phonesystems in the United States Japan Hong Kong and so forththe research of EMI effects on medical equipments in the3G band has appeared [11 12] In 2007 the InternationalElectrotechnical Committee (IEC) publishes the EN60601-1-2 standard and the immunity levels are recommendedas 3Vm and 10Vm for life-supporting equipment (egblood pressure monitors and infusion pumps) and non-life-supporting equipment (eg defibrillators) respectivelyIn view of the advances of electromagnetic compatibility(EMC) technologies some hospitals in Singapore and theUKrelax the EMI restriction recommended in the EN60601-1-2standard and mobile phones are allowed to be used in someareas of hospitals [13] Tang et al in [14] discuss the EMI testin view of the recently developed EMCofmedical equipment

and the test takes into account the EMI of GSM900 PCS1800and 3G mobile communication systems The testing resultsshow that ECGmonitors radiographic systems audio evokedpotential systems and ultrasonic fetal heart detectors aresensitive to EMI [14] Based on the previous literature it canbe concluded that the medical equipment sensitive to cellularphones includes fetal monitors infusion pumps syringepumps ECG monitors external pacemakers respiratorsanesthesia machines and defibrillators [15]

The other research topics focus on the EMI from deviceswithin a wireless local area network (WLAN) which usuallyworks at the frequency band around 24GHzThis frequencyband is different from the frequency band which mobilephones work at and the amount of EMI on a medicalequipment is related to frequency bands Given these reasonsthe research on EMI in the scenario of wireless healthcaremonitoring starts Krishnamoorthy et al in [16] measurethe EMI on medical equipment from patient and doctordevices which work around the 24GHZ frequency bandsthe measurement is undertaken in two hospitals The resultsshow that the maximal EMI record is 0552Vm whichis within the acceptable EMI range recommended by theEN60601-1-2 standard However the measurement in [16]has not considered the QoS of data transmitted by patientdevices and healthcare staff devices The policy on mobilephone utilization such as turning off mobile phone cannotbe applicable for patient devices and healthcare staff devicesin a wireless healthcare monitoring system [17] In wirelesshealthcare monitoring systems healthcare staff and patientsshould employ wireless devices for data transmission andcommunication and the restriction on transmit power mayreduce the quality of service (QoS) of data transmissionwhich may increase the risk of medical data loss Thereforea contradiction between transmit power restriction and QoSrequirements exists in wireless healthcare monitoring sys-tems In addition when multiple patient devices and health-care staff devices transmit data simultaneously the aggre-gated signals at medical equipment would cause a higherlevel of EMI to medical equipment including life-supportingequipment (eg blood pressure monitors and infusionpumps) and non-life-supporting equipment (eg defibrilla-tors) [1] Phunchongharn et al in [1] discuss the EMI inhospital environments in view of the QoS of patient devicesand healthcare staff devices The conclusion is that EMI onmost medical equipment is within the unacceptable range ifthe transmit power of a WLAN device is larger than 10mW

All the abovementioned researches do not consider thevehicular scenarios for healthcare applications which areinteresting to this paper and thus the medical sensors inthe test may not be vehicle-mounted and wearable medicalsensors In Section 31 we address a detailed experimentwhich includes the test of EMI impact on types of vehicle-mounted and wearable medical sensors

3 Game Model

A typical mobile hospital environment is composed of vehi-cles for E-health applications and these vehicles are mountedwith a fewmedical sensors which can help doctors tomonitor

Journal of Sensors 3

the condition of patients (see Figure 2) On the vehicle for E-health applications doctors healthcare staff and the relativesof patients may use mobile phones due to these two issues(1) doctors and nurses must report the conditions of patientsover phone to the staff in a hospital or in a medical centerto arrange the medical actions which will be taken at thearrival of patients (2) Patients or their relatives need tocontact their family members over mobile phone about thechange of clinical situations as well as important informationHowever the use of mobile phones may lead to EMI impacton nearbymedical sensors [18] EMI refers to the disturbanceof electrical circuits due to electromagnetic induction orelectromagnetic radiationwhich are emitted from an externalsource [19] The disturbance may cause the degradation ofcircuitrsquos performance and the degradation can lead to a totalloss of data

In the following we first present the implementation ofmedical data collection and transmission Then we addressan experiment to show the effects of EMI onmedical sensorsAlso we address the model of EMI impact in this paperas a constraint of outrage-optimization problem which isdetailed in Section 31

31 Implementation of Data Collection and Transmission Thetransmission of data is composed of two layers one layer isfrom sensors to a mobile phone via personal area networks(with the technologies of Bluetooth or Zigbee) within avehicle and the other layer is from a mobile phone on avehicle to the medical center via wide area network (WANeg 3G or 4G networks)The latter layer of data transmissioncan be implemented as regular communicators (eg MSNor Tencent QQ) So we focus on the implementation of theformer layer the data transmission from sensors to a mobilephone Specifically we implement the data collection andtransmission by designing an integrated circuit (IC) whichcan be embedded into a regular mobile phone

By and large the IC (its architecture is shown in Figure 1)is composed of six components namely the microcontrolunit (MCU) the communication module the display mod-ule the data acquisition module the network interface andthe power supply module The data acquisition module ismodified from an off-the-shelf compact module that runsdata acquisition algorithms and this module consists ofa gas-pump unit and a gas pressure sensor The cellularcommunication module takes charge of transmitting theacquired data to a remote data server via wireless networksThe core component of this module is a Subscriber IdentityModel (SIM300C) which enables the data to access bothGSM andGPRS communication networks As the core of ourpatient device MCU would store and run communicationprotocols and control signal processing programs In the ICthe controller we used is MSP430 from Texas Instrumentswhich is widely used for ultra low power applications Inaddition a power supply module offers a stable power supplyto the patient device The display module controls the screenthat shows all the information to the user The interface isresponsible for interaction between a mobile phone and theother phones or computers Specifically an interface could be

Display moduleCommunicationmodule

MCU

moduleBP acquisitionInterface

Power supply module

Figure 1 Architecture of an IC for data collection and transmission

EMI to medical sensors

Mobile station

Ultrasonographysensor

Holter

Ultrasonographysensor

Blood pressure sensor

Blood pressure sensor

Holter

Medical data transmission EMI impact

Vehicle for E-health

Vehicle for E-health

Hospital

Reporting patient condition (talking over phone)

Figure 2 The figure illustrates the Internet of vehicles for E-healthapplications

used either to transfer medical data from sensors to a mobilephone or to debug programs running on the mobile phone

32 Experiment of Testing EMI Effects In this experimentwe test the EMI impact on 50 types of vehicle-mounted andwearable medical sensors from the cellular phones operatedby China Mobile China Unicom China Telecom Thesecellular phones are with the technologies of GSM-9001800CDMA2000 and TD-LTE and their average transmit poweris 08W

4 Journal of Sensors

The test is carried out in an anechoic chamber in order toexclude EMI impact from the other sources of RF emissionsuch as from telecommunication systemsThe test proceduresare detailed as follows (a) tabletop sensors are placed ona table 80 cm above the floor and floor-standing sensorsare placed on the floor Both the tabletop sensors andthe floor sensors are vacillated to simulate the vacillationduring the moving of a vehicle (b) one investigator whooperates a mobile phone controls the maximal power output(08W) while another investigator monitors the workingstatus of medical sensors (c) the mobile phone is graduallybrought closer to the medical sensor If the degradation ofperformance of sensors occurs themobile phone is turned offto check if the performance degradation ceases which showswhether the degradation is reversible or irreversible (d) theEMI impact on medical sensors reversible or irreversibleas well as the distance between medical sensors and mobilephones at the degradation of performance is recorded

Test result shows that EMI from cellular phones causesthe performance degradation of 68 of medical sensorswithin a 2m distance away from the cellular phones Typicaldegradation in the test includes (a) artifact in images ofultrasound sensors (b) noise on biomedical signals such aselectrocardiograph (ECG) and electroencephalogram (EEG)(c) sensor malfunction in infusion pumps syringe pumpsand ventilators (d) change of operating mode of externalpacemakers such as from aynchronized to fixed rate Thisresult is in line with [1 2]

Most of the problems of performance degradation aredue to the component parasitics and it represents the strayreactive elements which have been found in every compo-nent whether a passive or active component Capacitors haveseries inductance which can lead to a series resonant circuitWound inductors have interwinding capacitance which canlead to a parallel resonant circuit These circuits resonate atthe frequencies from 5MHz to 1000MHz Besides the issue ofcomponent parasitics the other issues which may lead to theperformance degradation of medical sensors include groundimpedance poor cable shielding and stray internal couplingpaths [20ndash23]

33 Mobile Hospital Environment A typical mobile hospi-tal environment consists of both life-supporting and non-life-supporting medical sensors either wearable or vehicle-mounted sensors The medical data which are collected bymedical sensors are required to be sent to the doctors whoare staying in a hospital to make the plan of taking actionson the patient once the vehicle arrives at the hospital Alsothe medical staff on the vehicle need to report the conditionof patients over phone to doctors and the use of mobilephone may lead to EMI on medical sensors nearby The life-supporting medical sensors contain electronic componentswhich are sensitive to EMI so they are more sensitive tothe impact of EMI than non-life-supporting sensors Life-supporting medical sensors include wearable pacemakersand non-life-supporting medical sensors include blood pres-sure sensors and Holter for ECG monitoring

Both the abovementioned life-support sensors and non-life-support sensors may have different requirements on

the transmit power of a wireless user to ensure that theuserrsquos RF transmission causes an acceptable level of EMI onmedical sensors The maximal potential transmit power ofeach wireless user should satisfy all of these requirements Tothe best of our knowledge Phunchongharn et al in [1] firstlyaddress how to model the EMI effects on medical sensorsand calculate the maximal potential transmit power of awireless user subject to the EMI constraints Mathematicallythe constraints on transmit power of a wireless user can beshown in (1) for life-support medical sensors and non-life-support medical sensors respectively [1]

sum119894isin119866

1205831radic119875119894

119863119894(119901)

le 119864NLS (119901) for 119901 isin 1198721

sum119894isin119866

1205832radic119875119894

119863119894(119902)

le 119864LS (119902) for 119902 isin 1198722

(1)

where 119864NLS(119901) and 119864LS(119902) are the acceptable EMI levelsfor non-life-support sensor 119901 and life-support sensor 119902respectively 119875

119894is transmit power of wireless user 119894119863

119894(119901) and

119863119894(119902) are the distances between the transmitter of user 119894 and

non-life-support sensor 119901 or life-support sensor 119902 1205831and 120583

2

are constant and their values suggested by IEC 60601-1-2 are7 and 23 respectively [1]119866 represents the set of wireless usersin the Internet of vehicles119872

1represents the set of non-life-

support sensors while 1198722represents the set of life-support

sensorsLet

119860 =

(((((((((((

(

1205831

1198631 (1)

sdot sdot sdot1205831

119863119899 (1)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1205831

1198631(1198981)sdot sdot sdot

1205831

119863119899(1198981)

1205832

1198631 (1)

sdot sdot sdot1205832

119863119899 (1)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1205832

1198631(1198982)sdot sdot sdot

1205832

119863119899(1198982)

)))))))))))

)

(2)

and 119909119894= radic119875119894 we can represent (1) as

119860119883 le 119861 (3)

where1198981is the cardinality of119872

11198982is the cardinality of119872

2

119883 = [1199091 119909

1198981+1198982

]119879 119861 = [119864NLS(1) sdot sdot sdot 119864NLS(1198981) 119864LS(1) sdot sdot sdot

119864LS(1198982)]119879

Remark 1 When the number of rows of 119860 is equal to 119899 thatis1198981+1198982= 119899 then we can obtain the unique solution119883 =

119860minus1119861

Remark 2 When the number of rows of 119860 is less than 119899 thatis1198981+1198982lt 119899 then the linear equation is underdetermined

We select the optimal one from infinite solutions subject tothe maximization of sum

119894isin119866119875119894

Journal of Sensors 5

Remark 3 When the number of rows of 119860 is larger than119899 that is 119898

1+ 1198982

gt 119899 then the linear equation isoverdetermined We relax the constraints of (1) with the bestapproximation that is min

119883|119860119883 minus 119861| So119883 = (119860119879119860)

minus1119860119879119861

Remark 4 Given the set of wireless users 119866 the maximaltransmit power of any wireless user 119894 (denoted as 119875

119894(119866)) can

ensure that all of medical sensors are free from EMI effectswhen 119898

1+ 1198982le 119899 (see Remarks 1 and 2) and also ensure

that the total amount of EMI onmedical sensors isminimizedwhen 119898

1+ 1198982gt 119899 (see Remark 3) since under the latter

scenario the power allocation can ensure min119883|119860119883 minus 119861|

Definition 5 The maximal potential transmit power of user119894 (ie 119875

119894(119866)) to minimize the total amount of EMI on

medical sensors as obtained from Remark 4 is defined asthe maximal effective transmit power (METP) The METP(ie 119875

119894(119866) for user 119894) will be employed to establish the game

model in Section 32 (see Theorem 11) as well as to developthe joint power and rate control algorithm in Section 32 (seeRemark 8)

34 The Game Model In this section considering a cellularnetwork in which wireless users are randomly distributedin the coverage area we address a noncooperative jointtransmit power and rate control game In this game weemploy a commonly used utility which is proposed in [24]and can be characterized as a logarithmic function of powerand rate with a squared pricing item By and large threecommon requirements in wireless communications motivatethe proposal of utility in [24]

(i) Eachwireless user aims to achieve higher level of signalto interference plus noise ratio (SINR) which is defined as

SINR119894=

119875119894ℎ119894119894119877119894

sum119895 =119894119875119895ℎ119895119894+ 119873119894

(4)

where 119875119894and 119877

119894denote the transmit power and data rate

of user 119894 respectively ℎ119895119894

denotes the channel conditionbetween users 119894 and 119895119873

119894denotes the additive white Gaussian

noise(ii) Each wireless user aims to achieve a higher data rate(iii)When the interference level is high eachwireless user

is inclined to increase its power level or decrease its data rateThe proposed utility in [24] can exactly meet the three

common requirements in the wireless communication net-works Mathematically it can be presented as

119894(119875119894 119877119894) = log (120573

1119875119894+ 1205732119877119894) minus

120582

2(1205731

1205732

1198752

119894+1205732

1205731

1198772

119894) (5)

where 120582 is the pricing factor 1205731and 120573

2are adjustable

parametersThe game with utility of (5) can be modeled as

max0le119875119894le119875119894(119866)

119894(119875119894 119877119894) 119894 = 1 2 119873 (6)

where 119875119894(119866) is METP which is defined in Definition 5

Theorem 6 There exists a unique Nash equilibrium in thegame of (6) when 119875

119894(119866) = infin and at the Nash equilibrium

(119875lowast119894 119877lowast119894) the following equations hold

119875lowast

119894= radic

1

2

1205732

1205731120582 119877

lowast

119894= radic

1

2

1205731

1205732120582 (7)

Proof We show that the utility is a jointly concave functionof 119875119894and 119877

119894by calculating its second derivatives that is

1205972119894

1205971198752119894

= minus12057321

(1205731119875119894+ 1205732119877119894)2minus 120582

1205731

1205732

1205972119894

1205971198772119894

= minus1205732

2

(1205731119875119894+ 1205732119877119894)2minus 120582

1205732

1205731

1205972119894

120597119877119894120597119875119894

= minus12057311205732

(1205731119875119894+ 1205732119877119894)2

(8)

It is obvious that 12059721198941205971198752119894

le 0 12059721198941205971198772119894

le 0(12059721198941205971198752

119894)(12059721198941205971198772

119894) minus (1205972119894120597119877119894120597119875119894)2ge 0 are strict inequal-

itiesThus the utility is a strictly concave function on (119875119894 119877119894)

Also the utility is continuous on (119875119894 119877119894) Since the strategy

space of (119875119894 119877119894) is a compact convex and nonempty subset

of two-dimensional Euclidean space of real numbers fromTheorem 12 in [25] the proof of a unique Nash equilibriumof (6) follows

Recall the first derivative of 119906119894with respect to (119875

119894 119877119894) and

write120597119894

120597119875119894

= 0 997888rarr1205732

1205731119875119894+ 1205732119877119894

minus 120582119875119894= 0

120597119894

120597119877119894

= 0 997888rarr1205731

1205731119875119894+ 1205732119877119894

minus 120582119877119894= 0

(9)

We can conclude that the Nash equilibrium (119875lowast119894 119877lowast119894)

satisfies (7)

Remark 7 Theorem 6 indicates the iterative algorithm forupdating (119875

119894 119877119894) [24]

(119875119899+1

119894 119877119899+1

119894) = (IP (119875119899

119894 119877119899

119894) IR (119875119899

119894 119877119899

119894))

IP (119875119899119894 119877119899

119894) = radic

1

2

1205732

1205731120582

IR (119875119899119894 119877119899

119894) = radic

1

2

1205731

1205732120582

(10)

where 119899 denotes the 119899th iteration

The iterative power and rate updating algorithmproposedin [24] does not take into account the METP (119875

119894(119866) =

infin) thus the Nash equilibrium (119875lowast119894 119877lowast119894) could reach above

METP which would cause harmful EMI to medical sensorsIn the following we propose a novel iterative power and rateupdating algorithm to ensure that the proposed algorithmconverges to a fixed point below METP

6 Journal of Sensors

Remark 8 Theorem 6 indicates when 119875119894lt 119875119894(119866) that is the

transmit power of user 119894 is lower than its METP we have119877119894= radic(12)(120573

11205732120582) from (9) when 119875

119894= 119875119894(119866) that is

the transmit power of user 119894 reaches its METP we have 119877119894=

(minus1205731120582119875119894(119866) + radic(120573

1120582119875119894(119866))2+ 412057311205732120582)2120573

2120582 from (9)

35 Joint Power and Control AlgorithmRemark 9 In view of Remark 8 we propose the followingiterative algorithm for updating (119875

119894 119877119894)

(119875119899+1

119894 119877119899+1

119894) = (UP

(119875119899

119894 119877119899

119894) UR

(119875119899

119894 119877119899

119894))

UP(119875119899

119894 119877119899

119894) =

radic1

2

1205732

1205731120582 if 119875119899

119894le 119875119894 (119866)

119875119894 (119866) if 119875119899

119894gt 119875119894 (119866)

UR(119875119899

119894 119877119899

119894) =

radic1

2

1205731

1205732120582

if 119875119899119894le 119875119894 (119866)

minus1205731120582119875119894 (119866) + radic(1205731120582119875119894 (119866))

2

+ 412057311205732120582

21205732120582

if 119875119899119894gt 119875119894 (119866)

(11)

where 119899 denotes the 119899th iteration 119875119894(119866) is defined as

Definition 5

Algorithm in Remark 9 indicates that we force the trans-mit power to be 119875

119894(119866) when 119875119899

119894reaches above 119875

119894(119866) in order

to ensure the minimal amount of EMI on medical sensors

Lemma 10 (Brouwerrsquos Fixed Point Theorem) Let 119878 sube 119877119899 becompact and convex and 119865 119878 rarr 119878 a continuous functionThere exists a 119904 isin 119878 such that 119904 = 119865(119904)

Proof Refer to [26]

Theorem 11 The function UP(119875119899119894 119877119899119894) has a fixed point that

is there exists a power vector Plowast = [1198751 1198752 119875

119872] such that

Plowast = UP(Plowast)

Proof Since the functionUP(119875119899119894 119877119899119894) is a continuous function

of 119875119894 by Brouwerrsquos Fixed Point Theorem in Lemma 10

showing the existence of a fixed point is equal to showing theexistence of a compact and convex set 119878 such that UP 119878 rarr119878 In the following we fabricate such a set

When 119875119899119894le 119875119894(119866) UP(119875119899

119894 119877119899119894) = radic(12)(120573

21205731120582) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 ge 119892119894= radic(12)(119873

1198941205721120582ℎ119894119894)

Let 119892 = min119894119892119894 119897119895

= max119894(ℎ1198951198942120572119894120582ℎ119894119894) and

119897 = max(max119894119892119894max119894119897119894) We have UP(119875119899

119894 119877119899119894) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 le 119892 = radic119872119897 Then we

fabricate the set 119878 = 119892 le 119875119894le max119892 119875119866

119894 such that

UP 119878 rarr 119878 The proof follows

Theorem 11 indicates that a fixed point of UP(119875119899119894 119877119899119894)

always exists In the following we show that its fixed pointis unique and converges to the Nash equilibrium of game (6)

Definition 12 A function 119865(x) is defined as a standardfunction if it satisfies the following three conditions for allx ge 0 (1) positivity 119865(x) ge 0 (2) monotonicity if x1015840 ge xthen 119865(x1015840) ge 119865(x) (3) scalability for all 120575 gt 1 120575119865(x) gt119865(120575x)

Lemma 13 If a standard function has a fixed point then thefixed point is unique Also the standard function will globallyconverge to this unique fixed point

Proof Refer to [26]

Theorem 14 The joint power and rate control algorithm willalways converge to the unique Nash equilibrium of (6)

Proof By [26] if a standard function has a fixed point thenthe fixed point is unique We can easily show thatUP(119875119899

119894 119877119899119894)

is a standard function By Theorem 11 and Lemma 13 thefixed point of UP(119875119899

119894 119877119899119894) is unique

By [26] a standard function globally converges to itsunique fixed point Thus the standard function UP(119875119899

119894 119877119899119894)

will globally converge to its unique fixed point which isalso the Nash equilibrium of game by Remark 8 At theNash equilibrium the data rate and power need to meetthe relationship of (9) (see Theorem 6) and the algorithmin (10) exactly guarantees this relationship between datarate and power Thus the joint power and rate controlalgorithm always converges to the unique Nash equilibriumof game

4 Simulation and Discussion

We gather the data on Internet of vehicles from [27] in whicha connection of network represents a transmit-receive pair ofwireless users In the simulation the vehicle network contains50 nodes and each node has a probability of 01 using themobile phone Please note that in cities when an ambulanceis close to densely populated areas it is possible that 50terminals have EMI impact on medical devices at the sametime The average distance between terminals is 8 metersEach terminal ismovingwith an arbitrary direction at a speedof 10ms (36 kmh) We clarify the characteristics of channelmodels in Section 31 Also we normalize the level of EMI 119864LSor 119864NLS (see (1)) to unity and perform about 100000 Matlab-based experiments to present the results

41 Characteristics of Channel Models We select the com-monly used set of empirical channel models which is speci-fied in ITU-R recommendation M1225 [28] for simulationITU-R M1225 model is applicable for the test scenarios inurban and suburban areas outside the high rise core wherethe buildings are of nearly uniform height [28]

119871 = 40 (1 minus 4 times 10minus3Δℎ) log119877

minus 18 logΔℎ + 21 log119891 + 80(12)

Journal of Sensors 7

Table 1 Parameters of propagationmodels in ITU-R recommenda-tion M1225 [28]

Tap Relative delay (ns) Average power (dB) Doppler spectrum1 0 00 Rayleigh2 310 minus10 Rayleigh3 710 minus90 Rayleigh4 1090 minus100 Rayleigh5 1730 minus150 Rayleigh6 2510 minus200 Rayleigh

where 119877 [km] represents the distance between base stationandmobile station119891 [MHz] represents the carrier frequencyℎ [119898] represents the base station antenna height which ismeasured from the average rooftop level

Each terrestrial test environment can be modelled as achannel impulse response model based on a tapped-delayline The model is characterized by the number of taps thetime delay relative to the first tap the average power relativeto the strongest tap and the Doppler spectrum of each tapA majority of time-delay spreads are relatively small while afew ldquoworst caserdquo multipath characteristics cause much largerdelay spreads Table 1 identifies the propagation model foreach of 6 vehicular test cases In all of these test caseswe consider the strength and relative time delay of signalcomponents as well as Doppler shift and assume that eachof 6 vehicular test cases occurs with the same probabilitySpecifically the primary parameters to characterize each ofpropagation models include

(i) time delay-spread its structure and its statisticalvariability (eg probability distribution of time delayspread)

(ii) multipath fading characteristics (eg Doppler spec-trum Rician versus Rayleigh) for the envelope ofchannels

42 Proposed Algorithm across Networks In this section wecompare the convergence rate of our algorithm (11) under thescenarios of different random networks For simplicity weset 1205731= 1205732= 05 and investigate the convergence rate for

different networksIt is observed from Figure 3 that the algorithm of

(11) under the networks with highly concentrated trans-mitreceive nodes (eg Exponential network) quickly con-verges to the fixed point (with the Intel Core i7-2760QMprocessor the running time of each iteration is around000014 s so the total time of running the algorithm with6000 iterations is 084 s Given that the ambulance is movingat a speed of 10ms the algorithm is feasible when thechannel conditions are assumed to be invariant within adistance of 84m In a fast-varying mobile environment wecan use a more powerful processor to run the algorithm toensure its feasibility) while the algorithmunder the networkswithout highly concentrated transmitreceive nodes (egErdos-Renyi network) converges to the fixed point at a lowrate Indeed the algorithm under the exponential network

0 2 4 6 8 10 12 14 16 18 2005

055

06

065

07

075

08

085

09

Util

ity

Number of iterations (times103)

Figure 3 The figure illustrates the rate of convergence to the fixedpoint of our algorithm under different random networks Blueline with ldquoΔrdquo represents exponential network red line with ldquolowastrdquorepresents preferential attachment (scale-free) network dark linewith ldquoordquo represents Erdos-Renyi network

reaches the fixed point after 7000 iterations while its conver-gence appears after 12000 iterations under the Erdos-Renyinetwork

Another result observed from Figure 3 is that higher util-ity can be achieved by exponential network in which wirelessusers have only a single or few transmitreceive pairs thanby Erdos-Renyi network in which users have multiple trans-mitreceive pairs This is because a user establishs transmit-receive pairs with most of the other users in Erdos-Renyinetwork and thus one data transmission is easily influencedby the interference from the other transmissions However inthe exponential network the users establish transmit-receivepairs with only a single or few other users and they sufferlittle interference from the other transmissions

43 Impact of EMI We first address the advantages of jointpower and rate control to the increase of utility acrosswirelessusers For the comparison of utility between using joint powerand rate control as well as using power or rate control onlywe employ the strategy of power control (proposed in [1] bysetting 119877

119894as a constant) as well as rate control (by setting

119875119894as a constant) as a benchmark Figure 4 implies that the

joint power and rate control can gain a higher average utilitythan only using the control of power or the control of rateshowing the benefits of using joint power and rate control toincrease the utility Also the value of average utility dependson the ratio of 120573

1(1205731+ 1205732) and at the Nash equilibrium of

the game we have 119877119894(119877119894+ 119875119894) = 1205731(1205731+ 1205732) (see Theorem

6) It is also observed from Figure 4 that the value of utilityis symmetric with one peak at 120573

1= 1205732 this is because at

the Nash equilibrium the utility within the strategy spacecan be denoted as log(radic2120573

11205732120582) minus12058222 (by substituting (12)

into (6)) which is symmetric at the peak of 1205731= 1205732when

119875119894le 119875119894(119866)

In the following we address the benefits of using the pro-posed algorithm to the decrease of EMI on medical sensors

8 Journal of Sensors

0 01 02 03 04 05 06 07 08 09 1055

06

065

07

075

08

085

09

095

Util

ity

1205731(1205731 + 1205732)

Figure 4 The figure shows the impact of power and rate control on the utility Blue line with ldquoΔrdquo denotes power control only red line withldquolowastrdquo denotes rate control only dark line with ldquoordquo denotes joint power and rate control

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]Proposed algorithm

1205731(1205731 + 1205732)

EN

LS

(a)

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]

Proposed algorithm

1205731(1205731 + 1205732)

ELS

(b)

Figure 5The figure shows EMI caused by RF transmission using our algorithm versus algorithm in [24] the left shows the EMI on non-life-support sensors while the right shows the EMI on life-support sensors Blue and dashed line represents using algorithm in [24] dark andsolid line represents using our algorithm Line with ldquoΔrdquo represents the case of119898

1+ 1198982gt 119899 line with ldquoordquo represents the case of119898

1+ 1198982le 119899

Figure 5 shows the comparison of EMI on medical sensorscaused by RF transmission between using our proposed algo-rithm (Remark 9) and using the algorithm proposed in [24](Remark 7) Figure 5 implies that our proposed algorithm(EMI level below 01) can dramatically reduce the amount ofEMI on medical sensors compared to the algorithm in [24](EMI level up to 08) Also our algorithm can ensure thatmedical sensors are free from EMI when 119898

1+ 1198982le 119899 and

can ensure the minimal amount of EMI when 1198981+ 1198982gt 119899

To put it another way whenwe need to consider the EMI on alarge number ofmedical sensors (119898

1+1198982gt 119899) our algorithm

can minimize the amount of EMI on medical sensors thoughit cannot keep medical sensors free from EMI as under thescenario of a small number of medical sensors (119898

1+ 1198982le

119899)

5 Conclusions

We addressed a noncooperative game to maximize the utilityof wireless users by controlling their transmit power andrate under a mobile hospital scenario We proposed thejoint power and rate control algorithm and showed thatthe algorithm would globally converge to a unique Nashequilibrium of game Some of the key inferences drawn areas follows

(i) Proposed joint power and rate control algorithmcould dramatically improve the utility of wirelessusers and reduce the amount of EMI on medicalsensors compared to current algorithm in [24] whichis the most widely used power and rate controlalgorithm under nonmedical settings

Journal of Sensors 9

(ii) Under the networks with users who have highlyconcentrated transmitreceive pairs the power andrate control algorithm can converge to the fixed pointat a higher rate than under the networks in whichtransmitreceive pairs are evenly distributed amongwireless users

(iii) Networks with users who have highly concentratedtransmitreceive pairs can achieve a higher utilitythan the networks in which transmitreceive pairs areevenly distributed among wireless users

We are extending our results to the settings in whichwireless users can be of different prioritiesWewould also liketo extendour results to a dynamic setting that is the structureof Internet of vehicles is dynamically changing over time

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by National NaturalScience Foundation of China (no 61301100) and partiallysupported by a Grant from the National High TechnologyResearch and Development Program of China (863 Programno 2012AA02A614)

References

[1] P Phunchongharn D Niyato E Hossain and S CamorlingaldquoAn EMI-aware prioritized wireless access scheme for e-Healthapplications in hospital environmentsrdquo IEEE Transactions onInformation Technology in Biomedicine vol 14 no 5 pp 1247ndash1258 2010

[2] P Phunchongharn E Hossain and S Camorlinga ldquoElec-tromagnetic interference-aware transmission scheduling andpower control for dynamic wireless access in hospital envi-ronmentsrdquo IEEE Transactions on Information Technology inBiomedicine vol 15 no 6 pp 890ndash899 2011

[3] A Soomro and D Cavalcanti ldquoOpportunities and challengesin using WPAN and WLAN technologies in medical environ-mentsrdquo IEEE Communications Magazine vol 45 no 2 pp 114ndash122 2007

[4] L Zhou J Chen B Zhen I de la Torre and SMisra ldquoOn asyn-chronous flow scheduling for wireless body sensor networksrdquoin Proceedings of the 15th IEEE International Conference on e-Health Networking Applications amp Services (Healthcom rsquo13) pp366ndash370 Lisbon Portugal October 2013

[5] J J P C Rodrigues O R E Pereira and P A C S NevesldquoBiofeedback data visualization for body sensor networksrdquoJournal of Network and Computer Applications vol 34 no 1 pp151ndash158 2011

[6] M Hayajneh and C T Abdallah ldquoDistributed joint rate andpower control game-theoretic algorithms for wireless datardquoIEEE Communications Letters vol 8 no 8 pp 511ndash513 2004

[7] K-S Tan and I Hinberg ldquoRadiofrequency susceptibility testson medical equipmentrdquo in Proceedings of the 16th AnnualInternational Conference of the IEEE Engineering in Medicine

and Biology Society Engineering Advances New Opportunitiesfor Biomedical Engineers vol 2 pp 998ndash999 November 1994

[8] ldquoElectromagnetic compatibility of medical devices with mobilecommunicationsrdquo Medical Devices Bulletin DB9702 MedicalDevices Agency London UK 1997

[9] A J Trigano A AzoulayM Rochdi andA Campillo ldquoElectro-magnetic interference of external pacemakers by walkie-talkiesand digital cellular phones experimental studyrdquo Pacing andClinical Electrophysiology vol 22 no 4 pp 588ndash593 1999

[10] G Calcagnini P Bartolini M Floris et al ldquoElectromagneticinterference to infusion pumps from GSM mobile phonesrdquo inProceedings of the 26th Annual International Conference of theIEEE Engineering in Medicine and Biology Society (EMBC rsquo04)vol 2 pp 3515ndash3518 September 2004

[11] Y Chu and A Ganz ldquoA mobile teletrauma system using 3Gnetworksrdquo IEEE Transactions on Information Technology inBiomedicine vol 8 no 4 pp 456ndash462 2004

[12] E A V Navarro J R Mas J F Navajas and C P AlcegaldquoPerformance of a 3G-based mobile telemedicine systemrdquo inProceedings of the 3rd IEEE Consumer Communications andNetworking Conference (CCNC rsquo06) vol 2 pp 1023ndash1027January 2006

[13] E-Health Insider DH to lift hospital mobile phone ban 2007httpwwwe-health-insidercomnewsitemcfmID=2542

[14] C-K Tang K-H Chan L-C Fung and S-W Leung ldquoElectro-magnetic interference immunity testing of medical equipmentto second- and third-generationmobile phonesrdquo IEEE Transac-tions on Electromagnetic Compatibility vol 51 no 3 pp 659ndash664 2009

[15] M Ardavan K Schmitt and C W Trueman ldquoA preliminaryassessment of EMI control policies in hospitalsrdquo in Proceedingsof the 14th International Symposium on Antenna Technology andApplied Electromagnetics and the American ElectromagneticsConference (ANTEMAMEREM rsquo10) pp 1ndash6 July 2010

[16] S Krishnamoorthy J H Reed C R Anderson P M Robertand S Srikanteswara ldquoCharacterization of the 24GHz ISMband electromagnetic interference in a hospital environmentrdquoin Proceedings of the 25th Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society pp 3245ndash3248 September 2003

[17] D Witters and S Seidman ldquoEMC and wireless healthcarerdquo inProceedings of the Asia-Pacific Symposium on ElectromagneticCompatibility 2010

[18] S GMyerson ldquoMobile phones in hospitals are not as hazardousas believed and should be allowed at least in non-clinical areasrdquoThe British Medical Journal vol 326 no 7387 pp 460ndash4612003

[19] F Fiori Integrated Circuit Susceptibility to Conducted RF Inter-ference Compliance Engineering 2014

[20] W D Kimmel and D D Gerke Ten Common EMI Problems inMedical Electronics Medical Electronics Design 2005

[21] G Acampora D J Cook P Rashidi and A V Vasilakos ldquoAsurvey on ambient intelligence in healthcarerdquo Proceedings of theIEEE vol 101 no 12 pp 2470ndash2494 2013

[22] D He C Chen S Chan J Bu and A V Vasilakos ldquoReTrustattack-resistant and lightweight trust management for medicalsensor networksrdquo IEEE Transactions on Information Technologyin Biomedicine vol 16 no 4 pp 623ndash632 2012

[23] N Xiong A V Vasilakos L T Yang et al ldquoComparativeanalysis of quality of service and memory usage for adaptivefailure detectors in healthcare systemsrdquo IEEE Journal on SelectedAreas in Communications vol 27 no 4 pp 495ndash509 2009

10 Journal of Sensors

[24] M R Javan and A R Sharafat ldquoEfficient and distributed SINR-Based joint resource allocation and base station assignment inwireless CDMA networksrdquo IEEE Transactions on Communica-tions vol 59 no 12 pp 3388ndash3399 2011

[25] S Tadelis GameTheory Princeton University Press 2013[26] I Benedetti S Bolognini andAMartellotti ldquoMultivalued fixed

point theoremswithout strong compactness via a generalizationof midpoint convexityrdquo Fixed Point Theory vol 15 no 1 pp 3ndash22 2014

[27] J Leskovec K J LangADasgupta andMWMahoney ldquoCom-munity structure in large networks natural cluster sizes and theabsence of large well-defined clustersrdquo Internet Mathematicsvol 6 no 1 pp 29ndash123 2009

[28] ITU-R Recommendation M1225 Guidelines for Evaluation ofRadio Transmission Technologies for IMT-2000 1997

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Submit your manuscripts athttpwwwhindawicom

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Navigation and Observation

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DistributedSensor Networks

International Journal of

Journal of Sensors 3

the condition of patients (see Figure 2) On the vehicle for E-health applications doctors healthcare staff and the relativesof patients may use mobile phones due to these two issues(1) doctors and nurses must report the conditions of patientsover phone to the staff in a hospital or in a medical centerto arrange the medical actions which will be taken at thearrival of patients (2) Patients or their relatives need tocontact their family members over mobile phone about thechange of clinical situations as well as important informationHowever the use of mobile phones may lead to EMI impacton nearbymedical sensors [18] EMI refers to the disturbanceof electrical circuits due to electromagnetic induction orelectromagnetic radiationwhich are emitted from an externalsource [19] The disturbance may cause the degradation ofcircuitrsquos performance and the degradation can lead to a totalloss of data

In the following we first present the implementation ofmedical data collection and transmission Then we addressan experiment to show the effects of EMI onmedical sensorsAlso we address the model of EMI impact in this paperas a constraint of outrage-optimization problem which isdetailed in Section 31

31 Implementation of Data Collection and Transmission Thetransmission of data is composed of two layers one layer isfrom sensors to a mobile phone via personal area networks(with the technologies of Bluetooth or Zigbee) within avehicle and the other layer is from a mobile phone on avehicle to the medical center via wide area network (WANeg 3G or 4G networks)The latter layer of data transmissioncan be implemented as regular communicators (eg MSNor Tencent QQ) So we focus on the implementation of theformer layer the data transmission from sensors to a mobilephone Specifically we implement the data collection andtransmission by designing an integrated circuit (IC) whichcan be embedded into a regular mobile phone

By and large the IC (its architecture is shown in Figure 1)is composed of six components namely the microcontrolunit (MCU) the communication module the display mod-ule the data acquisition module the network interface andthe power supply module The data acquisition module ismodified from an off-the-shelf compact module that runsdata acquisition algorithms and this module consists ofa gas-pump unit and a gas pressure sensor The cellularcommunication module takes charge of transmitting theacquired data to a remote data server via wireless networksThe core component of this module is a Subscriber IdentityModel (SIM300C) which enables the data to access bothGSM andGPRS communication networks As the core of ourpatient device MCU would store and run communicationprotocols and control signal processing programs In the ICthe controller we used is MSP430 from Texas Instrumentswhich is widely used for ultra low power applications Inaddition a power supply module offers a stable power supplyto the patient device The display module controls the screenthat shows all the information to the user The interface isresponsible for interaction between a mobile phone and theother phones or computers Specifically an interface could be

Display moduleCommunicationmodule

MCU

moduleBP acquisitionInterface

Power supply module

Figure 1 Architecture of an IC for data collection and transmission

EMI to medical sensors

Mobile station

Ultrasonographysensor

Holter

Ultrasonographysensor

Blood pressure sensor

Blood pressure sensor

Holter

Medical data transmission EMI impact

Vehicle for E-health

Vehicle for E-health

Hospital

Reporting patient condition (talking over phone)

Figure 2 The figure illustrates the Internet of vehicles for E-healthapplications

used either to transfer medical data from sensors to a mobilephone or to debug programs running on the mobile phone

32 Experiment of Testing EMI Effects In this experimentwe test the EMI impact on 50 types of vehicle-mounted andwearable medical sensors from the cellular phones operatedby China Mobile China Unicom China Telecom Thesecellular phones are with the technologies of GSM-9001800CDMA2000 and TD-LTE and their average transmit poweris 08W

4 Journal of Sensors

The test is carried out in an anechoic chamber in order toexclude EMI impact from the other sources of RF emissionsuch as from telecommunication systemsThe test proceduresare detailed as follows (a) tabletop sensors are placed ona table 80 cm above the floor and floor-standing sensorsare placed on the floor Both the tabletop sensors andthe floor sensors are vacillated to simulate the vacillationduring the moving of a vehicle (b) one investigator whooperates a mobile phone controls the maximal power output(08W) while another investigator monitors the workingstatus of medical sensors (c) the mobile phone is graduallybrought closer to the medical sensor If the degradation ofperformance of sensors occurs themobile phone is turned offto check if the performance degradation ceases which showswhether the degradation is reversible or irreversible (d) theEMI impact on medical sensors reversible or irreversibleas well as the distance between medical sensors and mobilephones at the degradation of performance is recorded

Test result shows that EMI from cellular phones causesthe performance degradation of 68 of medical sensorswithin a 2m distance away from the cellular phones Typicaldegradation in the test includes (a) artifact in images ofultrasound sensors (b) noise on biomedical signals such aselectrocardiograph (ECG) and electroencephalogram (EEG)(c) sensor malfunction in infusion pumps syringe pumpsand ventilators (d) change of operating mode of externalpacemakers such as from aynchronized to fixed rate Thisresult is in line with [1 2]

Most of the problems of performance degradation aredue to the component parasitics and it represents the strayreactive elements which have been found in every compo-nent whether a passive or active component Capacitors haveseries inductance which can lead to a series resonant circuitWound inductors have interwinding capacitance which canlead to a parallel resonant circuit These circuits resonate atthe frequencies from 5MHz to 1000MHz Besides the issue ofcomponent parasitics the other issues which may lead to theperformance degradation of medical sensors include groundimpedance poor cable shielding and stray internal couplingpaths [20ndash23]

33 Mobile Hospital Environment A typical mobile hospi-tal environment consists of both life-supporting and non-life-supporting medical sensors either wearable or vehicle-mounted sensors The medical data which are collected bymedical sensors are required to be sent to the doctors whoare staying in a hospital to make the plan of taking actionson the patient once the vehicle arrives at the hospital Alsothe medical staff on the vehicle need to report the conditionof patients over phone to doctors and the use of mobilephone may lead to EMI on medical sensors nearby The life-supporting medical sensors contain electronic componentswhich are sensitive to EMI so they are more sensitive tothe impact of EMI than non-life-supporting sensors Life-supporting medical sensors include wearable pacemakersand non-life-supporting medical sensors include blood pres-sure sensors and Holter for ECG monitoring

Both the abovementioned life-support sensors and non-life-support sensors may have different requirements on

the transmit power of a wireless user to ensure that theuserrsquos RF transmission causes an acceptable level of EMI onmedical sensors The maximal potential transmit power ofeach wireless user should satisfy all of these requirements Tothe best of our knowledge Phunchongharn et al in [1] firstlyaddress how to model the EMI effects on medical sensorsand calculate the maximal potential transmit power of awireless user subject to the EMI constraints Mathematicallythe constraints on transmit power of a wireless user can beshown in (1) for life-support medical sensors and non-life-support medical sensors respectively [1]

sum119894isin119866

1205831radic119875119894

119863119894(119901)

le 119864NLS (119901) for 119901 isin 1198721

sum119894isin119866

1205832radic119875119894

119863119894(119902)

le 119864LS (119902) for 119902 isin 1198722

(1)

where 119864NLS(119901) and 119864LS(119902) are the acceptable EMI levelsfor non-life-support sensor 119901 and life-support sensor 119902respectively 119875

119894is transmit power of wireless user 119894119863

119894(119901) and

119863119894(119902) are the distances between the transmitter of user 119894 and

non-life-support sensor 119901 or life-support sensor 119902 1205831and 120583

2

are constant and their values suggested by IEC 60601-1-2 are7 and 23 respectively [1]119866 represents the set of wireless usersin the Internet of vehicles119872

1represents the set of non-life-

support sensors while 1198722represents the set of life-support

sensorsLet

119860 =

(((((((((((

(

1205831

1198631 (1)

sdot sdot sdot1205831

119863119899 (1)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1205831

1198631(1198981)sdot sdot sdot

1205831

119863119899(1198981)

1205832

1198631 (1)

sdot sdot sdot1205832

119863119899 (1)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1205832

1198631(1198982)sdot sdot sdot

1205832

119863119899(1198982)

)))))))))))

)

(2)

and 119909119894= radic119875119894 we can represent (1) as

119860119883 le 119861 (3)

where1198981is the cardinality of119872

11198982is the cardinality of119872

2

119883 = [1199091 119909

1198981+1198982

]119879 119861 = [119864NLS(1) sdot sdot sdot 119864NLS(1198981) 119864LS(1) sdot sdot sdot

119864LS(1198982)]119879

Remark 1 When the number of rows of 119860 is equal to 119899 thatis1198981+1198982= 119899 then we can obtain the unique solution119883 =

119860minus1119861

Remark 2 When the number of rows of 119860 is less than 119899 thatis1198981+1198982lt 119899 then the linear equation is underdetermined

We select the optimal one from infinite solutions subject tothe maximization of sum

119894isin119866119875119894

Journal of Sensors 5

Remark 3 When the number of rows of 119860 is larger than119899 that is 119898

1+ 1198982

gt 119899 then the linear equation isoverdetermined We relax the constraints of (1) with the bestapproximation that is min

119883|119860119883 minus 119861| So119883 = (119860119879119860)

minus1119860119879119861

Remark 4 Given the set of wireless users 119866 the maximaltransmit power of any wireless user 119894 (denoted as 119875

119894(119866)) can

ensure that all of medical sensors are free from EMI effectswhen 119898

1+ 1198982le 119899 (see Remarks 1 and 2) and also ensure

that the total amount of EMI onmedical sensors isminimizedwhen 119898

1+ 1198982gt 119899 (see Remark 3) since under the latter

scenario the power allocation can ensure min119883|119860119883 minus 119861|

Definition 5 The maximal potential transmit power of user119894 (ie 119875

119894(119866)) to minimize the total amount of EMI on

medical sensors as obtained from Remark 4 is defined asthe maximal effective transmit power (METP) The METP(ie 119875

119894(119866) for user 119894) will be employed to establish the game

model in Section 32 (see Theorem 11) as well as to developthe joint power and rate control algorithm in Section 32 (seeRemark 8)

34 The Game Model In this section considering a cellularnetwork in which wireless users are randomly distributedin the coverage area we address a noncooperative jointtransmit power and rate control game In this game weemploy a commonly used utility which is proposed in [24]and can be characterized as a logarithmic function of powerand rate with a squared pricing item By and large threecommon requirements in wireless communications motivatethe proposal of utility in [24]

(i) Eachwireless user aims to achieve higher level of signalto interference plus noise ratio (SINR) which is defined as

SINR119894=

119875119894ℎ119894119894119877119894

sum119895 =119894119875119895ℎ119895119894+ 119873119894

(4)

where 119875119894and 119877

119894denote the transmit power and data rate

of user 119894 respectively ℎ119895119894

denotes the channel conditionbetween users 119894 and 119895119873

119894denotes the additive white Gaussian

noise(ii) Each wireless user aims to achieve a higher data rate(iii)When the interference level is high eachwireless user

is inclined to increase its power level or decrease its data rateThe proposed utility in [24] can exactly meet the three

common requirements in the wireless communication net-works Mathematically it can be presented as

119894(119875119894 119877119894) = log (120573

1119875119894+ 1205732119877119894) minus

120582

2(1205731

1205732

1198752

119894+1205732

1205731

1198772

119894) (5)

where 120582 is the pricing factor 1205731and 120573

2are adjustable

parametersThe game with utility of (5) can be modeled as

max0le119875119894le119875119894(119866)

119894(119875119894 119877119894) 119894 = 1 2 119873 (6)

where 119875119894(119866) is METP which is defined in Definition 5

Theorem 6 There exists a unique Nash equilibrium in thegame of (6) when 119875

119894(119866) = infin and at the Nash equilibrium

(119875lowast119894 119877lowast119894) the following equations hold

119875lowast

119894= radic

1

2

1205732

1205731120582 119877

lowast

119894= radic

1

2

1205731

1205732120582 (7)

Proof We show that the utility is a jointly concave functionof 119875119894and 119877

119894by calculating its second derivatives that is

1205972119894

1205971198752119894

= minus12057321

(1205731119875119894+ 1205732119877119894)2minus 120582

1205731

1205732

1205972119894

1205971198772119894

= minus1205732

2

(1205731119875119894+ 1205732119877119894)2minus 120582

1205732

1205731

1205972119894

120597119877119894120597119875119894

= minus12057311205732

(1205731119875119894+ 1205732119877119894)2

(8)

It is obvious that 12059721198941205971198752119894

le 0 12059721198941205971198772119894

le 0(12059721198941205971198752

119894)(12059721198941205971198772

119894) minus (1205972119894120597119877119894120597119875119894)2ge 0 are strict inequal-

itiesThus the utility is a strictly concave function on (119875119894 119877119894)

Also the utility is continuous on (119875119894 119877119894) Since the strategy

space of (119875119894 119877119894) is a compact convex and nonempty subset

of two-dimensional Euclidean space of real numbers fromTheorem 12 in [25] the proof of a unique Nash equilibriumof (6) follows

Recall the first derivative of 119906119894with respect to (119875

119894 119877119894) and

write120597119894

120597119875119894

= 0 997888rarr1205732

1205731119875119894+ 1205732119877119894

minus 120582119875119894= 0

120597119894

120597119877119894

= 0 997888rarr1205731

1205731119875119894+ 1205732119877119894

minus 120582119877119894= 0

(9)

We can conclude that the Nash equilibrium (119875lowast119894 119877lowast119894)

satisfies (7)

Remark 7 Theorem 6 indicates the iterative algorithm forupdating (119875

119894 119877119894) [24]

(119875119899+1

119894 119877119899+1

119894) = (IP (119875119899

119894 119877119899

119894) IR (119875119899

119894 119877119899

119894))

IP (119875119899119894 119877119899

119894) = radic

1

2

1205732

1205731120582

IR (119875119899119894 119877119899

119894) = radic

1

2

1205731

1205732120582

(10)

where 119899 denotes the 119899th iteration

The iterative power and rate updating algorithmproposedin [24] does not take into account the METP (119875

119894(119866) =

infin) thus the Nash equilibrium (119875lowast119894 119877lowast119894) could reach above

METP which would cause harmful EMI to medical sensorsIn the following we propose a novel iterative power and rateupdating algorithm to ensure that the proposed algorithmconverges to a fixed point below METP

6 Journal of Sensors

Remark 8 Theorem 6 indicates when 119875119894lt 119875119894(119866) that is the

transmit power of user 119894 is lower than its METP we have119877119894= radic(12)(120573

11205732120582) from (9) when 119875

119894= 119875119894(119866) that is

the transmit power of user 119894 reaches its METP we have 119877119894=

(minus1205731120582119875119894(119866) + radic(120573

1120582119875119894(119866))2+ 412057311205732120582)2120573

2120582 from (9)

35 Joint Power and Control AlgorithmRemark 9 In view of Remark 8 we propose the followingiterative algorithm for updating (119875

119894 119877119894)

(119875119899+1

119894 119877119899+1

119894) = (UP

(119875119899

119894 119877119899

119894) UR

(119875119899

119894 119877119899

119894))

UP(119875119899

119894 119877119899

119894) =

radic1

2

1205732

1205731120582 if 119875119899

119894le 119875119894 (119866)

119875119894 (119866) if 119875119899

119894gt 119875119894 (119866)

UR(119875119899

119894 119877119899

119894) =

radic1

2

1205731

1205732120582

if 119875119899119894le 119875119894 (119866)

minus1205731120582119875119894 (119866) + radic(1205731120582119875119894 (119866))

2

+ 412057311205732120582

21205732120582

if 119875119899119894gt 119875119894 (119866)

(11)

where 119899 denotes the 119899th iteration 119875119894(119866) is defined as

Definition 5

Algorithm in Remark 9 indicates that we force the trans-mit power to be 119875

119894(119866) when 119875119899

119894reaches above 119875

119894(119866) in order

to ensure the minimal amount of EMI on medical sensors

Lemma 10 (Brouwerrsquos Fixed Point Theorem) Let 119878 sube 119877119899 becompact and convex and 119865 119878 rarr 119878 a continuous functionThere exists a 119904 isin 119878 such that 119904 = 119865(119904)

Proof Refer to [26]

Theorem 11 The function UP(119875119899119894 119877119899119894) has a fixed point that

is there exists a power vector Plowast = [1198751 1198752 119875

119872] such that

Plowast = UP(Plowast)

Proof Since the functionUP(119875119899119894 119877119899119894) is a continuous function

of 119875119894 by Brouwerrsquos Fixed Point Theorem in Lemma 10

showing the existence of a fixed point is equal to showing theexistence of a compact and convex set 119878 such that UP 119878 rarr119878 In the following we fabricate such a set

When 119875119899119894le 119875119894(119866) UP(119875119899

119894 119877119899119894) = radic(12)(120573

21205731120582) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 ge 119892119894= radic(12)(119873

1198941205721120582ℎ119894119894)

Let 119892 = min119894119892119894 119897119895

= max119894(ℎ1198951198942120572119894120582ℎ119894119894) and

119897 = max(max119894119892119894max119894119897119894) We have UP(119875119899

119894 119877119899119894) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 le 119892 = radic119872119897 Then we

fabricate the set 119878 = 119892 le 119875119894le max119892 119875119866

119894 such that

UP 119878 rarr 119878 The proof follows

Theorem 11 indicates that a fixed point of UP(119875119899119894 119877119899119894)

always exists In the following we show that its fixed pointis unique and converges to the Nash equilibrium of game (6)

Definition 12 A function 119865(x) is defined as a standardfunction if it satisfies the following three conditions for allx ge 0 (1) positivity 119865(x) ge 0 (2) monotonicity if x1015840 ge xthen 119865(x1015840) ge 119865(x) (3) scalability for all 120575 gt 1 120575119865(x) gt119865(120575x)

Lemma 13 If a standard function has a fixed point then thefixed point is unique Also the standard function will globallyconverge to this unique fixed point

Proof Refer to [26]

Theorem 14 The joint power and rate control algorithm willalways converge to the unique Nash equilibrium of (6)

Proof By [26] if a standard function has a fixed point thenthe fixed point is unique We can easily show thatUP(119875119899

119894 119877119899119894)

is a standard function By Theorem 11 and Lemma 13 thefixed point of UP(119875119899

119894 119877119899119894) is unique

By [26] a standard function globally converges to itsunique fixed point Thus the standard function UP(119875119899

119894 119877119899119894)

will globally converge to its unique fixed point which isalso the Nash equilibrium of game by Remark 8 At theNash equilibrium the data rate and power need to meetthe relationship of (9) (see Theorem 6) and the algorithmin (10) exactly guarantees this relationship between datarate and power Thus the joint power and rate controlalgorithm always converges to the unique Nash equilibriumof game

4 Simulation and Discussion

We gather the data on Internet of vehicles from [27] in whicha connection of network represents a transmit-receive pair ofwireless users In the simulation the vehicle network contains50 nodes and each node has a probability of 01 using themobile phone Please note that in cities when an ambulanceis close to densely populated areas it is possible that 50terminals have EMI impact on medical devices at the sametime The average distance between terminals is 8 metersEach terminal ismovingwith an arbitrary direction at a speedof 10ms (36 kmh) We clarify the characteristics of channelmodels in Section 31 Also we normalize the level of EMI 119864LSor 119864NLS (see (1)) to unity and perform about 100000 Matlab-based experiments to present the results

41 Characteristics of Channel Models We select the com-monly used set of empirical channel models which is speci-fied in ITU-R recommendation M1225 [28] for simulationITU-R M1225 model is applicable for the test scenarios inurban and suburban areas outside the high rise core wherethe buildings are of nearly uniform height [28]

119871 = 40 (1 minus 4 times 10minus3Δℎ) log119877

minus 18 logΔℎ + 21 log119891 + 80(12)

Journal of Sensors 7

Table 1 Parameters of propagationmodels in ITU-R recommenda-tion M1225 [28]

Tap Relative delay (ns) Average power (dB) Doppler spectrum1 0 00 Rayleigh2 310 minus10 Rayleigh3 710 minus90 Rayleigh4 1090 minus100 Rayleigh5 1730 minus150 Rayleigh6 2510 minus200 Rayleigh

where 119877 [km] represents the distance between base stationandmobile station119891 [MHz] represents the carrier frequencyℎ [119898] represents the base station antenna height which ismeasured from the average rooftop level

Each terrestrial test environment can be modelled as achannel impulse response model based on a tapped-delayline The model is characterized by the number of taps thetime delay relative to the first tap the average power relativeto the strongest tap and the Doppler spectrum of each tapA majority of time-delay spreads are relatively small while afew ldquoworst caserdquo multipath characteristics cause much largerdelay spreads Table 1 identifies the propagation model foreach of 6 vehicular test cases In all of these test caseswe consider the strength and relative time delay of signalcomponents as well as Doppler shift and assume that eachof 6 vehicular test cases occurs with the same probabilitySpecifically the primary parameters to characterize each ofpropagation models include

(i) time delay-spread its structure and its statisticalvariability (eg probability distribution of time delayspread)

(ii) multipath fading characteristics (eg Doppler spec-trum Rician versus Rayleigh) for the envelope ofchannels

42 Proposed Algorithm across Networks In this section wecompare the convergence rate of our algorithm (11) under thescenarios of different random networks For simplicity weset 1205731= 1205732= 05 and investigate the convergence rate for

different networksIt is observed from Figure 3 that the algorithm of

(11) under the networks with highly concentrated trans-mitreceive nodes (eg Exponential network) quickly con-verges to the fixed point (with the Intel Core i7-2760QMprocessor the running time of each iteration is around000014 s so the total time of running the algorithm with6000 iterations is 084 s Given that the ambulance is movingat a speed of 10ms the algorithm is feasible when thechannel conditions are assumed to be invariant within adistance of 84m In a fast-varying mobile environment wecan use a more powerful processor to run the algorithm toensure its feasibility) while the algorithmunder the networkswithout highly concentrated transmitreceive nodes (egErdos-Renyi network) converges to the fixed point at a lowrate Indeed the algorithm under the exponential network

0 2 4 6 8 10 12 14 16 18 2005

055

06

065

07

075

08

085

09

Util

ity

Number of iterations (times103)

Figure 3 The figure illustrates the rate of convergence to the fixedpoint of our algorithm under different random networks Blueline with ldquoΔrdquo represents exponential network red line with ldquolowastrdquorepresents preferential attachment (scale-free) network dark linewith ldquoordquo represents Erdos-Renyi network

reaches the fixed point after 7000 iterations while its conver-gence appears after 12000 iterations under the Erdos-Renyinetwork

Another result observed from Figure 3 is that higher util-ity can be achieved by exponential network in which wirelessusers have only a single or few transmitreceive pairs thanby Erdos-Renyi network in which users have multiple trans-mitreceive pairs This is because a user establishs transmit-receive pairs with most of the other users in Erdos-Renyinetwork and thus one data transmission is easily influencedby the interference from the other transmissions However inthe exponential network the users establish transmit-receivepairs with only a single or few other users and they sufferlittle interference from the other transmissions

43 Impact of EMI We first address the advantages of jointpower and rate control to the increase of utility acrosswirelessusers For the comparison of utility between using joint powerand rate control as well as using power or rate control onlywe employ the strategy of power control (proposed in [1] bysetting 119877

119894as a constant) as well as rate control (by setting

119875119894as a constant) as a benchmark Figure 4 implies that the

joint power and rate control can gain a higher average utilitythan only using the control of power or the control of rateshowing the benefits of using joint power and rate control toincrease the utility Also the value of average utility dependson the ratio of 120573

1(1205731+ 1205732) and at the Nash equilibrium of

the game we have 119877119894(119877119894+ 119875119894) = 1205731(1205731+ 1205732) (see Theorem

6) It is also observed from Figure 4 that the value of utilityis symmetric with one peak at 120573

1= 1205732 this is because at

the Nash equilibrium the utility within the strategy spacecan be denoted as log(radic2120573

11205732120582) minus12058222 (by substituting (12)

into (6)) which is symmetric at the peak of 1205731= 1205732when

119875119894le 119875119894(119866)

In the following we address the benefits of using the pro-posed algorithm to the decrease of EMI on medical sensors

8 Journal of Sensors

0 01 02 03 04 05 06 07 08 09 1055

06

065

07

075

08

085

09

095

Util

ity

1205731(1205731 + 1205732)

Figure 4 The figure shows the impact of power and rate control on the utility Blue line with ldquoΔrdquo denotes power control only red line withldquolowastrdquo denotes rate control only dark line with ldquoordquo denotes joint power and rate control

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]Proposed algorithm

1205731(1205731 + 1205732)

EN

LS

(a)

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]

Proposed algorithm

1205731(1205731 + 1205732)

ELS

(b)

Figure 5The figure shows EMI caused by RF transmission using our algorithm versus algorithm in [24] the left shows the EMI on non-life-support sensors while the right shows the EMI on life-support sensors Blue and dashed line represents using algorithm in [24] dark andsolid line represents using our algorithm Line with ldquoΔrdquo represents the case of119898

1+ 1198982gt 119899 line with ldquoordquo represents the case of119898

1+ 1198982le 119899

Figure 5 shows the comparison of EMI on medical sensorscaused by RF transmission between using our proposed algo-rithm (Remark 9) and using the algorithm proposed in [24](Remark 7) Figure 5 implies that our proposed algorithm(EMI level below 01) can dramatically reduce the amount ofEMI on medical sensors compared to the algorithm in [24](EMI level up to 08) Also our algorithm can ensure thatmedical sensors are free from EMI when 119898

1+ 1198982le 119899 and

can ensure the minimal amount of EMI when 1198981+ 1198982gt 119899

To put it another way whenwe need to consider the EMI on alarge number ofmedical sensors (119898

1+1198982gt 119899) our algorithm

can minimize the amount of EMI on medical sensors thoughit cannot keep medical sensors free from EMI as under thescenario of a small number of medical sensors (119898

1+ 1198982le

119899)

5 Conclusions

We addressed a noncooperative game to maximize the utilityof wireless users by controlling their transmit power andrate under a mobile hospital scenario We proposed thejoint power and rate control algorithm and showed thatthe algorithm would globally converge to a unique Nashequilibrium of game Some of the key inferences drawn areas follows

(i) Proposed joint power and rate control algorithmcould dramatically improve the utility of wirelessusers and reduce the amount of EMI on medicalsensors compared to current algorithm in [24] whichis the most widely used power and rate controlalgorithm under nonmedical settings

Journal of Sensors 9

(ii) Under the networks with users who have highlyconcentrated transmitreceive pairs the power andrate control algorithm can converge to the fixed pointat a higher rate than under the networks in whichtransmitreceive pairs are evenly distributed amongwireless users

(iii) Networks with users who have highly concentratedtransmitreceive pairs can achieve a higher utilitythan the networks in which transmitreceive pairs areevenly distributed among wireless users

We are extending our results to the settings in whichwireless users can be of different prioritiesWewould also liketo extendour results to a dynamic setting that is the structureof Internet of vehicles is dynamically changing over time

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by National NaturalScience Foundation of China (no 61301100) and partiallysupported by a Grant from the National High TechnologyResearch and Development Program of China (863 Programno 2012AA02A614)

References

[1] P Phunchongharn D Niyato E Hossain and S CamorlingaldquoAn EMI-aware prioritized wireless access scheme for e-Healthapplications in hospital environmentsrdquo IEEE Transactions onInformation Technology in Biomedicine vol 14 no 5 pp 1247ndash1258 2010

[2] P Phunchongharn E Hossain and S Camorlinga ldquoElec-tromagnetic interference-aware transmission scheduling andpower control for dynamic wireless access in hospital envi-ronmentsrdquo IEEE Transactions on Information Technology inBiomedicine vol 15 no 6 pp 890ndash899 2011

[3] A Soomro and D Cavalcanti ldquoOpportunities and challengesin using WPAN and WLAN technologies in medical environ-mentsrdquo IEEE Communications Magazine vol 45 no 2 pp 114ndash122 2007

[4] L Zhou J Chen B Zhen I de la Torre and SMisra ldquoOn asyn-chronous flow scheduling for wireless body sensor networksrdquoin Proceedings of the 15th IEEE International Conference on e-Health Networking Applications amp Services (Healthcom rsquo13) pp366ndash370 Lisbon Portugal October 2013

[5] J J P C Rodrigues O R E Pereira and P A C S NevesldquoBiofeedback data visualization for body sensor networksrdquoJournal of Network and Computer Applications vol 34 no 1 pp151ndash158 2011

[6] M Hayajneh and C T Abdallah ldquoDistributed joint rate andpower control game-theoretic algorithms for wireless datardquoIEEE Communications Letters vol 8 no 8 pp 511ndash513 2004

[7] K-S Tan and I Hinberg ldquoRadiofrequency susceptibility testson medical equipmentrdquo in Proceedings of the 16th AnnualInternational Conference of the IEEE Engineering in Medicine

and Biology Society Engineering Advances New Opportunitiesfor Biomedical Engineers vol 2 pp 998ndash999 November 1994

[8] ldquoElectromagnetic compatibility of medical devices with mobilecommunicationsrdquo Medical Devices Bulletin DB9702 MedicalDevices Agency London UK 1997

[9] A J Trigano A AzoulayM Rochdi andA Campillo ldquoElectro-magnetic interference of external pacemakers by walkie-talkiesand digital cellular phones experimental studyrdquo Pacing andClinical Electrophysiology vol 22 no 4 pp 588ndash593 1999

[10] G Calcagnini P Bartolini M Floris et al ldquoElectromagneticinterference to infusion pumps from GSM mobile phonesrdquo inProceedings of the 26th Annual International Conference of theIEEE Engineering in Medicine and Biology Society (EMBC rsquo04)vol 2 pp 3515ndash3518 September 2004

[11] Y Chu and A Ganz ldquoA mobile teletrauma system using 3Gnetworksrdquo IEEE Transactions on Information Technology inBiomedicine vol 8 no 4 pp 456ndash462 2004

[12] E A V Navarro J R Mas J F Navajas and C P AlcegaldquoPerformance of a 3G-based mobile telemedicine systemrdquo inProceedings of the 3rd IEEE Consumer Communications andNetworking Conference (CCNC rsquo06) vol 2 pp 1023ndash1027January 2006

[13] E-Health Insider DH to lift hospital mobile phone ban 2007httpwwwe-health-insidercomnewsitemcfmID=2542

[14] C-K Tang K-H Chan L-C Fung and S-W Leung ldquoElectro-magnetic interference immunity testing of medical equipmentto second- and third-generationmobile phonesrdquo IEEE Transac-tions on Electromagnetic Compatibility vol 51 no 3 pp 659ndash664 2009

[15] M Ardavan K Schmitt and C W Trueman ldquoA preliminaryassessment of EMI control policies in hospitalsrdquo in Proceedingsof the 14th International Symposium on Antenna Technology andApplied Electromagnetics and the American ElectromagneticsConference (ANTEMAMEREM rsquo10) pp 1ndash6 July 2010

[16] S Krishnamoorthy J H Reed C R Anderson P M Robertand S Srikanteswara ldquoCharacterization of the 24GHz ISMband electromagnetic interference in a hospital environmentrdquoin Proceedings of the 25th Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society pp 3245ndash3248 September 2003

[17] D Witters and S Seidman ldquoEMC and wireless healthcarerdquo inProceedings of the Asia-Pacific Symposium on ElectromagneticCompatibility 2010

[18] S GMyerson ldquoMobile phones in hospitals are not as hazardousas believed and should be allowed at least in non-clinical areasrdquoThe British Medical Journal vol 326 no 7387 pp 460ndash4612003

[19] F Fiori Integrated Circuit Susceptibility to Conducted RF Inter-ference Compliance Engineering 2014

[20] W D Kimmel and D D Gerke Ten Common EMI Problems inMedical Electronics Medical Electronics Design 2005

[21] G Acampora D J Cook P Rashidi and A V Vasilakos ldquoAsurvey on ambient intelligence in healthcarerdquo Proceedings of theIEEE vol 101 no 12 pp 2470ndash2494 2013

[22] D He C Chen S Chan J Bu and A V Vasilakos ldquoReTrustattack-resistant and lightweight trust management for medicalsensor networksrdquo IEEE Transactions on Information Technologyin Biomedicine vol 16 no 4 pp 623ndash632 2012

[23] N Xiong A V Vasilakos L T Yang et al ldquoComparativeanalysis of quality of service and memory usage for adaptivefailure detectors in healthcare systemsrdquo IEEE Journal on SelectedAreas in Communications vol 27 no 4 pp 495ndash509 2009

10 Journal of Sensors

[24] M R Javan and A R Sharafat ldquoEfficient and distributed SINR-Based joint resource allocation and base station assignment inwireless CDMA networksrdquo IEEE Transactions on Communica-tions vol 59 no 12 pp 3388ndash3399 2011

[25] S Tadelis GameTheory Princeton University Press 2013[26] I Benedetti S Bolognini andAMartellotti ldquoMultivalued fixed

point theoremswithout strong compactness via a generalizationof midpoint convexityrdquo Fixed Point Theory vol 15 no 1 pp 3ndash22 2014

[27] J Leskovec K J LangADasgupta andMWMahoney ldquoCom-munity structure in large networks natural cluster sizes and theabsence of large well-defined clustersrdquo Internet Mathematicsvol 6 no 1 pp 29ndash123 2009

[28] ITU-R Recommendation M1225 Guidelines for Evaluation ofRadio Transmission Technologies for IMT-2000 1997

International Journal of

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RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Journal of Sensors

The test is carried out in an anechoic chamber in order toexclude EMI impact from the other sources of RF emissionsuch as from telecommunication systemsThe test proceduresare detailed as follows (a) tabletop sensors are placed ona table 80 cm above the floor and floor-standing sensorsare placed on the floor Both the tabletop sensors andthe floor sensors are vacillated to simulate the vacillationduring the moving of a vehicle (b) one investigator whooperates a mobile phone controls the maximal power output(08W) while another investigator monitors the workingstatus of medical sensors (c) the mobile phone is graduallybrought closer to the medical sensor If the degradation ofperformance of sensors occurs themobile phone is turned offto check if the performance degradation ceases which showswhether the degradation is reversible or irreversible (d) theEMI impact on medical sensors reversible or irreversibleas well as the distance between medical sensors and mobilephones at the degradation of performance is recorded

Test result shows that EMI from cellular phones causesthe performance degradation of 68 of medical sensorswithin a 2m distance away from the cellular phones Typicaldegradation in the test includes (a) artifact in images ofultrasound sensors (b) noise on biomedical signals such aselectrocardiograph (ECG) and electroencephalogram (EEG)(c) sensor malfunction in infusion pumps syringe pumpsand ventilators (d) change of operating mode of externalpacemakers such as from aynchronized to fixed rate Thisresult is in line with [1 2]

Most of the problems of performance degradation aredue to the component parasitics and it represents the strayreactive elements which have been found in every compo-nent whether a passive or active component Capacitors haveseries inductance which can lead to a series resonant circuitWound inductors have interwinding capacitance which canlead to a parallel resonant circuit These circuits resonate atthe frequencies from 5MHz to 1000MHz Besides the issue ofcomponent parasitics the other issues which may lead to theperformance degradation of medical sensors include groundimpedance poor cable shielding and stray internal couplingpaths [20ndash23]

33 Mobile Hospital Environment A typical mobile hospi-tal environment consists of both life-supporting and non-life-supporting medical sensors either wearable or vehicle-mounted sensors The medical data which are collected bymedical sensors are required to be sent to the doctors whoare staying in a hospital to make the plan of taking actionson the patient once the vehicle arrives at the hospital Alsothe medical staff on the vehicle need to report the conditionof patients over phone to doctors and the use of mobilephone may lead to EMI on medical sensors nearby The life-supporting medical sensors contain electronic componentswhich are sensitive to EMI so they are more sensitive tothe impact of EMI than non-life-supporting sensors Life-supporting medical sensors include wearable pacemakersand non-life-supporting medical sensors include blood pres-sure sensors and Holter for ECG monitoring

Both the abovementioned life-support sensors and non-life-support sensors may have different requirements on

the transmit power of a wireless user to ensure that theuserrsquos RF transmission causes an acceptable level of EMI onmedical sensors The maximal potential transmit power ofeach wireless user should satisfy all of these requirements Tothe best of our knowledge Phunchongharn et al in [1] firstlyaddress how to model the EMI effects on medical sensorsand calculate the maximal potential transmit power of awireless user subject to the EMI constraints Mathematicallythe constraints on transmit power of a wireless user can beshown in (1) for life-support medical sensors and non-life-support medical sensors respectively [1]

sum119894isin119866

1205831radic119875119894

119863119894(119901)

le 119864NLS (119901) for 119901 isin 1198721

sum119894isin119866

1205832radic119875119894

119863119894(119902)

le 119864LS (119902) for 119902 isin 1198722

(1)

where 119864NLS(119901) and 119864LS(119902) are the acceptable EMI levelsfor non-life-support sensor 119901 and life-support sensor 119902respectively 119875

119894is transmit power of wireless user 119894119863

119894(119901) and

119863119894(119902) are the distances between the transmitter of user 119894 and

non-life-support sensor 119901 or life-support sensor 119902 1205831and 120583

2

are constant and their values suggested by IEC 60601-1-2 are7 and 23 respectively [1]119866 represents the set of wireless usersin the Internet of vehicles119872

1represents the set of non-life-

support sensors while 1198722represents the set of life-support

sensorsLet

119860 =

(((((((((((

(

1205831

1198631 (1)

sdot sdot sdot1205831

119863119899 (1)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1205831

1198631(1198981)sdot sdot sdot

1205831

119863119899(1198981)

1205832

1198631 (1)

sdot sdot sdot1205832

119863119899 (1)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1205832

1198631(1198982)sdot sdot sdot

1205832

119863119899(1198982)

)))))))))))

)

(2)

and 119909119894= radic119875119894 we can represent (1) as

119860119883 le 119861 (3)

where1198981is the cardinality of119872

11198982is the cardinality of119872

2

119883 = [1199091 119909

1198981+1198982

]119879 119861 = [119864NLS(1) sdot sdot sdot 119864NLS(1198981) 119864LS(1) sdot sdot sdot

119864LS(1198982)]119879

Remark 1 When the number of rows of 119860 is equal to 119899 thatis1198981+1198982= 119899 then we can obtain the unique solution119883 =

119860minus1119861

Remark 2 When the number of rows of 119860 is less than 119899 thatis1198981+1198982lt 119899 then the linear equation is underdetermined

We select the optimal one from infinite solutions subject tothe maximization of sum

119894isin119866119875119894

Journal of Sensors 5

Remark 3 When the number of rows of 119860 is larger than119899 that is 119898

1+ 1198982

gt 119899 then the linear equation isoverdetermined We relax the constraints of (1) with the bestapproximation that is min

119883|119860119883 minus 119861| So119883 = (119860119879119860)

minus1119860119879119861

Remark 4 Given the set of wireless users 119866 the maximaltransmit power of any wireless user 119894 (denoted as 119875

119894(119866)) can

ensure that all of medical sensors are free from EMI effectswhen 119898

1+ 1198982le 119899 (see Remarks 1 and 2) and also ensure

that the total amount of EMI onmedical sensors isminimizedwhen 119898

1+ 1198982gt 119899 (see Remark 3) since under the latter

scenario the power allocation can ensure min119883|119860119883 minus 119861|

Definition 5 The maximal potential transmit power of user119894 (ie 119875

119894(119866)) to minimize the total amount of EMI on

medical sensors as obtained from Remark 4 is defined asthe maximal effective transmit power (METP) The METP(ie 119875

119894(119866) for user 119894) will be employed to establish the game

model in Section 32 (see Theorem 11) as well as to developthe joint power and rate control algorithm in Section 32 (seeRemark 8)

34 The Game Model In this section considering a cellularnetwork in which wireless users are randomly distributedin the coverage area we address a noncooperative jointtransmit power and rate control game In this game weemploy a commonly used utility which is proposed in [24]and can be characterized as a logarithmic function of powerand rate with a squared pricing item By and large threecommon requirements in wireless communications motivatethe proposal of utility in [24]

(i) Eachwireless user aims to achieve higher level of signalto interference plus noise ratio (SINR) which is defined as

SINR119894=

119875119894ℎ119894119894119877119894

sum119895 =119894119875119895ℎ119895119894+ 119873119894

(4)

where 119875119894and 119877

119894denote the transmit power and data rate

of user 119894 respectively ℎ119895119894

denotes the channel conditionbetween users 119894 and 119895119873

119894denotes the additive white Gaussian

noise(ii) Each wireless user aims to achieve a higher data rate(iii)When the interference level is high eachwireless user

is inclined to increase its power level or decrease its data rateThe proposed utility in [24] can exactly meet the three

common requirements in the wireless communication net-works Mathematically it can be presented as

119894(119875119894 119877119894) = log (120573

1119875119894+ 1205732119877119894) minus

120582

2(1205731

1205732

1198752

119894+1205732

1205731

1198772

119894) (5)

where 120582 is the pricing factor 1205731and 120573

2are adjustable

parametersThe game with utility of (5) can be modeled as

max0le119875119894le119875119894(119866)

119894(119875119894 119877119894) 119894 = 1 2 119873 (6)

where 119875119894(119866) is METP which is defined in Definition 5

Theorem 6 There exists a unique Nash equilibrium in thegame of (6) when 119875

119894(119866) = infin and at the Nash equilibrium

(119875lowast119894 119877lowast119894) the following equations hold

119875lowast

119894= radic

1

2

1205732

1205731120582 119877

lowast

119894= radic

1

2

1205731

1205732120582 (7)

Proof We show that the utility is a jointly concave functionof 119875119894and 119877

119894by calculating its second derivatives that is

1205972119894

1205971198752119894

= minus12057321

(1205731119875119894+ 1205732119877119894)2minus 120582

1205731

1205732

1205972119894

1205971198772119894

= minus1205732

2

(1205731119875119894+ 1205732119877119894)2minus 120582

1205732

1205731

1205972119894

120597119877119894120597119875119894

= minus12057311205732

(1205731119875119894+ 1205732119877119894)2

(8)

It is obvious that 12059721198941205971198752119894

le 0 12059721198941205971198772119894

le 0(12059721198941205971198752

119894)(12059721198941205971198772

119894) minus (1205972119894120597119877119894120597119875119894)2ge 0 are strict inequal-

itiesThus the utility is a strictly concave function on (119875119894 119877119894)

Also the utility is continuous on (119875119894 119877119894) Since the strategy

space of (119875119894 119877119894) is a compact convex and nonempty subset

of two-dimensional Euclidean space of real numbers fromTheorem 12 in [25] the proof of a unique Nash equilibriumof (6) follows

Recall the first derivative of 119906119894with respect to (119875

119894 119877119894) and

write120597119894

120597119875119894

= 0 997888rarr1205732

1205731119875119894+ 1205732119877119894

minus 120582119875119894= 0

120597119894

120597119877119894

= 0 997888rarr1205731

1205731119875119894+ 1205732119877119894

minus 120582119877119894= 0

(9)

We can conclude that the Nash equilibrium (119875lowast119894 119877lowast119894)

satisfies (7)

Remark 7 Theorem 6 indicates the iterative algorithm forupdating (119875

119894 119877119894) [24]

(119875119899+1

119894 119877119899+1

119894) = (IP (119875119899

119894 119877119899

119894) IR (119875119899

119894 119877119899

119894))

IP (119875119899119894 119877119899

119894) = radic

1

2

1205732

1205731120582

IR (119875119899119894 119877119899

119894) = radic

1

2

1205731

1205732120582

(10)

where 119899 denotes the 119899th iteration

The iterative power and rate updating algorithmproposedin [24] does not take into account the METP (119875

119894(119866) =

infin) thus the Nash equilibrium (119875lowast119894 119877lowast119894) could reach above

METP which would cause harmful EMI to medical sensorsIn the following we propose a novel iterative power and rateupdating algorithm to ensure that the proposed algorithmconverges to a fixed point below METP

6 Journal of Sensors

Remark 8 Theorem 6 indicates when 119875119894lt 119875119894(119866) that is the

transmit power of user 119894 is lower than its METP we have119877119894= radic(12)(120573

11205732120582) from (9) when 119875

119894= 119875119894(119866) that is

the transmit power of user 119894 reaches its METP we have 119877119894=

(minus1205731120582119875119894(119866) + radic(120573

1120582119875119894(119866))2+ 412057311205732120582)2120573

2120582 from (9)

35 Joint Power and Control AlgorithmRemark 9 In view of Remark 8 we propose the followingiterative algorithm for updating (119875

119894 119877119894)

(119875119899+1

119894 119877119899+1

119894) = (UP

(119875119899

119894 119877119899

119894) UR

(119875119899

119894 119877119899

119894))

UP(119875119899

119894 119877119899

119894) =

radic1

2

1205732

1205731120582 if 119875119899

119894le 119875119894 (119866)

119875119894 (119866) if 119875119899

119894gt 119875119894 (119866)

UR(119875119899

119894 119877119899

119894) =

radic1

2

1205731

1205732120582

if 119875119899119894le 119875119894 (119866)

minus1205731120582119875119894 (119866) + radic(1205731120582119875119894 (119866))

2

+ 412057311205732120582

21205732120582

if 119875119899119894gt 119875119894 (119866)

(11)

where 119899 denotes the 119899th iteration 119875119894(119866) is defined as

Definition 5

Algorithm in Remark 9 indicates that we force the trans-mit power to be 119875

119894(119866) when 119875119899

119894reaches above 119875

119894(119866) in order

to ensure the minimal amount of EMI on medical sensors

Lemma 10 (Brouwerrsquos Fixed Point Theorem) Let 119878 sube 119877119899 becompact and convex and 119865 119878 rarr 119878 a continuous functionThere exists a 119904 isin 119878 such that 119904 = 119865(119904)

Proof Refer to [26]

Theorem 11 The function UP(119875119899119894 119877119899119894) has a fixed point that

is there exists a power vector Plowast = [1198751 1198752 119875

119872] such that

Plowast = UP(Plowast)

Proof Since the functionUP(119875119899119894 119877119899119894) is a continuous function

of 119875119894 by Brouwerrsquos Fixed Point Theorem in Lemma 10

showing the existence of a fixed point is equal to showing theexistence of a compact and convex set 119878 such that UP 119878 rarr119878 In the following we fabricate such a set

When 119875119899119894le 119875119894(119866) UP(119875119899

119894 119877119899119894) = radic(12)(120573

21205731120582) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 ge 119892119894= radic(12)(119873

1198941205721120582ℎ119894119894)

Let 119892 = min119894119892119894 119897119895

= max119894(ℎ1198951198942120572119894120582ℎ119894119894) and

119897 = max(max119894119892119894max119894119897119894) We have UP(119875119899

119894 119877119899119894) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 le 119892 = radic119872119897 Then we

fabricate the set 119878 = 119892 le 119875119894le max119892 119875119866

119894 such that

UP 119878 rarr 119878 The proof follows

Theorem 11 indicates that a fixed point of UP(119875119899119894 119877119899119894)

always exists In the following we show that its fixed pointis unique and converges to the Nash equilibrium of game (6)

Definition 12 A function 119865(x) is defined as a standardfunction if it satisfies the following three conditions for allx ge 0 (1) positivity 119865(x) ge 0 (2) monotonicity if x1015840 ge xthen 119865(x1015840) ge 119865(x) (3) scalability for all 120575 gt 1 120575119865(x) gt119865(120575x)

Lemma 13 If a standard function has a fixed point then thefixed point is unique Also the standard function will globallyconverge to this unique fixed point

Proof Refer to [26]

Theorem 14 The joint power and rate control algorithm willalways converge to the unique Nash equilibrium of (6)

Proof By [26] if a standard function has a fixed point thenthe fixed point is unique We can easily show thatUP(119875119899

119894 119877119899119894)

is a standard function By Theorem 11 and Lemma 13 thefixed point of UP(119875119899

119894 119877119899119894) is unique

By [26] a standard function globally converges to itsunique fixed point Thus the standard function UP(119875119899

119894 119877119899119894)

will globally converge to its unique fixed point which isalso the Nash equilibrium of game by Remark 8 At theNash equilibrium the data rate and power need to meetthe relationship of (9) (see Theorem 6) and the algorithmin (10) exactly guarantees this relationship between datarate and power Thus the joint power and rate controlalgorithm always converges to the unique Nash equilibriumof game

4 Simulation and Discussion

We gather the data on Internet of vehicles from [27] in whicha connection of network represents a transmit-receive pair ofwireless users In the simulation the vehicle network contains50 nodes and each node has a probability of 01 using themobile phone Please note that in cities when an ambulanceis close to densely populated areas it is possible that 50terminals have EMI impact on medical devices at the sametime The average distance between terminals is 8 metersEach terminal ismovingwith an arbitrary direction at a speedof 10ms (36 kmh) We clarify the characteristics of channelmodels in Section 31 Also we normalize the level of EMI 119864LSor 119864NLS (see (1)) to unity and perform about 100000 Matlab-based experiments to present the results

41 Characteristics of Channel Models We select the com-monly used set of empirical channel models which is speci-fied in ITU-R recommendation M1225 [28] for simulationITU-R M1225 model is applicable for the test scenarios inurban and suburban areas outside the high rise core wherethe buildings are of nearly uniform height [28]

119871 = 40 (1 minus 4 times 10minus3Δℎ) log119877

minus 18 logΔℎ + 21 log119891 + 80(12)

Journal of Sensors 7

Table 1 Parameters of propagationmodels in ITU-R recommenda-tion M1225 [28]

Tap Relative delay (ns) Average power (dB) Doppler spectrum1 0 00 Rayleigh2 310 minus10 Rayleigh3 710 minus90 Rayleigh4 1090 minus100 Rayleigh5 1730 minus150 Rayleigh6 2510 minus200 Rayleigh

where 119877 [km] represents the distance between base stationandmobile station119891 [MHz] represents the carrier frequencyℎ [119898] represents the base station antenna height which ismeasured from the average rooftop level

Each terrestrial test environment can be modelled as achannel impulse response model based on a tapped-delayline The model is characterized by the number of taps thetime delay relative to the first tap the average power relativeto the strongest tap and the Doppler spectrum of each tapA majority of time-delay spreads are relatively small while afew ldquoworst caserdquo multipath characteristics cause much largerdelay spreads Table 1 identifies the propagation model foreach of 6 vehicular test cases In all of these test caseswe consider the strength and relative time delay of signalcomponents as well as Doppler shift and assume that eachof 6 vehicular test cases occurs with the same probabilitySpecifically the primary parameters to characterize each ofpropagation models include

(i) time delay-spread its structure and its statisticalvariability (eg probability distribution of time delayspread)

(ii) multipath fading characteristics (eg Doppler spec-trum Rician versus Rayleigh) for the envelope ofchannels

42 Proposed Algorithm across Networks In this section wecompare the convergence rate of our algorithm (11) under thescenarios of different random networks For simplicity weset 1205731= 1205732= 05 and investigate the convergence rate for

different networksIt is observed from Figure 3 that the algorithm of

(11) under the networks with highly concentrated trans-mitreceive nodes (eg Exponential network) quickly con-verges to the fixed point (with the Intel Core i7-2760QMprocessor the running time of each iteration is around000014 s so the total time of running the algorithm with6000 iterations is 084 s Given that the ambulance is movingat a speed of 10ms the algorithm is feasible when thechannel conditions are assumed to be invariant within adistance of 84m In a fast-varying mobile environment wecan use a more powerful processor to run the algorithm toensure its feasibility) while the algorithmunder the networkswithout highly concentrated transmitreceive nodes (egErdos-Renyi network) converges to the fixed point at a lowrate Indeed the algorithm under the exponential network

0 2 4 6 8 10 12 14 16 18 2005

055

06

065

07

075

08

085

09

Util

ity

Number of iterations (times103)

Figure 3 The figure illustrates the rate of convergence to the fixedpoint of our algorithm under different random networks Blueline with ldquoΔrdquo represents exponential network red line with ldquolowastrdquorepresents preferential attachment (scale-free) network dark linewith ldquoordquo represents Erdos-Renyi network

reaches the fixed point after 7000 iterations while its conver-gence appears after 12000 iterations under the Erdos-Renyinetwork

Another result observed from Figure 3 is that higher util-ity can be achieved by exponential network in which wirelessusers have only a single or few transmitreceive pairs thanby Erdos-Renyi network in which users have multiple trans-mitreceive pairs This is because a user establishs transmit-receive pairs with most of the other users in Erdos-Renyinetwork and thus one data transmission is easily influencedby the interference from the other transmissions However inthe exponential network the users establish transmit-receivepairs with only a single or few other users and they sufferlittle interference from the other transmissions

43 Impact of EMI We first address the advantages of jointpower and rate control to the increase of utility acrosswirelessusers For the comparison of utility between using joint powerand rate control as well as using power or rate control onlywe employ the strategy of power control (proposed in [1] bysetting 119877

119894as a constant) as well as rate control (by setting

119875119894as a constant) as a benchmark Figure 4 implies that the

joint power and rate control can gain a higher average utilitythan only using the control of power or the control of rateshowing the benefits of using joint power and rate control toincrease the utility Also the value of average utility dependson the ratio of 120573

1(1205731+ 1205732) and at the Nash equilibrium of

the game we have 119877119894(119877119894+ 119875119894) = 1205731(1205731+ 1205732) (see Theorem

6) It is also observed from Figure 4 that the value of utilityis symmetric with one peak at 120573

1= 1205732 this is because at

the Nash equilibrium the utility within the strategy spacecan be denoted as log(radic2120573

11205732120582) minus12058222 (by substituting (12)

into (6)) which is symmetric at the peak of 1205731= 1205732when

119875119894le 119875119894(119866)

In the following we address the benefits of using the pro-posed algorithm to the decrease of EMI on medical sensors

8 Journal of Sensors

0 01 02 03 04 05 06 07 08 09 1055

06

065

07

075

08

085

09

095

Util

ity

1205731(1205731 + 1205732)

Figure 4 The figure shows the impact of power and rate control on the utility Blue line with ldquoΔrdquo denotes power control only red line withldquolowastrdquo denotes rate control only dark line with ldquoordquo denotes joint power and rate control

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]Proposed algorithm

1205731(1205731 + 1205732)

EN

LS

(a)

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]

Proposed algorithm

1205731(1205731 + 1205732)

ELS

(b)

Figure 5The figure shows EMI caused by RF transmission using our algorithm versus algorithm in [24] the left shows the EMI on non-life-support sensors while the right shows the EMI on life-support sensors Blue and dashed line represents using algorithm in [24] dark andsolid line represents using our algorithm Line with ldquoΔrdquo represents the case of119898

1+ 1198982gt 119899 line with ldquoordquo represents the case of119898

1+ 1198982le 119899

Figure 5 shows the comparison of EMI on medical sensorscaused by RF transmission between using our proposed algo-rithm (Remark 9) and using the algorithm proposed in [24](Remark 7) Figure 5 implies that our proposed algorithm(EMI level below 01) can dramatically reduce the amount ofEMI on medical sensors compared to the algorithm in [24](EMI level up to 08) Also our algorithm can ensure thatmedical sensors are free from EMI when 119898

1+ 1198982le 119899 and

can ensure the minimal amount of EMI when 1198981+ 1198982gt 119899

To put it another way whenwe need to consider the EMI on alarge number ofmedical sensors (119898

1+1198982gt 119899) our algorithm

can minimize the amount of EMI on medical sensors thoughit cannot keep medical sensors free from EMI as under thescenario of a small number of medical sensors (119898

1+ 1198982le

119899)

5 Conclusions

We addressed a noncooperative game to maximize the utilityof wireless users by controlling their transmit power andrate under a mobile hospital scenario We proposed thejoint power and rate control algorithm and showed thatthe algorithm would globally converge to a unique Nashequilibrium of game Some of the key inferences drawn areas follows

(i) Proposed joint power and rate control algorithmcould dramatically improve the utility of wirelessusers and reduce the amount of EMI on medicalsensors compared to current algorithm in [24] whichis the most widely used power and rate controlalgorithm under nonmedical settings

Journal of Sensors 9

(ii) Under the networks with users who have highlyconcentrated transmitreceive pairs the power andrate control algorithm can converge to the fixed pointat a higher rate than under the networks in whichtransmitreceive pairs are evenly distributed amongwireless users

(iii) Networks with users who have highly concentratedtransmitreceive pairs can achieve a higher utilitythan the networks in which transmitreceive pairs areevenly distributed among wireless users

We are extending our results to the settings in whichwireless users can be of different prioritiesWewould also liketo extendour results to a dynamic setting that is the structureof Internet of vehicles is dynamically changing over time

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by National NaturalScience Foundation of China (no 61301100) and partiallysupported by a Grant from the National High TechnologyResearch and Development Program of China (863 Programno 2012AA02A614)

References

[1] P Phunchongharn D Niyato E Hossain and S CamorlingaldquoAn EMI-aware prioritized wireless access scheme for e-Healthapplications in hospital environmentsrdquo IEEE Transactions onInformation Technology in Biomedicine vol 14 no 5 pp 1247ndash1258 2010

[2] P Phunchongharn E Hossain and S Camorlinga ldquoElec-tromagnetic interference-aware transmission scheduling andpower control for dynamic wireless access in hospital envi-ronmentsrdquo IEEE Transactions on Information Technology inBiomedicine vol 15 no 6 pp 890ndash899 2011

[3] A Soomro and D Cavalcanti ldquoOpportunities and challengesin using WPAN and WLAN technologies in medical environ-mentsrdquo IEEE Communications Magazine vol 45 no 2 pp 114ndash122 2007

[4] L Zhou J Chen B Zhen I de la Torre and SMisra ldquoOn asyn-chronous flow scheduling for wireless body sensor networksrdquoin Proceedings of the 15th IEEE International Conference on e-Health Networking Applications amp Services (Healthcom rsquo13) pp366ndash370 Lisbon Portugal October 2013

[5] J J P C Rodrigues O R E Pereira and P A C S NevesldquoBiofeedback data visualization for body sensor networksrdquoJournal of Network and Computer Applications vol 34 no 1 pp151ndash158 2011

[6] M Hayajneh and C T Abdallah ldquoDistributed joint rate andpower control game-theoretic algorithms for wireless datardquoIEEE Communications Letters vol 8 no 8 pp 511ndash513 2004

[7] K-S Tan and I Hinberg ldquoRadiofrequency susceptibility testson medical equipmentrdquo in Proceedings of the 16th AnnualInternational Conference of the IEEE Engineering in Medicine

and Biology Society Engineering Advances New Opportunitiesfor Biomedical Engineers vol 2 pp 998ndash999 November 1994

[8] ldquoElectromagnetic compatibility of medical devices with mobilecommunicationsrdquo Medical Devices Bulletin DB9702 MedicalDevices Agency London UK 1997

[9] A J Trigano A AzoulayM Rochdi andA Campillo ldquoElectro-magnetic interference of external pacemakers by walkie-talkiesand digital cellular phones experimental studyrdquo Pacing andClinical Electrophysiology vol 22 no 4 pp 588ndash593 1999

[10] G Calcagnini P Bartolini M Floris et al ldquoElectromagneticinterference to infusion pumps from GSM mobile phonesrdquo inProceedings of the 26th Annual International Conference of theIEEE Engineering in Medicine and Biology Society (EMBC rsquo04)vol 2 pp 3515ndash3518 September 2004

[11] Y Chu and A Ganz ldquoA mobile teletrauma system using 3Gnetworksrdquo IEEE Transactions on Information Technology inBiomedicine vol 8 no 4 pp 456ndash462 2004

[12] E A V Navarro J R Mas J F Navajas and C P AlcegaldquoPerformance of a 3G-based mobile telemedicine systemrdquo inProceedings of the 3rd IEEE Consumer Communications andNetworking Conference (CCNC rsquo06) vol 2 pp 1023ndash1027January 2006

[13] E-Health Insider DH to lift hospital mobile phone ban 2007httpwwwe-health-insidercomnewsitemcfmID=2542

[14] C-K Tang K-H Chan L-C Fung and S-W Leung ldquoElectro-magnetic interference immunity testing of medical equipmentto second- and third-generationmobile phonesrdquo IEEE Transac-tions on Electromagnetic Compatibility vol 51 no 3 pp 659ndash664 2009

[15] M Ardavan K Schmitt and C W Trueman ldquoA preliminaryassessment of EMI control policies in hospitalsrdquo in Proceedingsof the 14th International Symposium on Antenna Technology andApplied Electromagnetics and the American ElectromagneticsConference (ANTEMAMEREM rsquo10) pp 1ndash6 July 2010

[16] S Krishnamoorthy J H Reed C R Anderson P M Robertand S Srikanteswara ldquoCharacterization of the 24GHz ISMband electromagnetic interference in a hospital environmentrdquoin Proceedings of the 25th Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society pp 3245ndash3248 September 2003

[17] D Witters and S Seidman ldquoEMC and wireless healthcarerdquo inProceedings of the Asia-Pacific Symposium on ElectromagneticCompatibility 2010

[18] S GMyerson ldquoMobile phones in hospitals are not as hazardousas believed and should be allowed at least in non-clinical areasrdquoThe British Medical Journal vol 326 no 7387 pp 460ndash4612003

[19] F Fiori Integrated Circuit Susceptibility to Conducted RF Inter-ference Compliance Engineering 2014

[20] W D Kimmel and D D Gerke Ten Common EMI Problems inMedical Electronics Medical Electronics Design 2005

[21] G Acampora D J Cook P Rashidi and A V Vasilakos ldquoAsurvey on ambient intelligence in healthcarerdquo Proceedings of theIEEE vol 101 no 12 pp 2470ndash2494 2013

[22] D He C Chen S Chan J Bu and A V Vasilakos ldquoReTrustattack-resistant and lightweight trust management for medicalsensor networksrdquo IEEE Transactions on Information Technologyin Biomedicine vol 16 no 4 pp 623ndash632 2012

[23] N Xiong A V Vasilakos L T Yang et al ldquoComparativeanalysis of quality of service and memory usage for adaptivefailure detectors in healthcare systemsrdquo IEEE Journal on SelectedAreas in Communications vol 27 no 4 pp 495ndash509 2009

10 Journal of Sensors

[24] M R Javan and A R Sharafat ldquoEfficient and distributed SINR-Based joint resource allocation and base station assignment inwireless CDMA networksrdquo IEEE Transactions on Communica-tions vol 59 no 12 pp 3388ndash3399 2011

[25] S Tadelis GameTheory Princeton University Press 2013[26] I Benedetti S Bolognini andAMartellotti ldquoMultivalued fixed

point theoremswithout strong compactness via a generalizationof midpoint convexityrdquo Fixed Point Theory vol 15 no 1 pp 3ndash22 2014

[27] J Leskovec K J LangADasgupta andMWMahoney ldquoCom-munity structure in large networks natural cluster sizes and theabsence of large well-defined clustersrdquo Internet Mathematicsvol 6 no 1 pp 29ndash123 2009

[28] ITU-R Recommendation M1225 Guidelines for Evaluation ofRadio Transmission Technologies for IMT-2000 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 5

Remark 3 When the number of rows of 119860 is larger than119899 that is 119898

1+ 1198982

gt 119899 then the linear equation isoverdetermined We relax the constraints of (1) with the bestapproximation that is min

119883|119860119883 minus 119861| So119883 = (119860119879119860)

minus1119860119879119861

Remark 4 Given the set of wireless users 119866 the maximaltransmit power of any wireless user 119894 (denoted as 119875

119894(119866)) can

ensure that all of medical sensors are free from EMI effectswhen 119898

1+ 1198982le 119899 (see Remarks 1 and 2) and also ensure

that the total amount of EMI onmedical sensors isminimizedwhen 119898

1+ 1198982gt 119899 (see Remark 3) since under the latter

scenario the power allocation can ensure min119883|119860119883 minus 119861|

Definition 5 The maximal potential transmit power of user119894 (ie 119875

119894(119866)) to minimize the total amount of EMI on

medical sensors as obtained from Remark 4 is defined asthe maximal effective transmit power (METP) The METP(ie 119875

119894(119866) for user 119894) will be employed to establish the game

model in Section 32 (see Theorem 11) as well as to developthe joint power and rate control algorithm in Section 32 (seeRemark 8)

34 The Game Model In this section considering a cellularnetwork in which wireless users are randomly distributedin the coverage area we address a noncooperative jointtransmit power and rate control game In this game weemploy a commonly used utility which is proposed in [24]and can be characterized as a logarithmic function of powerand rate with a squared pricing item By and large threecommon requirements in wireless communications motivatethe proposal of utility in [24]

(i) Eachwireless user aims to achieve higher level of signalto interference plus noise ratio (SINR) which is defined as

SINR119894=

119875119894ℎ119894119894119877119894

sum119895 =119894119875119895ℎ119895119894+ 119873119894

(4)

where 119875119894and 119877

119894denote the transmit power and data rate

of user 119894 respectively ℎ119895119894

denotes the channel conditionbetween users 119894 and 119895119873

119894denotes the additive white Gaussian

noise(ii) Each wireless user aims to achieve a higher data rate(iii)When the interference level is high eachwireless user

is inclined to increase its power level or decrease its data rateThe proposed utility in [24] can exactly meet the three

common requirements in the wireless communication net-works Mathematically it can be presented as

119894(119875119894 119877119894) = log (120573

1119875119894+ 1205732119877119894) minus

120582

2(1205731

1205732

1198752

119894+1205732

1205731

1198772

119894) (5)

where 120582 is the pricing factor 1205731and 120573

2are adjustable

parametersThe game with utility of (5) can be modeled as

max0le119875119894le119875119894(119866)

119894(119875119894 119877119894) 119894 = 1 2 119873 (6)

where 119875119894(119866) is METP which is defined in Definition 5

Theorem 6 There exists a unique Nash equilibrium in thegame of (6) when 119875

119894(119866) = infin and at the Nash equilibrium

(119875lowast119894 119877lowast119894) the following equations hold

119875lowast

119894= radic

1

2

1205732

1205731120582 119877

lowast

119894= radic

1

2

1205731

1205732120582 (7)

Proof We show that the utility is a jointly concave functionof 119875119894and 119877

119894by calculating its second derivatives that is

1205972119894

1205971198752119894

= minus12057321

(1205731119875119894+ 1205732119877119894)2minus 120582

1205731

1205732

1205972119894

1205971198772119894

= minus1205732

2

(1205731119875119894+ 1205732119877119894)2minus 120582

1205732

1205731

1205972119894

120597119877119894120597119875119894

= minus12057311205732

(1205731119875119894+ 1205732119877119894)2

(8)

It is obvious that 12059721198941205971198752119894

le 0 12059721198941205971198772119894

le 0(12059721198941205971198752

119894)(12059721198941205971198772

119894) minus (1205972119894120597119877119894120597119875119894)2ge 0 are strict inequal-

itiesThus the utility is a strictly concave function on (119875119894 119877119894)

Also the utility is continuous on (119875119894 119877119894) Since the strategy

space of (119875119894 119877119894) is a compact convex and nonempty subset

of two-dimensional Euclidean space of real numbers fromTheorem 12 in [25] the proof of a unique Nash equilibriumof (6) follows

Recall the first derivative of 119906119894with respect to (119875

119894 119877119894) and

write120597119894

120597119875119894

= 0 997888rarr1205732

1205731119875119894+ 1205732119877119894

minus 120582119875119894= 0

120597119894

120597119877119894

= 0 997888rarr1205731

1205731119875119894+ 1205732119877119894

minus 120582119877119894= 0

(9)

We can conclude that the Nash equilibrium (119875lowast119894 119877lowast119894)

satisfies (7)

Remark 7 Theorem 6 indicates the iterative algorithm forupdating (119875

119894 119877119894) [24]

(119875119899+1

119894 119877119899+1

119894) = (IP (119875119899

119894 119877119899

119894) IR (119875119899

119894 119877119899

119894))

IP (119875119899119894 119877119899

119894) = radic

1

2

1205732

1205731120582

IR (119875119899119894 119877119899

119894) = radic

1

2

1205731

1205732120582

(10)

where 119899 denotes the 119899th iteration

The iterative power and rate updating algorithmproposedin [24] does not take into account the METP (119875

119894(119866) =

infin) thus the Nash equilibrium (119875lowast119894 119877lowast119894) could reach above

METP which would cause harmful EMI to medical sensorsIn the following we propose a novel iterative power and rateupdating algorithm to ensure that the proposed algorithmconverges to a fixed point below METP

6 Journal of Sensors

Remark 8 Theorem 6 indicates when 119875119894lt 119875119894(119866) that is the

transmit power of user 119894 is lower than its METP we have119877119894= radic(12)(120573

11205732120582) from (9) when 119875

119894= 119875119894(119866) that is

the transmit power of user 119894 reaches its METP we have 119877119894=

(minus1205731120582119875119894(119866) + radic(120573

1120582119875119894(119866))2+ 412057311205732120582)2120573

2120582 from (9)

35 Joint Power and Control AlgorithmRemark 9 In view of Remark 8 we propose the followingiterative algorithm for updating (119875

119894 119877119894)

(119875119899+1

119894 119877119899+1

119894) = (UP

(119875119899

119894 119877119899

119894) UR

(119875119899

119894 119877119899

119894))

UP(119875119899

119894 119877119899

119894) =

radic1

2

1205732

1205731120582 if 119875119899

119894le 119875119894 (119866)

119875119894 (119866) if 119875119899

119894gt 119875119894 (119866)

UR(119875119899

119894 119877119899

119894) =

radic1

2

1205731

1205732120582

if 119875119899119894le 119875119894 (119866)

minus1205731120582119875119894 (119866) + radic(1205731120582119875119894 (119866))

2

+ 412057311205732120582

21205732120582

if 119875119899119894gt 119875119894 (119866)

(11)

where 119899 denotes the 119899th iteration 119875119894(119866) is defined as

Definition 5

Algorithm in Remark 9 indicates that we force the trans-mit power to be 119875

119894(119866) when 119875119899

119894reaches above 119875

119894(119866) in order

to ensure the minimal amount of EMI on medical sensors

Lemma 10 (Brouwerrsquos Fixed Point Theorem) Let 119878 sube 119877119899 becompact and convex and 119865 119878 rarr 119878 a continuous functionThere exists a 119904 isin 119878 such that 119904 = 119865(119904)

Proof Refer to [26]

Theorem 11 The function UP(119875119899119894 119877119899119894) has a fixed point that

is there exists a power vector Plowast = [1198751 1198752 119875

119872] such that

Plowast = UP(Plowast)

Proof Since the functionUP(119875119899119894 119877119899119894) is a continuous function

of 119875119894 by Brouwerrsquos Fixed Point Theorem in Lemma 10

showing the existence of a fixed point is equal to showing theexistence of a compact and convex set 119878 such that UP 119878 rarr119878 In the following we fabricate such a set

When 119875119899119894le 119875119894(119866) UP(119875119899

119894 119877119899119894) = radic(12)(120573

21205731120582) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 ge 119892119894= radic(12)(119873

1198941205721120582ℎ119894119894)

Let 119892 = min119894119892119894 119897119895

= max119894(ℎ1198951198942120572119894120582ℎ119894119894) and

119897 = max(max119894119892119894max119894119897119894) We have UP(119875119899

119894 119877119899119894) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 le 119892 = radic119872119897 Then we

fabricate the set 119878 = 119892 le 119875119894le max119892 119875119866

119894 such that

UP 119878 rarr 119878 The proof follows

Theorem 11 indicates that a fixed point of UP(119875119899119894 119877119899119894)

always exists In the following we show that its fixed pointis unique and converges to the Nash equilibrium of game (6)

Definition 12 A function 119865(x) is defined as a standardfunction if it satisfies the following three conditions for allx ge 0 (1) positivity 119865(x) ge 0 (2) monotonicity if x1015840 ge xthen 119865(x1015840) ge 119865(x) (3) scalability for all 120575 gt 1 120575119865(x) gt119865(120575x)

Lemma 13 If a standard function has a fixed point then thefixed point is unique Also the standard function will globallyconverge to this unique fixed point

Proof Refer to [26]

Theorem 14 The joint power and rate control algorithm willalways converge to the unique Nash equilibrium of (6)

Proof By [26] if a standard function has a fixed point thenthe fixed point is unique We can easily show thatUP(119875119899

119894 119877119899119894)

is a standard function By Theorem 11 and Lemma 13 thefixed point of UP(119875119899

119894 119877119899119894) is unique

By [26] a standard function globally converges to itsunique fixed point Thus the standard function UP(119875119899

119894 119877119899119894)

will globally converge to its unique fixed point which isalso the Nash equilibrium of game by Remark 8 At theNash equilibrium the data rate and power need to meetthe relationship of (9) (see Theorem 6) and the algorithmin (10) exactly guarantees this relationship between datarate and power Thus the joint power and rate controlalgorithm always converges to the unique Nash equilibriumof game

4 Simulation and Discussion

We gather the data on Internet of vehicles from [27] in whicha connection of network represents a transmit-receive pair ofwireless users In the simulation the vehicle network contains50 nodes and each node has a probability of 01 using themobile phone Please note that in cities when an ambulanceis close to densely populated areas it is possible that 50terminals have EMI impact on medical devices at the sametime The average distance between terminals is 8 metersEach terminal ismovingwith an arbitrary direction at a speedof 10ms (36 kmh) We clarify the characteristics of channelmodels in Section 31 Also we normalize the level of EMI 119864LSor 119864NLS (see (1)) to unity and perform about 100000 Matlab-based experiments to present the results

41 Characteristics of Channel Models We select the com-monly used set of empirical channel models which is speci-fied in ITU-R recommendation M1225 [28] for simulationITU-R M1225 model is applicable for the test scenarios inurban and suburban areas outside the high rise core wherethe buildings are of nearly uniform height [28]

119871 = 40 (1 minus 4 times 10minus3Δℎ) log119877

minus 18 logΔℎ + 21 log119891 + 80(12)

Journal of Sensors 7

Table 1 Parameters of propagationmodels in ITU-R recommenda-tion M1225 [28]

Tap Relative delay (ns) Average power (dB) Doppler spectrum1 0 00 Rayleigh2 310 minus10 Rayleigh3 710 minus90 Rayleigh4 1090 minus100 Rayleigh5 1730 minus150 Rayleigh6 2510 minus200 Rayleigh

where 119877 [km] represents the distance between base stationandmobile station119891 [MHz] represents the carrier frequencyℎ [119898] represents the base station antenna height which ismeasured from the average rooftop level

Each terrestrial test environment can be modelled as achannel impulse response model based on a tapped-delayline The model is characterized by the number of taps thetime delay relative to the first tap the average power relativeto the strongest tap and the Doppler spectrum of each tapA majority of time-delay spreads are relatively small while afew ldquoworst caserdquo multipath characteristics cause much largerdelay spreads Table 1 identifies the propagation model foreach of 6 vehicular test cases In all of these test caseswe consider the strength and relative time delay of signalcomponents as well as Doppler shift and assume that eachof 6 vehicular test cases occurs with the same probabilitySpecifically the primary parameters to characterize each ofpropagation models include

(i) time delay-spread its structure and its statisticalvariability (eg probability distribution of time delayspread)

(ii) multipath fading characteristics (eg Doppler spec-trum Rician versus Rayleigh) for the envelope ofchannels

42 Proposed Algorithm across Networks In this section wecompare the convergence rate of our algorithm (11) under thescenarios of different random networks For simplicity weset 1205731= 1205732= 05 and investigate the convergence rate for

different networksIt is observed from Figure 3 that the algorithm of

(11) under the networks with highly concentrated trans-mitreceive nodes (eg Exponential network) quickly con-verges to the fixed point (with the Intel Core i7-2760QMprocessor the running time of each iteration is around000014 s so the total time of running the algorithm with6000 iterations is 084 s Given that the ambulance is movingat a speed of 10ms the algorithm is feasible when thechannel conditions are assumed to be invariant within adistance of 84m In a fast-varying mobile environment wecan use a more powerful processor to run the algorithm toensure its feasibility) while the algorithmunder the networkswithout highly concentrated transmitreceive nodes (egErdos-Renyi network) converges to the fixed point at a lowrate Indeed the algorithm under the exponential network

0 2 4 6 8 10 12 14 16 18 2005

055

06

065

07

075

08

085

09

Util

ity

Number of iterations (times103)

Figure 3 The figure illustrates the rate of convergence to the fixedpoint of our algorithm under different random networks Blueline with ldquoΔrdquo represents exponential network red line with ldquolowastrdquorepresents preferential attachment (scale-free) network dark linewith ldquoordquo represents Erdos-Renyi network

reaches the fixed point after 7000 iterations while its conver-gence appears after 12000 iterations under the Erdos-Renyinetwork

Another result observed from Figure 3 is that higher util-ity can be achieved by exponential network in which wirelessusers have only a single or few transmitreceive pairs thanby Erdos-Renyi network in which users have multiple trans-mitreceive pairs This is because a user establishs transmit-receive pairs with most of the other users in Erdos-Renyinetwork and thus one data transmission is easily influencedby the interference from the other transmissions However inthe exponential network the users establish transmit-receivepairs with only a single or few other users and they sufferlittle interference from the other transmissions

43 Impact of EMI We first address the advantages of jointpower and rate control to the increase of utility acrosswirelessusers For the comparison of utility between using joint powerand rate control as well as using power or rate control onlywe employ the strategy of power control (proposed in [1] bysetting 119877

119894as a constant) as well as rate control (by setting

119875119894as a constant) as a benchmark Figure 4 implies that the

joint power and rate control can gain a higher average utilitythan only using the control of power or the control of rateshowing the benefits of using joint power and rate control toincrease the utility Also the value of average utility dependson the ratio of 120573

1(1205731+ 1205732) and at the Nash equilibrium of

the game we have 119877119894(119877119894+ 119875119894) = 1205731(1205731+ 1205732) (see Theorem

6) It is also observed from Figure 4 that the value of utilityis symmetric with one peak at 120573

1= 1205732 this is because at

the Nash equilibrium the utility within the strategy spacecan be denoted as log(radic2120573

11205732120582) minus12058222 (by substituting (12)

into (6)) which is symmetric at the peak of 1205731= 1205732when

119875119894le 119875119894(119866)

In the following we address the benefits of using the pro-posed algorithm to the decrease of EMI on medical sensors

8 Journal of Sensors

0 01 02 03 04 05 06 07 08 09 1055

06

065

07

075

08

085

09

095

Util

ity

1205731(1205731 + 1205732)

Figure 4 The figure shows the impact of power and rate control on the utility Blue line with ldquoΔrdquo denotes power control only red line withldquolowastrdquo denotes rate control only dark line with ldquoordquo denotes joint power and rate control

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]Proposed algorithm

1205731(1205731 + 1205732)

EN

LS

(a)

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]

Proposed algorithm

1205731(1205731 + 1205732)

ELS

(b)

Figure 5The figure shows EMI caused by RF transmission using our algorithm versus algorithm in [24] the left shows the EMI on non-life-support sensors while the right shows the EMI on life-support sensors Blue and dashed line represents using algorithm in [24] dark andsolid line represents using our algorithm Line with ldquoΔrdquo represents the case of119898

1+ 1198982gt 119899 line with ldquoordquo represents the case of119898

1+ 1198982le 119899

Figure 5 shows the comparison of EMI on medical sensorscaused by RF transmission between using our proposed algo-rithm (Remark 9) and using the algorithm proposed in [24](Remark 7) Figure 5 implies that our proposed algorithm(EMI level below 01) can dramatically reduce the amount ofEMI on medical sensors compared to the algorithm in [24](EMI level up to 08) Also our algorithm can ensure thatmedical sensors are free from EMI when 119898

1+ 1198982le 119899 and

can ensure the minimal amount of EMI when 1198981+ 1198982gt 119899

To put it another way whenwe need to consider the EMI on alarge number ofmedical sensors (119898

1+1198982gt 119899) our algorithm

can minimize the amount of EMI on medical sensors thoughit cannot keep medical sensors free from EMI as under thescenario of a small number of medical sensors (119898

1+ 1198982le

119899)

5 Conclusions

We addressed a noncooperative game to maximize the utilityof wireless users by controlling their transmit power andrate under a mobile hospital scenario We proposed thejoint power and rate control algorithm and showed thatthe algorithm would globally converge to a unique Nashequilibrium of game Some of the key inferences drawn areas follows

(i) Proposed joint power and rate control algorithmcould dramatically improve the utility of wirelessusers and reduce the amount of EMI on medicalsensors compared to current algorithm in [24] whichis the most widely used power and rate controlalgorithm under nonmedical settings

Journal of Sensors 9

(ii) Under the networks with users who have highlyconcentrated transmitreceive pairs the power andrate control algorithm can converge to the fixed pointat a higher rate than under the networks in whichtransmitreceive pairs are evenly distributed amongwireless users

(iii) Networks with users who have highly concentratedtransmitreceive pairs can achieve a higher utilitythan the networks in which transmitreceive pairs areevenly distributed among wireless users

We are extending our results to the settings in whichwireless users can be of different prioritiesWewould also liketo extendour results to a dynamic setting that is the structureof Internet of vehicles is dynamically changing over time

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by National NaturalScience Foundation of China (no 61301100) and partiallysupported by a Grant from the National High TechnologyResearch and Development Program of China (863 Programno 2012AA02A614)

References

[1] P Phunchongharn D Niyato E Hossain and S CamorlingaldquoAn EMI-aware prioritized wireless access scheme for e-Healthapplications in hospital environmentsrdquo IEEE Transactions onInformation Technology in Biomedicine vol 14 no 5 pp 1247ndash1258 2010

[2] P Phunchongharn E Hossain and S Camorlinga ldquoElec-tromagnetic interference-aware transmission scheduling andpower control for dynamic wireless access in hospital envi-ronmentsrdquo IEEE Transactions on Information Technology inBiomedicine vol 15 no 6 pp 890ndash899 2011

[3] A Soomro and D Cavalcanti ldquoOpportunities and challengesin using WPAN and WLAN technologies in medical environ-mentsrdquo IEEE Communications Magazine vol 45 no 2 pp 114ndash122 2007

[4] L Zhou J Chen B Zhen I de la Torre and SMisra ldquoOn asyn-chronous flow scheduling for wireless body sensor networksrdquoin Proceedings of the 15th IEEE International Conference on e-Health Networking Applications amp Services (Healthcom rsquo13) pp366ndash370 Lisbon Portugal October 2013

[5] J J P C Rodrigues O R E Pereira and P A C S NevesldquoBiofeedback data visualization for body sensor networksrdquoJournal of Network and Computer Applications vol 34 no 1 pp151ndash158 2011

[6] M Hayajneh and C T Abdallah ldquoDistributed joint rate andpower control game-theoretic algorithms for wireless datardquoIEEE Communications Letters vol 8 no 8 pp 511ndash513 2004

[7] K-S Tan and I Hinberg ldquoRadiofrequency susceptibility testson medical equipmentrdquo in Proceedings of the 16th AnnualInternational Conference of the IEEE Engineering in Medicine

and Biology Society Engineering Advances New Opportunitiesfor Biomedical Engineers vol 2 pp 998ndash999 November 1994

[8] ldquoElectromagnetic compatibility of medical devices with mobilecommunicationsrdquo Medical Devices Bulletin DB9702 MedicalDevices Agency London UK 1997

[9] A J Trigano A AzoulayM Rochdi andA Campillo ldquoElectro-magnetic interference of external pacemakers by walkie-talkiesand digital cellular phones experimental studyrdquo Pacing andClinical Electrophysiology vol 22 no 4 pp 588ndash593 1999

[10] G Calcagnini P Bartolini M Floris et al ldquoElectromagneticinterference to infusion pumps from GSM mobile phonesrdquo inProceedings of the 26th Annual International Conference of theIEEE Engineering in Medicine and Biology Society (EMBC rsquo04)vol 2 pp 3515ndash3518 September 2004

[11] Y Chu and A Ganz ldquoA mobile teletrauma system using 3Gnetworksrdquo IEEE Transactions on Information Technology inBiomedicine vol 8 no 4 pp 456ndash462 2004

[12] E A V Navarro J R Mas J F Navajas and C P AlcegaldquoPerformance of a 3G-based mobile telemedicine systemrdquo inProceedings of the 3rd IEEE Consumer Communications andNetworking Conference (CCNC rsquo06) vol 2 pp 1023ndash1027January 2006

[13] E-Health Insider DH to lift hospital mobile phone ban 2007httpwwwe-health-insidercomnewsitemcfmID=2542

[14] C-K Tang K-H Chan L-C Fung and S-W Leung ldquoElectro-magnetic interference immunity testing of medical equipmentto second- and third-generationmobile phonesrdquo IEEE Transac-tions on Electromagnetic Compatibility vol 51 no 3 pp 659ndash664 2009

[15] M Ardavan K Schmitt and C W Trueman ldquoA preliminaryassessment of EMI control policies in hospitalsrdquo in Proceedingsof the 14th International Symposium on Antenna Technology andApplied Electromagnetics and the American ElectromagneticsConference (ANTEMAMEREM rsquo10) pp 1ndash6 July 2010

[16] S Krishnamoorthy J H Reed C R Anderson P M Robertand S Srikanteswara ldquoCharacterization of the 24GHz ISMband electromagnetic interference in a hospital environmentrdquoin Proceedings of the 25th Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society pp 3245ndash3248 September 2003

[17] D Witters and S Seidman ldquoEMC and wireless healthcarerdquo inProceedings of the Asia-Pacific Symposium on ElectromagneticCompatibility 2010

[18] S GMyerson ldquoMobile phones in hospitals are not as hazardousas believed and should be allowed at least in non-clinical areasrdquoThe British Medical Journal vol 326 no 7387 pp 460ndash4612003

[19] F Fiori Integrated Circuit Susceptibility to Conducted RF Inter-ference Compliance Engineering 2014

[20] W D Kimmel and D D Gerke Ten Common EMI Problems inMedical Electronics Medical Electronics Design 2005

[21] G Acampora D J Cook P Rashidi and A V Vasilakos ldquoAsurvey on ambient intelligence in healthcarerdquo Proceedings of theIEEE vol 101 no 12 pp 2470ndash2494 2013

[22] D He C Chen S Chan J Bu and A V Vasilakos ldquoReTrustattack-resistant and lightweight trust management for medicalsensor networksrdquo IEEE Transactions on Information Technologyin Biomedicine vol 16 no 4 pp 623ndash632 2012

[23] N Xiong A V Vasilakos L T Yang et al ldquoComparativeanalysis of quality of service and memory usage for adaptivefailure detectors in healthcare systemsrdquo IEEE Journal on SelectedAreas in Communications vol 27 no 4 pp 495ndash509 2009

10 Journal of Sensors

[24] M R Javan and A R Sharafat ldquoEfficient and distributed SINR-Based joint resource allocation and base station assignment inwireless CDMA networksrdquo IEEE Transactions on Communica-tions vol 59 no 12 pp 3388ndash3399 2011

[25] S Tadelis GameTheory Princeton University Press 2013[26] I Benedetti S Bolognini andAMartellotti ldquoMultivalued fixed

point theoremswithout strong compactness via a generalizationof midpoint convexityrdquo Fixed Point Theory vol 15 no 1 pp 3ndash22 2014

[27] J Leskovec K J LangADasgupta andMWMahoney ldquoCom-munity structure in large networks natural cluster sizes and theabsence of large well-defined clustersrdquo Internet Mathematicsvol 6 no 1 pp 29ndash123 2009

[28] ITU-R Recommendation M1225 Guidelines for Evaluation ofRadio Transmission Technologies for IMT-2000 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Journal of Sensors

Remark 8 Theorem 6 indicates when 119875119894lt 119875119894(119866) that is the

transmit power of user 119894 is lower than its METP we have119877119894= radic(12)(120573

11205732120582) from (9) when 119875

119894= 119875119894(119866) that is

the transmit power of user 119894 reaches its METP we have 119877119894=

(minus1205731120582119875119894(119866) + radic(120573

1120582119875119894(119866))2+ 412057311205732120582)2120573

2120582 from (9)

35 Joint Power and Control AlgorithmRemark 9 In view of Remark 8 we propose the followingiterative algorithm for updating (119875

119894 119877119894)

(119875119899+1

119894 119877119899+1

119894) = (UP

(119875119899

119894 119877119899

119894) UR

(119875119899

119894 119877119899

119894))

UP(119875119899

119894 119877119899

119894) =

radic1

2

1205732

1205731120582 if 119875119899

119894le 119875119894 (119866)

119875119894 (119866) if 119875119899

119894gt 119875119894 (119866)

UR(119875119899

119894 119877119899

119894) =

radic1

2

1205731

1205732120582

if 119875119899119894le 119875119894 (119866)

minus1205731120582119875119894 (119866) + radic(1205731120582119875119894 (119866))

2

+ 412057311205732120582

21205732120582

if 119875119899119894gt 119875119894 (119866)

(11)

where 119899 denotes the 119899th iteration 119875119894(119866) is defined as

Definition 5

Algorithm in Remark 9 indicates that we force the trans-mit power to be 119875

119894(119866) when 119875119899

119894reaches above 119875

119894(119866) in order

to ensure the minimal amount of EMI on medical sensors

Lemma 10 (Brouwerrsquos Fixed Point Theorem) Let 119878 sube 119877119899 becompact and convex and 119865 119878 rarr 119878 a continuous functionThere exists a 119904 isin 119878 such that 119904 = 119865(119904)

Proof Refer to [26]

Theorem 11 The function UP(119875119899119894 119877119899119894) has a fixed point that

is there exists a power vector Plowast = [1198751 1198752 119875

119872] such that

Plowast = UP(Plowast)

Proof Since the functionUP(119875119899119894 119877119899119894) is a continuous function

of 119875119894 by Brouwerrsquos Fixed Point Theorem in Lemma 10

showing the existence of a fixed point is equal to showing theexistence of a compact and convex set 119878 such that UP 119878 rarr119878 In the following we fabricate such a set

When 119875119899119894le 119875119894(119866) UP(119875119899

119894 119877119899119894) = radic(12)(120573

21205731120582) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 ge 119892119894= radic(12)(119873

1198941205721120582ℎ119894119894)

Let 119892 = min119894119892119894 119897119895

= max119894(ℎ1198951198942120572119894120582ℎ119894119894) and

119897 = max(max119894119892119894max119894119897119894) We have UP(119875119899

119894 119877119899119894) =

radic(12)(sum119895 =119894 119875119895ℎ119895119894 + 119873119894)1205721120582ℎ119894119894 le 119892 = radic119872119897 Then we

fabricate the set 119878 = 119892 le 119875119894le max119892 119875119866

119894 such that

UP 119878 rarr 119878 The proof follows

Theorem 11 indicates that a fixed point of UP(119875119899119894 119877119899119894)

always exists In the following we show that its fixed pointis unique and converges to the Nash equilibrium of game (6)

Definition 12 A function 119865(x) is defined as a standardfunction if it satisfies the following three conditions for allx ge 0 (1) positivity 119865(x) ge 0 (2) monotonicity if x1015840 ge xthen 119865(x1015840) ge 119865(x) (3) scalability for all 120575 gt 1 120575119865(x) gt119865(120575x)

Lemma 13 If a standard function has a fixed point then thefixed point is unique Also the standard function will globallyconverge to this unique fixed point

Proof Refer to [26]

Theorem 14 The joint power and rate control algorithm willalways converge to the unique Nash equilibrium of (6)

Proof By [26] if a standard function has a fixed point thenthe fixed point is unique We can easily show thatUP(119875119899

119894 119877119899119894)

is a standard function By Theorem 11 and Lemma 13 thefixed point of UP(119875119899

119894 119877119899119894) is unique

By [26] a standard function globally converges to itsunique fixed point Thus the standard function UP(119875119899

119894 119877119899119894)

will globally converge to its unique fixed point which isalso the Nash equilibrium of game by Remark 8 At theNash equilibrium the data rate and power need to meetthe relationship of (9) (see Theorem 6) and the algorithmin (10) exactly guarantees this relationship between datarate and power Thus the joint power and rate controlalgorithm always converges to the unique Nash equilibriumof game

4 Simulation and Discussion

We gather the data on Internet of vehicles from [27] in whicha connection of network represents a transmit-receive pair ofwireless users In the simulation the vehicle network contains50 nodes and each node has a probability of 01 using themobile phone Please note that in cities when an ambulanceis close to densely populated areas it is possible that 50terminals have EMI impact on medical devices at the sametime The average distance between terminals is 8 metersEach terminal ismovingwith an arbitrary direction at a speedof 10ms (36 kmh) We clarify the characteristics of channelmodels in Section 31 Also we normalize the level of EMI 119864LSor 119864NLS (see (1)) to unity and perform about 100000 Matlab-based experiments to present the results

41 Characteristics of Channel Models We select the com-monly used set of empirical channel models which is speci-fied in ITU-R recommendation M1225 [28] for simulationITU-R M1225 model is applicable for the test scenarios inurban and suburban areas outside the high rise core wherethe buildings are of nearly uniform height [28]

119871 = 40 (1 minus 4 times 10minus3Δℎ) log119877

minus 18 logΔℎ + 21 log119891 + 80(12)

Journal of Sensors 7

Table 1 Parameters of propagationmodels in ITU-R recommenda-tion M1225 [28]

Tap Relative delay (ns) Average power (dB) Doppler spectrum1 0 00 Rayleigh2 310 minus10 Rayleigh3 710 minus90 Rayleigh4 1090 minus100 Rayleigh5 1730 minus150 Rayleigh6 2510 minus200 Rayleigh

where 119877 [km] represents the distance between base stationandmobile station119891 [MHz] represents the carrier frequencyℎ [119898] represents the base station antenna height which ismeasured from the average rooftop level

Each terrestrial test environment can be modelled as achannel impulse response model based on a tapped-delayline The model is characterized by the number of taps thetime delay relative to the first tap the average power relativeto the strongest tap and the Doppler spectrum of each tapA majority of time-delay spreads are relatively small while afew ldquoworst caserdquo multipath characteristics cause much largerdelay spreads Table 1 identifies the propagation model foreach of 6 vehicular test cases In all of these test caseswe consider the strength and relative time delay of signalcomponents as well as Doppler shift and assume that eachof 6 vehicular test cases occurs with the same probabilitySpecifically the primary parameters to characterize each ofpropagation models include

(i) time delay-spread its structure and its statisticalvariability (eg probability distribution of time delayspread)

(ii) multipath fading characteristics (eg Doppler spec-trum Rician versus Rayleigh) for the envelope ofchannels

42 Proposed Algorithm across Networks In this section wecompare the convergence rate of our algorithm (11) under thescenarios of different random networks For simplicity weset 1205731= 1205732= 05 and investigate the convergence rate for

different networksIt is observed from Figure 3 that the algorithm of

(11) under the networks with highly concentrated trans-mitreceive nodes (eg Exponential network) quickly con-verges to the fixed point (with the Intel Core i7-2760QMprocessor the running time of each iteration is around000014 s so the total time of running the algorithm with6000 iterations is 084 s Given that the ambulance is movingat a speed of 10ms the algorithm is feasible when thechannel conditions are assumed to be invariant within adistance of 84m In a fast-varying mobile environment wecan use a more powerful processor to run the algorithm toensure its feasibility) while the algorithmunder the networkswithout highly concentrated transmitreceive nodes (egErdos-Renyi network) converges to the fixed point at a lowrate Indeed the algorithm under the exponential network

0 2 4 6 8 10 12 14 16 18 2005

055

06

065

07

075

08

085

09

Util

ity

Number of iterations (times103)

Figure 3 The figure illustrates the rate of convergence to the fixedpoint of our algorithm under different random networks Blueline with ldquoΔrdquo represents exponential network red line with ldquolowastrdquorepresents preferential attachment (scale-free) network dark linewith ldquoordquo represents Erdos-Renyi network

reaches the fixed point after 7000 iterations while its conver-gence appears after 12000 iterations under the Erdos-Renyinetwork

Another result observed from Figure 3 is that higher util-ity can be achieved by exponential network in which wirelessusers have only a single or few transmitreceive pairs thanby Erdos-Renyi network in which users have multiple trans-mitreceive pairs This is because a user establishs transmit-receive pairs with most of the other users in Erdos-Renyinetwork and thus one data transmission is easily influencedby the interference from the other transmissions However inthe exponential network the users establish transmit-receivepairs with only a single or few other users and they sufferlittle interference from the other transmissions

43 Impact of EMI We first address the advantages of jointpower and rate control to the increase of utility acrosswirelessusers For the comparison of utility between using joint powerand rate control as well as using power or rate control onlywe employ the strategy of power control (proposed in [1] bysetting 119877

119894as a constant) as well as rate control (by setting

119875119894as a constant) as a benchmark Figure 4 implies that the

joint power and rate control can gain a higher average utilitythan only using the control of power or the control of rateshowing the benefits of using joint power and rate control toincrease the utility Also the value of average utility dependson the ratio of 120573

1(1205731+ 1205732) and at the Nash equilibrium of

the game we have 119877119894(119877119894+ 119875119894) = 1205731(1205731+ 1205732) (see Theorem

6) It is also observed from Figure 4 that the value of utilityis symmetric with one peak at 120573

1= 1205732 this is because at

the Nash equilibrium the utility within the strategy spacecan be denoted as log(radic2120573

11205732120582) minus12058222 (by substituting (12)

into (6)) which is symmetric at the peak of 1205731= 1205732when

119875119894le 119875119894(119866)

In the following we address the benefits of using the pro-posed algorithm to the decrease of EMI on medical sensors

8 Journal of Sensors

0 01 02 03 04 05 06 07 08 09 1055

06

065

07

075

08

085

09

095

Util

ity

1205731(1205731 + 1205732)

Figure 4 The figure shows the impact of power and rate control on the utility Blue line with ldquoΔrdquo denotes power control only red line withldquolowastrdquo denotes rate control only dark line with ldquoordquo denotes joint power and rate control

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]Proposed algorithm

1205731(1205731 + 1205732)

EN

LS

(a)

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]

Proposed algorithm

1205731(1205731 + 1205732)

ELS

(b)

Figure 5The figure shows EMI caused by RF transmission using our algorithm versus algorithm in [24] the left shows the EMI on non-life-support sensors while the right shows the EMI on life-support sensors Blue and dashed line represents using algorithm in [24] dark andsolid line represents using our algorithm Line with ldquoΔrdquo represents the case of119898

1+ 1198982gt 119899 line with ldquoordquo represents the case of119898

1+ 1198982le 119899

Figure 5 shows the comparison of EMI on medical sensorscaused by RF transmission between using our proposed algo-rithm (Remark 9) and using the algorithm proposed in [24](Remark 7) Figure 5 implies that our proposed algorithm(EMI level below 01) can dramatically reduce the amount ofEMI on medical sensors compared to the algorithm in [24](EMI level up to 08) Also our algorithm can ensure thatmedical sensors are free from EMI when 119898

1+ 1198982le 119899 and

can ensure the minimal amount of EMI when 1198981+ 1198982gt 119899

To put it another way whenwe need to consider the EMI on alarge number ofmedical sensors (119898

1+1198982gt 119899) our algorithm

can minimize the amount of EMI on medical sensors thoughit cannot keep medical sensors free from EMI as under thescenario of a small number of medical sensors (119898

1+ 1198982le

119899)

5 Conclusions

We addressed a noncooperative game to maximize the utilityof wireless users by controlling their transmit power andrate under a mobile hospital scenario We proposed thejoint power and rate control algorithm and showed thatthe algorithm would globally converge to a unique Nashequilibrium of game Some of the key inferences drawn areas follows

(i) Proposed joint power and rate control algorithmcould dramatically improve the utility of wirelessusers and reduce the amount of EMI on medicalsensors compared to current algorithm in [24] whichis the most widely used power and rate controlalgorithm under nonmedical settings

Journal of Sensors 9

(ii) Under the networks with users who have highlyconcentrated transmitreceive pairs the power andrate control algorithm can converge to the fixed pointat a higher rate than under the networks in whichtransmitreceive pairs are evenly distributed amongwireless users

(iii) Networks with users who have highly concentratedtransmitreceive pairs can achieve a higher utilitythan the networks in which transmitreceive pairs areevenly distributed among wireless users

We are extending our results to the settings in whichwireless users can be of different prioritiesWewould also liketo extendour results to a dynamic setting that is the structureof Internet of vehicles is dynamically changing over time

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by National NaturalScience Foundation of China (no 61301100) and partiallysupported by a Grant from the National High TechnologyResearch and Development Program of China (863 Programno 2012AA02A614)

References

[1] P Phunchongharn D Niyato E Hossain and S CamorlingaldquoAn EMI-aware prioritized wireless access scheme for e-Healthapplications in hospital environmentsrdquo IEEE Transactions onInformation Technology in Biomedicine vol 14 no 5 pp 1247ndash1258 2010

[2] P Phunchongharn E Hossain and S Camorlinga ldquoElec-tromagnetic interference-aware transmission scheduling andpower control for dynamic wireless access in hospital envi-ronmentsrdquo IEEE Transactions on Information Technology inBiomedicine vol 15 no 6 pp 890ndash899 2011

[3] A Soomro and D Cavalcanti ldquoOpportunities and challengesin using WPAN and WLAN technologies in medical environ-mentsrdquo IEEE Communications Magazine vol 45 no 2 pp 114ndash122 2007

[4] L Zhou J Chen B Zhen I de la Torre and SMisra ldquoOn asyn-chronous flow scheduling for wireless body sensor networksrdquoin Proceedings of the 15th IEEE International Conference on e-Health Networking Applications amp Services (Healthcom rsquo13) pp366ndash370 Lisbon Portugal October 2013

[5] J J P C Rodrigues O R E Pereira and P A C S NevesldquoBiofeedback data visualization for body sensor networksrdquoJournal of Network and Computer Applications vol 34 no 1 pp151ndash158 2011

[6] M Hayajneh and C T Abdallah ldquoDistributed joint rate andpower control game-theoretic algorithms for wireless datardquoIEEE Communications Letters vol 8 no 8 pp 511ndash513 2004

[7] K-S Tan and I Hinberg ldquoRadiofrequency susceptibility testson medical equipmentrdquo in Proceedings of the 16th AnnualInternational Conference of the IEEE Engineering in Medicine

and Biology Society Engineering Advances New Opportunitiesfor Biomedical Engineers vol 2 pp 998ndash999 November 1994

[8] ldquoElectromagnetic compatibility of medical devices with mobilecommunicationsrdquo Medical Devices Bulletin DB9702 MedicalDevices Agency London UK 1997

[9] A J Trigano A AzoulayM Rochdi andA Campillo ldquoElectro-magnetic interference of external pacemakers by walkie-talkiesand digital cellular phones experimental studyrdquo Pacing andClinical Electrophysiology vol 22 no 4 pp 588ndash593 1999

[10] G Calcagnini P Bartolini M Floris et al ldquoElectromagneticinterference to infusion pumps from GSM mobile phonesrdquo inProceedings of the 26th Annual International Conference of theIEEE Engineering in Medicine and Biology Society (EMBC rsquo04)vol 2 pp 3515ndash3518 September 2004

[11] Y Chu and A Ganz ldquoA mobile teletrauma system using 3Gnetworksrdquo IEEE Transactions on Information Technology inBiomedicine vol 8 no 4 pp 456ndash462 2004

[12] E A V Navarro J R Mas J F Navajas and C P AlcegaldquoPerformance of a 3G-based mobile telemedicine systemrdquo inProceedings of the 3rd IEEE Consumer Communications andNetworking Conference (CCNC rsquo06) vol 2 pp 1023ndash1027January 2006

[13] E-Health Insider DH to lift hospital mobile phone ban 2007httpwwwe-health-insidercomnewsitemcfmID=2542

[14] C-K Tang K-H Chan L-C Fung and S-W Leung ldquoElectro-magnetic interference immunity testing of medical equipmentto second- and third-generationmobile phonesrdquo IEEE Transac-tions on Electromagnetic Compatibility vol 51 no 3 pp 659ndash664 2009

[15] M Ardavan K Schmitt and C W Trueman ldquoA preliminaryassessment of EMI control policies in hospitalsrdquo in Proceedingsof the 14th International Symposium on Antenna Technology andApplied Electromagnetics and the American ElectromagneticsConference (ANTEMAMEREM rsquo10) pp 1ndash6 July 2010

[16] S Krishnamoorthy J H Reed C R Anderson P M Robertand S Srikanteswara ldquoCharacterization of the 24GHz ISMband electromagnetic interference in a hospital environmentrdquoin Proceedings of the 25th Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society pp 3245ndash3248 September 2003

[17] D Witters and S Seidman ldquoEMC and wireless healthcarerdquo inProceedings of the Asia-Pacific Symposium on ElectromagneticCompatibility 2010

[18] S GMyerson ldquoMobile phones in hospitals are not as hazardousas believed and should be allowed at least in non-clinical areasrdquoThe British Medical Journal vol 326 no 7387 pp 460ndash4612003

[19] F Fiori Integrated Circuit Susceptibility to Conducted RF Inter-ference Compliance Engineering 2014

[20] W D Kimmel and D D Gerke Ten Common EMI Problems inMedical Electronics Medical Electronics Design 2005

[21] G Acampora D J Cook P Rashidi and A V Vasilakos ldquoAsurvey on ambient intelligence in healthcarerdquo Proceedings of theIEEE vol 101 no 12 pp 2470ndash2494 2013

[22] D He C Chen S Chan J Bu and A V Vasilakos ldquoReTrustattack-resistant and lightweight trust management for medicalsensor networksrdquo IEEE Transactions on Information Technologyin Biomedicine vol 16 no 4 pp 623ndash632 2012

[23] N Xiong A V Vasilakos L T Yang et al ldquoComparativeanalysis of quality of service and memory usage for adaptivefailure detectors in healthcare systemsrdquo IEEE Journal on SelectedAreas in Communications vol 27 no 4 pp 495ndash509 2009

10 Journal of Sensors

[24] M R Javan and A R Sharafat ldquoEfficient and distributed SINR-Based joint resource allocation and base station assignment inwireless CDMA networksrdquo IEEE Transactions on Communica-tions vol 59 no 12 pp 3388ndash3399 2011

[25] S Tadelis GameTheory Princeton University Press 2013[26] I Benedetti S Bolognini andAMartellotti ldquoMultivalued fixed

point theoremswithout strong compactness via a generalizationof midpoint convexityrdquo Fixed Point Theory vol 15 no 1 pp 3ndash22 2014

[27] J Leskovec K J LangADasgupta andMWMahoney ldquoCom-munity structure in large networks natural cluster sizes and theabsence of large well-defined clustersrdquo Internet Mathematicsvol 6 no 1 pp 29ndash123 2009

[28] ITU-R Recommendation M1225 Guidelines for Evaluation ofRadio Transmission Technologies for IMT-2000 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 7

Table 1 Parameters of propagationmodels in ITU-R recommenda-tion M1225 [28]

Tap Relative delay (ns) Average power (dB) Doppler spectrum1 0 00 Rayleigh2 310 minus10 Rayleigh3 710 minus90 Rayleigh4 1090 minus100 Rayleigh5 1730 minus150 Rayleigh6 2510 minus200 Rayleigh

where 119877 [km] represents the distance between base stationandmobile station119891 [MHz] represents the carrier frequencyℎ [119898] represents the base station antenna height which ismeasured from the average rooftop level

Each terrestrial test environment can be modelled as achannel impulse response model based on a tapped-delayline The model is characterized by the number of taps thetime delay relative to the first tap the average power relativeto the strongest tap and the Doppler spectrum of each tapA majority of time-delay spreads are relatively small while afew ldquoworst caserdquo multipath characteristics cause much largerdelay spreads Table 1 identifies the propagation model foreach of 6 vehicular test cases In all of these test caseswe consider the strength and relative time delay of signalcomponents as well as Doppler shift and assume that eachof 6 vehicular test cases occurs with the same probabilitySpecifically the primary parameters to characterize each ofpropagation models include

(i) time delay-spread its structure and its statisticalvariability (eg probability distribution of time delayspread)

(ii) multipath fading characteristics (eg Doppler spec-trum Rician versus Rayleigh) for the envelope ofchannels

42 Proposed Algorithm across Networks In this section wecompare the convergence rate of our algorithm (11) under thescenarios of different random networks For simplicity weset 1205731= 1205732= 05 and investigate the convergence rate for

different networksIt is observed from Figure 3 that the algorithm of

(11) under the networks with highly concentrated trans-mitreceive nodes (eg Exponential network) quickly con-verges to the fixed point (with the Intel Core i7-2760QMprocessor the running time of each iteration is around000014 s so the total time of running the algorithm with6000 iterations is 084 s Given that the ambulance is movingat a speed of 10ms the algorithm is feasible when thechannel conditions are assumed to be invariant within adistance of 84m In a fast-varying mobile environment wecan use a more powerful processor to run the algorithm toensure its feasibility) while the algorithmunder the networkswithout highly concentrated transmitreceive nodes (egErdos-Renyi network) converges to the fixed point at a lowrate Indeed the algorithm under the exponential network

0 2 4 6 8 10 12 14 16 18 2005

055

06

065

07

075

08

085

09

Util

ity

Number of iterations (times103)

Figure 3 The figure illustrates the rate of convergence to the fixedpoint of our algorithm under different random networks Blueline with ldquoΔrdquo represents exponential network red line with ldquolowastrdquorepresents preferential attachment (scale-free) network dark linewith ldquoordquo represents Erdos-Renyi network

reaches the fixed point after 7000 iterations while its conver-gence appears after 12000 iterations under the Erdos-Renyinetwork

Another result observed from Figure 3 is that higher util-ity can be achieved by exponential network in which wirelessusers have only a single or few transmitreceive pairs thanby Erdos-Renyi network in which users have multiple trans-mitreceive pairs This is because a user establishs transmit-receive pairs with most of the other users in Erdos-Renyinetwork and thus one data transmission is easily influencedby the interference from the other transmissions However inthe exponential network the users establish transmit-receivepairs with only a single or few other users and they sufferlittle interference from the other transmissions

43 Impact of EMI We first address the advantages of jointpower and rate control to the increase of utility acrosswirelessusers For the comparison of utility between using joint powerand rate control as well as using power or rate control onlywe employ the strategy of power control (proposed in [1] bysetting 119877

119894as a constant) as well as rate control (by setting

119875119894as a constant) as a benchmark Figure 4 implies that the

joint power and rate control can gain a higher average utilitythan only using the control of power or the control of rateshowing the benefits of using joint power and rate control toincrease the utility Also the value of average utility dependson the ratio of 120573

1(1205731+ 1205732) and at the Nash equilibrium of

the game we have 119877119894(119877119894+ 119875119894) = 1205731(1205731+ 1205732) (see Theorem

6) It is also observed from Figure 4 that the value of utilityis symmetric with one peak at 120573

1= 1205732 this is because at

the Nash equilibrium the utility within the strategy spacecan be denoted as log(radic2120573

11205732120582) minus12058222 (by substituting (12)

into (6)) which is symmetric at the peak of 1205731= 1205732when

119875119894le 119875119894(119866)

In the following we address the benefits of using the pro-posed algorithm to the decrease of EMI on medical sensors

8 Journal of Sensors

0 01 02 03 04 05 06 07 08 09 1055

06

065

07

075

08

085

09

095

Util

ity

1205731(1205731 + 1205732)

Figure 4 The figure shows the impact of power and rate control on the utility Blue line with ldquoΔrdquo denotes power control only red line withldquolowastrdquo denotes rate control only dark line with ldquoordquo denotes joint power and rate control

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]Proposed algorithm

1205731(1205731 + 1205732)

EN

LS

(a)

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]

Proposed algorithm

1205731(1205731 + 1205732)

ELS

(b)

Figure 5The figure shows EMI caused by RF transmission using our algorithm versus algorithm in [24] the left shows the EMI on non-life-support sensors while the right shows the EMI on life-support sensors Blue and dashed line represents using algorithm in [24] dark andsolid line represents using our algorithm Line with ldquoΔrdquo represents the case of119898

1+ 1198982gt 119899 line with ldquoordquo represents the case of119898

1+ 1198982le 119899

Figure 5 shows the comparison of EMI on medical sensorscaused by RF transmission between using our proposed algo-rithm (Remark 9) and using the algorithm proposed in [24](Remark 7) Figure 5 implies that our proposed algorithm(EMI level below 01) can dramatically reduce the amount ofEMI on medical sensors compared to the algorithm in [24](EMI level up to 08) Also our algorithm can ensure thatmedical sensors are free from EMI when 119898

1+ 1198982le 119899 and

can ensure the minimal amount of EMI when 1198981+ 1198982gt 119899

To put it another way whenwe need to consider the EMI on alarge number ofmedical sensors (119898

1+1198982gt 119899) our algorithm

can minimize the amount of EMI on medical sensors thoughit cannot keep medical sensors free from EMI as under thescenario of a small number of medical sensors (119898

1+ 1198982le

119899)

5 Conclusions

We addressed a noncooperative game to maximize the utilityof wireless users by controlling their transmit power andrate under a mobile hospital scenario We proposed thejoint power and rate control algorithm and showed thatthe algorithm would globally converge to a unique Nashequilibrium of game Some of the key inferences drawn areas follows

(i) Proposed joint power and rate control algorithmcould dramatically improve the utility of wirelessusers and reduce the amount of EMI on medicalsensors compared to current algorithm in [24] whichis the most widely used power and rate controlalgorithm under nonmedical settings

Journal of Sensors 9

(ii) Under the networks with users who have highlyconcentrated transmitreceive pairs the power andrate control algorithm can converge to the fixed pointat a higher rate than under the networks in whichtransmitreceive pairs are evenly distributed amongwireless users

(iii) Networks with users who have highly concentratedtransmitreceive pairs can achieve a higher utilitythan the networks in which transmitreceive pairs areevenly distributed among wireless users

We are extending our results to the settings in whichwireless users can be of different prioritiesWewould also liketo extendour results to a dynamic setting that is the structureof Internet of vehicles is dynamically changing over time

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by National NaturalScience Foundation of China (no 61301100) and partiallysupported by a Grant from the National High TechnologyResearch and Development Program of China (863 Programno 2012AA02A614)

References

[1] P Phunchongharn D Niyato E Hossain and S CamorlingaldquoAn EMI-aware prioritized wireless access scheme for e-Healthapplications in hospital environmentsrdquo IEEE Transactions onInformation Technology in Biomedicine vol 14 no 5 pp 1247ndash1258 2010

[2] P Phunchongharn E Hossain and S Camorlinga ldquoElec-tromagnetic interference-aware transmission scheduling andpower control for dynamic wireless access in hospital envi-ronmentsrdquo IEEE Transactions on Information Technology inBiomedicine vol 15 no 6 pp 890ndash899 2011

[3] A Soomro and D Cavalcanti ldquoOpportunities and challengesin using WPAN and WLAN technologies in medical environ-mentsrdquo IEEE Communications Magazine vol 45 no 2 pp 114ndash122 2007

[4] L Zhou J Chen B Zhen I de la Torre and SMisra ldquoOn asyn-chronous flow scheduling for wireless body sensor networksrdquoin Proceedings of the 15th IEEE International Conference on e-Health Networking Applications amp Services (Healthcom rsquo13) pp366ndash370 Lisbon Portugal October 2013

[5] J J P C Rodrigues O R E Pereira and P A C S NevesldquoBiofeedback data visualization for body sensor networksrdquoJournal of Network and Computer Applications vol 34 no 1 pp151ndash158 2011

[6] M Hayajneh and C T Abdallah ldquoDistributed joint rate andpower control game-theoretic algorithms for wireless datardquoIEEE Communications Letters vol 8 no 8 pp 511ndash513 2004

[7] K-S Tan and I Hinberg ldquoRadiofrequency susceptibility testson medical equipmentrdquo in Proceedings of the 16th AnnualInternational Conference of the IEEE Engineering in Medicine

and Biology Society Engineering Advances New Opportunitiesfor Biomedical Engineers vol 2 pp 998ndash999 November 1994

[8] ldquoElectromagnetic compatibility of medical devices with mobilecommunicationsrdquo Medical Devices Bulletin DB9702 MedicalDevices Agency London UK 1997

[9] A J Trigano A AzoulayM Rochdi andA Campillo ldquoElectro-magnetic interference of external pacemakers by walkie-talkiesand digital cellular phones experimental studyrdquo Pacing andClinical Electrophysiology vol 22 no 4 pp 588ndash593 1999

[10] G Calcagnini P Bartolini M Floris et al ldquoElectromagneticinterference to infusion pumps from GSM mobile phonesrdquo inProceedings of the 26th Annual International Conference of theIEEE Engineering in Medicine and Biology Society (EMBC rsquo04)vol 2 pp 3515ndash3518 September 2004

[11] Y Chu and A Ganz ldquoA mobile teletrauma system using 3Gnetworksrdquo IEEE Transactions on Information Technology inBiomedicine vol 8 no 4 pp 456ndash462 2004

[12] E A V Navarro J R Mas J F Navajas and C P AlcegaldquoPerformance of a 3G-based mobile telemedicine systemrdquo inProceedings of the 3rd IEEE Consumer Communications andNetworking Conference (CCNC rsquo06) vol 2 pp 1023ndash1027January 2006

[13] E-Health Insider DH to lift hospital mobile phone ban 2007httpwwwe-health-insidercomnewsitemcfmID=2542

[14] C-K Tang K-H Chan L-C Fung and S-W Leung ldquoElectro-magnetic interference immunity testing of medical equipmentto second- and third-generationmobile phonesrdquo IEEE Transac-tions on Electromagnetic Compatibility vol 51 no 3 pp 659ndash664 2009

[15] M Ardavan K Schmitt and C W Trueman ldquoA preliminaryassessment of EMI control policies in hospitalsrdquo in Proceedingsof the 14th International Symposium on Antenna Technology andApplied Electromagnetics and the American ElectromagneticsConference (ANTEMAMEREM rsquo10) pp 1ndash6 July 2010

[16] S Krishnamoorthy J H Reed C R Anderson P M Robertand S Srikanteswara ldquoCharacterization of the 24GHz ISMband electromagnetic interference in a hospital environmentrdquoin Proceedings of the 25th Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society pp 3245ndash3248 September 2003

[17] D Witters and S Seidman ldquoEMC and wireless healthcarerdquo inProceedings of the Asia-Pacific Symposium on ElectromagneticCompatibility 2010

[18] S GMyerson ldquoMobile phones in hospitals are not as hazardousas believed and should be allowed at least in non-clinical areasrdquoThe British Medical Journal vol 326 no 7387 pp 460ndash4612003

[19] F Fiori Integrated Circuit Susceptibility to Conducted RF Inter-ference Compliance Engineering 2014

[20] W D Kimmel and D D Gerke Ten Common EMI Problems inMedical Electronics Medical Electronics Design 2005

[21] G Acampora D J Cook P Rashidi and A V Vasilakos ldquoAsurvey on ambient intelligence in healthcarerdquo Proceedings of theIEEE vol 101 no 12 pp 2470ndash2494 2013

[22] D He C Chen S Chan J Bu and A V Vasilakos ldquoReTrustattack-resistant and lightweight trust management for medicalsensor networksrdquo IEEE Transactions on Information Technologyin Biomedicine vol 16 no 4 pp 623ndash632 2012

[23] N Xiong A V Vasilakos L T Yang et al ldquoComparativeanalysis of quality of service and memory usage for adaptivefailure detectors in healthcare systemsrdquo IEEE Journal on SelectedAreas in Communications vol 27 no 4 pp 495ndash509 2009

10 Journal of Sensors

[24] M R Javan and A R Sharafat ldquoEfficient and distributed SINR-Based joint resource allocation and base station assignment inwireless CDMA networksrdquo IEEE Transactions on Communica-tions vol 59 no 12 pp 3388ndash3399 2011

[25] S Tadelis GameTheory Princeton University Press 2013[26] I Benedetti S Bolognini andAMartellotti ldquoMultivalued fixed

point theoremswithout strong compactness via a generalizationof midpoint convexityrdquo Fixed Point Theory vol 15 no 1 pp 3ndash22 2014

[27] J Leskovec K J LangADasgupta andMWMahoney ldquoCom-munity structure in large networks natural cluster sizes and theabsence of large well-defined clustersrdquo Internet Mathematicsvol 6 no 1 pp 29ndash123 2009

[28] ITU-R Recommendation M1225 Guidelines for Evaluation ofRadio Transmission Technologies for IMT-2000 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Journal of Sensors

0 01 02 03 04 05 06 07 08 09 1055

06

065

07

075

08

085

09

095

Util

ity

1205731(1205731 + 1205732)

Figure 4 The figure shows the impact of power and rate control on the utility Blue line with ldquoΔrdquo denotes power control only red line withldquolowastrdquo denotes rate control only dark line with ldquoordquo denotes joint power and rate control

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]Proposed algorithm

1205731(1205731 + 1205732)

EN

LS

(a)

0 02 04 06 08 10

01

02

03

04

05

06

07

08

09

1

Algorithm in [5]

Proposed algorithm

1205731(1205731 + 1205732)

ELS

(b)

Figure 5The figure shows EMI caused by RF transmission using our algorithm versus algorithm in [24] the left shows the EMI on non-life-support sensors while the right shows the EMI on life-support sensors Blue and dashed line represents using algorithm in [24] dark andsolid line represents using our algorithm Line with ldquoΔrdquo represents the case of119898

1+ 1198982gt 119899 line with ldquoordquo represents the case of119898

1+ 1198982le 119899

Figure 5 shows the comparison of EMI on medical sensorscaused by RF transmission between using our proposed algo-rithm (Remark 9) and using the algorithm proposed in [24](Remark 7) Figure 5 implies that our proposed algorithm(EMI level below 01) can dramatically reduce the amount ofEMI on medical sensors compared to the algorithm in [24](EMI level up to 08) Also our algorithm can ensure thatmedical sensors are free from EMI when 119898

1+ 1198982le 119899 and

can ensure the minimal amount of EMI when 1198981+ 1198982gt 119899

To put it another way whenwe need to consider the EMI on alarge number ofmedical sensors (119898

1+1198982gt 119899) our algorithm

can minimize the amount of EMI on medical sensors thoughit cannot keep medical sensors free from EMI as under thescenario of a small number of medical sensors (119898

1+ 1198982le

119899)

5 Conclusions

We addressed a noncooperative game to maximize the utilityof wireless users by controlling their transmit power andrate under a mobile hospital scenario We proposed thejoint power and rate control algorithm and showed thatthe algorithm would globally converge to a unique Nashequilibrium of game Some of the key inferences drawn areas follows

(i) Proposed joint power and rate control algorithmcould dramatically improve the utility of wirelessusers and reduce the amount of EMI on medicalsensors compared to current algorithm in [24] whichis the most widely used power and rate controlalgorithm under nonmedical settings

Journal of Sensors 9

(ii) Under the networks with users who have highlyconcentrated transmitreceive pairs the power andrate control algorithm can converge to the fixed pointat a higher rate than under the networks in whichtransmitreceive pairs are evenly distributed amongwireless users

(iii) Networks with users who have highly concentratedtransmitreceive pairs can achieve a higher utilitythan the networks in which transmitreceive pairs areevenly distributed among wireless users

We are extending our results to the settings in whichwireless users can be of different prioritiesWewould also liketo extendour results to a dynamic setting that is the structureof Internet of vehicles is dynamically changing over time

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by National NaturalScience Foundation of China (no 61301100) and partiallysupported by a Grant from the National High TechnologyResearch and Development Program of China (863 Programno 2012AA02A614)

References

[1] P Phunchongharn D Niyato E Hossain and S CamorlingaldquoAn EMI-aware prioritized wireless access scheme for e-Healthapplications in hospital environmentsrdquo IEEE Transactions onInformation Technology in Biomedicine vol 14 no 5 pp 1247ndash1258 2010

[2] P Phunchongharn E Hossain and S Camorlinga ldquoElec-tromagnetic interference-aware transmission scheduling andpower control for dynamic wireless access in hospital envi-ronmentsrdquo IEEE Transactions on Information Technology inBiomedicine vol 15 no 6 pp 890ndash899 2011

[3] A Soomro and D Cavalcanti ldquoOpportunities and challengesin using WPAN and WLAN technologies in medical environ-mentsrdquo IEEE Communications Magazine vol 45 no 2 pp 114ndash122 2007

[4] L Zhou J Chen B Zhen I de la Torre and SMisra ldquoOn asyn-chronous flow scheduling for wireless body sensor networksrdquoin Proceedings of the 15th IEEE International Conference on e-Health Networking Applications amp Services (Healthcom rsquo13) pp366ndash370 Lisbon Portugal October 2013

[5] J J P C Rodrigues O R E Pereira and P A C S NevesldquoBiofeedback data visualization for body sensor networksrdquoJournal of Network and Computer Applications vol 34 no 1 pp151ndash158 2011

[6] M Hayajneh and C T Abdallah ldquoDistributed joint rate andpower control game-theoretic algorithms for wireless datardquoIEEE Communications Letters vol 8 no 8 pp 511ndash513 2004

[7] K-S Tan and I Hinberg ldquoRadiofrequency susceptibility testson medical equipmentrdquo in Proceedings of the 16th AnnualInternational Conference of the IEEE Engineering in Medicine

and Biology Society Engineering Advances New Opportunitiesfor Biomedical Engineers vol 2 pp 998ndash999 November 1994

[8] ldquoElectromagnetic compatibility of medical devices with mobilecommunicationsrdquo Medical Devices Bulletin DB9702 MedicalDevices Agency London UK 1997

[9] A J Trigano A AzoulayM Rochdi andA Campillo ldquoElectro-magnetic interference of external pacemakers by walkie-talkiesand digital cellular phones experimental studyrdquo Pacing andClinical Electrophysiology vol 22 no 4 pp 588ndash593 1999

[10] G Calcagnini P Bartolini M Floris et al ldquoElectromagneticinterference to infusion pumps from GSM mobile phonesrdquo inProceedings of the 26th Annual International Conference of theIEEE Engineering in Medicine and Biology Society (EMBC rsquo04)vol 2 pp 3515ndash3518 September 2004

[11] Y Chu and A Ganz ldquoA mobile teletrauma system using 3Gnetworksrdquo IEEE Transactions on Information Technology inBiomedicine vol 8 no 4 pp 456ndash462 2004

[12] E A V Navarro J R Mas J F Navajas and C P AlcegaldquoPerformance of a 3G-based mobile telemedicine systemrdquo inProceedings of the 3rd IEEE Consumer Communications andNetworking Conference (CCNC rsquo06) vol 2 pp 1023ndash1027January 2006

[13] E-Health Insider DH to lift hospital mobile phone ban 2007httpwwwe-health-insidercomnewsitemcfmID=2542

[14] C-K Tang K-H Chan L-C Fung and S-W Leung ldquoElectro-magnetic interference immunity testing of medical equipmentto second- and third-generationmobile phonesrdquo IEEE Transac-tions on Electromagnetic Compatibility vol 51 no 3 pp 659ndash664 2009

[15] M Ardavan K Schmitt and C W Trueman ldquoA preliminaryassessment of EMI control policies in hospitalsrdquo in Proceedingsof the 14th International Symposium on Antenna Technology andApplied Electromagnetics and the American ElectromagneticsConference (ANTEMAMEREM rsquo10) pp 1ndash6 July 2010

[16] S Krishnamoorthy J H Reed C R Anderson P M Robertand S Srikanteswara ldquoCharacterization of the 24GHz ISMband electromagnetic interference in a hospital environmentrdquoin Proceedings of the 25th Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society pp 3245ndash3248 September 2003

[17] D Witters and S Seidman ldquoEMC and wireless healthcarerdquo inProceedings of the Asia-Pacific Symposium on ElectromagneticCompatibility 2010

[18] S GMyerson ldquoMobile phones in hospitals are not as hazardousas believed and should be allowed at least in non-clinical areasrdquoThe British Medical Journal vol 326 no 7387 pp 460ndash4612003

[19] F Fiori Integrated Circuit Susceptibility to Conducted RF Inter-ference Compliance Engineering 2014

[20] W D Kimmel and D D Gerke Ten Common EMI Problems inMedical Electronics Medical Electronics Design 2005

[21] G Acampora D J Cook P Rashidi and A V Vasilakos ldquoAsurvey on ambient intelligence in healthcarerdquo Proceedings of theIEEE vol 101 no 12 pp 2470ndash2494 2013

[22] D He C Chen S Chan J Bu and A V Vasilakos ldquoReTrustattack-resistant and lightweight trust management for medicalsensor networksrdquo IEEE Transactions on Information Technologyin Biomedicine vol 16 no 4 pp 623ndash632 2012

[23] N Xiong A V Vasilakos L T Yang et al ldquoComparativeanalysis of quality of service and memory usage for adaptivefailure detectors in healthcare systemsrdquo IEEE Journal on SelectedAreas in Communications vol 27 no 4 pp 495ndash509 2009

10 Journal of Sensors

[24] M R Javan and A R Sharafat ldquoEfficient and distributed SINR-Based joint resource allocation and base station assignment inwireless CDMA networksrdquo IEEE Transactions on Communica-tions vol 59 no 12 pp 3388ndash3399 2011

[25] S Tadelis GameTheory Princeton University Press 2013[26] I Benedetti S Bolognini andAMartellotti ldquoMultivalued fixed

point theoremswithout strong compactness via a generalizationof midpoint convexityrdquo Fixed Point Theory vol 15 no 1 pp 3ndash22 2014

[27] J Leskovec K J LangADasgupta andMWMahoney ldquoCom-munity structure in large networks natural cluster sizes and theabsence of large well-defined clustersrdquo Internet Mathematicsvol 6 no 1 pp 29ndash123 2009

[28] ITU-R Recommendation M1225 Guidelines for Evaluation ofRadio Transmission Technologies for IMT-2000 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 9

(ii) Under the networks with users who have highlyconcentrated transmitreceive pairs the power andrate control algorithm can converge to the fixed pointat a higher rate than under the networks in whichtransmitreceive pairs are evenly distributed amongwireless users

(iii) Networks with users who have highly concentratedtransmitreceive pairs can achieve a higher utilitythan the networks in which transmitreceive pairs areevenly distributed among wireless users

We are extending our results to the settings in whichwireless users can be of different prioritiesWewould also liketo extendour results to a dynamic setting that is the structureof Internet of vehicles is dynamically changing over time

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partially supported by National NaturalScience Foundation of China (no 61301100) and partiallysupported by a Grant from the National High TechnologyResearch and Development Program of China (863 Programno 2012AA02A614)

References

[1] P Phunchongharn D Niyato E Hossain and S CamorlingaldquoAn EMI-aware prioritized wireless access scheme for e-Healthapplications in hospital environmentsrdquo IEEE Transactions onInformation Technology in Biomedicine vol 14 no 5 pp 1247ndash1258 2010

[2] P Phunchongharn E Hossain and S Camorlinga ldquoElec-tromagnetic interference-aware transmission scheduling andpower control for dynamic wireless access in hospital envi-ronmentsrdquo IEEE Transactions on Information Technology inBiomedicine vol 15 no 6 pp 890ndash899 2011

[3] A Soomro and D Cavalcanti ldquoOpportunities and challengesin using WPAN and WLAN technologies in medical environ-mentsrdquo IEEE Communications Magazine vol 45 no 2 pp 114ndash122 2007

[4] L Zhou J Chen B Zhen I de la Torre and SMisra ldquoOn asyn-chronous flow scheduling for wireless body sensor networksrdquoin Proceedings of the 15th IEEE International Conference on e-Health Networking Applications amp Services (Healthcom rsquo13) pp366ndash370 Lisbon Portugal October 2013

[5] J J P C Rodrigues O R E Pereira and P A C S NevesldquoBiofeedback data visualization for body sensor networksrdquoJournal of Network and Computer Applications vol 34 no 1 pp151ndash158 2011

[6] M Hayajneh and C T Abdallah ldquoDistributed joint rate andpower control game-theoretic algorithms for wireless datardquoIEEE Communications Letters vol 8 no 8 pp 511ndash513 2004

[7] K-S Tan and I Hinberg ldquoRadiofrequency susceptibility testson medical equipmentrdquo in Proceedings of the 16th AnnualInternational Conference of the IEEE Engineering in Medicine

and Biology Society Engineering Advances New Opportunitiesfor Biomedical Engineers vol 2 pp 998ndash999 November 1994

[8] ldquoElectromagnetic compatibility of medical devices with mobilecommunicationsrdquo Medical Devices Bulletin DB9702 MedicalDevices Agency London UK 1997

[9] A J Trigano A AzoulayM Rochdi andA Campillo ldquoElectro-magnetic interference of external pacemakers by walkie-talkiesand digital cellular phones experimental studyrdquo Pacing andClinical Electrophysiology vol 22 no 4 pp 588ndash593 1999

[10] G Calcagnini P Bartolini M Floris et al ldquoElectromagneticinterference to infusion pumps from GSM mobile phonesrdquo inProceedings of the 26th Annual International Conference of theIEEE Engineering in Medicine and Biology Society (EMBC rsquo04)vol 2 pp 3515ndash3518 September 2004

[11] Y Chu and A Ganz ldquoA mobile teletrauma system using 3Gnetworksrdquo IEEE Transactions on Information Technology inBiomedicine vol 8 no 4 pp 456ndash462 2004

[12] E A V Navarro J R Mas J F Navajas and C P AlcegaldquoPerformance of a 3G-based mobile telemedicine systemrdquo inProceedings of the 3rd IEEE Consumer Communications andNetworking Conference (CCNC rsquo06) vol 2 pp 1023ndash1027January 2006

[13] E-Health Insider DH to lift hospital mobile phone ban 2007httpwwwe-health-insidercomnewsitemcfmID=2542

[14] C-K Tang K-H Chan L-C Fung and S-W Leung ldquoElectro-magnetic interference immunity testing of medical equipmentto second- and third-generationmobile phonesrdquo IEEE Transac-tions on Electromagnetic Compatibility vol 51 no 3 pp 659ndash664 2009

[15] M Ardavan K Schmitt and C W Trueman ldquoA preliminaryassessment of EMI control policies in hospitalsrdquo in Proceedingsof the 14th International Symposium on Antenna Technology andApplied Electromagnetics and the American ElectromagneticsConference (ANTEMAMEREM rsquo10) pp 1ndash6 July 2010

[16] S Krishnamoorthy J H Reed C R Anderson P M Robertand S Srikanteswara ldquoCharacterization of the 24GHz ISMband electromagnetic interference in a hospital environmentrdquoin Proceedings of the 25th Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society pp 3245ndash3248 September 2003

[17] D Witters and S Seidman ldquoEMC and wireless healthcarerdquo inProceedings of the Asia-Pacific Symposium on ElectromagneticCompatibility 2010

[18] S GMyerson ldquoMobile phones in hospitals are not as hazardousas believed and should be allowed at least in non-clinical areasrdquoThe British Medical Journal vol 326 no 7387 pp 460ndash4612003

[19] F Fiori Integrated Circuit Susceptibility to Conducted RF Inter-ference Compliance Engineering 2014

[20] W D Kimmel and D D Gerke Ten Common EMI Problems inMedical Electronics Medical Electronics Design 2005

[21] G Acampora D J Cook P Rashidi and A V Vasilakos ldquoAsurvey on ambient intelligence in healthcarerdquo Proceedings of theIEEE vol 101 no 12 pp 2470ndash2494 2013

[22] D He C Chen S Chan J Bu and A V Vasilakos ldquoReTrustattack-resistant and lightweight trust management for medicalsensor networksrdquo IEEE Transactions on Information Technologyin Biomedicine vol 16 no 4 pp 623ndash632 2012

[23] N Xiong A V Vasilakos L T Yang et al ldquoComparativeanalysis of quality of service and memory usage for adaptivefailure detectors in healthcare systemsrdquo IEEE Journal on SelectedAreas in Communications vol 27 no 4 pp 495ndash509 2009

10 Journal of Sensors

[24] M R Javan and A R Sharafat ldquoEfficient and distributed SINR-Based joint resource allocation and base station assignment inwireless CDMA networksrdquo IEEE Transactions on Communica-tions vol 59 no 12 pp 3388ndash3399 2011

[25] S Tadelis GameTheory Princeton University Press 2013[26] I Benedetti S Bolognini andAMartellotti ldquoMultivalued fixed

point theoremswithout strong compactness via a generalizationof midpoint convexityrdquo Fixed Point Theory vol 15 no 1 pp 3ndash22 2014

[27] J Leskovec K J LangADasgupta andMWMahoney ldquoCom-munity structure in large networks natural cluster sizes and theabsence of large well-defined clustersrdquo Internet Mathematicsvol 6 no 1 pp 29ndash123 2009

[28] ITU-R Recommendation M1225 Guidelines for Evaluation ofRadio Transmission Technologies for IMT-2000 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Journal of Sensors

[24] M R Javan and A R Sharafat ldquoEfficient and distributed SINR-Based joint resource allocation and base station assignment inwireless CDMA networksrdquo IEEE Transactions on Communica-tions vol 59 no 12 pp 3388ndash3399 2011

[25] S Tadelis GameTheory Princeton University Press 2013[26] I Benedetti S Bolognini andAMartellotti ldquoMultivalued fixed

point theoremswithout strong compactness via a generalizationof midpoint convexityrdquo Fixed Point Theory vol 15 no 1 pp 3ndash22 2014

[27] J Leskovec K J LangADasgupta andMWMahoney ldquoCom-munity structure in large networks natural cluster sizes and theabsence of large well-defined clustersrdquo Internet Mathematicsvol 6 no 1 pp 29ndash123 2009

[28] ITU-R Recommendation M1225 Guidelines for Evaluation ofRadio Transmission Technologies for IMT-2000 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of