Joint optimization of physical layer parameters androuting in wireless mesh networks

Fouad A. Tobagi and Mukesh M. HiraDepartment of Electrical Engineering, Stanford University, Stanford, CA 94305

Email: {tobagi, mukesh}@stanford.edu

Abstract—Achieving the best performance in a wireless meshnetwork requires striking the right balance between the perfor-mance of links carrying traffic and the extent of spatial reuseof the wireless medium. The performance of a link dependson its transmit power and data rate as well as the level ofinterference caused by concurrent transmissions in the network;the latter is function of the Energy Detect (ED) threshold thatdetermines when a node may access the medium. Which links inthe network carry traffic is determined by the routing function;routing selects paths according to a link metric that reflects therelative performance of links (e.g., the expected transmission timeof a packet on the link). In this paper, we seek to maximize end-to-end network throughput by jointly optimizing physical layerparameters and routing.

We consider a random topology with a uniform node density.We consider that the signal attenuation between a pair of nodesis determined by a power law path loss model with an exponentequal to 3. Our findings are as follows. Consider first that thesame transmit power and same data rate are used on all links.For any transmit power, data rate and ED threshold setting, thehighest feasible load is obtained when the level of interferenceexperienced by links used by routing is the highest possible.For a given transmit power and data rate setting, there is anoptimum ED threshold that maximizes network performance. Atthe optimum ED threshold and maximum load, the range of linklengths used by routing is the lowest possible given the topologyand routing metric used. With an ED threshold higher than theoptimum, the same range of links is used by routing; however,the highest feasible load in this case is lower due to the factthat concurrent transmitters are allowed to be closer. With alower ED threshold, concurrent transmitters are forced to befarther apart, and thus longer links become more attractive; asa result, the range of link lengths used by routing is higher.Among all data rates, one particular data rate results in thebest network performance at the corresponding optimum EDthreshold. Finally, we find that adjusting the transmit powerdownwards for shorter links results in an improvement of about15%, while adjusting the data rate upward on shorter linksresults in a rather modest improvement.

I. INTRODUCTION

We consider in this paper wireless mesh networks basedon the IEEE 802.11 standard [1], [2]. The Media AccessControl protocol specified in the standard is based on CarrierSense Multiple Access (CSMA), whereby nodes refrain fromstarting a transmission when the medium is considered busy[3]. For example, a node would consider the medium busy ifit senses energy greater than a certain threshold referred to as

This work was partially supported by a research grant from the AcademicExcellence Alliance program between King Abdullah University of Scienceand Technology (KAUST) and Stanford University.

the Energy Detect (ED) threshold. When a node transmits apacket on the medium, neighboring nodes sense the mediumbusy and are blocked from transmitting; the set of nodesblocked depends on the transmit power and ED threshold.Blocking allows the transmission of a packet to have agood chance of success by avoiding strong interference fromneighboring nodes. The lower the ED threshold is, the loweris the interference and the more likely is the packet correctlyreceived by its intended receiver. Nodes that are not blockedmay transmit at the same time. That is, in a mesh networkthat spans a wide area, the wireless medium may be used bymultiple concurrent transmissions that are spaced apart in thenetwork. This aspect, referred to as spatial reuse, contributessignificantly to the aggregate throughput of the network. Toachieve the best overall performance, one must find the rightbalance between the need to improve the performance ofindividual links, and the need to achieve a high degree ofspatial reuse.

A typical mesh network consists of a set of nodes deployedin a physical space; the specific location of nodes is determinedby various physical factors and constraints. However, nodesmust be at some appropriate distance from each other to permitgood communication among these nodes. An example of adeployed mesh network is Google’s mesh network in MountainView, California [4]. It is thus reasonable to consider thatmesh networks can be represented by a random but uniformplacement of nodes in the space to be served according to acertain node density. Given such a mesh network, one needsto determine which links should be established, as well as theappropriate physical layer parameters that should be used onthese links; namely, transmit power and data rate. One shouldalso determine an appropriate value for the ED threshold. Withthe goal of achieving the best overall network performance inmind, this cannot be determined without bringing routing intothe picture. Indeed, which links get used to carry traffic andthus need to be established is determined by routing; so is thedistribution of traffic on links in the network.

Routing in a multi-hop network is based on finding min-imum cost paths; the cost of a path is the sum of costsof links in the path. In wired networks, the cost metricof a link is often considered to be the inverse of the linkbandwidth since it represents the amount of time that thelink is used by a packet transmission. In wireless networks,given the multiaccess/broadcast nature of the wireless medium,errors may occur in packet transmissions due to noise and

978-1-4244-8435-5/10/$26.00 ©2010 IEEE

interference, and a packet may be transmitted multiple timesbefore it is received correctly. Thus an appropriate metric isthe expected transmission time (ETT) averaged over multiplepacket transmissions [5]. This is in fact the default routingmetric specified in the IEEE 802.11s draft, and is referred toas the Air time metric. It may also be useful to account for thenumber of nodes NB that are blocked during the transmissiontime of a packet. In this case, an appropriate routing metricwould be the product ETT .NB , which represents use of themedium both in time and space [6].

We note, however, that the amount of resources used incarrying traffic in the network is a function of the physicallayer parameters. Indeed, the probability of success of a packettransmission on a link is function of the received signalstrength at the receiver (which is function of the transmitpower used by the transmitter), the data rate used, and thelevel and extent of interference experienced during the packetreception. The extent of interference is directly determined bythe set of interferers and their physical layer parameters. Theset of interferers is a function of the spatial reuse factor, whichis function of the transmit power used by the transmitting nodeand the ED threshold values used at other nodes.

We seek in this paper the best overall performance in amesh network by jointly optimizing routing and physical layerparameters. We first note that decreasing network resourcesneeded to support a traffic load translates to improved perfor-mance (i.e., higher network capacity). We thus consider theuse of ETT .NB as a link metric for routing, and optimizephysical layer parameters so as to further minimize networkresources used and increase network capacity.

The issue of spatial reuse in multihop wireless networks hasbeen addressed in the past. However, prior work is limited tonetwork scenarios consisting of specific links in the networkand traffic on these links. For example, in [7], the authorsfocus on links between transmitters and receivers that areseparated by the maximum transmission range and seek theoptimal blocking distance so as to maximize the aggregatethroughput of such links. Similarly, in [8], [9], the authorspropose heuristic algorithms for selection of physical layerparameters to maximize aggregate throughput of links, givena set of links carrying traffic. None of the prior work addressesthe distribution of traffic on links resulting from routing, andstudies the optimum physical layer parameters and their effectgiven how routing may adapt to these parameters.

The remainder of this paper is organized as follows. Insection II, we describe the system model considered, theanalytical model used in deriving numerical results, and thetraffic model used in assessing the performance of the network.In section III, we present numerical results and discuss theseresults. We conclude in section IV.

II. SYSTEM MODEL, ANALYTICAL MODEL AND TRAFFICMODEL

A. System Model

We consider a mesh network with 400 nodes deployed in anarea of 600m x 600m. One node is randomly located in each

30m x 30m square by selecting the coordinates of the nodeindependently and randomly in the 30m range. This approachfor generating a network topology is one way to meet therequirement that neighboring nodes be separated by a certainappropriate distance for them to be able to communicateproperly, yet accounts for physical constraints in the placementof nodes in space. The network is considered to be wrappedat its edges to eliminate bias in results due to nodes locatedclose to the edge(s). Path loss between nodes is consideredto follow the power law model with an exponent of γ = 3,representative of outdoor environments.

All nodes are equipped with omnidirectional antennas andfollow the IEEE 802.11. Medium access is according tothe Distributed Coordination Function (DCF) specified in thestandard. The RTS/CTS feature is not used. The Physicallayer is according to the IEEE 802.11a/g OFDM specificationwith a maximum transmit power of 29 dBm and the physicallayer rates of {6, 12, 24, 36, 48, 54} Mbps. Clear channelassessment is based on the energy level sensed; nodes considerthe medium busy when they sense an energy level greater thanthe ED Threshold.

In accordance with the IEEE 802.11 standard, packetsconsist of a preamble followed by a PLCP header and Phys-ical layer Service Data Unit (PSDU). Preamble and PLCPheader are transmitted at the lowest supported rate. Packetreception consists of several phases. The first phase consistsof synchronizing to the preamble; if this step is successful,then the receiver receives and decodes the PLCP header;if this is successful, then the receiver receives and decodesthe PSDU. The probability of error at each of these phasesdepends on the Signal to Interference plus Noise Ratio (SINR)during each of the phases. Noise is modeled as Additive WhiteGaussian Noise (AWGN) with a noise power of -101 dBmcorresponding to the channel bandwidth of 20 MHz specifiedin the IEEE 802.11 OFDM physical layer specification.

The receiver characteristics pertaining to synchronizationand packet reception are given in figures 1(a) and 1(b). Figure1(a) depicts the probability of synchronization error as a func-tion of SNR, and is obtained from measurements on a testbedin the absence of interference using Orinoco 802.11a/b/ginterface cards [10]. Figure 1(b) depicts the probability of errorin PSDU reception after synchronization is achieved, and isobtained by simulation [11]. This data has been verified tobe valid by measurement by the authors of [10]. As is oftendone in the literature, one may consider that interference canbe modeled as AWGN, and consider the above receiver modelto be valid for the combined effect of noise and interference.This is referred to as SNR-based receiver model.

However, we recognize that receiver performance in thepresence of interference may be different from that in the pres-ence of noise. Measurements conducted by the same authorsof [10] in the same environment have shown that the effect ofinterference due to transmissions from other nodes in the samenetwork may not be as severe as that of white noise of the samepower. Considering a high level of interference, exceedingnoise by 10 dB, measurement results have shown that the

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Fig. 1. Probability of synchronization error and packet error vs. SINR withinterference modeled as AWGN

synchronization error and PSDU error curves as a function ofSIR are those in the above model but shifted by 5 dB to the left.That is, equal error rates are achieved with an SIR 5 dB smallerthan SNR [12]. These results were confirmed to hold wheninterference is caused by a single interferer or two interferersoverlapping in time. There is reason to believe that they holdalso when the number of interferers is greater than two. Inany case, as indicated in section II-B below, the likelihoodof a transmission experiencing simultaneous interference frommore than two interferers in a mesh network is extremely low,and thus this model is applicable to our situation. As is shownbelow, using the maximum transmit power for transmissionon all links, when the SIR is sufficiently low to be of concern(i.e., errors in synchronization and/or in PSDU reception mayoccur), then the level of interference exceeds noise by 10 dB.We thus consider this model in our study, and refer to thismodel as the SIR-based receiver model.

B. Analytical model used for assessing performance

The most reliable way to assess the performance of wirelessmesh networks is by experimentation on real networks. Thisapproach is costly and often unavailable. Researchers havethus resorted to computer simulation. However, simulationtools are computation-intensive since they must track thestate of all packets, transceivers, and wireless channels inthe entire network at all times. Analytical modeling is verychallenging given the complexity of wireless mesh networks.For an analytical model to be useful and to provide meaningfulresults, it must capture the essential aspects of CSMA/CA ina multi-hop network setting, channel propagation and wirelesstransceivers, and must be computationally more efficient thansimulation. All prior work in modeling wireless mesh networksproved to be inadequate due either scalability (computationalfeasibility when it comes to large size networks) or capability(could not accommodate different physical layer parametervalues on different links, multiple links active from thesame node, asymmetric blocking, cumulative interference frommultiple interfering nodes, etc.). We have thus developed ananalytical model that captures all the important effects, yet iscomputationally efficient, and used this model to derive thenumerical results presented in this paper.

Given: (i) the set of nodes in a mesh network and the pathloss between all pairs of nodes, (ii) the transmit power anddata rate used on each link, (iii) the ED threshold used ateach node, and (iv) the rate of traffic on each link, the modeldetermines if the traffic load imposed is feasible or not. Ifthe traffic load is feasible, the model provides performancemeasures for each link; namely, the packet error rate and thefraction of time that the channel is sensed busy. The modelcan also be used to determine the highest traffic load that canbe supported for a given distribution of traffic on links. Thisis done by starting with a distribution of traffic on links that isfeasible, increasing the load in small steps, and evaluating theperformance variables at each step; the highest load is reachedwhen the fraction of time that the channel is sensed busy atsome link(s) approaches one.

The analytical model is based on the observation that, at anygiven time, the source of a link is in one of the following states:(i) the channel is sensed busy due to its own transmissionsor due to transmissions from other nodes; (ii) the channel issensed idle and its back-off timer is counting down idle slots;and (iii) the channel is sensed idle and its back-off timer is notcounting down idle slots. A traffic load is feasible if the trafficon each link carrying traffic is feasible. The traffic on a linkis feasible if the fraction of time that the source of the link isin states (i) and (ii) is less than one. These conditions resultin a system of equations that is solved iteratively. As long asthe load imposed on links is feasible, the iterative approachfor solving the system of equations is quite efficient.

With respect to the evaluation of the fraction of time thatthe channel is sensed busy due to transmissions on other links,it is important to account for single ongoing transmissions forwhich the received power exceeds the ED threshold, as wellas multiple simultaneously occurring transmissions for whichthe cumulative received power exceeds the ED threshold. Byanalyzing timelines of simulation runs, we observe that itsuffices to account for blocking due to cumulative energyreceived from up to two simultaneous transmissions.

The fraction of time spent in states (i) and (ii) dependson the total rate of traffic required to be carried on the links,including retransmissions. The probability of error for a packettransmission depends on the SINR experienced at the receiverduring the reception of the packet. Since transmissions oninterfering links can start and end at arbitrary times duringthe transmission on the target link, the interference powervaries during the reception of the packet. We assume in ourmodel that the probability of error for a packet is determinedby the lowest SINR during its reception regardless of thefraction of packet reception time over which the SINR isat this lowest value. However, the lowest SINR and hencethe probability of error varies from packet to packet sinceeach packet experiences interference from different sources.For a packet transmission undertaken on the target link, weevaluate the probabilities that the transmission overlaps withand hence experiences interference from individual interferinglinks and probabilities that the transmission overlaps simulta-neously with transmissions on pairs of interfering links. By

studying simulation results, we find that the likelihood thata transmission undertaken on a link overlaps simultaneouslywith three or more transmissions in the neighborhood of thereceiver is very low.

Our model also accounts for acknowledgements (ACKs)with respect to (i) time occupied by acknowledgements, (ii)possibility of errors in reception of ACKs and the impactof these errors on data packet transmissions, and (iii) theinterference caused by ACKs on data transmissions. Thenumerical results presented in this paper use a simplifiedversion of the model that accounts for time occupied by ACKs,but assumes that ACKs are always successful and ignores theinterference caused by ACKs on data transmissions.

We have extensively verified the results of our analyticalmodel by comparing them against those from a high-fidelitysimulator based on GloMoSim [13] for several network topolo-gies. Detailed equations can be found in [14].

C. Traffic Model

The performance of a wireless mesh network depends on theparticular usage scenario(s) supported. Typical usage scenariosinclude a combination of: (i) traditional data applications suchas web browsing, file transfers and downloads, and electronicmail, (ii) voice communication, and (iii) video streaming andconferencing. A general assessment of the performance ofmesh networks supporting any combination of these is quitecomplex. In this paper, we limit ourselves to stream-typetraffic as is the case with voice and video communication.We consider end-to-end traffic to consist of constant bit rateflows, where the rate and size of packets is determined bythe applications throughput and delay requirements. Voicetraffic typically consists of fixed size packets carrying datacorresponding to 20 ms of speech generated at equal intervalsof 20 ms. The amount of data carried in a packet is dependenton the voice encoding scheme: for G.711, the data rate is64 Kbps; for G.729, the rate is 8 Kbps. Video consists ofa succession of frames with a constant frame rate. Encodedframes differ in type (I, P and B types), and thus in the amountof data required to encode them and the role they play. Apacket may contain either a complete frame or a portion ofa frame depending on the encoded video data rate, the typeof frame in question, and the maximum packet size allowed.The data rate of a video stream varies widely depending onthe content and the desired quality, as well as the encodingscheme. In the context of wireless networks, it is reasonableto consider that the data rate per stream is in the range of 64Kbps to 384 Kbps.

In a real network supporting stream traffic, requests forcommunication are random in time and space. We consider inthis paper that: (i) the source node and destination node for arequest are randomly selected among all nodes in the network,(ii) the times at which such requests are made are random intime following a stochastic process (e.g., Poisson process),and (iii) the duration of the communication for each requestis also random (e.g., following an exponential distributionwith a certain mean duration). We also consider that the

flows corresponding to these requests maintain their routesfixed throughout the entire duration of the communication.Given a certain set of flows already present in the network,when a new request is generated, a path from the source tothe destination is selected according to the routing metric.Then a test is made to guarantee that the selected path canaccommodate the new flow. If the test is positive, the newflow is routed on the selected path; otherwise it is rejected.With these considerations, the capacity of the network may beexpressed in terms of the highest rate of requests that can besupported given a certain target rejection rate (e.g., 5%). Thecapacity of the network may also be expressed in terms of themaximum average number of flows that can be simultaneouslysupported, or equivalently in terms of the maximum aggregatedata load that can be supported, summing the throughput ofall flows.

Unfortunately, considering a dynamic model for arrivalsand departures proved to be compute intensive, even withthe analytical model we developed. Instead, we consider afixed number of flows between randomly selected sources anddestinations and find the highest possible aggregate load thatcan be supported under the constraint that all flows are of equalrates. This approach is satisfactory for our purpose; indeedif the number of flows considered is about the same as themaximum number of flows that can be supported given theapplication’s data rate per flow, then the result in terms ofnetwork capacity would be equivalent to that obtained withthe dynamic arrival and departure model. It should also besatisfactory for the study of interaction between routing andphysical layer parameters.

Using this approach, however, it is important to guaranteethat the paths used to route a set of flows are the same as (or atleast equivalent to) those that would be taken in the dynamicarrival and departure model, which naturally makes use ofthe traffic-dependent routing metric (ETT .NB). This is easilyachieved by using the following iterative procedure. Startingwith an empty network, we find paths between sources anddestinations assuming that the data rate associated with eachflow is zero. In this situation, transmission on links do notexperience any interference, and ETT for a link is based onlyon the link’s propagation characteristics and physical layerparameters (transmit power and data rate used). Fixing theseroutes, we find the maximum aggregate load supported by thenetwork by uniforming increasing the data rate on all flowsuntil one or more flows cannot be supported. Given the currentdistribution of traffic on links in the network and the resultinglevel of interference experienced by the various links, ETT isupdated for all links, and a new set of routes is found basedon the new values of link metrics. This is repeated until noincrease in aggregate throughput is possible.

We consider several traffic scenarios consisting of unidi-rectional flows between randomly chosen source-destinationpairs. Each scenario is specified by the number of flows, thepacket rate per flow and the packet size used. All flows use thesame packet size and have the same packet rate. We considerscenarios with (i) 75 flows and 200 flows with 1528 bytes per

packet as may be used in video streaming, and (ii) 75 flowswith a smaller packet size of 228 bytes that would representvoice encoded at 64Kbps using the G.711 encoding scheme.With such encoding, each packet contains 20 ms of speechin 160 bytes which after addition of headers at various layersamounts to 228 bytes. One packet every 20 ms correspondsto a MAC layer throughput requirement of 91.2 Kbps.

III. NUMERICAL RESULTS

We consider that all links use the maximum transmit powerspecified in the IEEE 802.11 standard for OFDM (P = 29dBm) and the same data rate R. We derive the networkcapacity that can be supported for different values of R and EDthreshold using the analytical tool described in section II-B.We determine network capacity by the highest packet rate perflow and express it in terms of the maximum aggregate end-to-end throughput achieved in the network. We show in figure2 the results corresponding to a traffic scenario consisting of200 flows and a packet size of 1528 bytes, using the SIR-basedreceiver model. For each value of R, there is an optimal valueof ED threshold that maximizes network capacity. The optimalvalue of ED threshold decreases with the data rate since ahigher rate requires a higher SINR. The results show that thecurve corresponding to 24 Mbps dominates all other rates.With the receiver model considered, the SIR requirement forsynchronization exceeds the SIR for correct reception of thePSDU for 6 and 12 Mbps data rates; as for the 24 Mbps datarate, the same is true except for PSDU reception error ratesbelow 0.2. Thus it is not surprising that the performance with24 Mbps is superior to 6 and 12 Mbps. As for data rates higherthan 24 Mbps, the smaller ED threshold which translates tolower spatial reuse factor contributes to the lower achievableoverall network performance. With R = 24Mbps, the highestnetwork capacity is obtained at an optimum value of EDthreshold = -80 dBm. The aggregate network throughput at theoptimum value of ED threshold is 14.1 Mbps correspondingto a per-flow throughput of 70.65 Kbps and a per-flow packetrate of 5.78 packets per second.

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We now are interested in seeing how sensitive the resultsare to the traffic scenario considered. We start by considering apacket size of 1528 bytes, and number of flows = 75 and 200,

three different sets of source-destination pairs in each case.We derive the maximum aggregate throughput for differentvalues of ED threshold around the optimum value of -80 dBmseen above. We show in table I the aggregate throughput,and verify that any difference in results is rather insignificant.With 12 Mbps for 75 flows of 1528 byte packets, the per-flow throughput is 160Kbps and the packet rate per flow is 13packets per second. This is roughly representative of a videostream with 15 frames per second and 1528 bytes per frame.

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TABLE IAGGREGATE THROUGHPUT (IN MBPS) FOR SETS OF FLOWS BETWEENRANDOM SOURCE-DESTINATION PAIRS. P = 29 DBM, R = 24 MBPS

We now consider a set of 75 flows with a packet size of228 byte, representative of voice traffic. As can be seen fromfigure 3, the maximum aggregate throughput is still obtainedusing a data rate of 24 Mbps at an ED threshold of -77 dBm.The highest aggregate throughput is 8.14 Mbps. The slightlyhigher value of optimum ED threshold may be attributed to thefact that the the the relationships between SIR and probabilityof error in reception of a 228 byte PSDU for different ratesare shifted towards lower values of SIR by 1 to 2 dB ascompared to those for 1528 byte packets. We note howeverthat even at an ED threshold of -80 dBm, the aggregatethroughput is not much lower. With an aggregate throughputof 8.14 Mbps, the per-flow throughput is 108 Kbps, slightlyhigher than the 91.2 Kbps required for G.711 voice traffic.The decrease in throughput with shorter 228 byte packets isattributed to higher per-packet overhead that is incurred fora larger number of smaller packets as compared to smallernumber of larger packets. The overhead consists of (i) fixedphysical layer packet overhead consisting of preamble andPLCP header and (ii) overhead in media access control interms of backoff, inter-frame spacings and acknowledgements.

We now look at what the results would be if one was touse the SNR-based receiver model that has a 5 dB higherrequirement in SINR for the same synchronization and PSDUerror rates. The higher SINR requirement requires that the EDthreshold be smaller; i.e., the set of nodes blocked be larger.Thus, for this comparison, we consider a larger network toensure that spatial reuse is still realizable in the network eventhough concurrent transmissions have to be farther apart. Wechoose a network occupying an area of 1200m x 1200m, againwith one node placed randomly in each 30m x 30m square. Weevaluate the highest aggregate throughput and the optimum EDthreshold using both the SNR-based and SIR-based receivermodels. In both cases, R = 24 Mbps is the optimum physical

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layer rate. The optimum ED threshold is -80 dBm for theSIR-based receiver model and -85 dBm for the SNR-basedreceiver model. We find the maximum aggregate throughputachieved is 21 Mbps and 11 Mbps respectively for the SIR-based and SNR-based receiver models. The lower throughputachieved with the SNR-based receiver model is attributed tothe lower degree of spatial reuse that can be achieved whenusing such a receiver model as compared to the SIR-basedreceiver model. This difference of a factor of two in maximumaggregate throughput is quite significant.

We now examine the links used by routing and theirperformance. For the scenario of 200 flows with 1528 bytesfor which results are shown in figure 2, we show in figure 4the distribution of link lengths for links used by routing at theoptimum (see curve labeled ED = -80 dBm). The links usedfall in the range of 15m to 45m with 80% of the links fallingin the narrow range of 25m to 43m.

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The performance of the links used at the optimum is shownin figure 5 as a scatter plot of the average PER as a function ofthe link length. The PER increases with the link length since:(i) the received signal strength decreases with the link length,and (ii) the level of interference experienced at the receiverincreases with the link length due to the fact that the receiveris closer to the interfering nodes. We illustrate the latter fact byshowing in figure 6 the complementary cumulative distributionfunction of the interference experienced by links of lengths15, 30 and 45 meters that are used for forwarding traffic(Note that, as stated in section II-B, interference here refers to

the highest level experienced during the reception of a packettransmitted on the link). The reason why no links longer than45 m get used at this optimum can be easily seen from figure7 in which we show the received signal strength and the levelof interference experienced (shown in terms the mean, themedian, and percentiles) as a function of link length, as wellas background noise N . Using the maximum transmit powerat all nodes, interference dominates noise by more than 10 dBrendering the SIR-based receiver model appropriate to use.According to the SIR-based receiver model the SIR has to begreater than 10 dB for the link performance to be meaningful.This condition is met by links shorter than 45 m.

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We now examine the situations where the ED threshold isdifferent from the optimum value of -80 dBm. For a higherED threshold of -68 dBm, nodes that are allowed to transmitsimultaneously can be closer to each other, increasing boththe likelihood of packet overlap and the level of interference.Accordingly, the maximum aggregate throughput achievableis lower than at optimum. The distribution of lengths of linksused by routing is the same as with the optimum ED threshold(see plot labeled ED threshold = -68 dBm in figure 4). Thissuggests that as far as routing is concerned, the shortestappropriate links are used. On the other hand, for an EDthreshold of -86 dBm, routing makes use of longer links thanat the optimum, as can be seen from figure 4. This is certainly

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Fig. 7. Signal power, noise and interference experienced at capacity by usedlinks, P = 29 dBm, ED threshold = -80 dBm, R = 24 Mbps

due to the fact that higher blocking range reduces the levelinterference experienced by links, rendering longer links moreattractive. The links used in routing in this case range from 30m to about 72 m. The overall decrease in maximum achievableload in this case is attributed to the lower degree of spatialreuse; this decrease, however, is not as severe as if routingwere to be limited to links shorter than 45 m, because routingadjusted its selection of links so as to decrease resources used.We find that if links longer than 45m are not established, theaggregate throughput for the set of 200 flows is 7.3 Mbpscompared to 11.3 Mbps if longer links are established andmade available to routing.

So far, we have considered that all links use the sametransmit power and physical layer rate. Given that SINR ishigher for shorter links, the question arises as to the possibleimprovement that one may get if shorter links were operated ateither higher data rate, or lower power. A higher rate translatesto a decrease in the transmission time of a packet on themedium. A decrease in transmit power translates to a decreasein NB . The gain in either case, however, may be offset by anincrease in packet error rate resulting from operating at higherdata rate or with a lower power.

We address first the adjustment of data rates. We consideras a starting point the optimum operating point with P = 29dBm, R = 24 Mbps on all links, ED threshold = -80 dBm,and the highest feasible traffic load for the set of 200 flowsstudied above. Since the range of link lengths used by routingis already the lowest possible, we claim that the ED thresholdshould be maintained at its optimum value. For each link, weevaluate the link metric ETT .NB for all data rates based onthe level of interference experienced as a result of the abovetraffic, and identify the data rate that minimizes the metric.The relationship between link length and optimum data rate isdisplayed in figure 8 in which we show the fraction of links ofa certain length that have a given data rate as their optimumrate. As evident from the figure, almost all links in the range25-45 meters have 24 Mbps as their optimum rate, almostall links in the range 15-25 meters have 48 Mbps, and linksshorter than 15 m have 54 Mbps as their optimum rate. Giventhat 90% of the links used in the above scenario were longer

than 25 m, the gain achieved by assigning the higher rates tothe shorter links is expected to be low. This is indeed the caseas seen from table II. A notable difference with the base case,however, is the rise in the percentage of links shorter than 25m that get used by routing (from 10% to over 20%) as can beseen from figure 9.

0 10 20 30 40 50 60 700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Link length (m)

Fra

ction o

f lin

ks o

pera

ting a

t part

icula

r P

HY

rate

6 Mbps

12 Mbps

24 Mbps

36 Mbps

48 Mbps

54 Mbps

Fig. 8. Fraction of links at a particular rate vs. length of links

Flowset

Number offlows

P = 29dBm, R= 24Mbps on alllinks

With rate adjust-ment

1 200 12.27 12.712 200 13.15 13.743 200 12.86 13.45

TABLE IIAGGREGATE THROUGHPUT BEFORE AND AFTER RATE ADJUSTMENT, P =

29 DBM ON ALL LINKS, ED THRESHOLD = -80 DBM

0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Link length (m)

CD

F

R = 24 Mbps on all links

With data rate adjustment

Fig. 9. CDF of lengths of links carrying traffic before and after rateadjustment; P = 29 dBm, ED threshold = -80 dBm

We now address adjustment in transmit power. From figure7, we see that shorter links have a higher SINR, which isalso reflected in the low average PER of such links in figure5. This suggests that the transmit power of such short linksmay be reduced to some extent while still maintaining goodperformance. We perform the following test to investigate theimprovement in network throughput that may be obtained byreducing the transmit power on shorter links. The transmitpower of links shorter than a certain length L is reduced suchthat the signal power received at the receiver of these linksis the same as that at the receiver of a link of length L.The transmit power for links of length ≥ L is maintainedat 29 dBm. The idea is to achieve the same SINR on these

shorter links as that on links of length L (Note that thelevel of interference experienced by the set of used links isapproximately the same as observed in figure 7). We observethat with R = 24 Mbps, ED threshold = -80 dBm, thehighest improvement in throughput is obtained when assigningtransmit powers on links in this manner with L = 35 m. Forthe scenario consisting of 200 flows with 1528 byte packetsfor which results with equal transmit power and data rate werepresented in figure 2, the aggregate throughput is improved to16.33 Mbps (an improvement of 15% compared to 14.1 Mbpswith P = 29 dBm on all links). Figure 10 shows the CCDFof interference experienced by transmissions on used links atcapacity with such a transmit power assignment. It can beseen that shorter links now experience more interference ascompared to when P = 29 dBm is used on all links, sincethey block fewer nodes with the reduction in their transmitpower. This results in an increase in average PER of shortlinks as shown in figure 11. However, shorter links becomemore attractive for routing due to the reduction in their NB

as seen in figure 12. The distribution of link lengths carryingtraffic is now skewed towards shorter links. With more shorterlinks used, the set of nodes blocked is smaller, leading to moreconcurrency and higher throughput despite the higher PER onshort links. Note that our test is only to show that indeedadjusting transmit power has more influence than data rate. Aneven higher improvement in throughput than that demonstratedmay be obtained by a more appropriate power assignment.

−95 −90 −85 −80 −75 −70 −65 −600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Interference (dBm)

CC

DF

Link length = 30 m(P = 29 dBm on all links)

Link length = 15 m(P = 29 dBm on all links)

Link length = 30 m(with transmit power adjustment)

Link length = 45 m(P = 29 dBm on all links)

Link length = 15 m(with transmit power adjustment)

Link length = 45 m(with transmit power adjustment)

Fig. 10. CCDF of interference experienced by used links with transmit poweradjustment (L = 35 m), R = 24 Mbps, ED threshold = -80 dBm

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Link length (m)

Ave

rag

e P

ER

Fig. 11. Average PER of links with transmit power adjustment (L = 35 m),R = 24 Mbps, ED threshold = -80 dBm

0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Link length (m)

CD

F

P = 29 dBm on all links

With transmit power adjustment

Fig. 12. CDF of lengths of links carrying traffic with transmit poweradjustment (L = 35 m), R = 24 Mbps, ED threshold = -80 dBm

IV. CONCLUSION

In this paper, we have addressed the joint optimization ofphysical layer parameters and routing to maximize networkcapacity. We have illustrated the role of routing in properlyselecting the links that are used for carrying traffic. Wefind the optimal values for physical layer parameters basedon the optimum selection of routes by routing, leading tobest network performance. Any optimization of physical layerparameters that does not account for the role of routing wouldlead to suboptimal network performance.

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