Transmission Power Levels Prediction forDistributed Topology Control Protocols within

Parameterized ScenariosSergio Kostin∗, Leonardo Bidese de Pinho and Claudio Luis de Amorim

Parallel Computing Lab – COPPE Systems Engineering ProgramFederal University of Rio de Janeiro

Rio de Janeiro, RJ, Brazil 21941–972, PO BOX 68.511Email: {kostin,leopinho,amorim}@cos.ufrj.br

Abstract—Distributed Topology Control Protocols(DTCP) for Wireless Sensor Networks (WSN) coordinatenodes’ decisions regarding their transmission ranges, inorder to set up a network with a certain connectivity, whilereducing nodes’ energy consumption and/or increasingnetwork capacity. The key issue in DTCP is to choosethe most suitable Transmission Power Level (TPL) amongthose available for each sensor node in a distributedmanner. We present a method to predict the TPLs forDTCP in realistic scenarios, which takes into accountseveral propagation phenomena, such as barriers andmultipath interference. To evaluate the effectivenessof our approach, we simulated the radio propagationpattern of a WSN in a scenario of multiple rooms. Ourresults suggested that our method allows to predict, withreasonable accuracy, the approximate TPLs distributionachieved by different DTCP approaches within a givenparameterized scenario.

I. INTRODUCTION

Over the last years, Wireless Sensor Networks (WSN)have established new information collection and broad-cast models, with a great potential for new applica-tions such as environmental monitoring and ”intelligent”buildings, just to name a few.

Nevertheless, a major hurdle in deploying a WSN isthe limited battery’s life of sensor nodes. As a result, theTransmission Power Level (TPL) often is the key factoraffecting the energy consumption, once that the nodesusually consume the same power when they are in thereceiving mode. Thus, estimating suitable TPLs can helpstrongly the resource management, by determining, forexample, when the sensor node’ battery will probablybecome flat.

In this work, we present a method that can pre-dict TPLs for Distributed Topology Control Protocols(DTCPs) in scenarios with obstacles. Our method cal-culates the discrete TPLs that should be used given a

∗Corresponding author. Also affiliated to the Military Instituteof Engineering – Praca Gen Tiburcio, 80 – Rio de Janeiro, RJ, BrazilEmail:kostin@ime.eb.br

certain deployment area of WSN with its configuration ofobstacles and a probabilistic distribution of sensor nodes.

Our method is based on two metrics we recentlyproposed [1]: the Blockage Rate (BR) and the UsefulArea Rate (UR), which are computed by a Site SpecificPropagation (SISP) tool, named Zerkalo. Roughly, BRaccounts for the interaction between transmitters andreceivers considering the path loss effects, the multipathinterference, and signal sensitivity due to the presenceof obstacles for a given probabilistic distribution ofreceivers’ position in the scenario. UR concerns withfree-space coverage and aspects of signal range in theWSN. In particular, the two metrics take into account theaverage values of the radiation parameters, including therate of electromagnetic emission blockage, the radiationrate outwards the scenario, the effect of multipath inter-ference, and the percentage of radiation effectively used.We use a combination of the two metrics to estimate theconnectivity as function of TPL.

To assess the effectiveness of our approach, we sim-ulated the deployment of a WSN in an indoor scenarioof multiple offices. Our results showed that our methodallows to estimate, with reasonable accuracy, the TPLdistribution that will be chosen by DTCPs for a param-eterized scenario. In summary, the main contributionsof this work are: i) a probabilistic spatial model re-garding connectivity aspects considering electromagneticphenomena; and ii) a method of estimating the TPLsdistribution for DTCPs in such environments.

The remainder of the paper is organized as follows.Section II briefly overviews related works, includingSISP models and Topology Control theory. In SectionIII, we introduce our technique for establishing thetransmission power levels in WSNs for a given scenario.Section IV describes our experimental methodology andanalyzes simulated results. Finally, our conclusions andongoing works are presented in Section V.

978-1-4244-2036-0/08/$25.00 c, 2008 IEEE

II. BRIEF OVERVIEW ON SISP MODELS ANDTOPOLOGY CONTROL THEORY

In this section we will present briefly SISP models thatallows more accurate simulations. Further, we describeaspects of Topology Control, in particular DTCPs, clas-sifying their categories according to the literature [2] andthe TPL strategy approaching. Finally, we fit our workin its specific field.

The simplest software approach for radio-wave prop-agation modeling at high frequencies (VHF to SHF)is semi-empirical, such as the well-known exponentialpath-loss model. Radiowave propagation models usingdetailed terrain databases are commonly referred as SiteSpecific Propagation models (SISP) [3]. Smaller scenar-ios (usually indoors) may benefit from more complexand accurate approaches such as ray-tracing modeling. Inthis technique, the main propagation paths (rays) are de-terministically found based on the common electromag-netic phenomena of reflection, refraction, and scattering,which includes diffraction. Ray-tracing is usually carriedout two-fold, using either greedy methods or imagetheory [4]. With the ever growing available numericalcapacity of computers, ray-tracing models have increas-ingly become more attractive as propagation predictiontools. Some researchers even expect that deterministicmodeling may prevail in a near future as the preferredapproach for propagation prediction, even outdoors [3].

Topology Control (TC) is the art of coordinatingnodes’ decisions regarding their transmission ranges, inorder to generate a network with the desired properties(e.g. connectivity) while reducing node energy consump-tion and/or increasing network capacity. A topology con-trol protocol should have some basic properties: be fullydistributed and asynchronous; be localized; generate atopology that preserves the original network connectivityand relies, if possible, on bidirectional links; generate atopology with small physical degree; and rely on ’low-quality’ information [2].

DTCPs can be classified DTCP in four differentcategories [2]: Location-based; Direction-based; Mobile-based; and Neighbor-based.

In Location-based Topology Control Protocols (e.g.LMST [5]), a subset of the nodes can estimate theirpositions either exchanging messages with the surround-ing anchor nodes or through nodes which are GPS-equipped. Knowing their relative positions, they canconstruct a graph based on this information. Direction-based Topology Control Protocols (for instance CTBC[6]) rely on the ability of the nodes to estimate therelative direction of their neighbors based on equippingnodes with more than one directional antenna. Mobile-based protocols (e.g., LINT [7]) must be fast, so thatit can keep up with the changes across the network.Finally, Neighbor-based Topology Control Protocols are

based on the node’s ability to determine the number andidentity of neighbors within their range and to build anorder on this neighbor set (based on distance such asKNEIGH [8] or on link quality, e. g., KNEIGHLEV [9]and XTC [10]). In a certain sense, this is the minimumamount of information needed by the nodes to build thenetwork topology, allowing a network construction withsimpler hardware.

As to the TPL initial value, DTCPs solutions useeither a bottom-up or a top-down approach. In CTBC[6] and KNEIGHLEV [9], the sensor nodes start from alower transmission power level (TPL) up to a highersuitable TPL that often is more economic but takeslonger to converge. Other protocols such as KNEIGH [8]and XTC [10], start with higher TPLs stepping downto a suitable TPL, thus spending more power thoughconverging faster.

However, often the TPL of a node cannot be set to anarbitrary level. Instead, the transmitters can only be setto a limited number of predefined power levels. DTCPsthat fit in this category are called Level-Based TopologyControl Protocols (LBTCP) [2]. Among several solu-tions of LBTCP we can cite CLUSTERPOW [11] andKNEIGHLEV [9].

In this context, the present work presents a novel wayto predict the TPLs distribution for LBTCP within aparameterized scenario for Distributed Neighbor-basedTopology Control Protocols, using XTC and KNEIGH-LEV as references, specially because they are significantexamples of state-of-the-art protocols that can be easilyimplemented in commodity hardware.

III. TRANSMISSION POWER CONTROL TECHNIQUE

In this section, we present the foundations of ourtechnique [1]. It is based on a Probabilistic SpatialDistribution Map (PSDM), the Blockage Rate (BR) andUseful Area Rate (UR). Later on, we show how todetermine the connectivity using BR and UR and a wayto use the technique. Finally, we tackle the prediction ofthe TPL distribution for neighbor-based approach.

A. Occupation Profile of a Scenario

BR and UR are calculated for each particular sce-nario. Often, we can use a Geographic InformationSystem (GIS) to build a PSDM. The idea behind PSDMis that distributed sensor nodes within a WSN scenariotend to form specific probabilistic occupation profiles.For example, pedestrians usually walk along sidewalks,gardens and parks. Cars are driven on roads, avenues andso on. Therefore, it is possible to derive the PSDM usingthe location of the sensor nodes distributed in a specificscenario, mobility models [12], or calculated by meansof a localization system [13] that indicates the probableregion where each sensor is located.

Fig. 1. Probabilistic Spatial Distribution Map (PSDM)

Fig. 2. Blockage Rate and Useful Area Rate

Figure 1 shows an example of a receiver device’sPSDM based on the relative weights of the distributedoccupation across the terrain by the nodes. These weightsare obtained from a given probability density. The dis-tribution can be function of time and number of nodes.It can also be conditional (P (A | B)). Specifically, inFigure 1 the area with p = 4, 2, 1, 0 represent streets,sidewalks, gardens, and a lake, respectively.

B. Blockage Rate (BR)

Figure 2 shows a typical situation where a certainobstacle blocks the electromagnetic signal of a trans-mitter t, establishing four distinct areas regarding thequality of signal reception: the receivers’ area (RA) - e.g.the area where the receivers are located; the theoretical

coverage area not contained in RA; the coverage areacontained in RA blocked by the obstacles (EB); and theunblocked area (ENB). Conceptually, BR expresses theratio between EB and the sum given by EB + ENB .

Formally, considering a specific transmitter class lo-cated at position s, and assuming a specific transmissionpower level 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 proba-bility that the jth receiver, rj , be found at x position,subjected to a t-type transmitter being located at positions. Note that the expression accommodates clustering(when devices tend to join) and repelling (when thereis a minimum distance among devices). The antennagains of transmitters and receivers are considered in thecalculation of the probabilities, as well as the receivers’sensitivity. The Function B accounts for the interactionbetween transmitters - t(s, pw) (transmitter t at s, emit-ting a signal with pw power level) - and receivers -(receiver rj) - within RA. The subscripts CF and NF

mean Considering F ading and Not considering F ading,respectively.

BCF ∈ {−1, 0, 1}. BCF returns 0 when the receiverrj(x) is in the theoretical coverage area of a transmittert at a pw power level, the received signal is abovethe data sensitivity level and the multipath interferenceis so weak that it is unable to degrade the data link(a power level threshold must be established to assistthis process). Otherwise BCF returns 1, either when thedegradation due to multipath is observed or the receivedsignal is below the data sensitivity level. BCF will return-1 when the receiver is outside the theoretical coveragearea, since multipath interference may also cause aconstructive effect (at aisles, for example), though theobstacle configuration is such that the transmitted signalis still able to reach the receiver rj .

BNF ∈ {0, 1}. BNF simply considers free-spacepropagation and the presence of obstacles against directrays. It returns 1 for all receivers rj(x) within thetheoretical coverage area of the transmitter t at positions - t(s, pw). Otherwise BNF equals zero, which occurswhen the receiver rj is at a position x such that itis either outside (beyond) the theoretical coverage areaof t, or behind any obstacle (no direct ray reaches thereceiver).

We calculate BR for a specific region, aka Trans-mitter Area (TA), computing the weighted average ofall BR(t(s, pw)) according to Equation 2. Other sta-tistical parameters such as standard deviation, median,maximum, minimum, etc., are also calculated in order

to provide the best possible description of the chosenscenario. We may also compute the first and the secondderivatives with respect to TPL (pw) to help with theanalysis on overcoming propagation barriers.

BR(TA, t, pw) =

∑s∈TA

P (t(s))BR(t(s, pw))∑s∈TA

P (t(s))(2)

C. Useful Area Rate (UR)

Figure 2 illustrates the notion of Useful Area Rate(UR) that expresses the ratio between the useful and thetheoretical coverage area of a transmitter node. The def-inition of useful coverage area comprises the theoreticalcoverage area of a transmitter that lies within the receiverarea ignoring the obstacles. Therefore, this metric is mostconcerned with free-space coverage and aspects of signalrange in the WSN, thus ignoring multipath effects andscattering. 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 interactionbetween the theoretical coverage area and the scenario’sobstacles. The subscripts CO and NO mean ConsideringObstacles and Not considering Obstacles, respectively.

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

UNO ∈ {0, 1}. UNO quantifies the coverage area,considering rj’s sensitivity. UR mainly aims at the losseffects of propagation paths, neglecting the probabilisticdistribution of receiver’s position that has already beenconsidered in BR.

D. How to Determine the Connectivity Degree using BRand UR

Consider CA(t(s, pw), rj) as the theoretical coveragearea of a transmitter t operating at a power level pwfor a specific receiver rj . Yet, assume D as the sensornode density and t(s, pw) = z. Then, we carry out thefollowing product to get a specific connectivity degreefor 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 madeto BR(TA, t(pw)), and calculate various statistical mo-ments. 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)

E. How to Apply the TechniqueThe computation of the metrics should be previously

performed before starting the WSN operation. Next, thetable of values must be stored in each sensor nodeeither manually or broadcasting it to them, which isthe preferred one, because it allows to address theinclusion/exclusion of obstacles in the scenarios afterthe WSN deployment. In the latter, broadcasting can beperformed either by peers that participate in the WSNor devices with location capabilities. Usually, BR andUR can be computed using either desktop computers orother high-performance computer systems (like clusters)depending on the WSN size. Thus, the sensor nodes usethose tables with connectivity data in order to choosesuitable TPLs. The complexity of choice is O(n), wheren is the number of discrete TPLs available.

These metrics should be used in a planned manner.Indiscriminate use of BR and UR in an heterogeneousenvironment would minimize energy savings benefits.Ideally, the metrics should be used in small clusters ofsensor nodes that can be automatically detected duringthe data processing by data mining techniques (e.g.Clustering) such as k-Medoid Method [14], in which thepoints with the smallest BR values would be consideredas cluster centers.

F. Predicting the TPL DistributionUsing the information explained in the previous sub-

section, we can predict the TPL distribution in thenetwork, specially in protocols that intend to conserveenergy, such as XTC and KNEIGHLEV.

The way to calculate the distribution is straight for-ward, according to Equation 6.

Dist(TA, k, pwi) = P (TA, k, pwi)− P (TA, k, pwi−1)(6)

Dist(TA, k, pwi) means the percentage of the trans-mitters inside a TA, which aims at connect to k nodesusing the TPL of pwi. P (TA, k, pwi) is the probabilityof a sensor s be connected to k neighbors transmittingat power level pwi.

IV. SIMULATION

In this section, we evaluate the benefits that BR andUR metrics can offer to establish the TPL scheme fora WSN. Specifically, we simulated the deployment ofa WSN in a scenario of multiple offices, for which wecomputed BR, UR, and C, and then used these resultsto determine the most efficient transmission power levelsfor the sensor nodes of the WSN for each scenario room.

Fig. 3. Radiation pattern of sensors in each scenario room

A. The Zerkalo Simulator and Simulation Parameters

We developed a simple SISP tool called Zerkalo(mirror in Russian) based on ray-tracing (images method[4]) that simulates the electromagnetic propagation in aparametrized scenario. Besides free-space propagation,Zerkalo also simulates the electromagnetic phenomenaof reflection and refraction by computing the multipathinterference due to reflections up to a desired order.Zerkalo’s algorithm complexity is O(nr), where r is thereflection order and n is the number of obstacles.

In the design of Zerkalo, we assumed the so-callednarrowband hypothesis considering that the transmittedsignal’s spectral content is narrow enough around thecarrier (dozens or hundreds of KHz depending on theconditions) so that the technique fading can be consid-ered flat [3]. The points most affected by this kind offading are those close to walls, specially the ones nearthe corners [15].

B. Test Scenario

The test scenario, illustrated in Figure 3, is composedof 9 rooms (15x15 m2 each), similarly arranged as inthe tic-tac-toe game. The rooms are apart by 15 cm widebrick walls with relative permittivity (εr) equal to 4.444[3].

We computed the metrics as defined in Section 3for transmitters at CENTRAL, CORNER, and LATERALrooms, considering up to second order reflections (asshown in [16], only the first reflection has signifi-cant power under most situations). Moreover, we havealso assumed the following test parameters: 0.122 mwavelength, receiver sensitivity is -70 dBm (receive

threshold), -85 dBm (carrier sense threshold), half wavedipole antennas (1.64 dB gain) for transmission andreception [3], the capture threshold is 10 dB, and theMAC is based on CSMA/CA. We have modeled theerror in the RSSI as 10% of receive power around thecorrect value. In the present test scenario, the antennas’heights were half way between floor and roof, such thatthe major propagation effects were concentrated on thehorizontal plane comprising all antennas, simplifying thepropagation problem to a 2D analysis.

Regarding the influence of interference, the BR metricuses a threshold value that defines whether or not toconsider a resulting fading. For the analysis presentedbelow, we assumed a threshold value of half the powerreceived in the main propagation path that is usually thedirect path. Specifically, if the (complex) sum of all themultipath phasors is below half of the main componentpower, then BCF = 0. Otherwise, BCF returns 1 or −1,for destructive or constructive interference, respectively.Figure 3 illustrates how Zerkalo computes path loss,with multipath interference and the radiation in the threerooms types located at the CENTER, the CORNER, andthe LATERAL, respectively. The darkest points in Figure3 show the most affected points by the multipath inter-ference, considering the transmitter relative position. Weassume that the nodes are placed uniformly at randomin the scenario with density occupation of all rooms asbeing 0.05 sensors by square meter.

C. Connectivity Aspects

We solved the Equation 4 with the above criteria forassessing the WSN connectivity. As a result, a tablewas built and stored in the sensor node with statisticalparameters, specially the cumulative distribution. Thesummarized results are represented as graphics as shownin Figure 4.

Let us assume that a given sensor node located in theCENTER ROOM should be interconnected to other 40sensor nodes. According to our technique, this sensornode will look up its table checking on possible valuesthat allow it to achieve that connectivity degree k.As can be seen in Figure 4, only TPLs set at leastto 2 dBm will attend the required connectivity withprobability greater than zero. If 6 dBm is chosen, thereis a probability about 50% of reaching 40 nodes. For8 dBm, the chance is greater than 75%. Finally, from10 dBm upwards the connectivity degree of 40 nodesis almost always reached. However, outliers events canhappen. For example, for k > 40 with TPL < 2dBmand k < 40 with TPL > 10dBm.

D. Prediction Results and Analysis

Considering that our methodology is focused onneighborhood approach, the most suitable comparison

Fig. 4. Connectivity degree x TPL

TABLE ICENTER ROOM (CER) TPL DISTRIBUTION FOR k=40

TPL P(CeR) D(CeR) D(XTC) D(KNL)0 - - - 0.082 0.04 0.04 0.02 0.254 0.18 0.14 0.07 0.516 0.50 0.32 0.25 0.148 0.83 0.33 0.30 0.0210 1 0.17 0.24 -12 1 - 0.07 -14 1 - 0.05 -16 1 - - -18 1 - - -

>18 1 - - -

TABLE IILATERAL ROOM (LR) TPL DISTRIBUTION FOR k=40

TPL P(LR) D(LR) D(XTC) D(KNL)0 - - - 0.022 0.02 0.02 0.04 0.224 0.14 0.12 0.09 0.486 0.47 0.33 0.02 0.238 0.73 0.26 0.03 0.0510 0.91 0.18 0.18 -12 0.99 0.08 0.26 -14 1 0.01 0.21 -16 1 - 0.09 -18 1 - 0.05 -

>18 1 - 0.03 -

TABLE IIICORNER ROOM (CR) TPL DISTRIBUTION FOR k=40

TPL P(CR) D(CR) D(XTC) D(KNL)0 - - - -2 - - - -4 - - - -6 - - - -8 0.09 0.09 - 0.10

10 0.25 0.16 0.07 0.2212 0.35 0.10 0.28 0.3614 0.40 0.05 0.18 0.2416 0.55 0.15 0.08 0.0618 0.75 0.20 0.12 0.02

>18 1 0.25 0.27 -

will be against Distributed Neighbors-based TopologyControl Protocols, such as KNEIGHLEV [9] (bottom-up approach) and XTC [10] (top-down approach). Inorder to check the correctness of our technique, weuse a implementation of XTC [10], without the step ofedge selection (regarding the two-hop optimization). Insuch a case, XTC preserves network connectivity in theworst case, while KNEIGHLEV gives only a probabilisticguarantee on network connectivity. Yet, both are basedon the concept of ’link quality’. In our case, the ’linkquality’ corresponded to a combination of RSSI andmultipath fading, as described earlier. We conducted 30random simulations for each DTCP according to theparameters of subsection IV-B.

The results respectively for CENTER (CeR), CORNER(CR) and LATERAL (LR) rooms are shown in Tables I,II and III. The first column (TPL) represents the TPL(in dBm). The second column (P(ROOM)) shows thecumulative discrete probability distribution of reachinga certain connectivity degree according to our method.The third column (D(ROOM)) represents the computedvalue of Equation 6 (probability mass function). Fourthand Fifth columns show the TPL distribution of XTCand KNEIGHLEV (KNL). The sum of the third, fourth,and fifth columns are less or equal to 1.

In all cases, our estimates fit between both distri-butions. The outside results from one-hop implemen-tation of XTC (related to the worst cases) are upperbounds for our estimates and the two-hop optimizationof KNEIGHLEV induces a result that is a lower bound forour estimation, that confirms the expectations of energysavings due to the optimization of the two-hop links.

The greater values outside of one hop implementationof XTC are also due to the hidden node problem thatoccurs in CSMA/CA protocols, that is aggravated inscenarios with obstacles. Considering that XTC appliesthe maximum power, this protocol will be more affectedthan KNEIGHLEV.

It is worth to highlight that the proposed methodallows the construction of protocols based on TPL plan-

ning instead of using feedback mechanisms. It would beparticularly useful in mobile environments, specially be-cause, as stated in [2], mobile DTCP must be fast to buildthe topology, so that it can catch up with the changesthat happen across the network. To be fast, a protocolshould exchange relatively few messages with neigh-boring nodes and should execute a simple algorithm tocompute the neighboring set. Both characteristics areprovided by our method. Although we concentrate oursimulation in indoor scenarios, our technique can be usedin outdoor environments (as shown in Figures 1 and 2),and also using other neighbor-based protocols differentfrom those adopted in this work.

V. CONCLUSION

This work has proposed a novel method for TPLs dis-tribution prediction for WSN in scenarios with obstacles.Our method is supported by two metrics, the BlockageRate (BR) and the Useful Area Rate (UR), whichare able to correlate WSN connectivity degree withdistributed sensor TPLs under the effects of propagationbarriers and multipath fading.

To evaluate the potential of our technique, we sim-ulated in details the electromagnetic propagation of aWSN test scenario of multiple rooms with obstacles. Thesimulated results showed that the method could estimatewith reasonable accuracy the TPL distribution in suchkind of environments.

As further works, we plan to extend our techniqueto work in mobile networks, in 3D scenarios, withdifferent antenna heights, and to aggregate other radioirregularities beyond multipath interference.

ACKNOWLEDGMENTS

The authors would like to thank Mauricio HenriqueCosta Dias for his collaboration to the development ofthis work, and the Brazilian R&D agencies – CNPq andFAPERJ – for their support.

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