An Approach for Wireless Sensor Networks TopologyControl in Indoor Scenarios

Sérgio KostinInstituto Militar de Engenharia

Praça Gen Tibúrcio, 80Rio de Janeiro, Brazilkostin@ime.eb.br

Ronaldo Moreira SallesInstituto Militar de Engenharia

Praça Gen Tibúrcio, 80Rio de Janeiro, Brazilsalles@ime.eb.br

Claudio Luis de AmorimPESC/COPPE/UFRJ

POB 68.511 – 21941.972Rio de Janeiro, Brazil

amorim@cos.ufrj.br

ABSTRACTThis work presents a new approach for topology control(TC) in wireless sensor networks (WSN) devised for indoorscenarios with obstacles and no feedback mechanisms. Thetechnique is supported by two novel metrics, namely Block-age Rate and Useful Area Rate, applicable to environmentswith well-defined obstacles described by Site Specific Propa-gation models. Simulation results in some realistic scenariosshowed that the technique allows to relate connectivity withtransmission power levels and to identify critical transmis-sion power levels. Also, it is shown that the technique isequivalent to an approximated mean value in terms of con-nectivity aspects.

Categories and Subject DescriptorsC.2.1 [Computer-Communication Networks]: NetworkArchitecture and Design—Wireless communication

General TermsPerformance, Measurement

KeywordsWireless Sensor Networks, Topology Control, Connectivity

1. INTRODUCTIONWireless sensor networks (WSN) have fostered new mod-

els of collecting and broadcasting information with great po-tential use in the areas of environmental monitoring and “in-telligent” buildings, to name a few. However, a major hurdlein deploying a WSN is the limited battery life of a sensornode, requiring every node of a WSN to control its trans-mission power in such a way to maximize connectivity withlower power consumption. The problem is that assuringa certain connectivity degree [27] while minimizing energyconsumption are conflicting goals, besides influencing otheraspects of the WSN operation as well[11].

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Traditional works on WSN deal with flat scenarios, ig-noring the characteristics of the environment. The mostcommon sketch in these works is a circle representing thetransmitting range. When dealing with obstacles, those ap-proaches tend to treat them as non transposable, howeverthis assumption is not verified in practice. In a practical realsituation in indoor scenarios, for example, the electromag-netic radiation is not totally blocked by a wall, but it passesthrough the obstacle, decaying its energy level, according tophysics laws.

Building Mobile WSN is yet more challenging, mainly be-cause of the frequently changes in topology. Besides, thereis the necessity of having more neighbors in order to keepthe overall network connected[24].

We evaluated a novel technique introduced in [12] andimproved in [13] that can determine effective transmissionpower levels for deploying WSNs in scenarios with obsta-cles, which can be used in mobile environments. Specifi-cally, given a certain area to deploy a WSN with its config-uration of obstacles and a probabilistic distribution of sen-sor nodes, the technique calculates the transmission powerlevel (TPL) that each sensor node should apply to mini-mize overall power consumption while supporting the de-fined connectivity degree. The technique uses two metrics:the Blockage Rate (BR) and the Useful Area Rate (UR).Roughly, BR is associated to the interaction among trans-mitters and receivers considering multipath interference andsignal sensitivity due to the presence of obstacles for a givenprobabilistic distribution of the receiver’s positions in thescenario. While UR concerns with the loss effects of a givenpropagation path. More specifically, these two metrics takeinto account the average values of radiation parameters, in-cluding the rate of electromagnetic emission blockage, theradiation rate outwards the scenario, the effect of multipathinterference, and the percentage of radiation effectively used.We use the two metrics to assess the tradeoff between con-nectivity gains and energy savings for each TPL value.

Studying the technique carefully, we realized that it couldfind critical Transmission Power Level, even in complex sce-narios. Another important point to investigate is whetherthe technique would represent an approximation of the meanTPL value in terms of connectivity. So that, the contribu-tion of this work is two-fold. Firstly, we apply and evaluatethe proposed technique in more realistic scenarios, speciallyfinding the critical TPLs. Then, for these scenarios we showthat the technique represents an approximation of the TPLmean value in terms of connectivity.

The remainder of the paper is organized as follows. Sec-

1

Figure 1: Probabilistic Spatial Distribution Map(PSDM)

tion 2 presents related work. In Section 3, we present ourtechnique for establishing the transmission power levels inWSNs for a given scenario. Section 4 describes our exper-imental methodology and analyzes simulation results. Themain contributions of this work are presented in Section 5and 6. Section 5 analyses the blockage aspects. Section 6presents the technique evaluation as a mean value. Finally,our conclusions and ongoing works are presented in Section7.

2. RELATED WORKIn this section we briefly present Site Specific Propagation

models (SISP) that allow more accurate simulations. Fur-ther, we describe aspects of Topology Control, in particularDistributed Topology Control Protocols (DTCPs), classify-ing them into categories according to the literature [24] andthe TPL strategy approach. Finally, we position our workin its specific field.

The simplest approach for radio-wave propagation model-ing at high frequencies (VHF to SHF) is semi-empirical, suchas the well-known exponential path loss model. Radiowavepropagation models using detailed terrain data-bases arecommonly referred as Site Specific Propagation models[23].Smaller scenarios (usually indoors) may benefit from morecomplex and accurate approaches such as ray-tracing mod-eling. In this technique, the main propagation paths (rays)are deterministically found based on the common electro-magnetic phenomena of reflection, refraction, and scatter-ing, which includes diffraction. Ray-tracing is usually car-ried out two-fold, using either greedy methods or image the-ory [25]. With the ever growing available numerical capacity

Figure 2: Blockage Rate and Useful Area Rate

of computers, ray-tracing models have increasingly becomemore attractive as propagation prediction tools. Some re-searchers even expect that deterministic modeling may pre-vail in a near future as the preferred approach for propaga-tion prediction, even outdoors [23].

Topology Control (TC) is the art of coordinating nodes’decisions regarding their transmission ranges, in order togenerate a network with the desired properties (e.g. con-nectivity) while reducing node energy consumption and/orincreasing network capacity. A topology control protocolshould have some basic properties: be fully distributed andasynchronous; be localized; generate a topology that pre-serves the original network connectivity and relies, if possi-ble, on bidirectional links; generate a topology with smallphysical degree; and rely on “low-quality” information [24].

According to Santi [24], DTCPs can be classified in fourdifferent categories: Location-based; Direction-based; Neigh-bor-based; and Mobile-based.

In Location-based Topology Control Protocols (e.g. LocalMinimum Spanning Tree - LMST [16]), a subset of the nodescan estimate their positions either exchanging messages withthe surrounding anchor nodes or through nodes which areGPS-equipped. Knowing their relative positions, they canconstruct a graph based on this information.

Direction-based Topology Control Protocols, such as theCone-Based Topology Control – CTBC [15] – rely on thenode’s ability to estimate the relative direction of their neigh-bors based on equipping nodes with more than one direc-tional antenna.

K Neighbors Level Based (KNeighLev[2]) and Signal-Strength Topology Control (S-XTC[7]) are Neighbor-basedTopology Control Protocols which are based on the node’sability to determine the number and identity of neighborswithin their range and on link quality to build an order onthis neighbor set.

KNeighLev and S-XTC are examples of state-of-the-artNeighbor-based DTCPs, which in fact are based on bidirec-tional links. They argue that the support of unidirectionallinks is in general technically difficult and expensive. How-ever, many times, the data exchange in WSNs are done by

2

Figure 3: The Kubisch scenario

broadcasting information. Akyildiz et al, in [1], state thatsensor nodes mainly use broadcast communication, such asGossip Algorithms [4], paradigm whereas most strict ad hocnetworks are based on point-to-point communications. Anexample is that S-XTC had to improve the original XTC,mainly because, in XTC, every node needs to exchange itsordered list with all reachable neighbors, the time neededfor this operation scales badly with the network density.

Mobile-based protocols (e.g. MobileGrid[17] and Lo-cal Information No Topology – LINT[22]) must be fast, sothat they can keep up with the changes across the network.Maintain bidirectional links is an expensive task, not onlyin terms of time but also medium access and energy (crucialfor WSNs).

Regarding to metrics applied to the topology control, wefound the following works specially related to the networkinginterference measures.

Burkhart et al, in[5], presented a data traffic independentmodel that accounts the network interference as a whole.That metric is named maximum edge coverage, which comesfrom the maximum number of nodes affected by a specificnetwork link. The paper also tried to prove that most cur-rently proposed topology control algorithms do not effec-tively constrain interference.

Maveni-Nejad and Li, in [18], proposed an alternative met-ric that corresponds to the network average interference. Inthis case, the interference is defined as the coverage sum ofall network links divided by the network number of nodes.

Iannone et al, in [10], took into account the TPL. If thenumber of neighbors is constant when a node increases or de-creases its TPL for P1 to P2, the interference measure shouldincrease/decrease. Yet, if two neighbors N1 and N2 trans-mit at the same TPL but have different number of neighbors,the interference caused by the nodes should differ in orderto reflect the difference in neighborhood.

It is important to note that all previous mentioned metricswere proposed for scenarios without obstacles and to thebest of our knowledge, they were not tested and evaluatedin specific and more real scenarios.

3. TRANSMISSION POWER CONTROLTECHNIQUE

In this section, we present the foundations of our tech-nique [12], [13]. It is based on a Probabilistic Spatial Dis-tribution Map (PSDM), the Blockage Rate (BR) and UsefulArea Rate (UR). Later on, we show how to determine theconnectivity using BR and UR and a way to employ thetechnique.

3.1 Occupation Profile of a Scenario

Figure 4: The Parallel Computing Laboratory(PCL) scenario

BR and UR are calculated for each particular scenario.Often, we can use a Geographic Information System (GIS)to build a PSDM. The idea behind PSDM is that distributedsensor nodes within a WSN scenario tend to form specificprobabilistic occupation profiles. For example, pedestriansusually walk along sidewalks, gardens and parks. Cars aremostly located on roads, avenues and so on. Therefore, it ispossible to derive the PSDM in different ways: using sensornodes location distributed in a specific scenario, mobilitymodels [6], or calculated by means of a localization system[9] that indicates the probable region where each sensor islocated.

Figure 1 shows an example of a receiver device’s PSDMbased on the relative weights of the distributed occupationacross the terrain by the nodes. These weights are obtainedfrom a given probability density. The distribution can bea function of time and number of nodes. It can also beconditional (P (A | B)). Specifically, in Figure 1 the areawith p = 4, 2, 1, 0 represent streets, sidewalks, gardens, anda lake, respectively.

This information could be obtained from morphologic maps,also referred to as clutter or land-use maps, or built duringthe network planning. PSDM is not always static, being afunction of time.

3.2 Blockage Rate (BR)Figure 2 shows a typical situation where a certain obstacle

blocks the electromagnetic signal of a transmitter t, estab-lishing four distinct areas regarding to the quality of signalreception: the receivers’ area (RA) - e.g. the area wherethe receivers are located; the theoretical coverage area notcontained in RA; the coverage area contained in RA blockedby the obstacles (EB); and the unblocked area (ENB). Con-ceptually, BR expresses the ratio between EB and the sumgiven by EB + ENB .

Formally, considering a specific transmitter class located

3

Figure 5: Path Loss in the PCL scenario

at position s, and assuming a specific transmission powerlevel pw, then BR(t(s, pw)) is defined by:

∑x∈RA

P (rj(x) | t(s))BCF (t(s, pw), rj(x)))∑x∈RA

P (rj(x) | t(s))BNF (t(s, pw), rj(x)))(1)

In Equation 1, P (rj(x) | t(s)) represents the probabilitythat the jth receiver, rj , be found at position x, subjectedto a t-type transmitter being located at position s. Notethat the expression accommodates clustering (when devicestend to join) and repelling (when there is a minimum dis-tance among devices). The antenna gains of transmittersand receivers are considered in the calculation of the proba-bilities, as well as the receivers’ sensitivity. The Function Baccounts for the interaction between transmitters - t(s, pw)(transmitter t at s, emitting a signal with pw power level)- and receivers - (receiver rj) - within RA. The subscripts

CF and NF mean Considering Fading and Not consideringFading, respectively.

BCF ∈ {−1, 0, 1}. BCF returns 0 when the receiver rj(x)is in the theoretical coverage area of a transmitter t at a pwpower level, the received signal is above the data sensitiv-ity level and the multipath interference is so weak that itis unable to degrade the data link (a power level thresholdmust be established to assist this process). Otherwise BCF

returns 1, either when the degradation due to multipath isobserved or the received signal is below the data sensitiv-ity level. BCF will return -1 when the receiver is outsidethe theoretical coverage area, since multipath interferencemay also cause a constructive effect (at aisles, for example),though the obstacle configuration is such that the transmit-ted signal is still able to reach the receiver rj .

BNF ∈ {0, 1}. BNF simply considers free-space propaga-tion and the presence of obstacles against direct rays. It re-turns 1 for all receivers rj(x) within the theoretical coveragearea of the transmitter t at position s - t(s, pw). OtherwiseBNF equals zero, which occurs when the receiver rj is at aposition x such that it is either outside (beyond) the theo-

retical coverage area of t, or behind any obstacle (no directray reaches the receiver).

According to Equation 2, we calculate BR for a specificregion, aka Transmitter Area (TA), computing the weightedaverage of all BR(t(s, pw)). Other statistical parameterssuch as standard deviation, median, maximum, minimum,etc., are also calculated in order to provide the best possibledescription of the chosen scenario. We may also compute thefirst and the second derivatives with respect to TPL (pw) tohelp with the analysis on overcoming propagation barriers.

BR(TA, t, pw) =

∑s∈TA

P (t(s))BR(t(s, pw))∑s∈TA

P (t(s))(2)

3.3 Useful Area Rate (UR)Figure 2 illustrates the notion of Useful Area Rate (UR)

that expresses the ratio between the useful and the theoret-ical coverage area of a transmitter node. The definition ofuseful coverage area comprises the theoretical coverage areaof a transmitter that lies within the receiver area, ignor-ing the obstacles. Therefore, this metric is most concernedwith free-space coverage and aspects of signal range in theWSN, thus disregarding multipath effects and scattering.Formally, given a certain transmitter class t, located at s,operating at a power level pw, UR(t(s, pw)) is defined by:∑

x∈RA

UCO(t(s, pw), rj(x))∑x∈TheoreticalRange

UNO(t(s, pw), rj(x))(3)

In Equation 3, Function U verifies the interaction betweenthe theoretical coverage area and the scenario’s obstacles.The subscripts CO and NO mean Considering Obstacles andN ot considering Obstacles, respectively.

UCO ∈ {0, 1}. Function UCO returns 1 when the receiverrj is in the theoretical coverage area, or in RA, either in aposition where P (rj(x) | t(s)) is not equal to 0. Otherwise,it returns 0.

UNO ∈ {0, 1}. UNO quantifies the coverage area, consid-ering rj ’s sensitivity. UR mainly aims at the loss effects ofpropagation paths, neglecting the probabilistic distributionof receiver’s position that has already been considered inBR.

3.4 How to Determine the ConnectivityDegree using BR and UR

Consider CA(t(s, pw), rj) as the theoretical coverage areaof a transmitter t operating at a power level pw for a specificreceiver rj . Yet, assume D as the sensor node density andt(s, pw) = z. Then, we carry out the following product toget a specific connectivity degree for a given position:

C(z) = (1−BR(z))UR(z)CA(z, rj)D (4)

We can expand Equation 4 to a region, as we made toBR(TA, t(pw)), and calculate various statistical moments.The mean, for example, is given by Equation 5.

C(TA, t(pw), D) =

∑s∈TA

P (t(s))C(t(s, pw), D)∑s∈TA

P (t(s))(5)

4

(a) TPL × Connectivity of Room A – Kubisch

(b) TPL × Connectivity of Room B – PCL

Figure 6: TPL × Connectivity

5

Figure 7: Blockage Rate of Room A and Room B

3.5 How to Apply the TechniqueThe computation of the metrics should be previously per-

formed before starting the WSN operation. Next, the lookuptable values must be stored in each sensor node either man-ually or broadcasting it to them. The broadcast is the rec-ommended storage procedure since it allows addressing theinclusion/exclusion of obstacles in the scenarios after theWSN deployment. Additionally, broadcasting can be per-formed either by peers that participate in the WSN or de-vices with location capabilities. Usually, BR and UR canbe computed using either desktop computers or other high-performance computer systems (like clusters) depending onthe WSN size. Thus, the sensor nodes use those tables withconnectivity data in order to choose suitable TPLs. Thecomplexity of this choice is O(n), where n is the number ofdiscrete TPLs available.

These metrics should be used in a planned manner. In-discriminate use of BR and UR in a heterogeneous environ-ment would minimize energy savings benefits. Ideally, themetrics should be used in small clusters of sensor nodes thatcan be automatically detected during the data processing bydata mining techniques (e.g. Clustering) such as k-MedoidMethod [8], in which the points with the smallest BR valueswould be considered as cluster centers.

4. SIMULATION

4.1 The Zerkalo Simulator and SimulationParameters

We developed a simple SISP tool called Zerkalo (mirrorin Russian) based on ray-tracing (images method [25]) thatsimulates the electromagnetic propagation in a parameter-ized scenario. Besides free-space propagation, Zerkalo alsosimulates the electromagnetic phenomena of reflection andrefraction by computing the multipath interference due toreflections up to a desired order. Zerkalo’s algorithm com-plexity is O(nr), where r is the reflection order and n is

the number of obstacles. This complexity value is usuallyexpected for ray-tracing based algorithms, such as the pro-posed one.

In the design of Zerkalo, we assumed the so-called nar-rowband hypothesis considering that the transmitted sig-nal’s spectral content is narrow enough around the carrier(dozens or hundreds of KHz depending on the conditions)so that the technique fading can be considered flat [23]. Thepoints most affected by this kind of fading scheme are thoseclose to walls, specially the ones near the corners [21].

Moreover, we have also assumed the following test param-eters: 0.122 m wavelength, receiver sensitivity is -70 dBm(receive threshold), -85 dBm (carrier sense threshold), halfwave dipole antennas (1.64 dB gain) for transmission andreception [23], and the capture threshold is 10 dB. We havemodeled the error in the RSSI as 10% of receiving poweraround the correct value. The transmission power levelsare given in discrete steps of 2dB varying from -20dBm to18dBm. In the present test scenario, the antennas’ heightswere half way between floor and roof, such that the ma-jor propagation effects were concentrated on the horizontalplane comprising all antennas, simplifying the propagationproblem to a 2D analysis.

For the simulations considering multipath, we assumed amultipath fading threshold value of half the power receivedin the main propagation path, which usually is the directpath. Specifically, whenever the (complex) sum of all mul-tipath phasors is up to such threshold (equivalent to a 3dB difference, at least), the signal will be codified, other-wise it will not. Yet, we considered up to the second orderreflections [20], [26].

In previous work[19], we developed a new hardware tomeasure precisely the energy costs of basic wireless commu-nication events. We noticed that the measurements of theParallel Computing Lab we made using the hardware werecomparable with the results provided by Zerkalo.

4.2 Evaluation Scenarios

6

Scenario PLEKubisch 3.08

LCP 3.69

Table 1: Path Loss Exponent

(a) Technique results in Kubisch

(b) Simulation results in Kubisch

Figure 8: Technique and Simulation Comparison inKubisch

The Kubisch scenario, as shown in Figure 3, was extractedfrom [14]. The physical layout (18x7 m2) consisted of fourrooms connected by a hallway as can be seen in the figure.In [14], the walls were assumed to be infinitesimally thin, sothat there were no obstacles to radio communication. As-suming a practical scenario, we considered that rooms wereapart by wood walls with εr = 4.000[23]. The Parallel Com-puting Laboratory (PCL) [19], as in Figure 4, is a typicaloffice (14.7x15 m2), divided by standard wood and glasswalls.

Figure 5 illustrates how our SiSP tool computes path loss,considering multipath fading.

Moreover, the Kubisch scenario has a Path Loss Exponent(PLE) equal to 3.08 and PCL’s PLE is equal to 3.69. Usu-ally, we associate TPL with connected nodes. However, inthis case, in order to show the coverage area to the reader,we will consider a homogeneous random distribution of 1sensor by square meter (D=1 in Equation 4).

4.3 Connectivity AspectsThe results of Equation 5 are shown in Figure 6. Due

to multipath effect, it is not possible to cover all office area(126 m2 for Kubisch Scenario and 197.46 m2 for ParallelComputing Laboratory).

Suppose we have a density of 0.1 sensor by m2, so thatwe have to divide the axis Nodes Connected in Figure 6 by10. Additionally, assume we want to connect to 6 sensors.According to our method, if a sensor would be in room A inKubisch scenario and would apply a TPL of -4dBm, therewould be a probability about 20% of reaching 6 sensors. If it

(a) Technique results in PCL

(b) Simulation results in PCL

Figure 9: Technique and Simulation Comparison inPCL

7

would apply 0dBm, this probability would increase to 50%.For TPLs greater than 4dBm, this probability would sur-pass 75%, but there would be no guarantee that the sensorwould reach 6 sensors, even if it would apply the maximumTPL available. An easier way to understand this example isfollowing the red line in Figure 6(a).

Using the same approach for PCL scenario, if the sen-sor would apply -8dBm, there would be a 20% probabilityof reaching 6 nodes. On the other hand, with -6dBm, thisprobability would increase to 50%, and with 2dBm, it prob-ably would reach its goal (see the red line in Figure 6(b)).

In spite of the fact that the Kubisch’s Path Loss Expo-nent (PLE) is smaller than the PCL’s PLE, because of theposition room B in PCL layout, the PCL layout itself (PCLhas a square format and Kubisch has a rectangular format)and the receiver’s/transmitter’s area (126 m2 for KubischScenario and 197.46 m2 for PCL) the results for the roomB of the Parallel Computing Laboratory are better in termsof the connectivity, specially because of UR. However, wewill see in the next section that Path Loss Exponent effectreflects directly to the Blockage Rate.

5. BLOCKAGE ASPECTS OF THETECHNIQUE

The results of Equation 2 (mean) are shown in Figure 7.In this computation, we perform the calculation twice, oneconsidering and other not considering multipath (MP) effect(according to the simulation parameters of Subsection 4.1).As expected, because Kubisch’s scenario has a smaller PLE,its Blockage Rate (BR) is generally smaller than the PCL’sBR. It was computed the first derivative (BR′) and the sec-ond derivative (BR′′) of the Blockage Rate, necessary to theTransmission Power Level (TPL) critical identification.

As expected, due to the Kubisch’s Path Loss Exponent(PLE) be lower than the PCL’s PLE, Kubisch’s BR is lowerthan PCL’s BR. Observing Figure 7 carefully, it is pos-sible to note an association to the wall overcoming (wall1, wall 2 and wall 3 in Figure 3), specially in the Kubischscenario, where it can be easily noticed (this overcoming isnot totally dependent on the wall, because the radiation de-pends also on the incident angle, according to the Fresnellaws). According to the Figure 7, it takes place at -12dBm,-6bBm e 2dBm (marked with circles in the Figure 7). Thesemarks can easily be computed through the signal variationof the first and the second derivative (inflection points andfunctions concavity). Different from Kubisch, these criti-cal points (associated to wall/barriers) are not so clear inthe Parallel Computing Laboratory (PCL). But accordingto our technique, we found three critical TPLs: -14dBm,-8dBm and 2dBm (also marked with circles in the Figure7).

Figure 7 shows that BR′ for both rooms stay positive until-6bBm in Kubisch and -8dBm in PCL, indicating the posi-tive tendency of BR. After these TPLs, the Blockage Rate(BR) for both scenarios decreases, increasing the connectiv-ity aspects (see Figure 6). It is mathematically explained bythe (1 − BR(z)) component of Equation (4) that becomeslower.

An important remark to be addressed at this point is thatmultipath interference actually increased BR when comparedto the equivalent rates calculated not considering multipathaccording to the hypothesis of Subsection 4.1 (see BRMP

Scenario Points inside the CI (Percentage)Kubisch 58.2%

LCP 65.7%

Table 2: Points Inside the CI

and BR curves in Figure 7). In other words, our methodprovides an efficient and simple way to account for the mul-tipath effects on the network connectivity, correcting other-wise optimistic predictions that would arise from simple freespace path loss analysis.

Since the narrowband hypothesis has been assumed, fre-quency selective fading is less frequent, but still likely tohappen. Under such particular situation, the link perfor-mance is severely degraded due to the intersymbol interfer-ence (ISI), which cannot be mitigated by simply increasingthe transmission power level.

6. TECHNIQUE EVALUATION AS A MEANVALUE

Our intuition was that the approach would represent anapproximation of Transmission Power Level (TPL) meanvalue in a simulation of multiple spacial random allocation.So that, we adapted the S-XTC protocol [7], in an asym-metric way, getting the connectivity in a single hop. Yet,each node should reach a certain node number (k) in spiteof the other part should be obliged to handshake the link.In other words, we assure that each node would have anout physical node connectivity degree [3] equal to k. We alsoeliminated the collision problem synchronizing in time thesensor node transmission. Aspects related to the collisionswere considered in [13].

6.1 Gathering DataFor achieving our goal, we choose a connectivity degree

equal to 6 (k=6) and conducted 2,000,000 random simula-tions, varying the sensor position, according to a uniformdistribution, with density equal to 0.1 sensor by m2. Lateron, we computed TPL mean value (in dBm).

The TPL chosen by our technique is computed by Equa-tion (4). There is an adaptation of this equation. Suppose,by hypothesis, that for a specific point the C(0dBm) = 5and C(2dBm) = 8. The chosen TPL would be 0.666dBm,to reach k=6.

In order to evaluate our technique, we compare the dataobtained by the method and the simulation. The results arepresented in Figures 8 and 9.

6.2 Approach evaluation as TPL mean valueapproximation

In order to analyze the technique, we computed the con-fidence interval (CI) among the obtained values, with confi-dence coefficient equal to 0.95 and 35 samples for each loca-tion (t34;0.025 = 2.0322). The results are described in Table2 and Figures 10 and 11. The z axis of Figures 10 and 11represents the point probability of not being in the CI (thedarkest points are those with greater probability of beinginside of CI).

According to Figures 10 and 11, it can be noticed that thecentral points got better results. It is due, mainly, to theminor multipath fading (highly sensitive to the position),minimizing the computing unpredictability.

8

Figure 10: Confidence Interval Analysis for theKubisch Scenario

Figure 11: Confidence Interval Analysis for thePCL Scenario

The principal reason for the eventual differences is becauseof the approximation described before.

Other important factors are the integration method andthe multipath fading complexity. Regarding the integrationmethod the smaller the granularity of computation the bet-ter is the result.

The most important conclusion is that results corroboratethe assertion that our metrics reflect the average behavior.Yet, the technique considers a complex phenomenon, suchas multipath fading. It should also be observed that the ad-vantage over simulation is that we can directly estimate theTPL for every density, without using feedback mechanisms.

7. CONCLUSIONThis work has evaluated a novel technique to support the

deployment of wireless sensor networks (WSN) in scenar-ios with obstacles. The technique allows achieving, in apower efficient manner, the desired connectivity of WSN un-der the effects of propagation barriers and multipath fadingby determining suitable TPLs for sensor nodes that mini-mize power consumption. Beyond the approach itself, onepossible application could be, for example, to establish (con-figure) the initial transmission power levels settings for thenetwork.

In order to evaluate the potential of the technique, weperformed a detailed simulation in different indoor test re-alistic scenarios. We found the critical Transmission Power

Levels in these scenarios and showed that the technique isan approximation of the mean value.

We are working in an extension of the technique in 3Dscenarios, to be even closer to a real situation, includingmobility models aspects (Doppler effect), and to aggregateother radio irregularities besides multipath interference andimproving the integration method in order to get better re-sults in terms of confidence intervals.

AcknowledgmentsThe authors would like to thanks Luıs Felipe Magalhaes deMoraes and Maurıcio Henrique Costa Dias for their collabo-ration to the development of this work, and CAPES/PROAPfor its financial support.

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