232D_1_[J5] Julan Hsu Rubin Wireless Comm and Mobile Computing Paper Reprint 2010

WIRELESS COMMUNICATIONS AND MOBILE COMPUTINGWirel. Commun. Mob. Comput. 2010; 10:129144Published online in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/wcm.900

Cross-layer design of joint routing and rate control inad hoc wireless networks

Ju-Lan Hsu, and Izhak RubinElectrical Engineering Department, University of California at Los Angeles, U.S.A.

Summary

We investigate multi-hop wireless networks in which nodes use adaptive modulation/coding schemes and 802.11-based CSMA/CA MAC. Each node independently selects its cross-layer parameter vector for each packet thatit forwards. It entails the setting of the transmission data rate and the identification of the neighboring node towhich the packet is forwarded (and thus the selection of the route). We present an analytical model to calculate,for each candidate parameter vector, the corresponding attainable throughput and transport throughput capacityrates. To enable throughput-effective network operations, we present cross-layer schemes under which each nodeconfigures its parameter vector by using the transport throughput capacity measures that it computes, for eachcandidate attached link, as key metrics. We present two such datagram-based cross-layer parameter vector selectionschemes, one of which makes use of observed channel status statistical data. We compare the networks throughputperformance behavior attained under the use of these schemes, demonstrating the performance enhancement thatis offered by schemes that use cross-layer adaptations that are guided by calculations of link transport throughputcapacity metrics. Copyright 2009 John Wiley & Sons, Ltd.

KEY WORDS: ad hoc networking; CSMA/CA; 802.11; cross-layer design

1. Introduction

In this paper, we study the impact of adaptivemodulation coding scheme data rate operations onthe throughput efficiency of the multi-hop wirelessnetworks. Transmissions at a higher data rate leadto shorter packet transmission times and thus maypotentially induce a higher throughput; however,they require a higher acceptable SINR (Signal toInterference and Noise Ratio) at the intended receivingnodes. This may lead to the use of shorter link layercommunication forwarding ranges. From network

Correspondence to: Ju-Lan Hsu, Electrical Engineering Department, University of California at Los Angeles, U.S.A.E-mail: [email protected]

layer point of view, a flow may thus have to betransported along a route that contains a larger numberof hops. This produces higher network internal trafficloads, which may in turn increase the interferencepower measured at the receiving nodes. Hence, byincreasing the data rate, one does not necessarilysecure an overall upgrade in the end-to-end throughputperformance behavior. It is not readily determined asto how one should make the best joint selection of thetransmission data rate in combination with the settingof the packets forwarding range, under prescribed orobserved network loading conditions.

Copyright 2009 John Wiley & Sons, Ltd.

130 J.-L. HSU AND I. RUBIN

We investigate our proposed methodology for theselection by each node of the cross-layer parametervector. Relative to a given communications link, theparameter vector used by a node in forwarding packetsacross a link to a neighboring node is defined to includetwo parameters; namely, the associated forwardingrange (i.e., the distance traveled by a signal propagatedacross the link), and the data rate to be used forthe transmission of a packet across the link. Themethodology is based on a computation of a relativelink level transport throughput capacity measure. Thetransport throughput capacity attained across a linkrelative to a specified flow is calculated as the productof the computed link throughput capacity rate (i.e.,the maximum throughput rate that can be carriedacross the link) and the effective progress range gainedwhen sending flow packets across the link. In thispaper, we select the cross-layer parameter vector sothat the corresponding transport throughput capacitymetric is optimized. We introduce two schemesto execute the selection, and show that their useleads to a distinctly upgraded cross-layer throughputoperation.

We consider first the operations involving a singlenetwork station. We assume this tagged station tomonitor (on a sliding window basis) certain keyelements that represent the activity of its neighboringlinks and nodes. Using such statistical data, wederive mathematical expressions for the performancebehavior experienced by packets and flows traversingthis node and its attached links. We then presentthe analytical results and investigate the impactingparametric factors using the derived mathematicalexpressions. When designing distributed mechanismsfor the selection of the parameter vector, to attainnetwork-wide upgraded performance behavior, onemust consider the impact of the operations executedat each node on those undertaken by other nodes. Wefirst examine the independent scheme, in which eachnode acts independently, based on its monitored statusindicators, without coordinating with other nodes. Wethen develop a second scheme under which each nodecomputes the parameter vector under the assumptionthat a fair occupancy of the channel takes place, insteadof using monitored network activity statistics. It isidentified as the homogeneous scheme. Our resultsdemonstrate that the homogeneous scheme yieldshighly enhanced network performance. Since it isdistributed, involving calculations that can be carriedout in realtime, we conclude it to provide efficientsetting of the parameter vector investigated in thispaper.

The organization of the rest of this paper is asfollows. Section 2 summarizes related works. In section3, we present the nodal-centric model and deriveformulas that characterize the system performancemeasures. In section 4, we present and examine theperformance of the two schemes for the setting ofthe parameter vector. We further investigate in 5 theperformance behavior of the network under a multitudeof networking scenarios when the latter scheme isemployed. Simulation evaluations are presented in 6and conclusions are drawn in 7.

2. Related Works

Typical routing protocols used for wireless ad hocnetworks employ minimum hop length routes. Suchmechanisms have been shown to often produce poorthroughput performance behavior [1]. To upgradethe performance exhibited, alternative routing metricshave been studied [2]. Recently, routing metrics havebeen proposed for use in multi-rate ad hoc wirelessnetworks (see Reference [311]). In [1213], routingmechanisms that act to balance the distribution oftraffic loads across the network have been devised.The algorithms presented in [1415] employ multiplepath routing. We have also noted published papers thatutilize optimization techniques for the selection of thecross-layer parameters [8,16]. Due to the complexitiesinvolved in modeling the behavior of such networks,we introduce in this paper a simplified analytical modelthat enables each node to compute in a low-complexitymanner the optimal parameter vector.

The network transport throughput capacity achiev-able by an ad hoc wireless network is noted inReference [17] to grow at an order of O(n1/2)bit-meters per second. When nodes are permittedto select the neighbor to which they forward thepackets, an optimal link forwarding distance levelhas been noted to exist (see Reference [18]). InReference [5], it is shown that routing over fewerbut longer hops may yield better energy efficiencythan that attained under nearest-neighbor routing. Thework in Reference [7] has investigated the selectionof an optimum physical carrier sensing range thatmaximizes the throughput performance in an 802.11-based ad hoc network operation. The impact of variabletransmission range levels realized under the use ofvariable data rates have been studied, assuming astatic interference process. In contrast, in our study,we examine the performance of the network whenthe interference processes may stochastically and

Copyright 2009 John Wiley & Sons, Ltd. Wirel. Commun. Mob. Comput. 2010; 10:129144DOI: 10.1002/wcm

RATE CONTROL IN AD HOC WIRELESS NETWORKS 131

dynamically fluctuate. Accordingly, we develop cross-layer algorithms that employ system state monitorsfor current selection of the best parameter vector. InReference [8], the authors have formulated a jointrouting and link scheduling (and rate allocation)optimization problem to find a path for a flow thatoffers the highest path capacity value. In connectionwith the analysis of CSMA/CA-based networks, wealso note the contributions in Reference [1925]. Tothe best of our knowledge, there are no publishedworks that provide comprehensive mathematical-basedapproaches for adaptive rate control and routing forad hoc networks that employ 802.11 based MACprotocols.

3. System Model and NodalPerformance Behavior Characterizations

Consider an ad hoc wireless multi-hop networkcarrying multiple end-to-end data packet flows. Inthis section, we focus on one tagged station andmathematically model its performance behavior asflows traverse this station through its attached links,under given, or monitored, network activity conditions.The analytical results are then used in subsequentsections to facilitate at each node the selection of theparameter vector that serves to yield upgraded networkperformance behavior.

3.1. Performance Measures and Metrics

For a given flow whose packets are distributed acrossa selected path, to express the potential utility gainedby flow packets when transmitted across a selectedlink using a selected data rate, it is advantageous touse the link transport throughput capacity rate as aperformance measure. To calculate this metric, weassume, for the sake of the computation, that this flowis currently the only one using the link resources. Thismetric is then calculated as the product of the computedthroughput capacity rate of the link and the underlyingprogress range made by the flow when directed acrossthe link. The progress range of a flow across alink is defined as the projection of the links length(forwarding range) across the line vector connectingthe source toward the destination. Under this definition,we note that a given link may provide different linktransport capacity levels when calculated with respectto different flows. While the link throughput capacitymeasures the maximum packet data rate that can besustained across the wireless link, and is thus a MAC-

level oriented metric, the link transport throughputcapacity index, when normalized by the end-to-endline-of-sight range between the flows source anddestination nodes, serves as an indication of the per-link contribution to the end-to-end throughput capacityfor a flow.

In this paper, to implement and evaluate a simplemechanism, we consider here each node to invokedatagram based mechanisms. Clearly, the algorithmspresented here can be further enhanced by theinclusion of such flow oriented end-to-end performanceconsiderations. One can extend the approachespresented here to include flow oriented operations aswell as the prescription of end-to-end QoS performanceconsiderations.

3.2. System Model

The nodal transmission power P is fixed at everystation. Half-duplex radios are assumed to be used.Nodes are spatially Poisson distributed. In general, fora prescribed modulation coding scheme (MCS) thatoperates at a data rate rc, we can describe, (1) therelation between rc and the required minimum SINRthreshold (rc) at the intended receiver, and (2), therelation between rc and the packet transmission timeduration T(rc), rc Rc. Rc denotes the set of data ratesoffered by the available MCS structures. We consider apower law path loss model. Thus, the corresponding (i,j) links distance dependent signal attenuation is set as:Gij = dij , where dij is the physical distance betweennodes i and j and is the attenuation factor, > 2. Otherattenuation functions can also be incorporated into ourmodel.

Assume packets to contain a payload whose averagelength is equal to b bits. We consider a systemthat employs 802.11 DCF (Distribution CoordinationFunction) CSMA/CA type MAC. We assume that theuse of RTS/CTS dialog is not invoked, as this isthe default state and the suggested configuration byrecent studies (see Reference [20]). A station i thatdesires to transmit its packet, proceeds first to sensethe radio channel. During the carrier sensing process,transmissions initiated by nodes located within itscarrier sensing area (identified as a disk area centeredat node i whose radius is equal to the carrier sensingdistance) are assumed to cause node i to defer itstransmission. We use CWj to denote the contentionwindow size in the jth backoff stage. The minimumand maximum window sizes are represented byCWmin = CW0 and CWmax = 2mCWmin respectively,where m is an integer. After CWmax is reached, the



window size is fixed. The retransmission limit is setequal to L, L > m. Note that the carrier sense range (CS)is assumed to be fixed and not a function of the data rate.Alternatively, one may jointly adapt the value assumedfor the carrier sensing range for each data rate (seeReference [26]).

3.3. Characterizing the CSMA/CA MACOperations from the Point of View of a TaggedStation

Consider a station i that desires to select the parametervector to be used for the forwarding of each ofits queued packets. Station i observes the channelstate of the wireless medium in its carrier sensingarea. Denote the number of stations (including itself)that currently contend for channel access, and thatreside in the considered carrier sensing area, by K.For our analytical derivation, the following two-level(combined collision-SINR based) interference model isused to determine successful packet reception events.A packet transmission made by station i to station j issuccessful if: (1) none of the other K-1 stations initiatesa packet transmission at the same slot as that selectedby station i; and (2) the SINR level at receiver j ishigher than a threshold (rc), where rc is the data rateemployed to transmit this packet. In this manner, weemploy a collision model to account for interferencesoriginated (by nodes residing) inside the carrier sensingarea, and a SINR model to account for interferencesoriginated outside the latter area. Under our model,we neglect the possibility of the intended transmissioncapturing the receiver when other simultaneouslyexecuted transmissions originated inside the senderscarrier sensing range take place. In this regard, thisapproximation provides a conservative estimate of theattained throughput performance. Practically, the latterapproximation has been shown to yield highly accuratethroughput performance behavior.

In the following, we carry out analysis toquantitatively describe station is behavior. Weintroduce a model that characterizes the underlyingsystem activity in terms of the following parameters:(1) The probability p0 that any of the other (K-1)stations starts to transmit at a given slot that belongsto the backoff period of station i. (2) The averagechannel occupancy time E[To], which represents thetime duration during which the medium is sensedbusy and thus made unavailable to station i, once anyof the K-1 other stations start to transmit its packet.Its value includes the time occupied for data (andACK if successful) transmission and the lengths of

the involved inter-frame spacing (DIFS and SIFS)periods. (3) A probability distribution function of thecumulative interference power level ID, originated bynodes residing outside node is carrier sense region,measured at receiver j.

In practice, node i can obtain these parameters bymonitoring its observed network activity states and byreceiving data from other nodes concerning activitiesin the neighborhood. Good estimates for the first twoare readily derived from direct state observations bystation i. Alternatively, the third parameter can beapproximated by combining direct activity measureswith assumptions of uniformity in the statisticalbehavior of nearby nodes. Such an approach is usedin Section 3.4.

Given that node i has selected a specific slot forthe transmission of its packet, we set 1- p to denotethe probability that this packet is received successfullyby its intended link layer receiver j and that its ACKis received successfully by node i. We set PDcapture todenote the conditional probability of the successfulreception of this packet under the impact of thecumulative interference at receiver j (originated outsidenode is carrier sensing zone). Given a successful datatransmission, we set PAcapture to denote the conditionalprobability of a successful ACK reception under theimpact of the cumulative interference detected at nodei (originated outside the latter carrier sensing zone). Weuse ID and IA to denote the power levels interfering withthe reception of the data and ACK packets, respectively,as detected at their corresponding intended receivers.Hence, we obtain the following:

p = 1 PDcapture PAcapture (1 p0), (3-1)

PDcapture = P{ID Pd/(rc) N}, (3-2)

PAcapture = {IA Pd/(rc) N}, (3-3)

where the forwarding range d represents the distancetraveled across the link connecting station i tostation j, P represents the transmission power level,and N represents the thermal noise power level. InEquations (3-2)(3-3), PDcapture and PAcapture denote theprobabilities that the SINR levels at the receivers ofnodes i and j, respectively, involving the respectivereceptions of the data and ACK packets, are larger thanor equal to the threshold .

The head-of-line delay (THOL), also identified as themedium access delay (see Reference [27]), expressesthe time period elapsed between the instant at which



the packet enters the head of the line position instation is transmission queue and the instant of time atwhich the station is ready to transmit the next packetacross this link. In computing THOL, included arethe time durations during which (1) station i backsoff, (2) the channel is busy and the backoff processis frozen and (3) station i acquires the medium fortransmitting its packet. Its expected value E[THOL] isgiven by

E[THOL] = (Te (1 p0) + E[To] p0)

(

Li=0

pi CWi 12

)+ E[Tb]

(L

i=0pi

), (3-4)

where

E[Tb] = pTc + (1 p)Ts, (3-5)

and Te, Tb, Ts, and Tc are respectively the slottime duration, node is channel occupancy time fora packet transmission, the mean time duration of asuccessful transmission, and the mean time durationconsumed by an unsuccessful transmission. Ts and Tcare further expressed in terms of SIFS (short inter-frame spacing), DIFS (distributed inter-frame spacing)and ACK durations. Thus,

Ts = E[T (rc)] + SIFS + ACK + DIFS. (3-6)

Tc = E[T (rc)] + DIFS + PDcapture (SIFS + ACK).

The packet queueing and transmission processing isdescribed by an M/G/1 queueing system model, forwhich the effective packet service time is set equal tothe message head-of-line delay THOL. The throughputcapacity attained across the communications link (i, j),denoted as CS , is calculated by dividing the payloaddata length by the mean head-of-line delay incurredby a packet transmitted across this link, accountingonly for successful transmissions. Its expression is thusgiven by Equations (3-7). Noting the dependence ofE[THOL] and p on the following parameters throughEquatoons (3-1)-(3-4), we further express CS in termsof the number of stations residing within node is CSregion (K), the forwarding range d of (i, j) link, and theemployed data rate rc, denoted as CS =CS(K,d,rc).

CS = CS(K, d, rc) = bE[THOL]

(1 pL+1). (3-7)

The transport capacity attained across the identifiedlink, such as the (i, j) link, assuming prescribedparameters (K,d,rc), with respect to a given flow, isdefined as the product of the throughput capacity acrossthe link multiplied by the averaged value of the linksrange when projected in the direction of the line vectorconnecting the flows source with the final destination,yielding:

CSt = CSt(K, d, rC) = CS(k, d, rC) d cos(),(3-8)

where d cos() expresses the described projection.

3.4. Characterizing the CumulativeInterference Process and the Probabilities ofCapture

Recall the parameters that need to be monitoredto enable the calculations introduced earlier in thisSection. Often, it is costly to implement a mechanismthat serves to monitor the cumulative interferencepower at a node. Hence, we also present here anapproach under which the interference power at anode is computationally estimated rather than beingmeasured. The evaluation results (as demonstratedlater) show that our method provides accuratepredictions of the performance behavior. Specifically,the cumulative power level (ID) induced by randominterference signals sensed at tagged node is linkreceiver j is expressed as the sum of two components,identified by the random variables IDin and IDout . IDindenotes the interference level originated by nodeslocated outside station is CS area but inside a diskarea centered at node j, with a radius equal to thecarrier sensing distance CS plus the forwarding ranged between nodes i and j. The latter area is denoted byAin (see Figure 1). In turn, the second component, IDout ,represents the interference power level originated bynodes located outside both the CS area of station i andthe Ain region. The probability of capture is thus givenas:

PDcapture = P{ID d/(rc) N/P}= P{IDin + IDout d/(rc) N/P}. (3-9)

This method is motivated by the work in Reference[28]. The results there identify the dominatingcontribution made by the most significant interferersand the imprecision of a pure Gaussian approximation



Fig. 1. Illustration of a transmission from node i to node j.

of the cumulative interference, when spatially Poissonnetworks are considered. For calculating the IDincomponent, we use the following approximation.Noting that the probability that two nodes residing inAin simultaneously initiate a transmission at the sameslot is quite low, we assume that at most one interferingnode can be active in Ain. Observing the area to berepresented by the disk of radius (CS + d), puncturedby the disk that represents node is CS area, we have:

Ain = (CS + d)2 C2S. (3-10)

Induced by the Poisson statistics characterizing nodalspatial locations, we note that under a prescribedrealized number of nodes across the area, nodallocations are governed by uniformly distributed i.i.d.random variables. Let X denote the distance betweennode j and a randomly selected nodal location in Ain.We note that a node k will be located at a distancefrom node j that is equal in the range (x,x+ dx) withprobability (2x/|Ain|)dx, where |Ain| denoted the areaof region Ain. The angular location of node k, withrespect to node j, is uniformly distributed over (0,2),and is represented as ; referring to Figure 1, we notethat is depicted there as the angle of the sector kjv. Theprobability density function (p.d.f.) of X is thereforewritten as:

fX(x) 2x 2 = C1x cos1(

d2 + x2 C2S

2dx

),

CS d x CS + d, (3-11)

where C1 is a normalizing constant. The randomvariable representing the interference power causedby an active node located in the Ain region is then

expressed as:

IDin ={

PX, with probability (1 eAin ).0, else. ,

(3-12)

where represents the probability that an active nodelocated in Ain region is transmitting at any instant oftime. denotes the active nodal spatial density. Onecan obtain by setting it to be equal to the averagefraction of time available to each active station inthe latter region for transmitting. However, because theconsidered region is outside station isCS area, it can beoperatively expensive to monitor or learn the activitiestherein. Alternatively, several approximations can bemade. One is to simply assume the activities observedby the nodes there are statistically similar to those bystation i. This approximation can be justified by notingclosely located nodes are likely to observe similarchannel activities. In this manner, by assuming thenodes locating in node is proximity to see the sameparameters, namely, the parameters p and E[Tb], isthus calculated as follows:

= Pr{non empty nodal queue}

(E[Tb] + p E[Tb]... + pL E[Tb]

)E[THOL]

, (3-13)

Pr{non empty nodal queue} ={

, when < 1.1, when 1. ,

where represents the utilization factor of the M/G/1queueing system that we use to model the nodalsystems, engaging in packet queueing and transmissionprocessing (i.e., expressing the fraction of time that thequeueing system is busy).

An even simpler approximation can be derived inthe following. Noting that the average number ofactive stations in a CS area can be approximatedas Pr{non-empty nodal queue} E[K], we may set to be equal to min{1,(E[K] Pr{non-empty nodalqueue})1}, ignoring unutilized idle slots.

As depicted in Figure 1, we use IDout to denote arandom variable that models the aggregate interferencecaused by nodes located at a range from node j thatis farther than (CS + d). The IDout component involvesactive nodes that are distributed across outside a diskarea, so that the results presented in Reference [28] canbe applied for the calculation, yielding the following



Gaussian distribution:

IDout N(P

2(CS + d)2 2 ,

P22(CS + d)22

2 2)

= N(D, 2D). (3-14)

Combining Equations (39)(314), we obtain thecapture probability to be expressed as follows:

PDcapture = Pr{IDin = 0} Pr{IDout d/ N/P}+ Pr{IDin > 0} Pr{IDin + IDout d/ N/P}.

Similarly, for the calculation of PAcapture, recall thatIA represents the aggregate interference power levelmonitored at station i, as caused by nodes locatedoutside the CS area of station i. We use a Gaussianapproximation technique for the calculation of thedistribution of this cumulative interference power level,noting that interfering nodes include active nodes thatare symmetrically located in a disk centered at node i(with radiusCS). The probability of capture is thereforegiven as:

IA N(

P2C2S

2 , P2 2C

22S

2 2

)

= N(A, 2A). (3-15)

PAcapture = P{IA d/(r0c ) N/P}. (3-16)

4. Designing Mechanisms forCross-Layer Joint Routing and RateControl

Using the model developed in Section 3, we aimto design a distributed mechanism for selecting theparameter vector at each node, for each packet that itforwards. We assume the network system to be highlyloaded and thus saturated with packet traffic, so thatwe aim to devise a cross-layer operation that yieldsupgraded network throughput capacity. Note that ina non-saturated network, one may want to select theparameter vector to yield an acceptable packet delayperformance. In the rest, we however focus on theformer objective in designing our parameter vectorselection algorithm.

For implementation simplicity, we consider thefollowing relatively simple distributed mechanisms.We note that the algorithms used here require eachnode to forward its packets to a neighboring node thatprovides positive progress toward the destination, andthus ensure the realization of loop-free routes. For eachpacket that a node receives and forwards, it considersall of its neighboring nodes (when operating at thelowest data rate). The corresponding parameter vectorthat is used to forward the packet is then determinedin accordance with one of the following candidateschemes.

Scheme 1independent transport-based scheme:the forwarding node continuously monitors andcalculates channel activity statistics (producingupdates of p0 and E[To]). Using these statistics, thenode computes the transport throughput metric foreach of its neighbors and selects the neighbor (andits corresponding parameter vector) that offers thehighest link transport capacity level. The computationsare performed by using the formulas presented inSection 3.

Scheme 2homogeneous transport-based scheme:For each neighbor, the forwarding station computes theparameter vector that yields the highest link transportthroughput capacity level. For this computation, ratherthan using monitored channel statistics, it proceedsby assuming all other nodes to be operating underthe same statistical conditions that characterize itsown behavior, even when this may not be the case.Such an assumption is motivated by access fairnessbehavior imposed by the CSMA/CA MAC when thenodal region operates in a highly loaded (or saturated)mode.

Scheme 3max progress scheme: the forwardingstation selects the node that provides the highest(positive) progress range toward the destination node.In communicating with the selected node, it employs adata rate that is equal to the highest feasible such ratethat enables the forwarding of the packet. This schemethus aims to forward packets along lower hop lengthroutes.

Scheme 4max transmit rate scheme: the forward-ing node strives to select the highest data rate thatenables it to forward a packet to a neighboring nodeyielding positive progress. If multiple neighbors canbe reached at this rate, the one that yields the highestprogress range is selected.

Scheme 5nearest neighbor scheme: for eachneighbor, the forwarding node selects the node that,among all nodes that yield positive progress towardthe destination node, is closest to itself. It then uses the



Table I. Summary of the five schemes.

Scheme Procedure

1 Independenttransport-based

Use the real-time monitored p0 andE[To] as inputs and followcalculations presented in Section 3 toselect the parameter vector.

2 Homogeneoustransport-based

Use homogeneous channelstatistics assumption and followcalculations presented in Section 5 toselect the parameter vector.

3 Max progressscheme

Select the forwarding node(s) thatprovides the highest positive progressrange and then select the one offeringthe highest feasible data rate.

4 Max transmit ratescheme

Select the highest data rate that canreach at least one of thepositive-progress making forwardingnodes. If multiple nodes can bereached at this data rate, select theone that provides the highestprogress range.

5 Nearest neighborscheme

Select the shortest-distance nodeamong those that yield positiveprogress range and then select thehighest feasible data rate.

highest transmission data rate that enables it to forwardthe packet to the selected node.

The computation of the parameter vector carriedout by each node in accordance with Scheme 2 ispresented in the following Section. The correspondingcomputations carried out by Schemes 35 arestraightforward. We also summarize the proceduresof the above schemes in Table I. The latter schemesprovide benchmark comparisons to Schemes 12.They do not base the selection of the parametervector on the computation of a transport throughputcapacity measure, as employed by Schemes 12. In theremainder of this section, we discuss (and illustrate viaa simple example) the potential advantages to be gainedby using Scheme 2 when compared to Scheme 1. InSection 4, we provide via simulations a comparison ofthe performance attained through the use of the abovefive schemes. We demonstrate the advantages gainedby the use of Scheme 2.

Even though many distinct mechanisms may be usedto select the parameter vector at each node, we expectthe use of Scheme 1 to be quite effective, when eachnode acts independently by basing its selections on itsmonitored status indicators, without coordinating withother nodes. However, we note through the followingillustrative scenario that the use of Scheme 1 may attimes lead to the selection of a sub-optimal parametervector.

Fig. 2. A 2-node illustrative example of the link transportcapacity versus employed forwarding range performance,under selective values of the nodes employed data rate levelrc and the employed data rate level (rc)- by the other nodelocated inside the nodes CS region. p0 is set equal to 0.0571in plotting the figure, derived under a 2-node contending

CSMA/CA MAC saturation operation.

We consider a simple example where two activestations that reside in each others CS region. Assumethat currently they are the only active stations inthe neighborhood. Assume that the nodes can select802.11a data rate values that are equal to either18 Mbps (low rate) or 36 Mbps (high rate). Consideran operation based on the use of Scheme 1. Assumethat the monitored state points out to each node therate employed by the other node. Then the node willproceed, for each of the two possible rates used bythe other node, to calculate the highest achievablelink transport throughput capacity level realized whenit operates at the high or low data rate levels. InFigure 2, we depict the results of these computationsas represented by four curves. We use solid and dashedlines, respectively, to present the performance attainedwhen the rate selected by the other node is equal tothe low- and high-rate value. We use +marked andx-marked curves to present the performance attainedwhen the node itself selects to use the high and lowrates, respectively. For illustration simplicity, assumethe nodal density to be sufficiently high so that theselected forwarding range can be implemented.

When Scheme 1 is employed, each node proceedsto select the parameter vector that yields the highesttransport capacity level. For this example, eachnode will consequently select to operate at the lowrate (noting it to yield higher transport capacityindependently of the rate used by the other node).The resulting realized transport throughput rate is then



given at each node by operating point V. Clearly, thisis not the overall optimal operating point of the systemeven if a fairness constraint is imposed. Operatingpoint V (under which both nodes have selected touse the high data rate) yields a strictly higher transportthroughput performance vector.

Performance upgrade can be attained when morecomplex schemes are considered. On the other hand,a parameter vector selection strategy that is simpleto implement and is rapidly converging certainly hasits value. Consequently, we consider in this papermechanisms that do not impose such coordination inthe selection of the parameter vector at each node.The homogeneous scheme presents such a simplifieddistributed structure. In the following, we explainthat nevertheless we expect this scheme to yieldexcellent throughput performance behavior since itis set to operate under the assumption of networkconditions that will be realized due to the employmentof the CSMA/CA MAC. To this end, assume a high-nodal density level, so that any desirable forwardingrange can be realized. We consider a symmetricnodal outfitting configuration so that all stationsemploy the same set of MCS. Note that the hiddenterminal problem is often eliminated under many multi-hop CSMA/CA operations, even without engagingRTS/CTS (see Reference [29]), and consequently theunderlying CSMA/CA mechanism imposes accessfairness (among active network nodes) when operatedin saturation mode, as illustrated in Reference [30].We assume each node to use a stationary parametervector policy that calculates the selection as a functionof its realized channel activity and/or throughput rates,or related observables. Assuming the network to beloaded to saturation (to assess the attainable throughputcapacity level), the actions undertaken by each node,as automatically induced by the MAC scheme, arestatistically similar to those undertaken by any othernode. Hence, each node will determine its parametervector in a manner that is statistically similar to thatperformed by each other node. Thus, each forwardingnode will proceed to select the same parameter vectoras that chosen by any other node. To optimize thenetwork-wide throughput performance, it is thereforebest for each node, in selecting its parameter vector,to recognize the symmetric behavior imposed by theCSMA/CA MAC scheme. Furthermore, by assuminga sufficiently high-nodal density level, the sameparameter vector will be selected by a node for theforwarding of packets that belong to different flows.

Under practical topological layouts, a node may notbe able to find a neighboring node that is located at a

range that is equal to the calculated optimal distancevalue. Selections made by certain nodes may differfrom those made by others. Consequently, a parametervector computation at a node that is based on theassumption that the computations at other nodes leadto the same result may lead to suboptimal performance.Nevertheless, this strategy provides a simple yeteffective alternative to that used by Scheme 1. UnderScheme 2, every node can be programmed to selectthe parameter vector automatically without needingto monitor channel activities. This is particularlydesirable when channel state monitoring is consideredto be non-cost-efficient. To justify the use of Scheme2 for a heterogeneous network, notice that the selectedstrategy can reflect the willingness of each node to offera fairness based level of cooperation. In Section 6, wepresent simulation based performance results that wellconfirm the performance effectiveness of Scheme 2,assuming nodes to employ no status monitoring meansand to not engage in cooperative behavior.

5. Characterizing the PerformanceBehavior Under the HomogeneousScheme

As discussed in Section 4, we use the homogeneousscheme to choose the parameter vector that maximizesthe attained link transport capacity. For each arrivingpacket, node i proceeds with the joint selection of thenext hop node j and the transmission data rate rc to beemployed.

5.1. Characterizing Multi-Hop CSMA/CAOperations Under the Homogeneous Scheme

To calculate the systems throughput performance, weneed to first calculate the underlying variables thatinclude the probability p0 and the average channeloccupancy time E[To]. We then apply the resultsderived in Section 3.2 to carry out performance analysisfor the system. For a station that is contending foraccess with K-1 other stations that are located in itscarrier sense area, recalling our assumption that thesystems offered traffic load is sufficiently high sothat it is driven to saturation state, the correspondingcontention rate p0 is expressed in terms of as follows:

p0 = 1 (1 )K1. (5-1)

Since, for calculating the parameter vector, eachstation assumes other stations to act in a homogeneous



fashion (i.e., to statistically exhibit behavior similar toits own), E[To] is then set to be equal to the meanchannel occupancy time realized at station i, to be givenby E[To] =E[Tb].

We employ the two-dimensional Markov chainmodel developed in [31] to characterize the backoffprocess. The detailed derivations are omitted here, andthe result is given below:

=[L

l=0CWl1

n=0CWl n

CWlpl]1 1 pL+1

1 p

=[L

l=0CWl 1

2pl]1 1 pL+1

1 p . (5-2)

Using the latter results, we solve the system ofequations given by Equations (3-1)-(3-3) and (5-1)-(5-2) through numerical computations. Notingfrom Equations (5-2) (see Reference [32]) that isnon-increasing function of p, and, from Equations (3-1)(3-3) and (5-1), that p is non-decreasing function of, we conclude that a unique fixed point is guaranteedto exist (see Reference [32] for more details).

To obtain K, we assume active nodal locations overthe area of operations to be two-dimensional Poissonspatial distribution with parameter . Note that, bydefinition, we K> 1. According to the spatial Poissonnodal distribution assumption, K is a random variablecharacterized by the following distribution function:

Pr{K = k} = (C2S)k1eC

2S

(k 1)! , k = 1, 2, . . .

(5-3)

Recall that Equations (37) expresses the linkthroughput capacity CS(K,d,rc) and is a function of thenumber of nodesK, forwarding distance d, and data raterc. We use Cs to express the link throughput capacityrate attained along such a link (link distance is d) byaveraging over the values assumed by K. Hence, wewrite:

CS = CS(d, rc) =

k=1 Pr(K = k) CS(k, d, rc).(5-4)

In a similar manner, the link transport capacity rateCSt = CSt(d, rc), averaging over the values assumedby K, with respect to a given flow direction, is

Table II. Data rate versus SINR threshold table for targetBER = 105.

Rate (Mbps) 6 9 12 18 24 36 48 54SNR (dB) 6.02 7.78 9.03 10.79 17.04 18.8 24.05 24.56

written as

CSt = CSt(d, rc) =

k=1 Pr(K = k)CS(k, d, rc) d cos() (5-5)

Note that the directional penalty factor (expressed bythe cosine term) depends on the relative nodal spatiallayout. Its realized value is effectively independentof the configured parameter vector. For illustrationalpurposes, we thus do not include this cosine factor inthe following figures.

5.2. Performance Results

We consider the underlying multi-MCS implemen-tation provided by IEEE 802.11a systems. The datarate and the corresponding required SINR levels forsuccessful reception, per MCS, are given in Table IIfor a targeted BER value of 105 [33]. For theIEEE 802.11a protocol, the PLCP preamble plus SIGduration and the data rate dependent overhead lengthinduced by the headers are denoted as T0 and b0,respectively. The average packet length b is assumedto be 1000 bytes. The remaining parameter setup levelsare summarized in Table III. The packet transmissiontime T is calculated by

T (rc) = T0 + (b + b0)/rc. (5-6)

The transmission power is fixed at 0.01 mW and thebackground noise power level is assumed to be equal to

Table III. System parameters.

Parameter Value

Transmission power 0.01 mWN 1e09 mWCWmin 32m 5L 6SIFS 16usDIFS 34usTe 9usACK 24usPHY overhead (T0) 20usPHY, MAC, IP header (b0) 406bits



Fig. 3. Link throughput capacity illustration versusforwarding range performance results for selected values of

rc when CS = 50 m.

109 mW. The effective communications ranges for theset of modulation coding schemes under considerationare given as: 39.8, 36.0, 33.4, 30.2, 21.1, 19.1, 14.1,and 13.7 m.

5.2.1. Parameter vector selection andperformance behavior under theHomogeneous Scheme

In Figure 3, the achievable link throughput capacityintensity (expressed in units of bits per second perunit area) is plotted versus the selected forwardingrange, for various data rate levels when the CSdistance is equal to 50 m. Notice that the protocoloverhead reduces the efficiency attained by high-datarate operations. In addition, the performance curvesrepresenting the high-data rate levels induce moreabrupt degradations as the forwarding range levelincreases.

In Figure 4, the link transport capacity level is plottedagainst the forwarding range, under selected data ratelevels, when the CS distance is set equal to 50 m.Corresponding to each data rate value, there exists aunique optimal forwarding range level. The optimalsuch level is observed to be equal to the longestforwarding range that enables the signal to be receivedat a sufficiently high-SINR level. The results depictedin Figure 4 show that the link transport capacityperformance becomes a more sensitive function ofthe forwarding range at higher data rate levels. Asone acts to dynamically adapt the parameter vector toactual locations of nodes (so that a node must selecta neighbor from those nodes that currently reside inits vicinity), only a subset of parameter vectors would

Fig. 4. Link transport capacity versus forwarding rangeperformance results for selected values of rc when

CS = 50 m.

remain under consideration. When constrained by thelocation of neighboring nodes that are located at short,intermediate, and long forwarding ranges, we observefrom Figure 4 that the best data rate level to choose isequal to 54 Mbps, 36 Mbps and 18 Mbps, respectively.When considering the availability of neighboring nodesat any selected range, we note from Figure 4, that theoptimal link transport capacity level is achieved byemploying a data rate that is equal to 36 Mbps.

5.2.2. The impact of carrier sensingsensitivity and nodal spatial density

We investigate the impact of the setting of theCS sensitivity level on the performance. Relateddiscussions can be found in Reference [7,3435].Figure 5 and Figure 6 show, respectively, thelink throughput capacity and link transport capacityperformance functions plotted versus the selectedforwarding ranges, for various CS ranges, whenrc = 18 Mbps. Note that the assigned CS sensitivitylevel must be configured to provide a node with asufficient number of stations to be located insideits CS region. Otherwise, the CSMA mechanismbecomes ineffective, leading to a MAC operation that iseffectively identical to that exhibited by a pure randomaccess (ALOHA type) protocol. In the latter case, werefer to Reference [36] for the characterization of theperformance behavior for multi-rate random accessmulti-hop networks. We set here the CS distance levelsto yield an average number of CS-neighborhood nodes(K) that is equal to at least 2, so that a station is able tofind at least one other station that is located in its CSregion.



Fig. 5. Link throughput capacity versus forwarding rangeperformance results for selected values of carrier sensing

distances, when rc = 18 Mbps.

Fig. 6. Link transport capacity versus forwarding rangeperformance results for selected values of carrier sensing

distances, when rc = 18 Mbps.

As illustrated in Figure 5, provided that a node canfind a neighboring forwarding node that is sufficientlyclose, the use of lowerCS distance leads to a higher linkthroughput capacity, at the expense of higher sensitivityof the achieved throughput rate to the selectedforwarding range. This is explained by noting that oneis able to achieve higher spatial reuse gains with shorterCS range levels, provided the selected forwarding rangeis not too high. Realistically, attainable performancelevel is dependent on the forwarding range selectionsthat can be realized. In Figure 6, we observe that foreach CS distance level, there exists a forwarding rangethat maximizes the link transport capacity.

It is also essential to evaluate the sensitivity levelof the attained throughput performance rate to thenodal layout configuration. In Figure 7, we show

Fig. 7. Link transport capacity versus forwarding rangeperformance results for selected values of nodal spatial

density, when carrier sensing distance is equal to 50 m.

link transport capacity depicted against the selectedforwarding range. Three sets of curves are shown,each set involving a prescribed data rate (18 Mbps,36 Mbps and 54 Mbps). In each set, we depict variousperformance curves, whereby each corresponds to agiven nodal spatial density level that ranges from0.0005/m2 to 0.01/m2. By setting the CS distance to50 m, the latter nodal density levels translate to anaverage number of CS-neighborhood nodes (K) thatranges from 4 to 79. We observe that the link transportcapacity increases marginally with nodal density whenthe density level is very low, but monotonicallydecreases with nodal density at higher density levels.Notice that in the latter case, the performancedegradation ratio, for each set of prescribed data rates,is approximately invariant to the forwarding rangelevel. Thus, the effects of forwarding range and nodaldensity are noted to be approximately decoupled. Thisis explained by noting that the carrier sensing-basedoperation regulates channel access activities so that theinterference level is properly controlled, regardless ofthe nodal spatial density. Thus, the key impact of nodaldensity is not on the packet capture probability, but israther on the occurrence of collision activities withinthe CS region. Furthermore, we find that even thoughthe link transport capacity varies with nodal density,the relative optimality of the operating point remainsapproximately unchanged.

Recall again that the results presented in this section,depicting the expected behavior of the link transportcapacity function are used as metrics employed in theselection of the parameter vector, when employing thehomogeneous scheme.



6. Simulation Performance Results andComparisons of Parameter VectorSelection Algorithms

We consider the same network system configurationand parameters as those used in Section 5. We haveused a discrete event based C++ simulator to conductvarious evaluations, under a multitude of cross-layerjoint routing and rate control strategies. This sectioncontains two parts. The first part is used to verify theprecision of our analytical model. The second part ofour evaluation is aimed to investigate the usefulnessof our analysis results in realistic scenarios wheremultiple traffic flows traverse the network. Assumingeach node to learn the location of its neighbors and thedirection toward destination nodes, each node proceedsto independently compute its parameter vector. Weexamine and compare the performance results byconsidering the five schemes introduced in Section 4.

6.1. Conrmation of the DerivedPerformance Formulas for the HomogenousScheme

We generate link layer homogeneous traffic processesthat load the system at a sufficiently high rate, causing itto be saturated. To validate our model, we first assumethe forwarding range to be set to a prescribed value.We randomly place 640 transmitter nodes in an areaof 800 m 800 m (so that = 0.001/m2), and thenplace link layer receivers away from their link layertransmitters at the prescribed range in a random angle.In Figure 8, we exhibit link throughput capacity versusforwarding range performance curves, for selecteddata rate levels, when the CS distance is set equal to50 m. We observe the performance values obtainedby simulation to be very close to those predicted bythe use of the analytical model. In Figure 9, the linktransport capacity performance functions are plottedagainst the selected forwarding range, for variousselected CS distance levels, when the data rate isset equal to 18 Mbps. We note that our analyticalexpressions again provide accurate prediction of thethroughput performance behavior of the system, exceptfor the case in which the CS distance is set to be verylow (i.e., 10 m (not shown here) or 20 m). In suchcases, we observe that the resulting average numberof forwarding stations that are located inside the CSregion around a station is low (being equal to about0.3 or 1.2). In this case, the CSMA/CA MAC iseffectively identical to that exhibited by a random

Fig. 8. Throughput capacity versus forwarding rangeperformance results obtained by simulations for selectedvalues of rc when the carrier sensing distance = 50 m.Simulation results are depicted in points and analysis results

are depicted in dashed lines.

Fig. 9. Transport throughput capacity versus forward-ing range performance results obtained by simulationsfor selected values of carrier sensing distances, whenrc = 18 Mbps. Simulation results are depicted in points and

analysis results are depicted in dashed lines.

access scheme. Note that for the case in which CS isconfigured to be equal to 20 m, our analytical modeltends to overestimate the peak performance value butstill accurately predicts the position of the peak. Inturn, we confirm the simulation results to be close tothose predicted by the ALOHA-based analytical modelpresented by us in Reference [36].

6.2. Distributed Combined Rate Control andRouting Algorithms

In the second set of simulations, we let the five schemesintroduced in Section 4 to be used independently bynetwork nodes to compute the parameter vector to



Fig. 10. Aggregate end-to-end normalized throughput performance under selected forwarding algorithms.

forward traversing packets across multihop routes totheir destinations. We randomly place 120 nodes ina 150 m 150 m area of operation and randomly setthe network to be loaded by four source-destinationflows. We note that at the lowest data rate a paththat covers a distance of 150 m will use about fourhops; at the highest data rate, such a path willemploy 12 hops. We configure the loading level tobe sufficiently high to lead to a saturated operation.For the effective communication range calculationscarried out by the protocols employed by Schemes35, we have considered a model that assumes thetotal noise plus interference power at the receiver tobe equal to (1) the noise power (N), (2) noise plus a3 dB margin, or (3) noise plus a 6 dB margin. Twentydistinct spatial topology realizations were generatedand used to evaluate the performance of the fiveschemes. The resulting aggregate (over all end-to-end flows) throughput performances (normalized) areshown in Figure 10. It is observed that Scheme 2outperforms every other mechanism for 12 out ofthe 20 experiments, while Scheme 1 does so forsix experiments. For 90% of the experiment cases,Schemes 12 together provide the best performancelevels. Schemes 3 and 4 display top performanceeach for a single case. Scheme 5 displays poorperformance behavior for most simulated cases. As wefurther increase the assumed supplemental interferencepower (beyond the 6 dB level), we have noticed(not shown here) the throughput performance level

to further degrade. The results thus clearly point outthe performance superiority exhibited by Scheme 2 inthe selection of the parameter vector. We also noticethat the performance levels attained under Scheme 2reach the 80th percentile level of the highest displayedlevel of all schemes for 95% of the time. Using theseresults, we conclude that the effectiveness of Scheme 2has also been well demonstrated under heterogeneoustraffic patterns and a multitude of heterogeneous spatialand temporal network conditions. We note that wehave considered here simplified datagram-based nexthop route selection implementations. Clearly, in certaincases, it can be more effective, if feasible, to discoverand configure end-to-end routes in a manner that takesinto consideration current topological, loading andcapacity availability conditions. Yet, such an operationis more complex and will be further investigated infuture studies.

7. Conclusions

We propose schemes for setting the cross-layeroperational parameters for multi-hop CSMA/CAwireless networks. The link transport capacity measureis used as a metric for the selection of the cross-layer parameters at each node. Each node jointlyselects, for each packet, the corresponding parametervector that involves the preferred data rate andforwarding link across the selected route. We develop



an analytical model that provides for such a selectionand performance evaluation to be executed. Wedemonstrate the validity of the analytical formalismdeveloped to select the parameter vectors. We confirmthe effectiveness of two proposed distributed datagram-based cross-layer schemes. Under the first scheme,each node uses channel state observations of twochannel statistical occupancy metrics to compute itspreferred parameter vector selections; under the secondone, the selections are based in each station onobservations that it makes relating to the statisticalbehavior of packet flows that it itself queues andprocesses. We show these methods and schemesto yield significantly enhanced performance. Ourmodels provide important guidelines for the designand implementation of such joint rate and routingadaptation algorithms.

Acknowledgements

This work was supported by the National ScienceFoundation (NSF) under Grant No. ANI-0087148, byUniversity of California/Nokia MICRO Grant No. 05-054, by UC Discovery/Booz-Allen Hamilton Grant NoCom06-10214, and by Taiwan Merit Scholarship No.TMS-094-1-A-02.

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Authors Biographies

Ju-Lan Hsu received the PhD degreefrom University of California at LosAngeles in 2008, in Electrical Engi-neering. She received the BSc fromNational Taiwan University in 2002 andthe MSc from University of California atLos Angeles in 2004, both in ElectricalEngineering. She currently works in theWireless Connectivity Lab of Samsung

Electronics America as a Senior Engineer. Her researchinterests include cross-layer mechanism designs, focusing onPHY, MAC and network layers, for ad hoc wireless networksand wireless LANs.

Izhak Rubin received the BSc and MScfrom the Technion-Israel Institute ofTechnology, Haifa, Israel, in 1964 and1968, respectively, and the PhD degreefrom Princeton University, Princeton,NJ, in 1970, all in Electrical Engineering.Since 1970, he has been on the facultyof the UCLA School of Engineeringand Applied Science (now the Henry

Samueli School of Engineering and Applied Science),where he is currently a Professor in the ElectricalEngineering Department. Dr Rubin has had extensiveresearch, publications, consulting, and industrial experiencein the design and analysis of commercial and militarycomputer communications and telecommunications systemsand networks. At UCLA, he leads the AutonomousIntelligent Networked Systems research group. He alsoteaches short courses in communication networks at UCLAExtension, and gives courses and lectures throughoutthe telecommunications and computer communicationsnetworking industry and for government organizations. Healso serves as President of IRI Computer CommunicationsCorporation, a leading team of computer communicationsand telecommunications experts engaged in softwaredevelopment and consulting services. During 19791980,Dr Rubin served as Acting Chief Scientist of the XeroxTelecommunications Network. He served as co-chairmanof the 1981 IEEE International Symposium on InformationTheory, as program chairman of the 1984 NSF-UCLAworkshop on personal communications, as program chairmanfor the 1987 IEEE INFOCOM conference, and as programco-chair of the IEEE 1993 workshop on Local andMetropolitan Area Networks. Dr Rubin is a Fellow ofIEEE, and has served as editor of the IEEE Transactionson Communications. He is serving as editor of the Baltzerjournal on Wireless Networks, of the SPIE/Baltzer OpticalNetworks magazine, of the Kluwer Photonic NetworkCommunications journal, and of the International Journal ofCommunications Systems published by Wiley Interscience.He has also served as guest editor of special issueson communications networks for key journals. He hascontributed chapters to texts on telecommunications systemsand networks.


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232D_1_[J5] Julan Hsu Rubin Wireless Comm and Mobile Computing Paper Reprint 2010