Research Article Time Power Switching Based Relaying...
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Research Article Time Power Switching Based Relaying Protocol in Energy Harvesting Mobile Node: Optimal Throughput Analysis Dinh-Thuan Do Duy Tan University (DTU), Da Nang 550000, Vietnam Correspondence should be addressed to Dinh-uan Do; [email protected] Received 9 March 2015; Revised 28 May 2015; Accepted 7 June 2015 Academic Editor: Jose Juan Pazos-Arias Copyright © 2015 Dinh-uan Do. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We propose a new protocol for energy harvesting at relay mobile node in wireless communications called energy harvesting cooperative networks (EHCN). In particular, we investigate how the harvested power at relay mobile node affects outage probability and throughput performance. Specifically, we develop outage and throughput performance characterizations in terms of time and power factors in the proposed time power switching based relaying (TPSR) protocol. A simple, highly accurate closed-form formula of outage probability is also derived. It is shown that the optimal throughput of the EHCN is critically dependent on time switching and power splitting factor of the TPSR protocol. In addition, we extend the proposed protocol performance in ideal case of receiver. e tightness of our proposed protocol is determined through Monte Carlo simulation results. Finally, our results provide useful guidelines for the design of the energy harvesting enabled relay mobile node in the EHCN. 1. Introduction In recent years, energy harvesting through radio frequency (RF) signal has received significant attention in [1–7] as a promising solution to prolonging the lifetime of energy- constrained cooperative networks. Compared with tradi- tional energy supplies such as batteries that have limited operation time and are energy constrained, mobile node with energy harvested from external natural resources such as radio frequency (RF) signal radiation will respond to growing concerns about the high cost of wireless communication networks and inconvenience of replacing or recharging fixed energy supplies [8]. e benefit of this solution lies in the fact that RF signals can be used for information and energy transmission at the same time [6, 9]. In particular, the development of the wireless power transmission brings about the ability to share power, leading to the concept of a new network as the EHCN. Interestingly, mobile devices in the EHCN will combine capability of wireless communication and energy harvesting in order to ensure seamless wireless communication without the need of using external energy sources. As a result, the mobile relay node can harvest energy and processes information simultaneously. More specifically, the authors in [6] proposed two pro- tocols of an amplify-and-forward (AF) relaying system for energy harvesting and information processing as follows: (i) Time switching based relaying (TSR) protocol where the receiver switches between information processing and energy harvesting. (ii) Power splitting based relaying (PSR) protocol where the receiver splits the received signal in two parts for information processing and energy harvesting. Both protocols have been applied in [7] to calculate the throughput of decode-and-forward (DF) relaying systems. In [9], the authors presented a harvest-then-cooperate (HTC) protocol, in which the relay mobile node harvests energy from the access point (AP) in the downlink and works cooperatively in the uplink for the source’s information transmission. Regarding energy harvesting enabled full- duplex relaying system, the authors in [10] studied the outage probability and ergodic capacity for both the amplify-and- forward (AF) and decode-and-forward (DF) protocols. In addition, the wireless information and power transfer (WIPT) systems for two-way relaying network use the AF Hindawi Publishing Corporation Mobile Information Systems Volume 2015, Article ID 769286, 8 pages http://dx.doi.org/10.1155/2015/769286
Transcript of Research Article Time Power Switching Based Relaying...
Research ArticleTime Power Switching Based Relaying Protocol in EnergyHarvesting Mobile Node Optimal Throughput Analysis
Dinh-Thuan Do
Duy Tan University (DTU) Da Nang 550000 Vietnam
Correspondence should be addressed to Dinh-Thuan Do dodinhthuangmailcom
Received 9 March 2015 Revised 28 May 2015 Accepted 7 June 2015
Academic Editor Jose Juan Pazos-Arias
Copyright copy 2015 Dinh-Thuan Do This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
We propose a new protocol for energy harvesting at relay mobile node in wireless communications called energy harvestingcooperative networks (EHCN) In particular we investigate how the harvested power at relaymobile node affects outage probabilityand throughput performance Specifically we develop outage and throughput performance characterizations in terms of time andpower factors in the proposed time power switching based relaying (TPSR) protocol A simple highly accurate closed-form formulaof outage probability is also derived It is shown that the optimal throughput of the EHCN is critically dependent on time switchingand power splitting factor of the TPSR protocol In addition we extend the proposed protocol performance in ideal case of receiverThe tightness of our proposed protocol is determined through Monte Carlo simulation results Finally our results provide usefulguidelines for the design of the energy harvesting enabled relay mobile node in the EHCN
1 Introduction
In recent years energy harvesting through radio frequency(RF) signal has received significant attention in [1ndash7] as apromising solution to prolonging the lifetime of energy-constrained cooperative networks Compared with tradi-tional energy supplies such as batteries that have limitedoperation time and are energy constrained mobile node withenergy harvested from external natural resources such asradio frequency (RF) signal radiationwill respond to growingconcerns about the high cost of wireless communicationnetworks and inconvenience of replacing or recharging fixedenergy supplies [8] The benefit of this solution lies in thefact that RF signals can be used for information and energytransmission at the same time [6 9] In particular thedevelopment of the wireless power transmission brings aboutthe ability to share power leading to the concept of a newnetwork as the EHCN Interestingly mobile devices in theEHCN will combine capability of wireless communicationand energy harvesting in order to ensure seamless wirelesscommunication without the need of using external energysources As a result the mobile relay node can harvest energyand processes information simultaneously
More specifically the authors in [6] proposed two pro-tocols of an amplify-and-forward (AF) relaying system forenergy harvesting and information processing as follows
(i) Time switching based relaying (TSR) protocol wherethe receiver switches between information processingand energy harvesting
(ii) Power splitting based relaying (PSR) protocol wherethe receiver splits the received signal in two parts forinformation processing and energy harvesting
Both protocols have been applied in [7] to calculate thethroughput of decode-and-forward (DF) relaying systems In[9] the authors presented a harvest-then-cooperate (HTC)protocol in which the relay mobile node harvests energyfrom the access point (AP) in the downlink and workscooperatively in the uplink for the sourcersquos informationtransmission Regarding energy harvesting enabled full-duplex relaying system the authors in [10] studied the outageprobability and ergodic capacity for both the amplify-and-forward (AF) and decode-and-forward (DF) protocols
In addition the wireless information and power transfer(WIPT) systems for two-way relaying network use the AF
Hindawi Publishing CorporationMobile Information SystemsVolume 2015 Article ID 769286 8 pageshttpdxdoiorg1011552015769286
2 Mobile Information Systems
scheme where two sources exchange information via anenergy harvesting relay mobile node [11] The authors in[12] have developed a low-complexity antenna switchingtechnique for WIPT in MIMO (multiple-input multiple-output) channel at relay mobile node and the solutions forWIPT in a multiuser MISO (multiple-input single-output)interference channel are also analyzed in [13]
In this work the EHCN in [6] has been extended incase of generic energy harvesting protocol In particularwe propose a time power switching based relaying protocolfor determining both time switching and power splittingfactors subject to maximized throughput performance Ourproposed protocol can be seen as a general model for energyharvesting enabled relay mobile node in the EHCN
The rest of this paper is organized as follows Section 2introduces the overall system model of energy harvestingenabled mobile node in the EHCN Section 3 presents theproposed protocols and analytic expression of the achievablethroughput In Section 4 the paper analyzes the throughputperformance with an ideal relay receiver Section 5 addressesthe numerical results of the optimal throughputwith differentvalues of time switching and power splitting factors FinallySection 6 concludes the paper
2 System Model
We consider a simple EHCN for energy harvesting andinformation transmission using AF scheme which is shownin Figure 1 where the information is transferred from thesource node 119878 (ie access point (AP) inWiFi networks) to thedestination mobile node 119863 through an energy-constrainedintermediate relay mobile node 119877 Each mobile node andsource is equipped with one single antenna and works inthe half-duplex mode We assume there is no direct linkbetween the source and the destination mobile node Thusan intermediatemobile relay assists information transmissionbetween the source and the mobile destination
Relay Model We make the following assumptions regardingrelay mobile node
(i) The relaymobile node has no other embedded energysupply and thus needs to first harvest energy fromthe AP for information processing in the next hoptransmission In practice harvested power can bestored in batteries and then is supplied as a source oftransmitting power in order to forward informationfrom the AP to the destination mobile node
(ii) The receiver structure of relaymobile node is designedfor simultaneous energy harvesting and informationprocessing and it adopts the time power switchingbased relaying protocol
Channel Model We assume that channel state information(CSI) can be obtained thanks to the advanced channelestimation algorithm which was well defined in previousworks Channel model in the EHCN is characterized as flatRayleigh fading We denote the distances from the source to
Energy harvestingInformation transmission
Source
Relay
DestinationDS
d1 d2
hShD
PS PD
R
Figure 1 The system model
the relay and from the relay to the destination mobile nodeby 1198891 and 1198892 respectively
Energy Harvesting Protocol
(i) We propose time power switching based relaying(TPSR) protocol for the considered network whichis shown in Figure 2 In the TPSR protocol 119879
denotes the block time in which the information istransmitted from the AP to the destination mobilenode and 0 lt 120572 lt 1 denotes the fraction of the blocktime switching in which the first portion of time 120572119879
is used for energy harvesting process and informationtransmission between the AP and the relay mobilenode In context of power splitting 119875 depicts the totalpower of the transmitted signal and 0 lt 120573 lt 1denotes the fraction of the power splitting ratio inenergy harvesting scheme in which TPSR divides thepower of the received signal into two parts namely120573119875 and (1minus120573)119875 with the former being used for energyharvesting and the latter being used for the sourceto relay information transmission while 120572119879 denotesa time switching ratio of the received signal at therelaymobile node for simultaneous energy harvestingand information transmission between the AP andthe relay mobile node and the remaining block timeof (1 minus 120572)119879 is used for information transmissionin the second hop Specifically these parameters aredesigned as in Figure 2
(ii) In this paper the WiFi systems following the EHCNtechnology utilizes amplify-and-forward (AF) relay-ing protocol at the relay mobile node due to itsimplementation simplicity
In the following section we consider the application ofthe TPSR protocol for the EHCN in which the relay mobilenode is powered by the energy harvested from source node(ie AP) Moreover we derive a closed-form expression ofachievable throughput in different cases of time and powerfractions in the proposed TPSR protocol
Mobile Information Systems 3
T
RrarrD
information transmission
Energy harvesting at R(120573P)
SrarrR information transmission((1 minus 120573)P)
120572T (1 minus 120572)T
Figure 2 The diagram of the TPSR protocol for energy harvestingand information processing at the relay mobile node
3 TPSR in the EHCN
31 TPSR Protocol In the EHCN relay mobile node scav-enges energy from all signals around and assists the com-munication between the AP and destination mobile node Inthis section we assume a reference systemmodel depicted inFigure 1 in which the harvested energy transferred from theAP is stored in the battery of the relay in the first hop and usedfor the transmission of relay mobile node in the next hop Togain further insights into the performance we will analyzethe achievable throughput of the proposed TPSR protocol
In TPSR protocol we design two stages namely energystage (ES) and information stage (IS) Aiming to obtainwireless energy in ES the power of received signal 119910
119877can be
divided into two parts for energy harvesting and informationprocessing in the proposed TPSR protocol Based on theenergy harvesting enabled receiver architecture as shown inFigure 3 the signal received 119910RE at the input of the energyharvesting receiver is expressed as
119910RE =1
radic119889119898
1
radic120573119875119878ℎ119878119909119878+ radic120573119899
119877 (1)
where 120573 is the power splitting ratio for energy harvesting 119898is the path loss exponent factor 119875
119878is the transmitted power
of the source node ℎ119878denotes channel coefficient between
source and relay mobile node while 119909119878denotes transmitted
signal from source and 119899119877
sim 119862119873(0 1205902119877) denotes the total
additive white Gaussian noise (AWGN) introduced at therelay mobile node by the receiving antenna and signal bandconversion [6]
The energy processing module in the relay mobile nodeconverts incoming signal in (1) to a direct current (DC) signal119894DC by a rectifier which includes a Schottky diode and a low-pass filter (LPF) As illustrated in Figure 3 the direct currentsignal is used to charge the battery and to supply informationtransmission [14] Hence the energy harvested in the TPSRprotocol is given by
119864TPSRℎ
= 120578119864 119894DC 120572120573119879 = 120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1120572120573119879 (2)
where 119864sdot denotes expectation operation and 0 lt 120578 le 1depicts the energy harvesting efficiency at the energy receiverand it depends on the rectifier and the energy harvestingcircuitry
In IS of the proposed TPSR protocol the energy scav-enged from the previous stage (ie ES) is power supply for
Rectifier BatteryEnergy harvesting
RF to baseband conversion
Baseband processing
Information receiver
Time powerswitching
Information transmitter
+
+
+
nrec
nC
120572T
(1minus120572
)T
yR
nA
radic120573yR
radic1 minus 120573yR
Figure 3 Receiver architecture for the TPSR protocol at the relaymobile node
information processing in the second hop of the EHCNCompared with harvesting energy receiver the receivedsignal at the input of the information processing receiver inthe TPSR protocol is written as
119910119877
=1
radic119889119898
1
radic(1 minus 120573) 119875119878ℎ119878119909119878+ radic(1 minus 120573)119899
119877 (3)
By applying the AF relaying protocol the relay amplifiesthe received messages by a factor 119866 defined as
119866 =1
radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 + 1205902119877
(4)
After processing the received signal at relay mobile nodethe AF based relay amplifies the source signal and forwardsit to the destination mobile node with power of 119875
119877 which
depends on the amount of energy harvested during the ESThe received signal at the destination mobile node 119910
119863 can
be expressed as
119910119863
=radic119875119877ℎ119863119866
radic119889119898
2
119910119877
+ 119899119863 (5)
where 119899119863
sim 119862119873(0 1205902119863) denotes the additive white Gaussian
noise (AWGN) introduced at the destination mobile nodeNext by substituting 119910
119877and 119866 from (3) and (4) into (5) 119910
119863
can be rewritten as
119910119863
=
radic(1 minus 120573) 119875119877119875119878ℎ119878ℎ119863119909119878
radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
2 + 119889119898
1 1205902119877
+
radic119875119877119889119898
1 ℎ119863119899119877
radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
2 + 119889119898
1 1205902119877
+ 119899119863
(6)
On the other hand the relay mobile node transmits theamplified signal using the harvested energy 119864
TPSRℎ
duringenergy harvesting time (ES) as a source of power for (1minus 120572)119879
time and hence the transmitted power from the relay mobilenode 119875
119877is calculated by
119875119877
=119864TPSRℎ
(1 minus 120572) 119879= 120578
119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1
120572120573
1 minus 120572 (7)
4 Mobile Information Systems
By substituting the transmitted power 119875119877from (7) into
(6) we obtain the received signal at the destination mobilenode 119910
119863which is illustrated as
119910119863
=
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2120572120573 (1 minus 120573) 119875
119878ℎ119878ℎ119863119909119878
radic119889119898
1 119889119898
2 (1 minus 120572)radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Signal part
+
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2120572120573119889119898
1 ℎ119863119899119877
radic119889119898
2 (1 minus 120572)radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877
+ 119899119863
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Noise part
(8)
Next by calculation of power of signal part and power ofnoise part we obtain the end-to-end SNR at the destinationas follows
SNR119863
=120578120572120573 (1 minus 120573) 119875
119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
1205781205721205731003816100381610038161003816ℎ119863
1003816100381610038161003816
2119889119898
1 1205902119877
+ (1 minus 120572) (1 minus 120573) 119889119898
1 119889119898
2 1205902119863
+ (1 minus 120572) 11988921198981 120590
21198771205902119863119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 (9)
32Throughput Analysis In this work we consider the delay-limited transmissionmode where the achievable throughput120591TPSR is determined by evaluating the outage probability
119875TPSRout of the system with a fixed source transmission rate 119877
(bpsHz)We have119877 ≜ (12)log2(1+SNR0) and denote SNR0as the threshold signal-to-noise ratio for exact data detectionat the destination Moreover in order to analyze the outageprobability of the TPSR protocol at the destination mobilenode we first obtain the instantaneous mutual informationbetween the relay and the destination mobile node which isgiven by
119868119877119863
≜ (12) log2 (1+ SNR
119863) (10)
where SNR119863is the signal-to-noise ratio at the destination
mobile node and then we formulate the outage probability ofthe system as the probability that the instantaneous mutualinformation 119868
119877119863is below fixed source transmission rate 119877
Therefore the outage probability of the system can be shownas
119875TPSRout = Pr (119868
119877119863lt 119877) = Pr (SNR
119863lt SNR0) (11)
where Pr(sdot) is probability operation and the value SNR0can be calculated by SNR0 = 22119877 minus 1 Specifically wederive the closed-form SNR
119863as the following expression
because we can ignore the infinitesimal element with respectto (1 minus 120572)119889
21198981 120590
21198771205902119863119875119878|ℎ119878|2
asymp 0 at high SNR Therefore theapproximate outage probability 119875
TPSRout can be determined by
119875TPSRout
asymp Pr(120578120572120573 (1 minus 120573) 119875
119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
1205781205721205731003816100381610038161003816ℎ119863
1003816100381610038161003816
2119889119898
1 1205902119877
+ (1 minus 120572) (1 minus 120573) 119889119898
1 119889119898
2 1205902119863
lt SNR0) = Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2
lt(1 minus 120572) (1 minus 120573) 119889
119898
1 119889119898
2 1205902119863SNR0
120578120572120573 (1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2minus 120578120572120573119889
119898
1 1205902119877SNR0
)
(12)
According to (12) we have the following proposition
Proposition 1 Let parameters for simplicity be 120596 ≜
120578120572120573119889119898
1 12059021198771198781198731198770 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 119889119898
2 12059021198631198781198731198770 and 120595 ≜
120578120572120573(1 minus 120573)119875119878 The outage probability of the destination mobile
node for the TPSR protocol in the energy harvesting networksis given by
119875119879119875119878119877
119900119906119905
= 119875119903 (1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
)
= 1minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120582ℎ119878
120582ℎ119863
1198701 (radic4120579
120595120582ℎ119878
120582ℎ119863
)
(13)
where 120582ℎ119878
and 120582ℎ119863
are the mean of the exponential randomvariables of |ℎ
119878|2 and |ℎ
119863|2 respectively and 119870
119899(sdot) is the modi-
fied Bessel function of the second kind with the order 119899 definedin [15]
Proof See the Appendix
The achievable throughput 120591TPSR of the TPSR protocol
with the fixed rate 119877 at the destination is demonstrated by
120591TPSR
= (1minus 119875TPSRout ) 119877
(1 minus 120572) 119879
119879
= (1minus 119875TPSRout ) 119877 (1minus 120572)
(14)
Therefore the optimal throughput can be found by simu-lation due to its complexity while the tractable expressions ofthe optimal throughput can be obtained in two special casesas analysis in the next subsection
Mobile Information Systems 5
33 Optimal Throughput Analysis In this paper we assumethat the CSI can be obtained by channel estimation Inprinciple the AP sends a RTS (request-to-send) packet whichis compatible with IEEE 80211 wireless LAN standards Basedon the RTS information the full CSI can be estimated On theother hand the power splitting and time switching factorsin the proposed energy harvesting also can be extractedthrough RTS mechanism When the relay and destinationhave the knowledge of ℎ
119878and ℎ
119863 respectively maximizing
the throughput can be described as
120591opt = argmax120572120573
120591TPSR
= argmax120572120573
119877 (1minus 120572)
sdot (exp(minus120596
120595120582ℎ119878
) radic4120579
120595120582ℎ119878
120582ℎ119863
1198701 (radic4120579
120595120582ℎ119878
120582ℎ119863
))
(15)
In addition we adopt the offline store-and-transmitprotocol [15] the relay stores the harvested energy at the fixedlevel and then forwards information to the destination thanksto its scavenged energy In particular the required power 1198750for further information process at the relay can be expressedas
1198750 =12057812057201205730119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1 (1 minus 120572) (16)
where 1205720 and 1205730 denote time and power allocation coeffi-cients which are known by RTS mechanism
Interestingly due to the complexity of the involvedexpression in (15) we derive the closed-form expression ofthroughput in case of high SNR (ie 1205902
119877119875119878
rarr 0) By apply-ing the following approximation 119890
minus119909sim 1minus119909 and1198701(119909) sim 1119909
as 119909 rarr 0 we obtain new formula of optimal throughput asfollows
120591opt = argmax120572120573
119877 (1minus 120572) (1minus exp(minus120596
120595120582ℎ119878
))
= argmax120572120573
119877 (1minus 120572) (1minus1205902119877SNR0
(1 minus 120573) 119875119878120582ℎ119878
)
(17)
Next there are two cases of optimization problems whichare considered as the tractable expressions of the optimalthroughput after some manipulations
Case 1 The fixed power allocation and high SNR are asfollows
120591opt = 119877 (1minus1198750
120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
21205730 + 1198750119889
119898
1
)
sdot (1minus1205902119877SNR0
(1 minus 1205730) 119875119878120582ℎ119878
)
(18)
Case 2 Thefixed time allocation and high SNR are as follows
120591opt = 119877 (1minus 1205720)
sdot (1minus1205902119877SNR0
(1 minus 1198750 (1 minus 120572) 119889119898
1 120572120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2) 119875119878120582ℎ119878
)
(19)
4 Ideal Relay Receiver
In this section we assume the scenario with an ideal relayreceiver at the relay mobile node where simultaneous energyharvesting and information transmission between the sourceand the destination mobile node are extracted by the samereceived signal Half of the block time 1198792 is used to harvestenergy and process the information at the relay mobile nodeThe remaining half 1198792 is used for the relay to destinationmobile node information transmission [6]
We consider the energy harvesting collected from sourcenode and denote it as 119864
idealℎ
given by
119864idealℎ
=120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1(
119879
2) (20)
Similarly we obtain the received signal 1199101015840119877at the input of
the ideal receiver as the following expression
1199101015840
119877=
1
radic119889119898
1
radic119875119878ℎ119878119909119878+ 119899119877 (21)
In this ideal case the relay mobile node amplifies thereceived signal by a factor 119866
1015840 which is defined by
1198661015840=
1
radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 + 1205902119877
(22)
Based on principle of ideal receiver the transmittedpower from the relay mobile node 119875
1015840
119877can be given by
1198751015840
119877=
119864idealℎ
1198792=
120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1 (23)
where 1198792 is the communication time from the relay mobilenode to the destination mobile node in the block of time 119879
seconds As a result substituting the values of 1198751015840
119877 1198661015840 and 119910
1015840
119877
from (23) (22) and (21) into (6) the received signal at thedestination 1199101015840
119863 is given by
1199101015840
119863
=
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119875119878ℎ119878ℎ119863119909119878
radic119889119898
1 radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Signal part
+
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 ℎ119863119899119877
radic119889119898
1 radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877
+ 119899119863
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Noise part
(24)
In the following we calculate the SNR at the destinationmobile node which is modeled as
SNR1015840119863
=120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
120578119889119898
11003816100381610038161003816ℎ119863
1003816100381610038161003816
21205902119877
+ 119889119898
1 1205902119863
+ 11988921198981 120590
21198771205902119863119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 (25)
6 Mobile Information Systems
Similar to the analysis in previous section the throughputis determined by evaluating the outage probability Interest-ingly the closed-form expression of119875ideal
out can be calculated as119875TPSRout
119875idealout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (26)
where 119875idealout can be calculated as in the Appendix with 120579 ≜
119889119898
1 1205902119863SNR0 120595 ≜ 120578119875
119878 and 120596 ≜ 120578119889
119898
1 1205902119877SNR0 In this case
we also consider the delay-limited transmission mode forevaluating the throughput 120591
ideal at the destination which isgiven by
120591ideal
= (1minus 119875idealout )
119877
2 (27)
5 Numerical Results
In this section we present numerical results in order toillustrate the solution to the optimization throughput prob-lems of the AF energy harvesting enabled relaying schemein the proposed TPSR protocol namely the optimal value ofthroughput 120591 optimal value of signal processing time 120572 andpower splitting ratio 120573
In these simulations we set up common parameters asfollows the distances 1198891 and 1198892 are normalized to be 1 (ie1198891 = 1198892 = 1) the energy harvesting efficiency 120578 = 07 thefixed transmission rate of the source 119877 = 4 (bpsHz) sourcetransmission power 119875
119878= 2 (Watt) destination transmission
power 119875119863
= 2 (Watt) and path loss exponent 119898 = 27In all simulations 120582
ℎ119878and 120582
ℎ119863are denoted as the mean
values of the exponential random variables |ℎ119878|2 and |ℎ
119863|2
respectively and set to 1The simulation results depend on theexpressions for outage probability in (12) which is evaluatedby averaging these calculations over 105 random realizationsof the Rayleigh fading channels of ℎ
119878and ℎ119863
As observation Figures 4 and 5 show that simulationresults of achievable throughput perfectly match the analyt-ical results for the optimal values range of 0 lt 120572 lt 1and 0 lt 120573 lt 1 for the TPSR protocol In this illustrationsimilar noise variances at the relay and destination mobilenodes are assumed that is 120590
2119877
= 1205902119863
= 1205902
= 001 Ascan be seen from Figure 4 the throughput increases from 0to 125 when 120572 increases from 001 to 035 but later it startsdecreasing as 120572 increases from its optimal value (for 120573 = 07)and the throughput increases from 0 to 095 as 120572 increasesfrom 001 to 045 but then decreases as 120572 increases from itsoptimal value (for 120573 = 03) In Figure 5 the throughputincreases from 0 to 125 as 120573 increases from 001 to 07 butlater it starts decreasing as 120573 increases (for 120572 = 03) andthe throughput increases from 0 to 084 as 120573 increases from001 to 06 but then decreases as 120573 increases from its optimalvalue (for 120572 = 07) Interestingly in the case when value of 120572
increases we obtain optimal throughput only if 120573 decreasesand vice versa We can explain important results that thevalue of 120572 is smaller than the optimal value of 120572 whichmeans that there is less time for energy harvesting and more
0 02
02
04
04
06
06
08
08
10
1
12
14TPSR protocol
AnalyticalApproximateSimulation
120572
120573 = 07
120573 = 03
Thro
ughp
ut120591
TPSR
(bps
Hz)
Figure 4 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of the block time switching
TPSR protocol
AnalyticalApproximateSimulation
0 02 04 06 08 1
02
04
06
08
0
1
12
14
120572 = 07
120572 = 03
120573
Thro
ughp
ut120591
TPSR
(bits
sH
z)
Figure 5 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of power splitting
time for information transmission As a result less energy isharvested and throughput achieved at the destination mobilenode is greater In contrast when the value of120572 is greater thanthe optimal 120572 there is more time for energy harvesting butless time for information transmission Furthermore whenthe value of 120573 is smaller than the optimal 120573 there is less
Mobile Information Systems 7
power available for energy harvesting and more power forprocessing the received signal Thus high signal strengthis observed at the relay mobile node and results in higherthroughput at the destination mobile node In addition incase the value of120573 is greater than the optimal120573 more power iswasted on energy harvesting and less power for informationtransmission from the source to relay mobile node
For comparison Figure 6 depicts the optimal throughput120591 of the TPSR protocol and the ideal receiver for differentvalues of noise variance 120590
2 In fact the simulation resultshows that the throughput in the ideal case always outper-forms that in the TPSR caseThe optimal throughput roughlyremains constant when noise variance changes from minus40 dBto minus30 dB In contrast the systemrsquos throughput performancedecreases dramatically when a larger number of noise vari-ances occur
6 Conclusions
This paper proposes TPSR protocol and the design of thereceiver architecture for wireless energy harvesting andinformation transmission in the EHCN In addition theoutage performance of the AF relaying scheme where therelay mobile node harvests energy from source node throughthe received RF signal and then uses harvested energy toamplify the information and forward the source signal tothe destination mobile node has been derived For sim-plicity in computation we also develop the closed-formexpression of the achievable throughput at the destinationMore importantly the optimal values of time switching andpower splitting ratio for energy harvesting in the proposedTPSR protocol which are chosen in order to maximize thethroughput of the system were also numerically investigated
Appendix
In the following we derive the outage probability in (12)which is given by (A1) where 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 1205902119863SNR0
120595 ≜ 120578120572120573(1 minus 120573)119875119878 and 120596 ≜ 120578120572120573119889
119898
1 1205902119877SNR0
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A1)
It is observed and also can be verified that the factor inthe denominator 120595|ℎ
119878|2
minus 120596 = 0 Thus 119875TPSRout is rewritten in
two cases as follows(i) If |ℎ
119878|2
gt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A2)
(ii) If |ℎ119878|2
lt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) = 1 (A3)
TPSRIdeal receiver
18
16
14
12
1
08
06
04
02
0minus40 minus35 minus30 minus25 minus20 minus15 minus10
1205902 (dB)
Opt
imal
thro
ughp
ut120591
d1 = d2 = 1 PS = PD = 2 120578 = 07
Figure 6 The optimal throughput achieved for the TPSR protocoland the ideal receiver by the different value of noise
We obtain the equality Pr(|ℎ119863|2
gt 120579(120595|ℎ119878|2minus120596)) = 1 due
to the fact that if the value of |ℎ119878|2
lt 120596120595 with 120596120595 being thefactor in denominator 120595|ℎ
119878|2
minus 120596 will be a negative numberand probability of |ℎ
119863|2 being greater than some negative
number is always equal to 1Therefore119875TPSRout can be rewritten
as
119875TPSRout = int
120596120595
0Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
= int
120596120595
0119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1minus expminus120579
(120595120574 minus 120596) 120582ℎ119863
)
sdot 119901|ℎ119878|
2 (120574) 119889120574
(A4)
where 120574 is the integration variable 119901|ℎ119878|
2(120574) ≜ (1120582ℎ119878
)119890minus120574120582ℎ119878
is the probability density function (PDF) of exponentialdistributed random variable |ℎ
119878|2 and 119865
|ℎ119863|2(120574) ≜ Pr(|ℎ
119863|2
lt
120574) = 1minus119890minus120574120582ℎ119863 is the cumulative distribution function (CDF)
of the exponential distributed random variable |ℎ119863|2 Thus
119875TPSRout can be calculated by
119875TPSRout = 1
minus1
120582ℎ119878
int
infin
120596120595
expminus120574
120582ℎ119878
minus120579
(120595120574 minus 120596) 120582ℎ119863
119889120574
(A5)
8 Mobile Information Systems
Let us define a new integration variable 120583 = 120595120574minus120596 Thusoutage probability is given by [15]
119875TPSRout = 1minus
1120595120582ℎ119878
exp(minus120596
120595120582ℎ119878
)
sdot int
infin
120583=0exp(minus
120583
120595120582ℎ119878
minus120579
120583120582ℎ119863
) 119889120583 = 1
minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120574ℎ119878
120574ℎ119863
1198701 (radic4120579
120595120574ℎ119878
120574ℎ119863
)
(A6)
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] D Li C Shen and Z Qiu ldquoSum rate maximization and energyharvesting for two-way af relay systems with imperfect CSIrdquoin Proceedings of the 38th IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo13) pp 4958ndash4962 Vancouver Canada May 2013
[2] O Orhan and E Erkip ldquoThroughput maximization for energyharvesting two-hop networksrdquo in Proceedings of the IEEEInternational Symposium on Information Theory (ISITrsquo13) pp1596ndash1600 Istanbul Turkey July 2013
[3] P Mangayarkarasi J Raja and S Jayashri ldquoAn efficient energyharvesting scheme to maximize the throughput of the wirelessrelay networkwithTSR andPSRprotocolrdquo International Journalof Electronics and Communications vol 69 no 5 pp 841ndash8502015
[4] J Li C Ma Y Luo Y Cheng J Wu and C Chen ldquoJointoptimization of transmit power and energy harvesting for relay-basedM2M two-way communicationsrdquo International Journal ofDistributed Sensor Networks In press
[5] N Nomikos D N Skoutas D Vouyioukas C Verikoukisand C Skianis ldquoCapacity maximization through energy-awaremulti-mode relayingrdquo Wireless Personal Communications vol74 no 1 pp 83ndash99 2014
[6] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[7] A A Nasir X Zhou S Durrani and R A Kennedy ldquoThrough-put and ergodic capacity of wireless energy harvesting basedDF relaying networkrdquo in Proceedings of the IEEE InternationalConference on Communications (ICCrsquo14) pp 4066ndash4071 IEEESydney Australia June 2014
[8] X LuW Xu S Li J Lin and Z He ldquoSimultaneous informationand power transfer for relay-assisted cognitive radio networksrdquoin Proceedings of the IEEE International Conference on Commu-nications Workshops (ICC 14) pp 331ndash336 Sydney AustraliaJune 2014
[9] H H Chen Y Li J L Rebelatto B F Uchoa-Filhoand andB Vucetic ldquoHarvest-then-cooperate wireless-powered cooper-ative communicationsrdquo IEEE Transactions on Signal Processingvol 63 no 7 pp 1700ndash1711 2015
[10] C Zhong H A Suraweera G Zjeng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[11] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[12] I Krikidis S Sasaki S Timotheou and Z Ding ldquoA low com-plexity antenna switching for joint wireless information andenergy transfer in MIMO relay channelsrdquo IEEE Transactions onCommunications vol 62 no 5 pp 1577ndash1587 2014
[13] C Shen W-C Li and T-H Chang ldquoWireless information andenergy transfer in multi-antenna interference channelrdquo IEEETransactions on Signal Processing vol 62 no 23 pp 6249ndash62642014
[14] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4767 2013
[15] I S Gradshteyn and I M Ryzhik Table of Integrals Series andProducts ElsevierAcademic Press 7th edition 2007
Submit your manuscripts athttpwwwhindawicom
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Applied Computational Intelligence and Soft Computing
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Electrical and Computer Engineering
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Human-ComputerInteraction
Advances in
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2 Mobile Information Systems
scheme where two sources exchange information via anenergy harvesting relay mobile node [11] The authors in[12] have developed a low-complexity antenna switchingtechnique for WIPT in MIMO (multiple-input multiple-output) channel at relay mobile node and the solutions forWIPT in a multiuser MISO (multiple-input single-output)interference channel are also analyzed in [13]
In this work the EHCN in [6] has been extended incase of generic energy harvesting protocol In particularwe propose a time power switching based relaying protocolfor determining both time switching and power splittingfactors subject to maximized throughput performance Ourproposed protocol can be seen as a general model for energyharvesting enabled relay mobile node in the EHCN
The rest of this paper is organized as follows Section 2introduces the overall system model of energy harvestingenabled mobile node in the EHCN Section 3 presents theproposed protocols and analytic expression of the achievablethroughput In Section 4 the paper analyzes the throughputperformance with an ideal relay receiver Section 5 addressesthe numerical results of the optimal throughputwith differentvalues of time switching and power splitting factors FinallySection 6 concludes the paper
2 System Model
We consider a simple EHCN for energy harvesting andinformation transmission using AF scheme which is shownin Figure 1 where the information is transferred from thesource node 119878 (ie access point (AP) inWiFi networks) to thedestination mobile node 119863 through an energy-constrainedintermediate relay mobile node 119877 Each mobile node andsource is equipped with one single antenna and works inthe half-duplex mode We assume there is no direct linkbetween the source and the destination mobile node Thusan intermediatemobile relay assists information transmissionbetween the source and the mobile destination
Relay Model We make the following assumptions regardingrelay mobile node
(i) The relaymobile node has no other embedded energysupply and thus needs to first harvest energy fromthe AP for information processing in the next hoptransmission In practice harvested power can bestored in batteries and then is supplied as a source oftransmitting power in order to forward informationfrom the AP to the destination mobile node
(ii) The receiver structure of relaymobile node is designedfor simultaneous energy harvesting and informationprocessing and it adopts the time power switchingbased relaying protocol
Channel Model We assume that channel state information(CSI) can be obtained thanks to the advanced channelestimation algorithm which was well defined in previousworks Channel model in the EHCN is characterized as flatRayleigh fading We denote the distances from the source to
Energy harvestingInformation transmission
Source
Relay
DestinationDS
d1 d2
hShD
PS PD
R
Figure 1 The system model
the relay and from the relay to the destination mobile nodeby 1198891 and 1198892 respectively
Energy Harvesting Protocol
(i) We propose time power switching based relaying(TPSR) protocol for the considered network whichis shown in Figure 2 In the TPSR protocol 119879
denotes the block time in which the information istransmitted from the AP to the destination mobilenode and 0 lt 120572 lt 1 denotes the fraction of the blocktime switching in which the first portion of time 120572119879
is used for energy harvesting process and informationtransmission between the AP and the relay mobilenode In context of power splitting 119875 depicts the totalpower of the transmitted signal and 0 lt 120573 lt 1denotes the fraction of the power splitting ratio inenergy harvesting scheme in which TPSR divides thepower of the received signal into two parts namely120573119875 and (1minus120573)119875 with the former being used for energyharvesting and the latter being used for the sourceto relay information transmission while 120572119879 denotesa time switching ratio of the received signal at therelaymobile node for simultaneous energy harvestingand information transmission between the AP andthe relay mobile node and the remaining block timeof (1 minus 120572)119879 is used for information transmissionin the second hop Specifically these parameters aredesigned as in Figure 2
(ii) In this paper the WiFi systems following the EHCNtechnology utilizes amplify-and-forward (AF) relay-ing protocol at the relay mobile node due to itsimplementation simplicity
In the following section we consider the application ofthe TPSR protocol for the EHCN in which the relay mobilenode is powered by the energy harvested from source node(ie AP) Moreover we derive a closed-form expression ofachievable throughput in different cases of time and powerfractions in the proposed TPSR protocol
Mobile Information Systems 3
T
RrarrD
information transmission
Energy harvesting at R(120573P)
SrarrR information transmission((1 minus 120573)P)
120572T (1 minus 120572)T
Figure 2 The diagram of the TPSR protocol for energy harvestingand information processing at the relay mobile node
3 TPSR in the EHCN
31 TPSR Protocol In the EHCN relay mobile node scav-enges energy from all signals around and assists the com-munication between the AP and destination mobile node Inthis section we assume a reference systemmodel depicted inFigure 1 in which the harvested energy transferred from theAP is stored in the battery of the relay in the first hop and usedfor the transmission of relay mobile node in the next hop Togain further insights into the performance we will analyzethe achievable throughput of the proposed TPSR protocol
In TPSR protocol we design two stages namely energystage (ES) and information stage (IS) Aiming to obtainwireless energy in ES the power of received signal 119910
119877can be
divided into two parts for energy harvesting and informationprocessing in the proposed TPSR protocol Based on theenergy harvesting enabled receiver architecture as shown inFigure 3 the signal received 119910RE at the input of the energyharvesting receiver is expressed as
119910RE =1
radic119889119898
1
radic120573119875119878ℎ119878119909119878+ radic120573119899
119877 (1)
where 120573 is the power splitting ratio for energy harvesting 119898is the path loss exponent factor 119875
119878is the transmitted power
of the source node ℎ119878denotes channel coefficient between
source and relay mobile node while 119909119878denotes transmitted
signal from source and 119899119877
sim 119862119873(0 1205902119877) denotes the total
additive white Gaussian noise (AWGN) introduced at therelay mobile node by the receiving antenna and signal bandconversion [6]
The energy processing module in the relay mobile nodeconverts incoming signal in (1) to a direct current (DC) signal119894DC by a rectifier which includes a Schottky diode and a low-pass filter (LPF) As illustrated in Figure 3 the direct currentsignal is used to charge the battery and to supply informationtransmission [14] Hence the energy harvested in the TPSRprotocol is given by
119864TPSRℎ
= 120578119864 119894DC 120572120573119879 = 120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1120572120573119879 (2)
where 119864sdot denotes expectation operation and 0 lt 120578 le 1depicts the energy harvesting efficiency at the energy receiverand it depends on the rectifier and the energy harvestingcircuitry
In IS of the proposed TPSR protocol the energy scav-enged from the previous stage (ie ES) is power supply for
Rectifier BatteryEnergy harvesting
RF to baseband conversion
Baseband processing
Information receiver
Time powerswitching
Information transmitter
+
+
+
nrec
nC
120572T
(1minus120572
)T
yR
nA
radic120573yR
radic1 minus 120573yR
Figure 3 Receiver architecture for the TPSR protocol at the relaymobile node
information processing in the second hop of the EHCNCompared with harvesting energy receiver the receivedsignal at the input of the information processing receiver inthe TPSR protocol is written as
119910119877
=1
radic119889119898
1
radic(1 minus 120573) 119875119878ℎ119878119909119878+ radic(1 minus 120573)119899
119877 (3)
By applying the AF relaying protocol the relay amplifiesthe received messages by a factor 119866 defined as
119866 =1
radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 + 1205902119877
(4)
After processing the received signal at relay mobile nodethe AF based relay amplifies the source signal and forwardsit to the destination mobile node with power of 119875
119877 which
depends on the amount of energy harvested during the ESThe received signal at the destination mobile node 119910
119863 can
be expressed as
119910119863
=radic119875119877ℎ119863119866
radic119889119898
2
119910119877
+ 119899119863 (5)
where 119899119863
sim 119862119873(0 1205902119863) denotes the additive white Gaussian
noise (AWGN) introduced at the destination mobile nodeNext by substituting 119910
119877and 119866 from (3) and (4) into (5) 119910
119863
can be rewritten as
119910119863
=
radic(1 minus 120573) 119875119877119875119878ℎ119878ℎ119863119909119878
radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
2 + 119889119898
1 1205902119877
+
radic119875119877119889119898
1 ℎ119863119899119877
radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
2 + 119889119898
1 1205902119877
+ 119899119863
(6)
On the other hand the relay mobile node transmits theamplified signal using the harvested energy 119864
TPSRℎ
duringenergy harvesting time (ES) as a source of power for (1minus 120572)119879
time and hence the transmitted power from the relay mobilenode 119875
119877is calculated by
119875119877
=119864TPSRℎ
(1 minus 120572) 119879= 120578
119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1
120572120573
1 minus 120572 (7)
4 Mobile Information Systems
By substituting the transmitted power 119875119877from (7) into
(6) we obtain the received signal at the destination mobilenode 119910
119863which is illustrated as
119910119863
=
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2120572120573 (1 minus 120573) 119875
119878ℎ119878ℎ119863119909119878
radic119889119898
1 119889119898
2 (1 minus 120572)radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Signal part
+
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2120572120573119889119898
1 ℎ119863119899119877
radic119889119898
2 (1 minus 120572)radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877
+ 119899119863
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Noise part
(8)
Next by calculation of power of signal part and power ofnoise part we obtain the end-to-end SNR at the destinationas follows
SNR119863
=120578120572120573 (1 minus 120573) 119875
119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
1205781205721205731003816100381610038161003816ℎ119863
1003816100381610038161003816
2119889119898
1 1205902119877
+ (1 minus 120572) (1 minus 120573) 119889119898
1 119889119898
2 1205902119863
+ (1 minus 120572) 11988921198981 120590
21198771205902119863119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 (9)
32Throughput Analysis In this work we consider the delay-limited transmissionmode where the achievable throughput120591TPSR is determined by evaluating the outage probability
119875TPSRout of the system with a fixed source transmission rate 119877
(bpsHz)We have119877 ≜ (12)log2(1+SNR0) and denote SNR0as the threshold signal-to-noise ratio for exact data detectionat the destination Moreover in order to analyze the outageprobability of the TPSR protocol at the destination mobilenode we first obtain the instantaneous mutual informationbetween the relay and the destination mobile node which isgiven by
119868119877119863
≜ (12) log2 (1+ SNR
119863) (10)
where SNR119863is the signal-to-noise ratio at the destination
mobile node and then we formulate the outage probability ofthe system as the probability that the instantaneous mutualinformation 119868
119877119863is below fixed source transmission rate 119877
Therefore the outage probability of the system can be shownas
119875TPSRout = Pr (119868
119877119863lt 119877) = Pr (SNR
119863lt SNR0) (11)
where Pr(sdot) is probability operation and the value SNR0can be calculated by SNR0 = 22119877 minus 1 Specifically wederive the closed-form SNR
119863as the following expression
because we can ignore the infinitesimal element with respectto (1 minus 120572)119889
21198981 120590
21198771205902119863119875119878|ℎ119878|2
asymp 0 at high SNR Therefore theapproximate outage probability 119875
TPSRout can be determined by
119875TPSRout
asymp Pr(120578120572120573 (1 minus 120573) 119875
119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
1205781205721205731003816100381610038161003816ℎ119863
1003816100381610038161003816
2119889119898
1 1205902119877
+ (1 minus 120572) (1 minus 120573) 119889119898
1 119889119898
2 1205902119863
lt SNR0) = Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2
lt(1 minus 120572) (1 minus 120573) 119889
119898
1 119889119898
2 1205902119863SNR0
120578120572120573 (1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2minus 120578120572120573119889
119898
1 1205902119877SNR0
)
(12)
According to (12) we have the following proposition
Proposition 1 Let parameters for simplicity be 120596 ≜
120578120572120573119889119898
1 12059021198771198781198731198770 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 119889119898
2 12059021198631198781198731198770 and 120595 ≜
120578120572120573(1 minus 120573)119875119878 The outage probability of the destination mobile
node for the TPSR protocol in the energy harvesting networksis given by
119875119879119875119878119877
119900119906119905
= 119875119903 (1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
)
= 1minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120582ℎ119878
120582ℎ119863
1198701 (radic4120579
120595120582ℎ119878
120582ℎ119863
)
(13)
where 120582ℎ119878
and 120582ℎ119863
are the mean of the exponential randomvariables of |ℎ
119878|2 and |ℎ
119863|2 respectively and 119870
119899(sdot) is the modi-
fied Bessel function of the second kind with the order 119899 definedin [15]
Proof See the Appendix
The achievable throughput 120591TPSR of the TPSR protocol
with the fixed rate 119877 at the destination is demonstrated by
120591TPSR
= (1minus 119875TPSRout ) 119877
(1 minus 120572) 119879
119879
= (1minus 119875TPSRout ) 119877 (1minus 120572)
(14)
Therefore the optimal throughput can be found by simu-lation due to its complexity while the tractable expressions ofthe optimal throughput can be obtained in two special casesas analysis in the next subsection
Mobile Information Systems 5
33 Optimal Throughput Analysis In this paper we assumethat the CSI can be obtained by channel estimation Inprinciple the AP sends a RTS (request-to-send) packet whichis compatible with IEEE 80211 wireless LAN standards Basedon the RTS information the full CSI can be estimated On theother hand the power splitting and time switching factorsin the proposed energy harvesting also can be extractedthrough RTS mechanism When the relay and destinationhave the knowledge of ℎ
119878and ℎ
119863 respectively maximizing
the throughput can be described as
120591opt = argmax120572120573
120591TPSR
= argmax120572120573
119877 (1minus 120572)
sdot (exp(minus120596
120595120582ℎ119878
) radic4120579
120595120582ℎ119878
120582ℎ119863
1198701 (radic4120579
120595120582ℎ119878
120582ℎ119863
))
(15)
In addition we adopt the offline store-and-transmitprotocol [15] the relay stores the harvested energy at the fixedlevel and then forwards information to the destination thanksto its scavenged energy In particular the required power 1198750for further information process at the relay can be expressedas
1198750 =12057812057201205730119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1 (1 minus 120572) (16)
where 1205720 and 1205730 denote time and power allocation coeffi-cients which are known by RTS mechanism
Interestingly due to the complexity of the involvedexpression in (15) we derive the closed-form expression ofthroughput in case of high SNR (ie 1205902
119877119875119878
rarr 0) By apply-ing the following approximation 119890
minus119909sim 1minus119909 and1198701(119909) sim 1119909
as 119909 rarr 0 we obtain new formula of optimal throughput asfollows
120591opt = argmax120572120573
119877 (1minus 120572) (1minus exp(minus120596
120595120582ℎ119878
))
= argmax120572120573
119877 (1minus 120572) (1minus1205902119877SNR0
(1 minus 120573) 119875119878120582ℎ119878
)
(17)
Next there are two cases of optimization problems whichare considered as the tractable expressions of the optimalthroughput after some manipulations
Case 1 The fixed power allocation and high SNR are asfollows
120591opt = 119877 (1minus1198750
120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
21205730 + 1198750119889
119898
1
)
sdot (1minus1205902119877SNR0
(1 minus 1205730) 119875119878120582ℎ119878
)
(18)
Case 2 Thefixed time allocation and high SNR are as follows
120591opt = 119877 (1minus 1205720)
sdot (1minus1205902119877SNR0
(1 minus 1198750 (1 minus 120572) 119889119898
1 120572120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2) 119875119878120582ℎ119878
)
(19)
4 Ideal Relay Receiver
In this section we assume the scenario with an ideal relayreceiver at the relay mobile node where simultaneous energyharvesting and information transmission between the sourceand the destination mobile node are extracted by the samereceived signal Half of the block time 1198792 is used to harvestenergy and process the information at the relay mobile nodeThe remaining half 1198792 is used for the relay to destinationmobile node information transmission [6]
We consider the energy harvesting collected from sourcenode and denote it as 119864
idealℎ
given by
119864idealℎ
=120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1(
119879
2) (20)
Similarly we obtain the received signal 1199101015840119877at the input of
the ideal receiver as the following expression
1199101015840
119877=
1
radic119889119898
1
radic119875119878ℎ119878119909119878+ 119899119877 (21)
In this ideal case the relay mobile node amplifies thereceived signal by a factor 119866
1015840 which is defined by
1198661015840=
1
radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 + 1205902119877
(22)
Based on principle of ideal receiver the transmittedpower from the relay mobile node 119875
1015840
119877can be given by
1198751015840
119877=
119864idealℎ
1198792=
120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1 (23)
where 1198792 is the communication time from the relay mobilenode to the destination mobile node in the block of time 119879
seconds As a result substituting the values of 1198751015840
119877 1198661015840 and 119910
1015840
119877
from (23) (22) and (21) into (6) the received signal at thedestination 1199101015840
119863 is given by
1199101015840
119863
=
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119875119878ℎ119878ℎ119863119909119878
radic119889119898
1 radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Signal part
+
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 ℎ119863119899119877
radic119889119898
1 radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877
+ 119899119863
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Noise part
(24)
In the following we calculate the SNR at the destinationmobile node which is modeled as
SNR1015840119863
=120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
120578119889119898
11003816100381610038161003816ℎ119863
1003816100381610038161003816
21205902119877
+ 119889119898
1 1205902119863
+ 11988921198981 120590
21198771205902119863119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 (25)
6 Mobile Information Systems
Similar to the analysis in previous section the throughputis determined by evaluating the outage probability Interest-ingly the closed-form expression of119875ideal
out can be calculated as119875TPSRout
119875idealout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (26)
where 119875idealout can be calculated as in the Appendix with 120579 ≜
119889119898
1 1205902119863SNR0 120595 ≜ 120578119875
119878 and 120596 ≜ 120578119889
119898
1 1205902119877SNR0 In this case
we also consider the delay-limited transmission mode forevaluating the throughput 120591
ideal at the destination which isgiven by
120591ideal
= (1minus 119875idealout )
119877
2 (27)
5 Numerical Results
In this section we present numerical results in order toillustrate the solution to the optimization throughput prob-lems of the AF energy harvesting enabled relaying schemein the proposed TPSR protocol namely the optimal value ofthroughput 120591 optimal value of signal processing time 120572 andpower splitting ratio 120573
In these simulations we set up common parameters asfollows the distances 1198891 and 1198892 are normalized to be 1 (ie1198891 = 1198892 = 1) the energy harvesting efficiency 120578 = 07 thefixed transmission rate of the source 119877 = 4 (bpsHz) sourcetransmission power 119875
119878= 2 (Watt) destination transmission
power 119875119863
= 2 (Watt) and path loss exponent 119898 = 27In all simulations 120582
ℎ119878and 120582
ℎ119863are denoted as the mean
values of the exponential random variables |ℎ119878|2 and |ℎ
119863|2
respectively and set to 1The simulation results depend on theexpressions for outage probability in (12) which is evaluatedby averaging these calculations over 105 random realizationsof the Rayleigh fading channels of ℎ
119878and ℎ119863
As observation Figures 4 and 5 show that simulationresults of achievable throughput perfectly match the analyt-ical results for the optimal values range of 0 lt 120572 lt 1and 0 lt 120573 lt 1 for the TPSR protocol In this illustrationsimilar noise variances at the relay and destination mobilenodes are assumed that is 120590
2119877
= 1205902119863
= 1205902
= 001 Ascan be seen from Figure 4 the throughput increases from 0to 125 when 120572 increases from 001 to 035 but later it startsdecreasing as 120572 increases from its optimal value (for 120573 = 07)and the throughput increases from 0 to 095 as 120572 increasesfrom 001 to 045 but then decreases as 120572 increases from itsoptimal value (for 120573 = 03) In Figure 5 the throughputincreases from 0 to 125 as 120573 increases from 001 to 07 butlater it starts decreasing as 120573 increases (for 120572 = 03) andthe throughput increases from 0 to 084 as 120573 increases from001 to 06 but then decreases as 120573 increases from its optimalvalue (for 120572 = 07) Interestingly in the case when value of 120572
increases we obtain optimal throughput only if 120573 decreasesand vice versa We can explain important results that thevalue of 120572 is smaller than the optimal value of 120572 whichmeans that there is less time for energy harvesting and more
0 02
02
04
04
06
06
08
08
10
1
12
14TPSR protocol
AnalyticalApproximateSimulation
120572
120573 = 07
120573 = 03
Thro
ughp
ut120591
TPSR
(bps
Hz)
Figure 4 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of the block time switching
TPSR protocol
AnalyticalApproximateSimulation
0 02 04 06 08 1
02
04
06
08
0
1
12
14
120572 = 07
120572 = 03
120573
Thro
ughp
ut120591
TPSR
(bits
sH
z)
Figure 5 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of power splitting
time for information transmission As a result less energy isharvested and throughput achieved at the destination mobilenode is greater In contrast when the value of120572 is greater thanthe optimal 120572 there is more time for energy harvesting butless time for information transmission Furthermore whenthe value of 120573 is smaller than the optimal 120573 there is less
Mobile Information Systems 7
power available for energy harvesting and more power forprocessing the received signal Thus high signal strengthis observed at the relay mobile node and results in higherthroughput at the destination mobile node In addition incase the value of120573 is greater than the optimal120573 more power iswasted on energy harvesting and less power for informationtransmission from the source to relay mobile node
For comparison Figure 6 depicts the optimal throughput120591 of the TPSR protocol and the ideal receiver for differentvalues of noise variance 120590
2 In fact the simulation resultshows that the throughput in the ideal case always outper-forms that in the TPSR caseThe optimal throughput roughlyremains constant when noise variance changes from minus40 dBto minus30 dB In contrast the systemrsquos throughput performancedecreases dramatically when a larger number of noise vari-ances occur
6 Conclusions
This paper proposes TPSR protocol and the design of thereceiver architecture for wireless energy harvesting andinformation transmission in the EHCN In addition theoutage performance of the AF relaying scheme where therelay mobile node harvests energy from source node throughthe received RF signal and then uses harvested energy toamplify the information and forward the source signal tothe destination mobile node has been derived For sim-plicity in computation we also develop the closed-formexpression of the achievable throughput at the destinationMore importantly the optimal values of time switching andpower splitting ratio for energy harvesting in the proposedTPSR protocol which are chosen in order to maximize thethroughput of the system were also numerically investigated
Appendix
In the following we derive the outage probability in (12)which is given by (A1) where 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 1205902119863SNR0
120595 ≜ 120578120572120573(1 minus 120573)119875119878 and 120596 ≜ 120578120572120573119889
119898
1 1205902119877SNR0
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A1)
It is observed and also can be verified that the factor inthe denominator 120595|ℎ
119878|2
minus 120596 = 0 Thus 119875TPSRout is rewritten in
two cases as follows(i) If |ℎ
119878|2
gt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A2)
(ii) If |ℎ119878|2
lt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) = 1 (A3)
TPSRIdeal receiver
18
16
14
12
1
08
06
04
02
0minus40 minus35 minus30 minus25 minus20 minus15 minus10
1205902 (dB)
Opt
imal
thro
ughp
ut120591
d1 = d2 = 1 PS = PD = 2 120578 = 07
Figure 6 The optimal throughput achieved for the TPSR protocoland the ideal receiver by the different value of noise
We obtain the equality Pr(|ℎ119863|2
gt 120579(120595|ℎ119878|2minus120596)) = 1 due
to the fact that if the value of |ℎ119878|2
lt 120596120595 with 120596120595 being thefactor in denominator 120595|ℎ
119878|2
minus 120596 will be a negative numberand probability of |ℎ
119863|2 being greater than some negative
number is always equal to 1Therefore119875TPSRout can be rewritten
as
119875TPSRout = int
120596120595
0Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
= int
120596120595
0119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1minus expminus120579
(120595120574 minus 120596) 120582ℎ119863
)
sdot 119901|ℎ119878|
2 (120574) 119889120574
(A4)
where 120574 is the integration variable 119901|ℎ119878|
2(120574) ≜ (1120582ℎ119878
)119890minus120574120582ℎ119878
is the probability density function (PDF) of exponentialdistributed random variable |ℎ
119878|2 and 119865
|ℎ119863|2(120574) ≜ Pr(|ℎ
119863|2
lt
120574) = 1minus119890minus120574120582ℎ119863 is the cumulative distribution function (CDF)
of the exponential distributed random variable |ℎ119863|2 Thus
119875TPSRout can be calculated by
119875TPSRout = 1
minus1
120582ℎ119878
int
infin
120596120595
expminus120574
120582ℎ119878
minus120579
(120595120574 minus 120596) 120582ℎ119863
119889120574
(A5)
8 Mobile Information Systems
Let us define a new integration variable 120583 = 120595120574minus120596 Thusoutage probability is given by [15]
119875TPSRout = 1minus
1120595120582ℎ119878
exp(minus120596
120595120582ℎ119878
)
sdot int
infin
120583=0exp(minus
120583
120595120582ℎ119878
minus120579
120583120582ℎ119863
) 119889120583 = 1
minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120574ℎ119878
120574ℎ119863
1198701 (radic4120579
120595120574ℎ119878
120574ℎ119863
)
(A6)
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] D Li C Shen and Z Qiu ldquoSum rate maximization and energyharvesting for two-way af relay systems with imperfect CSIrdquoin Proceedings of the 38th IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo13) pp 4958ndash4962 Vancouver Canada May 2013
[2] O Orhan and E Erkip ldquoThroughput maximization for energyharvesting two-hop networksrdquo in Proceedings of the IEEEInternational Symposium on Information Theory (ISITrsquo13) pp1596ndash1600 Istanbul Turkey July 2013
[3] P Mangayarkarasi J Raja and S Jayashri ldquoAn efficient energyharvesting scheme to maximize the throughput of the wirelessrelay networkwithTSR andPSRprotocolrdquo International Journalof Electronics and Communications vol 69 no 5 pp 841ndash8502015
[4] J Li C Ma Y Luo Y Cheng J Wu and C Chen ldquoJointoptimization of transmit power and energy harvesting for relay-basedM2M two-way communicationsrdquo International Journal ofDistributed Sensor Networks In press
[5] N Nomikos D N Skoutas D Vouyioukas C Verikoukisand C Skianis ldquoCapacity maximization through energy-awaremulti-mode relayingrdquo Wireless Personal Communications vol74 no 1 pp 83ndash99 2014
[6] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[7] A A Nasir X Zhou S Durrani and R A Kennedy ldquoThrough-put and ergodic capacity of wireless energy harvesting basedDF relaying networkrdquo in Proceedings of the IEEE InternationalConference on Communications (ICCrsquo14) pp 4066ndash4071 IEEESydney Australia June 2014
[8] X LuW Xu S Li J Lin and Z He ldquoSimultaneous informationand power transfer for relay-assisted cognitive radio networksrdquoin Proceedings of the IEEE International Conference on Commu-nications Workshops (ICC 14) pp 331ndash336 Sydney AustraliaJune 2014
[9] H H Chen Y Li J L Rebelatto B F Uchoa-Filhoand andB Vucetic ldquoHarvest-then-cooperate wireless-powered cooper-ative communicationsrdquo IEEE Transactions on Signal Processingvol 63 no 7 pp 1700ndash1711 2015
[10] C Zhong H A Suraweera G Zjeng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[11] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[12] I Krikidis S Sasaki S Timotheou and Z Ding ldquoA low com-plexity antenna switching for joint wireless information andenergy transfer in MIMO relay channelsrdquo IEEE Transactions onCommunications vol 62 no 5 pp 1577ndash1587 2014
[13] C Shen W-C Li and T-H Chang ldquoWireless information andenergy transfer in multi-antenna interference channelrdquo IEEETransactions on Signal Processing vol 62 no 23 pp 6249ndash62642014
[14] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4767 2013
[15] I S Gradshteyn and I M Ryzhik Table of Integrals Series andProducts ElsevierAcademic Press 7th edition 2007
Submit your manuscripts athttpwwwhindawicom
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Mobile Information Systems 3
T
RrarrD
information transmission
Energy harvesting at R(120573P)
SrarrR information transmission((1 minus 120573)P)
120572T (1 minus 120572)T
Figure 2 The diagram of the TPSR protocol for energy harvestingand information processing at the relay mobile node
3 TPSR in the EHCN
31 TPSR Protocol In the EHCN relay mobile node scav-enges energy from all signals around and assists the com-munication between the AP and destination mobile node Inthis section we assume a reference systemmodel depicted inFigure 1 in which the harvested energy transferred from theAP is stored in the battery of the relay in the first hop and usedfor the transmission of relay mobile node in the next hop Togain further insights into the performance we will analyzethe achievable throughput of the proposed TPSR protocol
In TPSR protocol we design two stages namely energystage (ES) and information stage (IS) Aiming to obtainwireless energy in ES the power of received signal 119910
119877can be
divided into two parts for energy harvesting and informationprocessing in the proposed TPSR protocol Based on theenergy harvesting enabled receiver architecture as shown inFigure 3 the signal received 119910RE at the input of the energyharvesting receiver is expressed as
119910RE =1
radic119889119898
1
radic120573119875119878ℎ119878119909119878+ radic120573119899
119877 (1)
where 120573 is the power splitting ratio for energy harvesting 119898is the path loss exponent factor 119875
119878is the transmitted power
of the source node ℎ119878denotes channel coefficient between
source and relay mobile node while 119909119878denotes transmitted
signal from source and 119899119877
sim 119862119873(0 1205902119877) denotes the total
additive white Gaussian noise (AWGN) introduced at therelay mobile node by the receiving antenna and signal bandconversion [6]
The energy processing module in the relay mobile nodeconverts incoming signal in (1) to a direct current (DC) signal119894DC by a rectifier which includes a Schottky diode and a low-pass filter (LPF) As illustrated in Figure 3 the direct currentsignal is used to charge the battery and to supply informationtransmission [14] Hence the energy harvested in the TPSRprotocol is given by
119864TPSRℎ
= 120578119864 119894DC 120572120573119879 = 120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1120572120573119879 (2)
where 119864sdot denotes expectation operation and 0 lt 120578 le 1depicts the energy harvesting efficiency at the energy receiverand it depends on the rectifier and the energy harvestingcircuitry
In IS of the proposed TPSR protocol the energy scav-enged from the previous stage (ie ES) is power supply for
Rectifier BatteryEnergy harvesting
RF to baseband conversion
Baseband processing
Information receiver
Time powerswitching
Information transmitter
+
+
+
nrec
nC
120572T
(1minus120572
)T
yR
nA
radic120573yR
radic1 minus 120573yR
Figure 3 Receiver architecture for the TPSR protocol at the relaymobile node
information processing in the second hop of the EHCNCompared with harvesting energy receiver the receivedsignal at the input of the information processing receiver inthe TPSR protocol is written as
119910119877
=1
radic119889119898
1
radic(1 minus 120573) 119875119878ℎ119878119909119878+ radic(1 minus 120573)119899
119877 (3)
By applying the AF relaying protocol the relay amplifiesthe received messages by a factor 119866 defined as
119866 =1
radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 + 1205902119877
(4)
After processing the received signal at relay mobile nodethe AF based relay amplifies the source signal and forwardsit to the destination mobile node with power of 119875
119877 which
depends on the amount of energy harvested during the ESThe received signal at the destination mobile node 119910
119863 can
be expressed as
119910119863
=radic119875119877ℎ119863119866
radic119889119898
2
119910119877
+ 119899119863 (5)
where 119899119863
sim 119862119873(0 1205902119863) denotes the additive white Gaussian
noise (AWGN) introduced at the destination mobile nodeNext by substituting 119910
119877and 119866 from (3) and (4) into (5) 119910
119863
can be rewritten as
119910119863
=
radic(1 minus 120573) 119875119877119875119878ℎ119878ℎ119863119909119878
radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
2 + 119889119898
1 1205902119877
+
radic119875119877119889119898
1 ℎ119863119899119877
radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
2 + 119889119898
1 1205902119877
+ 119899119863
(6)
On the other hand the relay mobile node transmits theamplified signal using the harvested energy 119864
TPSRℎ
duringenergy harvesting time (ES) as a source of power for (1minus 120572)119879
time and hence the transmitted power from the relay mobilenode 119875
119877is calculated by
119875119877
=119864TPSRℎ
(1 minus 120572) 119879= 120578
119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1
120572120573
1 minus 120572 (7)
4 Mobile Information Systems
By substituting the transmitted power 119875119877from (7) into
(6) we obtain the received signal at the destination mobilenode 119910
119863which is illustrated as
119910119863
=
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2120572120573 (1 minus 120573) 119875
119878ℎ119878ℎ119863119909119878
radic119889119898
1 119889119898
2 (1 minus 120572)radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Signal part
+
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2120572120573119889119898
1 ℎ119863119899119877
radic119889119898
2 (1 minus 120572)radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877
+ 119899119863
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Noise part
(8)
Next by calculation of power of signal part and power ofnoise part we obtain the end-to-end SNR at the destinationas follows
SNR119863
=120578120572120573 (1 minus 120573) 119875
119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
1205781205721205731003816100381610038161003816ℎ119863
1003816100381610038161003816
2119889119898
1 1205902119877
+ (1 minus 120572) (1 minus 120573) 119889119898
1 119889119898
2 1205902119863
+ (1 minus 120572) 11988921198981 120590
21198771205902119863119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 (9)
32Throughput Analysis In this work we consider the delay-limited transmissionmode where the achievable throughput120591TPSR is determined by evaluating the outage probability
119875TPSRout of the system with a fixed source transmission rate 119877
(bpsHz)We have119877 ≜ (12)log2(1+SNR0) and denote SNR0as the threshold signal-to-noise ratio for exact data detectionat the destination Moreover in order to analyze the outageprobability of the TPSR protocol at the destination mobilenode we first obtain the instantaneous mutual informationbetween the relay and the destination mobile node which isgiven by
119868119877119863
≜ (12) log2 (1+ SNR
119863) (10)
where SNR119863is the signal-to-noise ratio at the destination
mobile node and then we formulate the outage probability ofthe system as the probability that the instantaneous mutualinformation 119868
119877119863is below fixed source transmission rate 119877
Therefore the outage probability of the system can be shownas
119875TPSRout = Pr (119868
119877119863lt 119877) = Pr (SNR
119863lt SNR0) (11)
where Pr(sdot) is probability operation and the value SNR0can be calculated by SNR0 = 22119877 minus 1 Specifically wederive the closed-form SNR
119863as the following expression
because we can ignore the infinitesimal element with respectto (1 minus 120572)119889
21198981 120590
21198771205902119863119875119878|ℎ119878|2
asymp 0 at high SNR Therefore theapproximate outage probability 119875
TPSRout can be determined by
119875TPSRout
asymp Pr(120578120572120573 (1 minus 120573) 119875
119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
1205781205721205731003816100381610038161003816ℎ119863
1003816100381610038161003816
2119889119898
1 1205902119877
+ (1 minus 120572) (1 minus 120573) 119889119898
1 119889119898
2 1205902119863
lt SNR0) = Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2
lt(1 minus 120572) (1 minus 120573) 119889
119898
1 119889119898
2 1205902119863SNR0
120578120572120573 (1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2minus 120578120572120573119889
119898
1 1205902119877SNR0
)
(12)
According to (12) we have the following proposition
Proposition 1 Let parameters for simplicity be 120596 ≜
120578120572120573119889119898
1 12059021198771198781198731198770 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 119889119898
2 12059021198631198781198731198770 and 120595 ≜
120578120572120573(1 minus 120573)119875119878 The outage probability of the destination mobile
node for the TPSR protocol in the energy harvesting networksis given by
119875119879119875119878119877
119900119906119905
= 119875119903 (1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
)
= 1minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120582ℎ119878
120582ℎ119863
1198701 (radic4120579
120595120582ℎ119878
120582ℎ119863
)
(13)
where 120582ℎ119878
and 120582ℎ119863
are the mean of the exponential randomvariables of |ℎ
119878|2 and |ℎ
119863|2 respectively and 119870
119899(sdot) is the modi-
fied Bessel function of the second kind with the order 119899 definedin [15]
Proof See the Appendix
The achievable throughput 120591TPSR of the TPSR protocol
with the fixed rate 119877 at the destination is demonstrated by
120591TPSR
= (1minus 119875TPSRout ) 119877
(1 minus 120572) 119879
119879
= (1minus 119875TPSRout ) 119877 (1minus 120572)
(14)
Therefore the optimal throughput can be found by simu-lation due to its complexity while the tractable expressions ofthe optimal throughput can be obtained in two special casesas analysis in the next subsection
Mobile Information Systems 5
33 Optimal Throughput Analysis In this paper we assumethat the CSI can be obtained by channel estimation Inprinciple the AP sends a RTS (request-to-send) packet whichis compatible with IEEE 80211 wireless LAN standards Basedon the RTS information the full CSI can be estimated On theother hand the power splitting and time switching factorsin the proposed energy harvesting also can be extractedthrough RTS mechanism When the relay and destinationhave the knowledge of ℎ
119878and ℎ
119863 respectively maximizing
the throughput can be described as
120591opt = argmax120572120573
120591TPSR
= argmax120572120573
119877 (1minus 120572)
sdot (exp(minus120596
120595120582ℎ119878
) radic4120579
120595120582ℎ119878
120582ℎ119863
1198701 (radic4120579
120595120582ℎ119878
120582ℎ119863
))
(15)
In addition we adopt the offline store-and-transmitprotocol [15] the relay stores the harvested energy at the fixedlevel and then forwards information to the destination thanksto its scavenged energy In particular the required power 1198750for further information process at the relay can be expressedas
1198750 =12057812057201205730119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1 (1 minus 120572) (16)
where 1205720 and 1205730 denote time and power allocation coeffi-cients which are known by RTS mechanism
Interestingly due to the complexity of the involvedexpression in (15) we derive the closed-form expression ofthroughput in case of high SNR (ie 1205902
119877119875119878
rarr 0) By apply-ing the following approximation 119890
minus119909sim 1minus119909 and1198701(119909) sim 1119909
as 119909 rarr 0 we obtain new formula of optimal throughput asfollows
120591opt = argmax120572120573
119877 (1minus 120572) (1minus exp(minus120596
120595120582ℎ119878
))
= argmax120572120573
119877 (1minus 120572) (1minus1205902119877SNR0
(1 minus 120573) 119875119878120582ℎ119878
)
(17)
Next there are two cases of optimization problems whichare considered as the tractable expressions of the optimalthroughput after some manipulations
Case 1 The fixed power allocation and high SNR are asfollows
120591opt = 119877 (1minus1198750
120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
21205730 + 1198750119889
119898
1
)
sdot (1minus1205902119877SNR0
(1 minus 1205730) 119875119878120582ℎ119878
)
(18)
Case 2 Thefixed time allocation and high SNR are as follows
120591opt = 119877 (1minus 1205720)
sdot (1minus1205902119877SNR0
(1 minus 1198750 (1 minus 120572) 119889119898
1 120572120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2) 119875119878120582ℎ119878
)
(19)
4 Ideal Relay Receiver
In this section we assume the scenario with an ideal relayreceiver at the relay mobile node where simultaneous energyharvesting and information transmission between the sourceand the destination mobile node are extracted by the samereceived signal Half of the block time 1198792 is used to harvestenergy and process the information at the relay mobile nodeThe remaining half 1198792 is used for the relay to destinationmobile node information transmission [6]
We consider the energy harvesting collected from sourcenode and denote it as 119864
idealℎ
given by
119864idealℎ
=120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1(
119879
2) (20)
Similarly we obtain the received signal 1199101015840119877at the input of
the ideal receiver as the following expression
1199101015840
119877=
1
radic119889119898
1
radic119875119878ℎ119878119909119878+ 119899119877 (21)
In this ideal case the relay mobile node amplifies thereceived signal by a factor 119866
1015840 which is defined by
1198661015840=
1
radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 + 1205902119877
(22)
Based on principle of ideal receiver the transmittedpower from the relay mobile node 119875
1015840
119877can be given by
1198751015840
119877=
119864idealℎ
1198792=
120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1 (23)
where 1198792 is the communication time from the relay mobilenode to the destination mobile node in the block of time 119879
seconds As a result substituting the values of 1198751015840
119877 1198661015840 and 119910
1015840
119877
from (23) (22) and (21) into (6) the received signal at thedestination 1199101015840
119863 is given by
1199101015840
119863
=
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119875119878ℎ119878ℎ119863119909119878
radic119889119898
1 radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Signal part
+
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 ℎ119863119899119877
radic119889119898
1 radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877
+ 119899119863
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Noise part
(24)
In the following we calculate the SNR at the destinationmobile node which is modeled as
SNR1015840119863
=120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
120578119889119898
11003816100381610038161003816ℎ119863
1003816100381610038161003816
21205902119877
+ 119889119898
1 1205902119863
+ 11988921198981 120590
21198771205902119863119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 (25)
6 Mobile Information Systems
Similar to the analysis in previous section the throughputis determined by evaluating the outage probability Interest-ingly the closed-form expression of119875ideal
out can be calculated as119875TPSRout
119875idealout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (26)
where 119875idealout can be calculated as in the Appendix with 120579 ≜
119889119898
1 1205902119863SNR0 120595 ≜ 120578119875
119878 and 120596 ≜ 120578119889
119898
1 1205902119877SNR0 In this case
we also consider the delay-limited transmission mode forevaluating the throughput 120591
ideal at the destination which isgiven by
120591ideal
= (1minus 119875idealout )
119877
2 (27)
5 Numerical Results
In this section we present numerical results in order toillustrate the solution to the optimization throughput prob-lems of the AF energy harvesting enabled relaying schemein the proposed TPSR protocol namely the optimal value ofthroughput 120591 optimal value of signal processing time 120572 andpower splitting ratio 120573
In these simulations we set up common parameters asfollows the distances 1198891 and 1198892 are normalized to be 1 (ie1198891 = 1198892 = 1) the energy harvesting efficiency 120578 = 07 thefixed transmission rate of the source 119877 = 4 (bpsHz) sourcetransmission power 119875
119878= 2 (Watt) destination transmission
power 119875119863
= 2 (Watt) and path loss exponent 119898 = 27In all simulations 120582
ℎ119878and 120582
ℎ119863are denoted as the mean
values of the exponential random variables |ℎ119878|2 and |ℎ
119863|2
respectively and set to 1The simulation results depend on theexpressions for outage probability in (12) which is evaluatedby averaging these calculations over 105 random realizationsof the Rayleigh fading channels of ℎ
119878and ℎ119863
As observation Figures 4 and 5 show that simulationresults of achievable throughput perfectly match the analyt-ical results for the optimal values range of 0 lt 120572 lt 1and 0 lt 120573 lt 1 for the TPSR protocol In this illustrationsimilar noise variances at the relay and destination mobilenodes are assumed that is 120590
2119877
= 1205902119863
= 1205902
= 001 Ascan be seen from Figure 4 the throughput increases from 0to 125 when 120572 increases from 001 to 035 but later it startsdecreasing as 120572 increases from its optimal value (for 120573 = 07)and the throughput increases from 0 to 095 as 120572 increasesfrom 001 to 045 but then decreases as 120572 increases from itsoptimal value (for 120573 = 03) In Figure 5 the throughputincreases from 0 to 125 as 120573 increases from 001 to 07 butlater it starts decreasing as 120573 increases (for 120572 = 03) andthe throughput increases from 0 to 084 as 120573 increases from001 to 06 but then decreases as 120573 increases from its optimalvalue (for 120572 = 07) Interestingly in the case when value of 120572
increases we obtain optimal throughput only if 120573 decreasesand vice versa We can explain important results that thevalue of 120572 is smaller than the optimal value of 120572 whichmeans that there is less time for energy harvesting and more
0 02
02
04
04
06
06
08
08
10
1
12
14TPSR protocol
AnalyticalApproximateSimulation
120572
120573 = 07
120573 = 03
Thro
ughp
ut120591
TPSR
(bps
Hz)
Figure 4 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of the block time switching
TPSR protocol
AnalyticalApproximateSimulation
0 02 04 06 08 1
02
04
06
08
0
1
12
14
120572 = 07
120572 = 03
120573
Thro
ughp
ut120591
TPSR
(bits
sH
z)
Figure 5 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of power splitting
time for information transmission As a result less energy isharvested and throughput achieved at the destination mobilenode is greater In contrast when the value of120572 is greater thanthe optimal 120572 there is more time for energy harvesting butless time for information transmission Furthermore whenthe value of 120573 is smaller than the optimal 120573 there is less
Mobile Information Systems 7
power available for energy harvesting and more power forprocessing the received signal Thus high signal strengthis observed at the relay mobile node and results in higherthroughput at the destination mobile node In addition incase the value of120573 is greater than the optimal120573 more power iswasted on energy harvesting and less power for informationtransmission from the source to relay mobile node
For comparison Figure 6 depicts the optimal throughput120591 of the TPSR protocol and the ideal receiver for differentvalues of noise variance 120590
2 In fact the simulation resultshows that the throughput in the ideal case always outper-forms that in the TPSR caseThe optimal throughput roughlyremains constant when noise variance changes from minus40 dBto minus30 dB In contrast the systemrsquos throughput performancedecreases dramatically when a larger number of noise vari-ances occur
6 Conclusions
This paper proposes TPSR protocol and the design of thereceiver architecture for wireless energy harvesting andinformation transmission in the EHCN In addition theoutage performance of the AF relaying scheme where therelay mobile node harvests energy from source node throughthe received RF signal and then uses harvested energy toamplify the information and forward the source signal tothe destination mobile node has been derived For sim-plicity in computation we also develop the closed-formexpression of the achievable throughput at the destinationMore importantly the optimal values of time switching andpower splitting ratio for energy harvesting in the proposedTPSR protocol which are chosen in order to maximize thethroughput of the system were also numerically investigated
Appendix
In the following we derive the outage probability in (12)which is given by (A1) where 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 1205902119863SNR0
120595 ≜ 120578120572120573(1 minus 120573)119875119878 and 120596 ≜ 120578120572120573119889
119898
1 1205902119877SNR0
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A1)
It is observed and also can be verified that the factor inthe denominator 120595|ℎ
119878|2
minus 120596 = 0 Thus 119875TPSRout is rewritten in
two cases as follows(i) If |ℎ
119878|2
gt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A2)
(ii) If |ℎ119878|2
lt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) = 1 (A3)
TPSRIdeal receiver
18
16
14
12
1
08
06
04
02
0minus40 minus35 minus30 minus25 minus20 minus15 minus10
1205902 (dB)
Opt
imal
thro
ughp
ut120591
d1 = d2 = 1 PS = PD = 2 120578 = 07
Figure 6 The optimal throughput achieved for the TPSR protocoland the ideal receiver by the different value of noise
We obtain the equality Pr(|ℎ119863|2
gt 120579(120595|ℎ119878|2minus120596)) = 1 due
to the fact that if the value of |ℎ119878|2
lt 120596120595 with 120596120595 being thefactor in denominator 120595|ℎ
119878|2
minus 120596 will be a negative numberand probability of |ℎ
119863|2 being greater than some negative
number is always equal to 1Therefore119875TPSRout can be rewritten
as
119875TPSRout = int
120596120595
0Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
= int
120596120595
0119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1minus expminus120579
(120595120574 minus 120596) 120582ℎ119863
)
sdot 119901|ℎ119878|
2 (120574) 119889120574
(A4)
where 120574 is the integration variable 119901|ℎ119878|
2(120574) ≜ (1120582ℎ119878
)119890minus120574120582ℎ119878
is the probability density function (PDF) of exponentialdistributed random variable |ℎ
119878|2 and 119865
|ℎ119863|2(120574) ≜ Pr(|ℎ
119863|2
lt
120574) = 1minus119890minus120574120582ℎ119863 is the cumulative distribution function (CDF)
of the exponential distributed random variable |ℎ119863|2 Thus
119875TPSRout can be calculated by
119875TPSRout = 1
minus1
120582ℎ119878
int
infin
120596120595
expminus120574
120582ℎ119878
minus120579
(120595120574 minus 120596) 120582ℎ119863
119889120574
(A5)
8 Mobile Information Systems
Let us define a new integration variable 120583 = 120595120574minus120596 Thusoutage probability is given by [15]
119875TPSRout = 1minus
1120595120582ℎ119878
exp(minus120596
120595120582ℎ119878
)
sdot int
infin
120583=0exp(minus
120583
120595120582ℎ119878
minus120579
120583120582ℎ119863
) 119889120583 = 1
minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120574ℎ119878
120574ℎ119863
1198701 (radic4120579
120595120574ℎ119878
120574ℎ119863
)
(A6)
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] D Li C Shen and Z Qiu ldquoSum rate maximization and energyharvesting for two-way af relay systems with imperfect CSIrdquoin Proceedings of the 38th IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo13) pp 4958ndash4962 Vancouver Canada May 2013
[2] O Orhan and E Erkip ldquoThroughput maximization for energyharvesting two-hop networksrdquo in Proceedings of the IEEEInternational Symposium on Information Theory (ISITrsquo13) pp1596ndash1600 Istanbul Turkey July 2013
[3] P Mangayarkarasi J Raja and S Jayashri ldquoAn efficient energyharvesting scheme to maximize the throughput of the wirelessrelay networkwithTSR andPSRprotocolrdquo International Journalof Electronics and Communications vol 69 no 5 pp 841ndash8502015
[4] J Li C Ma Y Luo Y Cheng J Wu and C Chen ldquoJointoptimization of transmit power and energy harvesting for relay-basedM2M two-way communicationsrdquo International Journal ofDistributed Sensor Networks In press
[5] N Nomikos D N Skoutas D Vouyioukas C Verikoukisand C Skianis ldquoCapacity maximization through energy-awaremulti-mode relayingrdquo Wireless Personal Communications vol74 no 1 pp 83ndash99 2014
[6] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[7] A A Nasir X Zhou S Durrani and R A Kennedy ldquoThrough-put and ergodic capacity of wireless energy harvesting basedDF relaying networkrdquo in Proceedings of the IEEE InternationalConference on Communications (ICCrsquo14) pp 4066ndash4071 IEEESydney Australia June 2014
[8] X LuW Xu S Li J Lin and Z He ldquoSimultaneous informationand power transfer for relay-assisted cognitive radio networksrdquoin Proceedings of the IEEE International Conference on Commu-nications Workshops (ICC 14) pp 331ndash336 Sydney AustraliaJune 2014
[9] H H Chen Y Li J L Rebelatto B F Uchoa-Filhoand andB Vucetic ldquoHarvest-then-cooperate wireless-powered cooper-ative communicationsrdquo IEEE Transactions on Signal Processingvol 63 no 7 pp 1700ndash1711 2015
[10] C Zhong H A Suraweera G Zjeng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[11] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[12] I Krikidis S Sasaki S Timotheou and Z Ding ldquoA low com-plexity antenna switching for joint wireless information andenergy transfer in MIMO relay channelsrdquo IEEE Transactions onCommunications vol 62 no 5 pp 1577ndash1587 2014
[13] C Shen W-C Li and T-H Chang ldquoWireless information andenergy transfer in multi-antenna interference channelrdquo IEEETransactions on Signal Processing vol 62 no 23 pp 6249ndash62642014
[14] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4767 2013
[15] I S Gradshteyn and I M Ryzhik Table of Integrals Series andProducts ElsevierAcademic Press 7th edition 2007
Submit your manuscripts athttpwwwhindawicom
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Human-ComputerInteraction
Advances in
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4 Mobile Information Systems
By substituting the transmitted power 119875119877from (7) into
(6) we obtain the received signal at the destination mobilenode 119910
119863which is illustrated as
119910119863
=
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2120572120573 (1 minus 120573) 119875
119878ℎ119878ℎ119863119909119878
radic119889119898
1 119889119898
2 (1 minus 120572)radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Signal part
+
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2120572120573119889119898
1 ℎ119863119899119877
radic119889119898
2 (1 minus 120572)radic(1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877
+ 119899119863
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Noise part
(8)
Next by calculation of power of signal part and power ofnoise part we obtain the end-to-end SNR at the destinationas follows
SNR119863
=120578120572120573 (1 minus 120573) 119875
119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
1205781205721205731003816100381610038161003816ℎ119863
1003816100381610038161003816
2119889119898
1 1205902119877
+ (1 minus 120572) (1 minus 120573) 119889119898
1 119889119898
2 1205902119863
+ (1 minus 120572) 11988921198981 120590
21198771205902119863119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 (9)
32Throughput Analysis In this work we consider the delay-limited transmissionmode where the achievable throughput120591TPSR is determined by evaluating the outage probability
119875TPSRout of the system with a fixed source transmission rate 119877
(bpsHz)We have119877 ≜ (12)log2(1+SNR0) and denote SNR0as the threshold signal-to-noise ratio for exact data detectionat the destination Moreover in order to analyze the outageprobability of the TPSR protocol at the destination mobilenode we first obtain the instantaneous mutual informationbetween the relay and the destination mobile node which isgiven by
119868119877119863
≜ (12) log2 (1+ SNR
119863) (10)
where SNR119863is the signal-to-noise ratio at the destination
mobile node and then we formulate the outage probability ofthe system as the probability that the instantaneous mutualinformation 119868
119877119863is below fixed source transmission rate 119877
Therefore the outage probability of the system can be shownas
119875TPSRout = Pr (119868
119877119863lt 119877) = Pr (SNR
119863lt SNR0) (11)
where Pr(sdot) is probability operation and the value SNR0can be calculated by SNR0 = 22119877 minus 1 Specifically wederive the closed-form SNR
119863as the following expression
because we can ignore the infinitesimal element with respectto (1 minus 120572)119889
21198981 120590
21198771205902119863119875119878|ℎ119878|2
asymp 0 at high SNR Therefore theapproximate outage probability 119875
TPSRout can be determined by
119875TPSRout
asymp Pr(120578120572120573 (1 minus 120573) 119875
119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
1205781205721205731003816100381610038161003816ℎ119863
1003816100381610038161003816
2119889119898
1 1205902119877
+ (1 minus 120572) (1 minus 120573) 119889119898
1 119889119898
2 1205902119863
lt SNR0) = Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2
lt(1 minus 120572) (1 minus 120573) 119889
119898
1 119889119898
2 1205902119863SNR0
120578120572120573 (1 minus 120573) 119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2minus 120578120572120573119889
119898
1 1205902119877SNR0
)
(12)
According to (12) we have the following proposition
Proposition 1 Let parameters for simplicity be 120596 ≜
120578120572120573119889119898
1 12059021198771198781198731198770 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 119889119898
2 12059021198631198781198731198770 and 120595 ≜
120578120572120573(1 minus 120573)119875119878 The outage probability of the destination mobile
node for the TPSR protocol in the energy harvesting networksis given by
119875119879119875119878119877
119900119906119905
= 119875119903 (1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
)
= 1minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120582ℎ119878
120582ℎ119863
1198701 (radic4120579
120595120582ℎ119878
120582ℎ119863
)
(13)
where 120582ℎ119878
and 120582ℎ119863
are the mean of the exponential randomvariables of |ℎ
119878|2 and |ℎ
119863|2 respectively and 119870
119899(sdot) is the modi-
fied Bessel function of the second kind with the order 119899 definedin [15]
Proof See the Appendix
The achievable throughput 120591TPSR of the TPSR protocol
with the fixed rate 119877 at the destination is demonstrated by
120591TPSR
= (1minus 119875TPSRout ) 119877
(1 minus 120572) 119879
119879
= (1minus 119875TPSRout ) 119877 (1minus 120572)
(14)
Therefore the optimal throughput can be found by simu-lation due to its complexity while the tractable expressions ofthe optimal throughput can be obtained in two special casesas analysis in the next subsection
Mobile Information Systems 5
33 Optimal Throughput Analysis In this paper we assumethat the CSI can be obtained by channel estimation Inprinciple the AP sends a RTS (request-to-send) packet whichis compatible with IEEE 80211 wireless LAN standards Basedon the RTS information the full CSI can be estimated On theother hand the power splitting and time switching factorsin the proposed energy harvesting also can be extractedthrough RTS mechanism When the relay and destinationhave the knowledge of ℎ
119878and ℎ
119863 respectively maximizing
the throughput can be described as
120591opt = argmax120572120573
120591TPSR
= argmax120572120573
119877 (1minus 120572)
sdot (exp(minus120596
120595120582ℎ119878
) radic4120579
120595120582ℎ119878
120582ℎ119863
1198701 (radic4120579
120595120582ℎ119878
120582ℎ119863
))
(15)
In addition we adopt the offline store-and-transmitprotocol [15] the relay stores the harvested energy at the fixedlevel and then forwards information to the destination thanksto its scavenged energy In particular the required power 1198750for further information process at the relay can be expressedas
1198750 =12057812057201205730119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1 (1 minus 120572) (16)
where 1205720 and 1205730 denote time and power allocation coeffi-cients which are known by RTS mechanism
Interestingly due to the complexity of the involvedexpression in (15) we derive the closed-form expression ofthroughput in case of high SNR (ie 1205902
119877119875119878
rarr 0) By apply-ing the following approximation 119890
minus119909sim 1minus119909 and1198701(119909) sim 1119909
as 119909 rarr 0 we obtain new formula of optimal throughput asfollows
120591opt = argmax120572120573
119877 (1minus 120572) (1minus exp(minus120596
120595120582ℎ119878
))
= argmax120572120573
119877 (1minus 120572) (1minus1205902119877SNR0
(1 minus 120573) 119875119878120582ℎ119878
)
(17)
Next there are two cases of optimization problems whichare considered as the tractable expressions of the optimalthroughput after some manipulations
Case 1 The fixed power allocation and high SNR are asfollows
120591opt = 119877 (1minus1198750
120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
21205730 + 1198750119889
119898
1
)
sdot (1minus1205902119877SNR0
(1 minus 1205730) 119875119878120582ℎ119878
)
(18)
Case 2 Thefixed time allocation and high SNR are as follows
120591opt = 119877 (1minus 1205720)
sdot (1minus1205902119877SNR0
(1 minus 1198750 (1 minus 120572) 119889119898
1 120572120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2) 119875119878120582ℎ119878
)
(19)
4 Ideal Relay Receiver
In this section we assume the scenario with an ideal relayreceiver at the relay mobile node where simultaneous energyharvesting and information transmission between the sourceand the destination mobile node are extracted by the samereceived signal Half of the block time 1198792 is used to harvestenergy and process the information at the relay mobile nodeThe remaining half 1198792 is used for the relay to destinationmobile node information transmission [6]
We consider the energy harvesting collected from sourcenode and denote it as 119864
idealℎ
given by
119864idealℎ
=120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1(
119879
2) (20)
Similarly we obtain the received signal 1199101015840119877at the input of
the ideal receiver as the following expression
1199101015840
119877=
1
radic119889119898
1
radic119875119878ℎ119878119909119878+ 119899119877 (21)
In this ideal case the relay mobile node amplifies thereceived signal by a factor 119866
1015840 which is defined by
1198661015840=
1
radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 + 1205902119877
(22)
Based on principle of ideal receiver the transmittedpower from the relay mobile node 119875
1015840
119877can be given by
1198751015840
119877=
119864idealℎ
1198792=
120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1 (23)
where 1198792 is the communication time from the relay mobilenode to the destination mobile node in the block of time 119879
seconds As a result substituting the values of 1198751015840
119877 1198661015840 and 119910
1015840
119877
from (23) (22) and (21) into (6) the received signal at thedestination 1199101015840
119863 is given by
1199101015840
119863
=
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119875119878ℎ119878ℎ119863119909119878
radic119889119898
1 radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Signal part
+
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 ℎ119863119899119877
radic119889119898
1 radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877
+ 119899119863
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Noise part
(24)
In the following we calculate the SNR at the destinationmobile node which is modeled as
SNR1015840119863
=120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
120578119889119898
11003816100381610038161003816ℎ119863
1003816100381610038161003816
21205902119877
+ 119889119898
1 1205902119863
+ 11988921198981 120590
21198771205902119863119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 (25)
6 Mobile Information Systems
Similar to the analysis in previous section the throughputis determined by evaluating the outage probability Interest-ingly the closed-form expression of119875ideal
out can be calculated as119875TPSRout
119875idealout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (26)
where 119875idealout can be calculated as in the Appendix with 120579 ≜
119889119898
1 1205902119863SNR0 120595 ≜ 120578119875
119878 and 120596 ≜ 120578119889
119898
1 1205902119877SNR0 In this case
we also consider the delay-limited transmission mode forevaluating the throughput 120591
ideal at the destination which isgiven by
120591ideal
= (1minus 119875idealout )
119877
2 (27)
5 Numerical Results
In this section we present numerical results in order toillustrate the solution to the optimization throughput prob-lems of the AF energy harvesting enabled relaying schemein the proposed TPSR protocol namely the optimal value ofthroughput 120591 optimal value of signal processing time 120572 andpower splitting ratio 120573
In these simulations we set up common parameters asfollows the distances 1198891 and 1198892 are normalized to be 1 (ie1198891 = 1198892 = 1) the energy harvesting efficiency 120578 = 07 thefixed transmission rate of the source 119877 = 4 (bpsHz) sourcetransmission power 119875
119878= 2 (Watt) destination transmission
power 119875119863
= 2 (Watt) and path loss exponent 119898 = 27In all simulations 120582
ℎ119878and 120582
ℎ119863are denoted as the mean
values of the exponential random variables |ℎ119878|2 and |ℎ
119863|2
respectively and set to 1The simulation results depend on theexpressions for outage probability in (12) which is evaluatedby averaging these calculations over 105 random realizationsof the Rayleigh fading channels of ℎ
119878and ℎ119863
As observation Figures 4 and 5 show that simulationresults of achievable throughput perfectly match the analyt-ical results for the optimal values range of 0 lt 120572 lt 1and 0 lt 120573 lt 1 for the TPSR protocol In this illustrationsimilar noise variances at the relay and destination mobilenodes are assumed that is 120590
2119877
= 1205902119863
= 1205902
= 001 Ascan be seen from Figure 4 the throughput increases from 0to 125 when 120572 increases from 001 to 035 but later it startsdecreasing as 120572 increases from its optimal value (for 120573 = 07)and the throughput increases from 0 to 095 as 120572 increasesfrom 001 to 045 but then decreases as 120572 increases from itsoptimal value (for 120573 = 03) In Figure 5 the throughputincreases from 0 to 125 as 120573 increases from 001 to 07 butlater it starts decreasing as 120573 increases (for 120572 = 03) andthe throughput increases from 0 to 084 as 120573 increases from001 to 06 but then decreases as 120573 increases from its optimalvalue (for 120572 = 07) Interestingly in the case when value of 120572
increases we obtain optimal throughput only if 120573 decreasesand vice versa We can explain important results that thevalue of 120572 is smaller than the optimal value of 120572 whichmeans that there is less time for energy harvesting and more
0 02
02
04
04
06
06
08
08
10
1
12
14TPSR protocol
AnalyticalApproximateSimulation
120572
120573 = 07
120573 = 03
Thro
ughp
ut120591
TPSR
(bps
Hz)
Figure 4 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of the block time switching
TPSR protocol
AnalyticalApproximateSimulation
0 02 04 06 08 1
02
04
06
08
0
1
12
14
120572 = 07
120572 = 03
120573
Thro
ughp
ut120591
TPSR
(bits
sH
z)
Figure 5 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of power splitting
time for information transmission As a result less energy isharvested and throughput achieved at the destination mobilenode is greater In contrast when the value of120572 is greater thanthe optimal 120572 there is more time for energy harvesting butless time for information transmission Furthermore whenthe value of 120573 is smaller than the optimal 120573 there is less
Mobile Information Systems 7
power available for energy harvesting and more power forprocessing the received signal Thus high signal strengthis observed at the relay mobile node and results in higherthroughput at the destination mobile node In addition incase the value of120573 is greater than the optimal120573 more power iswasted on energy harvesting and less power for informationtransmission from the source to relay mobile node
For comparison Figure 6 depicts the optimal throughput120591 of the TPSR protocol and the ideal receiver for differentvalues of noise variance 120590
2 In fact the simulation resultshows that the throughput in the ideal case always outper-forms that in the TPSR caseThe optimal throughput roughlyremains constant when noise variance changes from minus40 dBto minus30 dB In contrast the systemrsquos throughput performancedecreases dramatically when a larger number of noise vari-ances occur
6 Conclusions
This paper proposes TPSR protocol and the design of thereceiver architecture for wireless energy harvesting andinformation transmission in the EHCN In addition theoutage performance of the AF relaying scheme where therelay mobile node harvests energy from source node throughthe received RF signal and then uses harvested energy toamplify the information and forward the source signal tothe destination mobile node has been derived For sim-plicity in computation we also develop the closed-formexpression of the achievable throughput at the destinationMore importantly the optimal values of time switching andpower splitting ratio for energy harvesting in the proposedTPSR protocol which are chosen in order to maximize thethroughput of the system were also numerically investigated
Appendix
In the following we derive the outage probability in (12)which is given by (A1) where 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 1205902119863SNR0
120595 ≜ 120578120572120573(1 minus 120573)119875119878 and 120596 ≜ 120578120572120573119889
119898
1 1205902119877SNR0
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A1)
It is observed and also can be verified that the factor inthe denominator 120595|ℎ
119878|2
minus 120596 = 0 Thus 119875TPSRout is rewritten in
two cases as follows(i) If |ℎ
119878|2
gt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A2)
(ii) If |ℎ119878|2
lt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) = 1 (A3)
TPSRIdeal receiver
18
16
14
12
1
08
06
04
02
0minus40 minus35 minus30 minus25 minus20 minus15 minus10
1205902 (dB)
Opt
imal
thro
ughp
ut120591
d1 = d2 = 1 PS = PD = 2 120578 = 07
Figure 6 The optimal throughput achieved for the TPSR protocoland the ideal receiver by the different value of noise
We obtain the equality Pr(|ℎ119863|2
gt 120579(120595|ℎ119878|2minus120596)) = 1 due
to the fact that if the value of |ℎ119878|2
lt 120596120595 with 120596120595 being thefactor in denominator 120595|ℎ
119878|2
minus 120596 will be a negative numberand probability of |ℎ
119863|2 being greater than some negative
number is always equal to 1Therefore119875TPSRout can be rewritten
as
119875TPSRout = int
120596120595
0Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
= int
120596120595
0119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1minus expminus120579
(120595120574 minus 120596) 120582ℎ119863
)
sdot 119901|ℎ119878|
2 (120574) 119889120574
(A4)
where 120574 is the integration variable 119901|ℎ119878|
2(120574) ≜ (1120582ℎ119878
)119890minus120574120582ℎ119878
is the probability density function (PDF) of exponentialdistributed random variable |ℎ
119878|2 and 119865
|ℎ119863|2(120574) ≜ Pr(|ℎ
119863|2
lt
120574) = 1minus119890minus120574120582ℎ119863 is the cumulative distribution function (CDF)
of the exponential distributed random variable |ℎ119863|2 Thus
119875TPSRout can be calculated by
119875TPSRout = 1
minus1
120582ℎ119878
int
infin
120596120595
expminus120574
120582ℎ119878
minus120579
(120595120574 minus 120596) 120582ℎ119863
119889120574
(A5)
8 Mobile Information Systems
Let us define a new integration variable 120583 = 120595120574minus120596 Thusoutage probability is given by [15]
119875TPSRout = 1minus
1120595120582ℎ119878
exp(minus120596
120595120582ℎ119878
)
sdot int
infin
120583=0exp(minus
120583
120595120582ℎ119878
minus120579
120583120582ℎ119863
) 119889120583 = 1
minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120574ℎ119878
120574ℎ119863
1198701 (radic4120579
120595120574ℎ119878
120574ℎ119863
)
(A6)
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] D Li C Shen and Z Qiu ldquoSum rate maximization and energyharvesting for two-way af relay systems with imperfect CSIrdquoin Proceedings of the 38th IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo13) pp 4958ndash4962 Vancouver Canada May 2013
[2] O Orhan and E Erkip ldquoThroughput maximization for energyharvesting two-hop networksrdquo in Proceedings of the IEEEInternational Symposium on Information Theory (ISITrsquo13) pp1596ndash1600 Istanbul Turkey July 2013
[3] P Mangayarkarasi J Raja and S Jayashri ldquoAn efficient energyharvesting scheme to maximize the throughput of the wirelessrelay networkwithTSR andPSRprotocolrdquo International Journalof Electronics and Communications vol 69 no 5 pp 841ndash8502015
[4] J Li C Ma Y Luo Y Cheng J Wu and C Chen ldquoJointoptimization of transmit power and energy harvesting for relay-basedM2M two-way communicationsrdquo International Journal ofDistributed Sensor Networks In press
[5] N Nomikos D N Skoutas D Vouyioukas C Verikoukisand C Skianis ldquoCapacity maximization through energy-awaremulti-mode relayingrdquo Wireless Personal Communications vol74 no 1 pp 83ndash99 2014
[6] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[7] A A Nasir X Zhou S Durrani and R A Kennedy ldquoThrough-put and ergodic capacity of wireless energy harvesting basedDF relaying networkrdquo in Proceedings of the IEEE InternationalConference on Communications (ICCrsquo14) pp 4066ndash4071 IEEESydney Australia June 2014
[8] X LuW Xu S Li J Lin and Z He ldquoSimultaneous informationand power transfer for relay-assisted cognitive radio networksrdquoin Proceedings of the IEEE International Conference on Commu-nications Workshops (ICC 14) pp 331ndash336 Sydney AustraliaJune 2014
[9] H H Chen Y Li J L Rebelatto B F Uchoa-Filhoand andB Vucetic ldquoHarvest-then-cooperate wireless-powered cooper-ative communicationsrdquo IEEE Transactions on Signal Processingvol 63 no 7 pp 1700ndash1711 2015
[10] C Zhong H A Suraweera G Zjeng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[11] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[12] I Krikidis S Sasaki S Timotheou and Z Ding ldquoA low com-plexity antenna switching for joint wireless information andenergy transfer in MIMO relay channelsrdquo IEEE Transactions onCommunications vol 62 no 5 pp 1577ndash1587 2014
[13] C Shen W-C Li and T-H Chang ldquoWireless information andenergy transfer in multi-antenna interference channelrdquo IEEETransactions on Signal Processing vol 62 no 23 pp 6249ndash62642014
[14] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4767 2013
[15] I S Gradshteyn and I M Ryzhik Table of Integrals Series andProducts ElsevierAcademic Press 7th edition 2007
Submit your manuscripts athttpwwwhindawicom
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Electrical and Computer Engineering
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 5
33 Optimal Throughput Analysis In this paper we assumethat the CSI can be obtained by channel estimation Inprinciple the AP sends a RTS (request-to-send) packet whichis compatible with IEEE 80211 wireless LAN standards Basedon the RTS information the full CSI can be estimated On theother hand the power splitting and time switching factorsin the proposed energy harvesting also can be extractedthrough RTS mechanism When the relay and destinationhave the knowledge of ℎ
119878and ℎ
119863 respectively maximizing
the throughput can be described as
120591opt = argmax120572120573
120591TPSR
= argmax120572120573
119877 (1minus 120572)
sdot (exp(minus120596
120595120582ℎ119878
) radic4120579
120595120582ℎ119878
120582ℎ119863
1198701 (radic4120579
120595120582ℎ119878
120582ℎ119863
))
(15)
In addition we adopt the offline store-and-transmitprotocol [15] the relay stores the harvested energy at the fixedlevel and then forwards information to the destination thanksto its scavenged energy In particular the required power 1198750for further information process at the relay can be expressedas
1198750 =12057812057201205730119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1 (1 minus 120572) (16)
where 1205720 and 1205730 denote time and power allocation coeffi-cients which are known by RTS mechanism
Interestingly due to the complexity of the involvedexpression in (15) we derive the closed-form expression ofthroughput in case of high SNR (ie 1205902
119877119875119878
rarr 0) By apply-ing the following approximation 119890
minus119909sim 1minus119909 and1198701(119909) sim 1119909
as 119909 rarr 0 we obtain new formula of optimal throughput asfollows
120591opt = argmax120572120573
119877 (1minus 120572) (1minus exp(minus120596
120595120582ℎ119878
))
= argmax120572120573
119877 (1minus 120572) (1minus1205902119877SNR0
(1 minus 120573) 119875119878120582ℎ119878
)
(17)
Next there are two cases of optimization problems whichare considered as the tractable expressions of the optimalthroughput after some manipulations
Case 1 The fixed power allocation and high SNR are asfollows
120591opt = 119877 (1minus1198750
120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
21205730 + 1198750119889
119898
1
)
sdot (1minus1205902119877SNR0
(1 minus 1205730) 119875119878120582ℎ119878
)
(18)
Case 2 Thefixed time allocation and high SNR are as follows
120591opt = 119877 (1minus 1205720)
sdot (1minus1205902119877SNR0
(1 minus 1198750 (1 minus 120572) 119889119898
1 120572120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2) 119875119878120582ℎ119878
)
(19)
4 Ideal Relay Receiver
In this section we assume the scenario with an ideal relayreceiver at the relay mobile node where simultaneous energyharvesting and information transmission between the sourceand the destination mobile node are extracted by the samereceived signal Half of the block time 1198792 is used to harvestenergy and process the information at the relay mobile nodeThe remaining half 1198792 is used for the relay to destinationmobile node information transmission [6]
We consider the energy harvesting collected from sourcenode and denote it as 119864
idealℎ
given by
119864idealℎ
=120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1(
119879
2) (20)
Similarly we obtain the received signal 1199101015840119877at the input of
the ideal receiver as the following expression
1199101015840
119877=
1
radic119889119898
1
radic119875119878ℎ119878119909119878+ 119899119877 (21)
In this ideal case the relay mobile node amplifies thereceived signal by a factor 119866
1015840 which is defined by
1198661015840=
1
radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 + 1205902119877
(22)
Based on principle of ideal receiver the transmittedpower from the relay mobile node 119875
1015840
119877can be given by
1198751015840
119877=
119864idealℎ
1198792=
120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2
119889119898
1 (23)
where 1198792 is the communication time from the relay mobilenode to the destination mobile node in the block of time 119879
seconds As a result substituting the values of 1198751015840
119877 1198661015840 and 119910
1015840
119877
from (23) (22) and (21) into (6) the received signal at thedestination 1199101015840
119863 is given by
1199101015840
119863
=
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119875119878ℎ119878ℎ119863119909119878
radic119889119898
1 radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Signal part
+
radic120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2119889119898
1 ℎ119863119899119877
radic119889119898
1 radic119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2+ 119889119898
1 1205902119877
+ 119899119863
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
Noise part
(24)
In the following we calculate the SNR at the destinationmobile node which is modeled as
SNR1015840119863
=120578119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 1003816100381610038161003816ℎ1198631003816100381610038161003816
2
120578119889119898
11003816100381610038161003816ℎ119863
1003816100381610038161003816
21205902119877
+ 119889119898
1 1205902119863
+ 11988921198981 120590
21198771205902119863119875119878
1003816100381610038161003816ℎ1198781003816100381610038161003816
2 (25)
6 Mobile Information Systems
Similar to the analysis in previous section the throughputis determined by evaluating the outage probability Interest-ingly the closed-form expression of119875ideal
out can be calculated as119875TPSRout
119875idealout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (26)
where 119875idealout can be calculated as in the Appendix with 120579 ≜
119889119898
1 1205902119863SNR0 120595 ≜ 120578119875
119878 and 120596 ≜ 120578119889
119898
1 1205902119877SNR0 In this case
we also consider the delay-limited transmission mode forevaluating the throughput 120591
ideal at the destination which isgiven by
120591ideal
= (1minus 119875idealout )
119877
2 (27)
5 Numerical Results
In this section we present numerical results in order toillustrate the solution to the optimization throughput prob-lems of the AF energy harvesting enabled relaying schemein the proposed TPSR protocol namely the optimal value ofthroughput 120591 optimal value of signal processing time 120572 andpower splitting ratio 120573
In these simulations we set up common parameters asfollows the distances 1198891 and 1198892 are normalized to be 1 (ie1198891 = 1198892 = 1) the energy harvesting efficiency 120578 = 07 thefixed transmission rate of the source 119877 = 4 (bpsHz) sourcetransmission power 119875
119878= 2 (Watt) destination transmission
power 119875119863
= 2 (Watt) and path loss exponent 119898 = 27In all simulations 120582
ℎ119878and 120582
ℎ119863are denoted as the mean
values of the exponential random variables |ℎ119878|2 and |ℎ
119863|2
respectively and set to 1The simulation results depend on theexpressions for outage probability in (12) which is evaluatedby averaging these calculations over 105 random realizationsof the Rayleigh fading channels of ℎ
119878and ℎ119863
As observation Figures 4 and 5 show that simulationresults of achievable throughput perfectly match the analyt-ical results for the optimal values range of 0 lt 120572 lt 1and 0 lt 120573 lt 1 for the TPSR protocol In this illustrationsimilar noise variances at the relay and destination mobilenodes are assumed that is 120590
2119877
= 1205902119863
= 1205902
= 001 Ascan be seen from Figure 4 the throughput increases from 0to 125 when 120572 increases from 001 to 035 but later it startsdecreasing as 120572 increases from its optimal value (for 120573 = 07)and the throughput increases from 0 to 095 as 120572 increasesfrom 001 to 045 but then decreases as 120572 increases from itsoptimal value (for 120573 = 03) In Figure 5 the throughputincreases from 0 to 125 as 120573 increases from 001 to 07 butlater it starts decreasing as 120573 increases (for 120572 = 03) andthe throughput increases from 0 to 084 as 120573 increases from001 to 06 but then decreases as 120573 increases from its optimalvalue (for 120572 = 07) Interestingly in the case when value of 120572
increases we obtain optimal throughput only if 120573 decreasesand vice versa We can explain important results that thevalue of 120572 is smaller than the optimal value of 120572 whichmeans that there is less time for energy harvesting and more
0 02
02
04
04
06
06
08
08
10
1
12
14TPSR protocol
AnalyticalApproximateSimulation
120572
120573 = 07
120573 = 03
Thro
ughp
ut120591
TPSR
(bps
Hz)
Figure 4 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of the block time switching
TPSR protocol
AnalyticalApproximateSimulation
0 02 04 06 08 1
02
04
06
08
0
1
12
14
120572 = 07
120572 = 03
120573
Thro
ughp
ut120591
TPSR
(bits
sH
z)
Figure 5 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of power splitting
time for information transmission As a result less energy isharvested and throughput achieved at the destination mobilenode is greater In contrast when the value of120572 is greater thanthe optimal 120572 there is more time for energy harvesting butless time for information transmission Furthermore whenthe value of 120573 is smaller than the optimal 120573 there is less
Mobile Information Systems 7
power available for energy harvesting and more power forprocessing the received signal Thus high signal strengthis observed at the relay mobile node and results in higherthroughput at the destination mobile node In addition incase the value of120573 is greater than the optimal120573 more power iswasted on energy harvesting and less power for informationtransmission from the source to relay mobile node
For comparison Figure 6 depicts the optimal throughput120591 of the TPSR protocol and the ideal receiver for differentvalues of noise variance 120590
2 In fact the simulation resultshows that the throughput in the ideal case always outper-forms that in the TPSR caseThe optimal throughput roughlyremains constant when noise variance changes from minus40 dBto minus30 dB In contrast the systemrsquos throughput performancedecreases dramatically when a larger number of noise vari-ances occur
6 Conclusions
This paper proposes TPSR protocol and the design of thereceiver architecture for wireless energy harvesting andinformation transmission in the EHCN In addition theoutage performance of the AF relaying scheme where therelay mobile node harvests energy from source node throughthe received RF signal and then uses harvested energy toamplify the information and forward the source signal tothe destination mobile node has been derived For sim-plicity in computation we also develop the closed-formexpression of the achievable throughput at the destinationMore importantly the optimal values of time switching andpower splitting ratio for energy harvesting in the proposedTPSR protocol which are chosen in order to maximize thethroughput of the system were also numerically investigated
Appendix
In the following we derive the outage probability in (12)which is given by (A1) where 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 1205902119863SNR0
120595 ≜ 120578120572120573(1 minus 120573)119875119878 and 120596 ≜ 120578120572120573119889
119898
1 1205902119877SNR0
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A1)
It is observed and also can be verified that the factor inthe denominator 120595|ℎ
119878|2
minus 120596 = 0 Thus 119875TPSRout is rewritten in
two cases as follows(i) If |ℎ
119878|2
gt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A2)
(ii) If |ℎ119878|2
lt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) = 1 (A3)
TPSRIdeal receiver
18
16
14
12
1
08
06
04
02
0minus40 minus35 minus30 minus25 minus20 minus15 minus10
1205902 (dB)
Opt
imal
thro
ughp
ut120591
d1 = d2 = 1 PS = PD = 2 120578 = 07
Figure 6 The optimal throughput achieved for the TPSR protocoland the ideal receiver by the different value of noise
We obtain the equality Pr(|ℎ119863|2
gt 120579(120595|ℎ119878|2minus120596)) = 1 due
to the fact that if the value of |ℎ119878|2
lt 120596120595 with 120596120595 being thefactor in denominator 120595|ℎ
119878|2
minus 120596 will be a negative numberand probability of |ℎ
119863|2 being greater than some negative
number is always equal to 1Therefore119875TPSRout can be rewritten
as
119875TPSRout = int
120596120595
0Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
= int
120596120595
0119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1minus expminus120579
(120595120574 minus 120596) 120582ℎ119863
)
sdot 119901|ℎ119878|
2 (120574) 119889120574
(A4)
where 120574 is the integration variable 119901|ℎ119878|
2(120574) ≜ (1120582ℎ119878
)119890minus120574120582ℎ119878
is the probability density function (PDF) of exponentialdistributed random variable |ℎ
119878|2 and 119865
|ℎ119863|2(120574) ≜ Pr(|ℎ
119863|2
lt
120574) = 1minus119890minus120574120582ℎ119863 is the cumulative distribution function (CDF)
of the exponential distributed random variable |ℎ119863|2 Thus
119875TPSRout can be calculated by
119875TPSRout = 1
minus1
120582ℎ119878
int
infin
120596120595
expminus120574
120582ℎ119878
minus120579
(120595120574 minus 120596) 120582ℎ119863
119889120574
(A5)
8 Mobile Information Systems
Let us define a new integration variable 120583 = 120595120574minus120596 Thusoutage probability is given by [15]
119875TPSRout = 1minus
1120595120582ℎ119878
exp(minus120596
120595120582ℎ119878
)
sdot int
infin
120583=0exp(minus
120583
120595120582ℎ119878
minus120579
120583120582ℎ119863
) 119889120583 = 1
minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120574ℎ119878
120574ℎ119863
1198701 (radic4120579
120595120574ℎ119878
120574ℎ119863
)
(A6)
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] D Li C Shen and Z Qiu ldquoSum rate maximization and energyharvesting for two-way af relay systems with imperfect CSIrdquoin Proceedings of the 38th IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo13) pp 4958ndash4962 Vancouver Canada May 2013
[2] O Orhan and E Erkip ldquoThroughput maximization for energyharvesting two-hop networksrdquo in Proceedings of the IEEEInternational Symposium on Information Theory (ISITrsquo13) pp1596ndash1600 Istanbul Turkey July 2013
[3] P Mangayarkarasi J Raja and S Jayashri ldquoAn efficient energyharvesting scheme to maximize the throughput of the wirelessrelay networkwithTSR andPSRprotocolrdquo International Journalof Electronics and Communications vol 69 no 5 pp 841ndash8502015
[4] J Li C Ma Y Luo Y Cheng J Wu and C Chen ldquoJointoptimization of transmit power and energy harvesting for relay-basedM2M two-way communicationsrdquo International Journal ofDistributed Sensor Networks In press
[5] N Nomikos D N Skoutas D Vouyioukas C Verikoukisand C Skianis ldquoCapacity maximization through energy-awaremulti-mode relayingrdquo Wireless Personal Communications vol74 no 1 pp 83ndash99 2014
[6] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[7] A A Nasir X Zhou S Durrani and R A Kennedy ldquoThrough-put and ergodic capacity of wireless energy harvesting basedDF relaying networkrdquo in Proceedings of the IEEE InternationalConference on Communications (ICCrsquo14) pp 4066ndash4071 IEEESydney Australia June 2014
[8] X LuW Xu S Li J Lin and Z He ldquoSimultaneous informationand power transfer for relay-assisted cognitive radio networksrdquoin Proceedings of the IEEE International Conference on Commu-nications Workshops (ICC 14) pp 331ndash336 Sydney AustraliaJune 2014
[9] H H Chen Y Li J L Rebelatto B F Uchoa-Filhoand andB Vucetic ldquoHarvest-then-cooperate wireless-powered cooper-ative communicationsrdquo IEEE Transactions on Signal Processingvol 63 no 7 pp 1700ndash1711 2015
[10] C Zhong H A Suraweera G Zjeng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[11] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[12] I Krikidis S Sasaki S Timotheou and Z Ding ldquoA low com-plexity antenna switching for joint wireless information andenergy transfer in MIMO relay channelsrdquo IEEE Transactions onCommunications vol 62 no 5 pp 1577ndash1587 2014
[13] C Shen W-C Li and T-H Chang ldquoWireless information andenergy transfer in multi-antenna interference channelrdquo IEEETransactions on Signal Processing vol 62 no 23 pp 6249ndash62642014
[14] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4767 2013
[15] I S Gradshteyn and I M Ryzhik Table of Integrals Series andProducts ElsevierAcademic Press 7th edition 2007
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
6 Mobile Information Systems
Similar to the analysis in previous section the throughputis determined by evaluating the outage probability Interest-ingly the closed-form expression of119875ideal
out can be calculated as119875TPSRout
119875idealout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (26)
where 119875idealout can be calculated as in the Appendix with 120579 ≜
119889119898
1 1205902119863SNR0 120595 ≜ 120578119875
119878 and 120596 ≜ 120578119889
119898
1 1205902119877SNR0 In this case
we also consider the delay-limited transmission mode forevaluating the throughput 120591
ideal at the destination which isgiven by
120591ideal
= (1minus 119875idealout )
119877
2 (27)
5 Numerical Results
In this section we present numerical results in order toillustrate the solution to the optimization throughput prob-lems of the AF energy harvesting enabled relaying schemein the proposed TPSR protocol namely the optimal value ofthroughput 120591 optimal value of signal processing time 120572 andpower splitting ratio 120573
In these simulations we set up common parameters asfollows the distances 1198891 and 1198892 are normalized to be 1 (ie1198891 = 1198892 = 1) the energy harvesting efficiency 120578 = 07 thefixed transmission rate of the source 119877 = 4 (bpsHz) sourcetransmission power 119875
119878= 2 (Watt) destination transmission
power 119875119863
= 2 (Watt) and path loss exponent 119898 = 27In all simulations 120582
ℎ119878and 120582
ℎ119863are denoted as the mean
values of the exponential random variables |ℎ119878|2 and |ℎ
119863|2
respectively and set to 1The simulation results depend on theexpressions for outage probability in (12) which is evaluatedby averaging these calculations over 105 random realizationsof the Rayleigh fading channels of ℎ
119878and ℎ119863
As observation Figures 4 and 5 show that simulationresults of achievable throughput perfectly match the analyt-ical results for the optimal values range of 0 lt 120572 lt 1and 0 lt 120573 lt 1 for the TPSR protocol In this illustrationsimilar noise variances at the relay and destination mobilenodes are assumed that is 120590
2119877
= 1205902119863
= 1205902
= 001 Ascan be seen from Figure 4 the throughput increases from 0to 125 when 120572 increases from 001 to 035 but later it startsdecreasing as 120572 increases from its optimal value (for 120573 = 07)and the throughput increases from 0 to 095 as 120572 increasesfrom 001 to 045 but then decreases as 120572 increases from itsoptimal value (for 120573 = 03) In Figure 5 the throughputincreases from 0 to 125 as 120573 increases from 001 to 07 butlater it starts decreasing as 120573 increases (for 120572 = 03) andthe throughput increases from 0 to 084 as 120573 increases from001 to 06 but then decreases as 120573 increases from its optimalvalue (for 120572 = 07) Interestingly in the case when value of 120572
increases we obtain optimal throughput only if 120573 decreasesand vice versa We can explain important results that thevalue of 120572 is smaller than the optimal value of 120572 whichmeans that there is less time for energy harvesting and more
0 02
02
04
04
06
06
08
08
10
1
12
14TPSR protocol
AnalyticalApproximateSimulation
120572
120573 = 07
120573 = 03
Thro
ughp
ut120591
TPSR
(bps
Hz)
Figure 4 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of the block time switching
TPSR protocol
AnalyticalApproximateSimulation
0 02 04 06 08 1
02
04
06
08
0
1
12
14
120572 = 07
120572 = 03
120573
Thro
ughp
ut120591
TPSR
(bits
sH
z)
Figure 5 Simulation based and analytical throughput 120591 at thedestination with respect to the fraction of power splitting
time for information transmission As a result less energy isharvested and throughput achieved at the destination mobilenode is greater In contrast when the value of120572 is greater thanthe optimal 120572 there is more time for energy harvesting butless time for information transmission Furthermore whenthe value of 120573 is smaller than the optimal 120573 there is less
Mobile Information Systems 7
power available for energy harvesting and more power forprocessing the received signal Thus high signal strengthis observed at the relay mobile node and results in higherthroughput at the destination mobile node In addition incase the value of120573 is greater than the optimal120573 more power iswasted on energy harvesting and less power for informationtransmission from the source to relay mobile node
For comparison Figure 6 depicts the optimal throughput120591 of the TPSR protocol and the ideal receiver for differentvalues of noise variance 120590
2 In fact the simulation resultshows that the throughput in the ideal case always outper-forms that in the TPSR caseThe optimal throughput roughlyremains constant when noise variance changes from minus40 dBto minus30 dB In contrast the systemrsquos throughput performancedecreases dramatically when a larger number of noise vari-ances occur
6 Conclusions
This paper proposes TPSR protocol and the design of thereceiver architecture for wireless energy harvesting andinformation transmission in the EHCN In addition theoutage performance of the AF relaying scheme where therelay mobile node harvests energy from source node throughthe received RF signal and then uses harvested energy toamplify the information and forward the source signal tothe destination mobile node has been derived For sim-plicity in computation we also develop the closed-formexpression of the achievable throughput at the destinationMore importantly the optimal values of time switching andpower splitting ratio for energy harvesting in the proposedTPSR protocol which are chosen in order to maximize thethroughput of the system were also numerically investigated
Appendix
In the following we derive the outage probability in (12)which is given by (A1) where 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 1205902119863SNR0
120595 ≜ 120578120572120573(1 minus 120573)119875119878 and 120596 ≜ 120578120572120573119889
119898
1 1205902119877SNR0
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A1)
It is observed and also can be verified that the factor inthe denominator 120595|ℎ
119878|2
minus 120596 = 0 Thus 119875TPSRout is rewritten in
two cases as follows(i) If |ℎ
119878|2
gt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A2)
(ii) If |ℎ119878|2
lt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) = 1 (A3)
TPSRIdeal receiver
18
16
14
12
1
08
06
04
02
0minus40 minus35 minus30 minus25 minus20 minus15 minus10
1205902 (dB)
Opt
imal
thro
ughp
ut120591
d1 = d2 = 1 PS = PD = 2 120578 = 07
Figure 6 The optimal throughput achieved for the TPSR protocoland the ideal receiver by the different value of noise
We obtain the equality Pr(|ℎ119863|2
gt 120579(120595|ℎ119878|2minus120596)) = 1 due
to the fact that if the value of |ℎ119878|2
lt 120596120595 with 120596120595 being thefactor in denominator 120595|ℎ
119878|2
minus 120596 will be a negative numberand probability of |ℎ
119863|2 being greater than some negative
number is always equal to 1Therefore119875TPSRout can be rewritten
as
119875TPSRout = int
120596120595
0Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
= int
120596120595
0119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1minus expminus120579
(120595120574 minus 120596) 120582ℎ119863
)
sdot 119901|ℎ119878|
2 (120574) 119889120574
(A4)
where 120574 is the integration variable 119901|ℎ119878|
2(120574) ≜ (1120582ℎ119878
)119890minus120574120582ℎ119878
is the probability density function (PDF) of exponentialdistributed random variable |ℎ
119878|2 and 119865
|ℎ119863|2(120574) ≜ Pr(|ℎ
119863|2
lt
120574) = 1minus119890minus120574120582ℎ119863 is the cumulative distribution function (CDF)
of the exponential distributed random variable |ℎ119863|2 Thus
119875TPSRout can be calculated by
119875TPSRout = 1
minus1
120582ℎ119878
int
infin
120596120595
expminus120574
120582ℎ119878
minus120579
(120595120574 minus 120596) 120582ℎ119863
119889120574
(A5)
8 Mobile Information Systems
Let us define a new integration variable 120583 = 120595120574minus120596 Thusoutage probability is given by [15]
119875TPSRout = 1minus
1120595120582ℎ119878
exp(minus120596
120595120582ℎ119878
)
sdot int
infin
120583=0exp(minus
120583
120595120582ℎ119878
minus120579
120583120582ℎ119863
) 119889120583 = 1
minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120574ℎ119878
120574ℎ119863
1198701 (radic4120579
120595120574ℎ119878
120574ℎ119863
)
(A6)
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] D Li C Shen and Z Qiu ldquoSum rate maximization and energyharvesting for two-way af relay systems with imperfect CSIrdquoin Proceedings of the 38th IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo13) pp 4958ndash4962 Vancouver Canada May 2013
[2] O Orhan and E Erkip ldquoThroughput maximization for energyharvesting two-hop networksrdquo in Proceedings of the IEEEInternational Symposium on Information Theory (ISITrsquo13) pp1596ndash1600 Istanbul Turkey July 2013
[3] P Mangayarkarasi J Raja and S Jayashri ldquoAn efficient energyharvesting scheme to maximize the throughput of the wirelessrelay networkwithTSR andPSRprotocolrdquo International Journalof Electronics and Communications vol 69 no 5 pp 841ndash8502015
[4] J Li C Ma Y Luo Y Cheng J Wu and C Chen ldquoJointoptimization of transmit power and energy harvesting for relay-basedM2M two-way communicationsrdquo International Journal ofDistributed Sensor Networks In press
[5] N Nomikos D N Skoutas D Vouyioukas C Verikoukisand C Skianis ldquoCapacity maximization through energy-awaremulti-mode relayingrdquo Wireless Personal Communications vol74 no 1 pp 83ndash99 2014
[6] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[7] A A Nasir X Zhou S Durrani and R A Kennedy ldquoThrough-put and ergodic capacity of wireless energy harvesting basedDF relaying networkrdquo in Proceedings of the IEEE InternationalConference on Communications (ICCrsquo14) pp 4066ndash4071 IEEESydney Australia June 2014
[8] X LuW Xu S Li J Lin and Z He ldquoSimultaneous informationand power transfer for relay-assisted cognitive radio networksrdquoin Proceedings of the IEEE International Conference on Commu-nications Workshops (ICC 14) pp 331ndash336 Sydney AustraliaJune 2014
[9] H H Chen Y Li J L Rebelatto B F Uchoa-Filhoand andB Vucetic ldquoHarvest-then-cooperate wireless-powered cooper-ative communicationsrdquo IEEE Transactions on Signal Processingvol 63 no 7 pp 1700ndash1711 2015
[10] C Zhong H A Suraweera G Zjeng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[11] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[12] I Krikidis S Sasaki S Timotheou and Z Ding ldquoA low com-plexity antenna switching for joint wireless information andenergy transfer in MIMO relay channelsrdquo IEEE Transactions onCommunications vol 62 no 5 pp 1577ndash1587 2014
[13] C Shen W-C Li and T-H Chang ldquoWireless information andenergy transfer in multi-antenna interference channelrdquo IEEETransactions on Signal Processing vol 62 no 23 pp 6249ndash62642014
[14] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4767 2013
[15] I S Gradshteyn and I M Ryzhik Table of Integrals Series andProducts ElsevierAcademic Press 7th edition 2007
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 7
power available for energy harvesting and more power forprocessing the received signal Thus high signal strengthis observed at the relay mobile node and results in higherthroughput at the destination mobile node In addition incase the value of120573 is greater than the optimal120573 more power iswasted on energy harvesting and less power for informationtransmission from the source to relay mobile node
For comparison Figure 6 depicts the optimal throughput120591 of the TPSR protocol and the ideal receiver for differentvalues of noise variance 120590
2 In fact the simulation resultshows that the throughput in the ideal case always outper-forms that in the TPSR caseThe optimal throughput roughlyremains constant when noise variance changes from minus40 dBto minus30 dB In contrast the systemrsquos throughput performancedecreases dramatically when a larger number of noise vari-ances occur
6 Conclusions
This paper proposes TPSR protocol and the design of thereceiver architecture for wireless energy harvesting andinformation transmission in the EHCN In addition theoutage performance of the AF relaying scheme where therelay mobile node harvests energy from source node throughthe received RF signal and then uses harvested energy toamplify the information and forward the source signal tothe destination mobile node has been derived For sim-plicity in computation we also develop the closed-formexpression of the achievable throughput at the destinationMore importantly the optimal values of time switching andpower splitting ratio for energy harvesting in the proposedTPSR protocol which are chosen in order to maximize thethroughput of the system were also numerically investigated
Appendix
In the following we derive the outage probability in (12)which is given by (A1) where 120579 ≜ (1 minus 120572)(1 minus 120573)119889
119898
1 1205902119863SNR0
120595 ≜ 120578120572120573(1 minus 120573)119875119878 and 120596 ≜ 120578120572120573119889
119898
1 1205902119877SNR0
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A1)
It is observed and also can be verified that the factor inthe denominator 120595|ℎ
119878|2
minus 120596 = 0 Thus 119875TPSRout is rewritten in
two cases as follows(i) If |ℎ
119878|2
gt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2lt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) (A2)
(ii) If |ℎ119878|2
lt 120596120595
119875TPSRout = Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
1205951003816100381610038161003816ℎ119878
1003816100381610038161003816
2minus 120596
) = 1 (A3)
TPSRIdeal receiver
18
16
14
12
1
08
06
04
02
0minus40 minus35 minus30 minus25 minus20 minus15 minus10
1205902 (dB)
Opt
imal
thro
ughp
ut120591
d1 = d2 = 1 PS = PD = 2 120578 = 07
Figure 6 The optimal throughput achieved for the TPSR protocoland the ideal receiver by the different value of noise
We obtain the equality Pr(|ℎ119863|2
gt 120579(120595|ℎ119878|2minus120596)) = 1 due
to the fact that if the value of |ℎ119878|2
lt 120596120595 with 120596120595 being thefactor in denominator 120595|ℎ
119878|2
minus 120596 will be a negative numberand probability of |ℎ
119863|2 being greater than some negative
number is always equal to 1Therefore119875TPSRout can be rewritten
as
119875TPSRout = int
120596120595
0Pr(
1003816100381610038161003816ℎ1198631003816100381610038161003816
2gt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1003816100381610038161003816ℎ119863
1003816100381610038161003816
2lt
120579
120595120574 minus 120596) 119901|ℎ119878|
2 (120574) 119889120574
= int
120596120595
0119901|ℎ119878|
2 (120574) 119889120574
+ int
infin
120596120595
Pr(1minus expminus120579
(120595120574 minus 120596) 120582ℎ119863
)
sdot 119901|ℎ119878|
2 (120574) 119889120574
(A4)
where 120574 is the integration variable 119901|ℎ119878|
2(120574) ≜ (1120582ℎ119878
)119890minus120574120582ℎ119878
is the probability density function (PDF) of exponentialdistributed random variable |ℎ
119878|2 and 119865
|ℎ119863|2(120574) ≜ Pr(|ℎ
119863|2
lt
120574) = 1minus119890minus120574120582ℎ119863 is the cumulative distribution function (CDF)
of the exponential distributed random variable |ℎ119863|2 Thus
119875TPSRout can be calculated by
119875TPSRout = 1
minus1
120582ℎ119878
int
infin
120596120595
expminus120574
120582ℎ119878
minus120579
(120595120574 minus 120596) 120582ℎ119863
119889120574
(A5)
8 Mobile Information Systems
Let us define a new integration variable 120583 = 120595120574minus120596 Thusoutage probability is given by [15]
119875TPSRout = 1minus
1120595120582ℎ119878
exp(minus120596
120595120582ℎ119878
)
sdot int
infin
120583=0exp(minus
120583
120595120582ℎ119878
minus120579
120583120582ℎ119863
) 119889120583 = 1
minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120574ℎ119878
120574ℎ119863
1198701 (radic4120579
120595120574ℎ119878
120574ℎ119863
)
(A6)
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] D Li C Shen and Z Qiu ldquoSum rate maximization and energyharvesting for two-way af relay systems with imperfect CSIrdquoin Proceedings of the 38th IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo13) pp 4958ndash4962 Vancouver Canada May 2013
[2] O Orhan and E Erkip ldquoThroughput maximization for energyharvesting two-hop networksrdquo in Proceedings of the IEEEInternational Symposium on Information Theory (ISITrsquo13) pp1596ndash1600 Istanbul Turkey July 2013
[3] P Mangayarkarasi J Raja and S Jayashri ldquoAn efficient energyharvesting scheme to maximize the throughput of the wirelessrelay networkwithTSR andPSRprotocolrdquo International Journalof Electronics and Communications vol 69 no 5 pp 841ndash8502015
[4] J Li C Ma Y Luo Y Cheng J Wu and C Chen ldquoJointoptimization of transmit power and energy harvesting for relay-basedM2M two-way communicationsrdquo International Journal ofDistributed Sensor Networks In press
[5] N Nomikos D N Skoutas D Vouyioukas C Verikoukisand C Skianis ldquoCapacity maximization through energy-awaremulti-mode relayingrdquo Wireless Personal Communications vol74 no 1 pp 83ndash99 2014
[6] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[7] A A Nasir X Zhou S Durrani and R A Kennedy ldquoThrough-put and ergodic capacity of wireless energy harvesting basedDF relaying networkrdquo in Proceedings of the IEEE InternationalConference on Communications (ICCrsquo14) pp 4066ndash4071 IEEESydney Australia June 2014
[8] X LuW Xu S Li J Lin and Z He ldquoSimultaneous informationand power transfer for relay-assisted cognitive radio networksrdquoin Proceedings of the IEEE International Conference on Commu-nications Workshops (ICC 14) pp 331ndash336 Sydney AustraliaJune 2014
[9] H H Chen Y Li J L Rebelatto B F Uchoa-Filhoand andB Vucetic ldquoHarvest-then-cooperate wireless-powered cooper-ative communicationsrdquo IEEE Transactions on Signal Processingvol 63 no 7 pp 1700ndash1711 2015
[10] C Zhong H A Suraweera G Zjeng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[11] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[12] I Krikidis S Sasaki S Timotheou and Z Ding ldquoA low com-plexity antenna switching for joint wireless information andenergy transfer in MIMO relay channelsrdquo IEEE Transactions onCommunications vol 62 no 5 pp 1577ndash1587 2014
[13] C Shen W-C Li and T-H Chang ldquoWireless information andenergy transfer in multi-antenna interference channelrdquo IEEETransactions on Signal Processing vol 62 no 23 pp 6249ndash62642014
[14] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4767 2013
[15] I S Gradshteyn and I M Ryzhik Table of Integrals Series andProducts ElsevierAcademic Press 7th edition 2007
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
8 Mobile Information Systems
Let us define a new integration variable 120583 = 120595120574minus120596 Thusoutage probability is given by [15]
119875TPSRout = 1minus
1120595120582ℎ119878
exp(minus120596
120595120582ℎ119878
)
sdot int
infin
120583=0exp(minus
120583
120595120582ℎ119878
minus120579
120583120582ℎ119863
) 119889120583 = 1
minus exp(minus120596
120595120582ℎ119878
) radic4120579
120595120574ℎ119878
120574ℎ119863
1198701 (radic4120579
120595120574ℎ119878
120574ℎ119863
)
(A6)
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] D Li C Shen and Z Qiu ldquoSum rate maximization and energyharvesting for two-way af relay systems with imperfect CSIrdquoin Proceedings of the 38th IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo13) pp 4958ndash4962 Vancouver Canada May 2013
[2] O Orhan and E Erkip ldquoThroughput maximization for energyharvesting two-hop networksrdquo in Proceedings of the IEEEInternational Symposium on Information Theory (ISITrsquo13) pp1596ndash1600 Istanbul Turkey July 2013
[3] P Mangayarkarasi J Raja and S Jayashri ldquoAn efficient energyharvesting scheme to maximize the throughput of the wirelessrelay networkwithTSR andPSRprotocolrdquo International Journalof Electronics and Communications vol 69 no 5 pp 841ndash8502015
[4] J Li C Ma Y Luo Y Cheng J Wu and C Chen ldquoJointoptimization of transmit power and energy harvesting for relay-basedM2M two-way communicationsrdquo International Journal ofDistributed Sensor Networks In press
[5] N Nomikos D N Skoutas D Vouyioukas C Verikoukisand C Skianis ldquoCapacity maximization through energy-awaremulti-mode relayingrdquo Wireless Personal Communications vol74 no 1 pp 83ndash99 2014
[6] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[7] A A Nasir X Zhou S Durrani and R A Kennedy ldquoThrough-put and ergodic capacity of wireless energy harvesting basedDF relaying networkrdquo in Proceedings of the IEEE InternationalConference on Communications (ICCrsquo14) pp 4066ndash4071 IEEESydney Australia June 2014
[8] X LuW Xu S Li J Lin and Z He ldquoSimultaneous informationand power transfer for relay-assisted cognitive radio networksrdquoin Proceedings of the IEEE International Conference on Commu-nications Workshops (ICC 14) pp 331ndash336 Sydney AustraliaJune 2014
[9] H H Chen Y Li J L Rebelatto B F Uchoa-Filhoand andB Vucetic ldquoHarvest-then-cooperate wireless-powered cooper-ative communicationsrdquo IEEE Transactions on Signal Processingvol 63 no 7 pp 1700ndash1711 2015
[10] C Zhong H A Suraweera G Zjeng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[11] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[12] I Krikidis S Sasaki S Timotheou and Z Ding ldquoA low com-plexity antenna switching for joint wireless information andenergy transfer in MIMO relay channelsrdquo IEEE Transactions onCommunications vol 62 no 5 pp 1577ndash1587 2014
[13] C Shen W-C Li and T-H Chang ldquoWireless information andenergy transfer in multi-antenna interference channelrdquo IEEETransactions on Signal Processing vol 62 no 23 pp 6249ndash62642014
[14] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4767 2013
[15] I S Gradshteyn and I M Ryzhik Table of Integrals Series andProducts ElsevierAcademic Press 7th edition 2007
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
