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Distributed Algorithms for Transmission PowerControl in Wireless Sensor Networks

Martin Kubisch, Holger Karl, Adam WoliszTelecommunication Networks Group

Technische Universit at BerlinSekr. FT 5-2, Einsteinufer 25

10587 Berlin, Germanykubisch|karl|wolisz@ee.tu-berlin.de

Lizhi Charlie Zhong, Jan RabaeyBerkeley Wireless Research CenterUniversity of California Berkeley

2108 Allston Way, Suite 200Berkeley, CA 94704-1302

czhong|jan@eecs.berkeley.edu

Abstract Two algorithms for dynamically adjusting trans-mission power level on a per-node basis have been evaluatedusing a simulative approach. Network lifetime, convergencespeed as well as resulting network connectivity have beenobtained for these two algorithms using a particular indoorsensor environment. The network lifetime metrics of these twolocal algorithms are also benchmarked against power controlalgorithms using global information. We show that these twoalgorithms outperform xed power level assignment and aregenerally within a lifetime of two of a globally computedsolution.

Keywords: Relaying, energy efciency, sensor networks

I. INTRODUCTION

Sensor networks [1] networks of tiny nodes equippedwith limited sensing, computing, and radio communicationcapabilities are a technological vision that is currentlyreceiving a lot of attention from several research commu-nities. In a typical scenario, such sensor networks woulduse wireless communication to transmit their observationvalues to a given monitor station which would serve as a

user interface.A joint characteristic of most application scenarios is that

sensors only have a limited energy supply which might noteven be rechargeable, hence they have to work as energy-efciently as possible. One option is to reduce transmissionpower using intermediate nodes as relays instead of directcommunication with a remote node. While such relayinghas its own disadvantages (energy is now also consumedfor intermediate reception and transmission), relaying canbe benecial for improving energy efciency [2].

Yet arbitrarily reducing transmission power is not possi-ble; at least, some direct neighbors of a sensor node mustbe reachable to provide the possibilities to perform relayingand to form a connected network via relaying. Therefore itis important to nd algorithms which determine appropriatetransmission power levels for every node. In addition,because of the size and dynamics of sensor networks,these algorithms should be distributed ones, relying only onlocally available information and therewith being scalableas the network growths.

We present two distributed (local) algorithms that deter-mine an individual transmission power level for each nodeof a xed, non-mobile wireless sensor network. The same

power is used when sending to any neighbor, irrespectiveof whether some neighbors are closer than others. Onereason to do so is the time and hence energy expenditurethat is require to set the amplier to different powerlevels. Algorithmically, the use of different power levelsdepending on the intended receivers is easily possible.

The distributed computation happens in an initializationphase, and the resulting power levels are then used for thedata communication within the network. As this distributedcalculation does not warranty a full connected network, itmay be reasonable to leave few (communication expensive)nodes out in order to spend this energy for a network lifetime extension.

As the local algorithms would not be deployed asstand-alone, instead they would be integrated with othermechanism using the same information, e.g., locating of sensors, neither a particular MAC protocol nor a dedicatedprotocol for route discovery is used. But to evaluate thealgorithms in terms of network lifetime, data transfer must

be realized, hence any MAC protocol intended to work withmust provide correct data delivery. The routing tables arecomputed using the per-node power level achieved and theshortest-path routing based on Dijkstras algorithm [3]. Oneparticularly interesting aspect is the fact that power assign-ment algorithms can result in asymmetric communicationrelationships. Hence, the routing protocol applied in realsystems must be able to handle such a situation.

As the local algorithms can result in networks not beingfully connected, it is hard to compare local and globalalgorithms in terms of network lifetime 1 (time until therst sensor node dies; all nodes start with the same xedamount of energy). The solution is to consider the nodes notbeing connected as dead nodes, hence, a global algorithmruns until one node more than the number of not connectednodes (from the local case) died. For the local algorithmsthe lifetime is over when the rst node of the largestconnected part of the network runs out of energy. But ascan be seen in Section III-B, the average number of nodesnot being connected is far below one percent, which in the

1 Alternatively, time to network partition could be used, but as the localalgorithms can end up with some nodes not being connected it is notcomparable

appeared in Wireless Communications and Networking Conference (WCNC), New Orleans, LA, March 2003 IEEE

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scenarios used means below one node. Hence, we neglectedthis effect and consider always the dead of the rst nodeas our gure of merit and optimization criterion.

The remainder of this paper is organized as follows.Section II describes both local algorithms considered aswell as the global algorithms which serve as comparisoncases. Section III outlines the simulation setup we usedto study these algorithms and presents simulation results.Section IV gives an overview of related work. Finally,Section V presents conclusions and directions for futurework.

I I . P ROBLEM SOLUTIONS

In the following, ve different approaches are introduced.The rst two are the local algorithms which can be appliedto sensor networks in a distributed manner, whereas theother three (global) algorithms are comparison cases whichmake use of global knowledge and hence always achieveoptimal solutions, according to their respective restrictions.The global algorithms are used to show the effectivenessof the local algorithms.

A. Threshold in number of neighbors

The local mean algorithm (LMA) works in the follow-ing way: All nodes start with the same initial transmissionpower ( TransPwr ). Every node periodically broadcasts alife message ( LifeMsg ) including its unique identity. Allthe other nodes, which receive such a LifeMsg , replywith a life acknowledge message ( LifeAckMsg ) includingthe address of the LifeMsg sender. Before a node issuesthe next LifeMsg it counts the number of LifeAckMsg sreceived ( NodeResp ). If NodeResp is less than a mini-mum threshold ( NodeMinThresh ), the node increases itstransmission power by a certain amount ( A inc ) for every

missing neighbor; the transmission power is not increasedby more than B max in a single step. 2 If NodeResp is largerthan a maximum threshold ( NodeMaxThresh ), it decreasesits transmission power by a certain amount ( Adec ) for everysupernumerary neighbor; the transmission power is notdecreased by less then B min in a single step. 3 If NodeRespis between NodeMinThresh and NodeMaxThresh thenode does not change its transmission power anymore; ithas converged. While this algorithm has a periodic nature, itis important to note that no close synchronization of nodesor global time base is required; the notion of periodicity isa purely local one.

B. Threshold in mean number of neighborsThe local mean of neighbors algorithm (LMN) works

similar to LMA except that it adds some information tothe LifeAckMsg and it denes NodeResp in a differentway. In addition to the address from the received LifeMsg ,the LifeAckMsg also contains its own, most recently

2 Formally: TransPwr min {B max TransPwr , A inc (NodeMinThresh NodeResp) TransPwr }.

3 Formally: TransPwr max {B min TransPwr , A dec (1 (NodeResp NodeMaxThresh) TransPwr }.

computed, number of neighbors. The node receiving theLifeAckMsg s calculates a mean value from its neighborsnumber of neighbors the new NodeResp , which in turnis used to adjust the transmission power. E.g., when nodeA sends a LifeMsg , the nodes B , C and D receive thismessage and respond with a LifeAckMsg containing theirmost recent NodeResp (B =6; C =4; D =3). As node Areceives all these LifeAckMsg it creates the mean out of the number of responses (three neighbors B,C,D ) andtheir mean number of neighbors (6;4;3), which is thenew NodeResp for A (here 4). If this new NodeRespis below NodeMinThresh or above NodeMaxThresh thetransmission power adaption is done as described in SectionII-A.

C. Fixed transmission power

The most simplest algorithm is to assign an arbitrarilychosen transmission power level to all sensor nodes, muchlike it would be done at production time for sensors that donot have power control at all. In the following we assumethat the target conguration (i.e., the density of nodes)is known and hence the minimum transmission powerproviding a fully connected network is known as well. Thisvalue is used as xed transmission power. Additionallylarger transmission values are used to show the effect of using to much a power.

D. Global solution with equal transmission power

The Equal Transmission Power (ETP) algorithm alsoassigns a uniform power to all nodes, but chooses theminimal value that ensures a fully connected network forthis particular scenario. To nd the minimum transmissionpower, the following algorithm is used:

1) Among the node pairs that are not yet connected,

choose the one with the smallest distance.2) Set transmission power of all nodes to a value suf-cient to connect these two nodes.

3) Check connectivity of the resulting network and whenthe network is connected, the minimum power levelis found; otherwise start from 1.

This power value represents the smallest value for a fullyconnected sensor network with xed transmission rangeand it also results in symmetric communication links. Thisalgorithm uses global information and it is not evident howto implement a corresponding local algorithm that achievesthe same results.

E. Global solution with diverse transmission power The global solution with Diverse Transmission Power

(DTP) algorithm creates a connected network but does notset all transmission ranges to the same value. Instead it triesto nd a minimum power level for every node individually.The algorithm works in the following way:

1) Among the node pairs that are not yet connected,choose the one with the smallest distance.

2) Set transmission power of these two nodes to a valuesufcient to connect them.

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3) Check connectivity of the resulting network and whenthe network is not connected start from 1.

This algorithm minimizes the overall transmission powerconsumption for the entire network, but it may resultin asymmetric communication links, e.g., one node canreceive data from a far neighbor which uses a highertransmission power, but can not answer directly due to itssmaller transmission power.

Even though it is possible to construct networks wherethis algorithm does not nd minimum power levels for allnodes, DTP vastly outperforms any other global algorithmthat we have considered. Therefore, we use DTP as acomparison case. Similarly to the ETP algorithm, thisalgorithm also uses global knowledge, and equivalent localimplementations are not obvious.

III . S IMULATION RESULTS

A. Investigation scenario

In order to evaluate and compare these algorithms, wesimulated the energy consumption and resulting network lifetime for a particular indoor sensor network scenario.

The simulator used for this task was written using theOMNeT++ [4] simulation tool.During the data communication phase, energy is con-

sumed for both transmitting and receiving data packets aswell as for idle phases. The power consumption during theidle phase is 0.1 W, for receiving 0.5 mW, for sending1 mW; 4 a sensor nodes initial energy supply is 100 J. Atan assumed bit rate of 10 kbit/s, these values correspond to1 J and 0.5 J to send and receive a bit, respectively. Thetransmission power levels are set by the above algorithmssuch that transmission errors only happen with negligibleprobability (more precisely, a node is only considered toreceive from a neighbor if the SNR at its antenna is at least

-90 dBm), hence transmission errors are not considered.The physical layout consists of four rooms connectedby a hallway as shown in Figure 1. All rooms are 3.5 mhigh, the grey bars indicate doors (1 m wide; assumed toreach up to the ceiling), the black dots show the positionof two monitor nodes (acting as the user interface andbeing the master station which poll the sensors over thenetwork), which are positioned 1.2 m above the ground.Walls are assumed to be innitesimally thin, constituting noobstacle for radio communication. The path loss coefcientof the channel is set to 2. Based on this layout, 32 differentplacements of sensor nodes were generated by placing 318nodes randomly on the walls, ceilings, and oors (using a

uniform node distribution).For each of these placements, every algorithm computes

the transmission power level assignments for each sensornode. According to this assignments, edges between thenodes able to overhear each other are calculated and withDijkstras algorithm [3] the routing table entries for everynode are calculated. For the ETP and DTP algorithms as

4 the assumption is that a sending node can wake up nodes in its vicinityby using a low-bandwidth signaling channel that is easy to demodulateeven for a low-power receiver, e.g. the Frisbee model in [5]

Room Room Room Room

Hallway

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2 m

4m 4m 4m 6m

18m

Fig. 1. Physical room layout. Grey bars represent doors, black circlesrepresent monitor nodes.

well as for the xed transmission power, this results ina single conguration of power level assignments. Thenal transmission power level for the local algorithmsdepends on the initial transmission power to be used byeach node and the number of cycles an algorithm runs.

The initial power value is varied linearly in 56 steps froma transmission range of 25 mm to 1.4 m. For each of theseinitial power levels, the initialization phase is computedusing 100 cycles with either LMA or LMN. Even thoughboth algorithm settle down earlier, this number was usedto avoid instable routes.

The local algorithms use a transmission power increasevalue ( A inc ) of 10% with an upper bound ( B max ) of twotimes the old transmission power and a decay value ( Adec )of 2% with a lower bound ( B min ) of half the old value(more aggressive values let the implementation oscillate).

Note that the energy consumption during this initializa-tion phase is not taken into account. Information needed for

the algorithms are also available in other, sensor-network-related protocols [6], thus it can get this information with-out additional overhead and the consumption is negligible.

After the initialization, the data communication phaseis simulated. The trafc in the network consists of re-quest/replies initiated by the monitor. These requests aredirected at a randomly chosen sensor node (the monitoris assumed to have sufcient information about the sen-sors). The nodes receive the request and answer with an(arbitrary) reply value. These requests are sent every half a second, alternating between the two monitor nodes.

These simulation runs result in a total of 32 network lifetime samples for the global algorithms and 32 56 sam-ples for the local algorithms; network lifetimes, condencelevels for the average lifetime and comparisons are shownin Section III-C. But rst, the question of convergencespeed of the local algorithms as well as whether thesealgorithms reach a fully connected network is interesting.

B. Convergence and connectivity

The local algorithms LMA and LMN use a number of iterations before settling down to particular transmissionpower levels. An individual node has converged when

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its number of neighbors is between NodeMinThresh andNodeMaxThresh . As determined by K LEINROCK andSILVESTER in [7] the mean number of neighbors assuringa good connectivity should be 5.89 and preliminary experi-ments with the global algorithm, as described in Section II-E, showed that the number of neighbors of most nodes isbetween four and seven; these values were therefore usedas thresholds for the local algorithms.

A desirable property of such an algorithm would bethat all nodes converge very quickly. Evidently, the ini-tial transmission power (equivalent to the initial range of transmission) plays an important role for these algorithms.Figure 2 shows that most nodes converge within a smallnumber of cycles and some few nodes take up to 50 cycles.For certain initial power levels, it also happens that a very

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small number of nodes do not converge at all. As anexample, consider a case where a single node is located faraway from a cluster of nodes that quickly form a connectedgroup before they receive the far nodes LifeMsg .

While a larger value of NodeMaxThresh increases thelikelihood of a connected network, it also results in largertransmission power levels.

Figure 3 shows the percentage of nodes that were notreachable from the monitor stations for the local algorithmsfrom Sections II-A and II-B. The largest value is 1.65% forLMA and 0.04% for LMN, and on the average, 0.003%are not connected considering LMN and 0.37% when onlytaking into account LMA. 5 These results suggest that LMN

creates a much stronger connected network than LMA.

C. Network lifetime

The most interesting performance metric for such asensor network is the network lifetime: the longer everysingle node is capable to communicate, the better thetransmission power levels were chosen. In order to give

5 Note that these numbers are averaged over different initial transmissionpower levels, hence percentages do not correspond to an integer numberof nodes.

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Fig. 3. Percentage of nodes not connected for different network congurations

a rough idea of possible network lifetimes achievablein our conguration, Figure 4 shows the results for thesimple xed assignments of transmission powers (powervalues corresponding to transmission ranges of 3, 5, and

7 m were used; therewith the used networks were fullyconnected) as well as the case for the global ETP algorithm.As expected, ETP outperforms the xed value algorithmsand achieves an average network lifetime of about 48800seconds, while the xed network algorithms achievementsare considerably below that. It is also interesting to seethat the lifetime of the network depends heavily on theactual network conguration; differences are up to 50%.More interesting is the comparison between the global and

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Fig. 4. Network lifetimes for different congurations for xed transmis-sion power and equal transmission power assignments

the local algorithms in Figure 5. It comes as no surprisethat DTP vastly outperforms all other algorithms with itsglobal knowledge. As a general impression, the lifetimeachieved by DTP is up to 209% longer than that obtainedby LMN and even higher for LMA. On average, DTPachieves network lifetimes that are about twice as long asLMA, LMN, and ETP. Figure 5 also suggests that the localalgorithms and the ETP algorithm perform quite similarly.

Figure 6 shows the condence intervals for the meannetwork lifetime at a 95% condence level. Applying asimple graphical interpretation, we can infer that ETP

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outperforms both local algorithms. This stems from the factthat ETP uses global information, but it is important to note

that LMN does not only create a much stronger connectednetwork, it also performs in mean by 14% better than LMA.Moreover, the local algorithms are almost competitive withthe global ones.

IV. R ELATED WORK

In recent publications the problem of power control wasaddressed while assuming information on the angle of reception [8] or the nodes knowledge of its location [9][10].In these publications more complicated algorithms than inthis paper are used, but as they use additional informationa comparison can only be made using the same metric.

As there are similar approaches to solve the problemof power control as in this work [11][12], they differin that E LBATT et al. needs a separate and contention-free feedback channel and uses a cellular TDMA system.KRISHNAMACHARI et al. uses an algorithm with an expo-nential grow in control messages in the number of nodes.

In [13] R AMANATHAN and ROSALES -HAIN providedthe idea for the rst algorithm used in this paper, but theyused the algorithm to examine network throughput anddelay in a two dimensional space with a smaller set of nodes.

V. C ONCLUSIONS

We can state that using heuristics, which consider thenumber of neighbors a node has, result in a sufcientlyconnected network, provide improvements in network life-time over simple xed assignments and are in the rangeof symmetric algorithms using perfect knowledge. Whilethe presented local algorithms are not able to outperformsophisticated ones, they perform usually within a factor of two considering the lifetime.

Additionally, these algorithms are structured similarly toother mechanisms that are conjectured to be deployed insensor networks, e.g., locationing mechanisms. It wouldhence be possible to integrate these algorithms and toamortize their joint resource consumption.

A number of interesting questions remain for futurework, e.g., to use the number of neighbors in the announce-ment messages and to weight this information againstthe transmission power with which it was sent or how anon-reliable MAC inuences the algorithms. We intend toinvestigate these areas in the near future.

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