PROVIDING high-rate and reliable communications is an

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1 1764 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 12, DECEMBER 26 OMAR: Utlzg Multuser Dversty Wreless Ad Hoc Networks Jafeg Wag, Studet Member, IEEE, Hogqag Zha, Studet Member, IEEE, Yuguag Fag, Seor Member, IEEE, Joh M. Shea, Seor Member, IEEE, ad Dapeg Wu, Seor Member, IEEE Abstract Oe of the most promsg approaches to mprovg commucato effcecy wreless commucato systems s the use of multuser dversty. Although t has bee wdely vestgated ad show feasble ad effcet cellular etworks, there s lttle work for the ad hoc etworks, especally real protocol ad algorthm desg. I ths paper, we propose a ovel scheme, amely, the Opportustc Medum Access ad Auto Rate (OMAR), to effcetly utlze the shared medum IEEE based ad hoc etworks by takg advatage of dversty, dstrbuted schedulg, ad adaptvty. I a ad hoc etwork, especally a heterogeeous ad hoc etwork or a mesh etwork, some odes may eed to commucate wth multple oe-hop odes. We allow such a ode wth a certa umber of lks to fucto as a clusterhead to locally coordate multuser commucatos. We troduce a CDF-based (Cumulatve Dstrbuto Fucto) K-ary opportustc splttg algorthm ad a dstrbuted stochastc schedulg algorthm to resolve tra ad tercluster collsos, respectvely. Faress s formulated ad solved terms of socal optmalty wth ad across clusters. Aalytcal ad smulato results show that our scheme ca sgfcatly mprove commucato effcecy whle provdg socal faress. Idex Terms Wreless ad hoc etworks, multuser dversty, opportustc medum access, auto rate, cross-layer optmzato. Ç 1 INTRODUCTION PROVIDING hgh-rate ad relable commucatos s a mportat desg goal wreless ad hoc etworks. However, lmted spectrum, tme-varyg propagato characterstcs, hostle terferece, ad dstrbuted multple access, together wth complexty ad eergy costrats, mpose sgfcat challeges developg techques to acheve ths objectve. Oe of the most effectve approaches to combatg scarce spectrum resources ad chael varatos s the use of multuser dversty, whch s made possble because dfferet users usually have dfferet stataeous chael gas for the same shared medum. Opportustc multuser commucatos utlze the physcal-layer formato fed back from multple users to optmze the medum access cotrol, packet schedulg [1], [2], [3], [4], ad rate adaptato [5], [6]. By allowg the users wth good lk qualtes to trasmt data usg approprately chose modulato schemes, throughput ad eergy effcecy ca be greatly mproved. Dversty techques have bee wdely vestgated ad show feasble ad effcet frastructure-based wreless etworks [7], [8], [9], [1], [11]; however, these schemes may ot be applcable multhop ad hoc etworks because there s o base stato to act as the cetral cotroller ad o dedcated cotrol chael to feed back the chael state a tmely fasho. Moreover, ad hoc etworks, the medum access cotrol s dstrbuted ad. The authors are wth the Departmet of Electrcal ad Computer Egeerg, Uversty of Florda, Gaesvlle, FL E-mal: jfwag@ufl.edu, zha@ece1.ufl.edu, {fag, jshea, wu}@ece.ufl.edu. Mauscrpt receved 15 Feb. 25; revsed 22 Nov. 25; accepted 19 Mar. 26; publshed ole 16 Oct. 26. For formato o obtag reprts of ths artcle, please sed e-mal to: tmc@computer.org, ad referece IEEECS Log Number TMC each ode radomly accesses the shared medum wthout pror chael formato. Most recet work o dversty ad hoc etworks s lmted to multpath dversty [16], [17], [18], [19], [2],.e., usg multple paths to opportustcally forward packets to ehace ed-to-ed relablty. Research o mult-output lk dversty ad mult-put lk dversty s stll ope. The mult-output lk dversty s the output multuser dversty from oe to may (from a ode to multple eghbors). A correspodg case of the mult-output lk dversty ad hoc etworks s the dowlk dversty the cellular etworks. Smlarly, the mult-put lk dversty s the put multuser dversty from may to oe (from multple eghbors to a ode), whch correspods to uplk dversty the cellular etworks. As far as we kow, there s lttle work that provdes realstc study o how to acheve these two types of dversty through MAC protocol desg. Wth the above observatos, we preset a ovel based MAC protocol that explots these two kds of multuser dversty to mprove chael effcecy ad eergy effcecy. The proposed scheme s desged to work effcetly for multhop ad hoc etworks, especally heterogeeous ad hoc etworks ad mesh etworks, where multple odes eed to commucate wth a relatvely powerful ode the dstrbuted maer. Sce opportustc medum access may easly lead to ufaress, we address the faress terms of socal optmalty. The basc dea of our proposed scheme s as follows: Each ode wth a certa umber of lks s eabled to form a cluster ad fucto as the clusterhead to coordate multuser commucatos locally. I each cycle of data trasmsso, the clusterhead tates medum access (wth certa probablty a multcluster scearo to esure tercluster faress), ad the the cluster members (we call them users the followg) dstrbutedly make medum /6/$2. ß 26 IEEE Publshed by the IEEE CS, CASS, ComSoc, IES, & SPS

2 WANG ET AL.: OMAR: UTILIZING MULTIUSER DIVERSITY IN WIRELESS AD HOC NETWORKS 1765 Fg. 1. (a) A llustrato of mult-output lk dversty. (b) A llustrato of mult-put lk dversty. access decsos based o the observed stataeous chael codtos. A CDF-based K-ary opportustc splttg algorthm s used to guaratee that oly the user wth the best ormalzed stataeous chael qualty wll w the chael. After successful collso resoluto, a rate-adaptato techque s employed to acheve the hghest relable data rate for the selected user. I ths way, we facltate the explotato of lk dversty durg the process of collso avodace. I our prevous work [12], [13], we dscussed MAC ehacemet to utlze output lk dversty. The scheme proposed ths paper dffers from our prevous work ts throughput scalg ad socal optmalty. Two papers mostly related to ours are by Q ad Berry [14], [15]. They preseted a chael-aware Aloha protocol ad a bary opportustc splttg algorthm, whch s oe of the frst schemes that address the utlzato of multuser dversty a dstrbuted way. The cotrbuto our paper has the followg features: Frst, we target the IEEE based multhop ad hoc etworks, the desg of whch s much dfferet from that of Aloha-based sgle-hop etworks. Secod, we exted the CDF-based bary opportustc splttg algorthm to the weghted CDF-based K-ray opportustc splttg algorthm so that geeral optmzato goals ca be acheved a more effcet way. Thrd, we propose a dstrbuted tercluster collso resoluto scheme to acheve the systemwde socal optmalty multhop ad hoc etworks. Our desg s le wth the (DCF mode) stadard that our scheme herts smlar mechasms to probe the chael ad avod collsos ad the smlar dea to resolve collsos. Thus, our scheme ca be easly corporated to future stadards. Theoretcal aalyss ad smulato results demostrate that our scheme ca sgfcatly mprove commucato effcecy whle provdg socal faress ad ca sgfcatly crease eergy effcecy ad throughput. The rest of paper s orgazed as follows: I Secto 2, we llustrate our motvato ad detfy the desg challeges. We the preset the framework of our scheme Secto 3 ad the basc CDF-based opportustc medum access scheme Secto 4. The basc scheme s exteded to the weghted CDF-based opportustc medum access scheme Secto 5. I Secto 6, we dscuss the tercluster collso resoluto wth the objectve of socal optmalty. Aalytcal ad smulato results are provded Secto 7. Fally, we coclude the paper Secto 8. 2 MOTIVATION AND DESIGN CHALLENGES 2.1 Motvato The ad hoc etworks we cosder ths paper are qute geeral. It could be a homogeeous ad hoc etwork, a heterogeeous ad hoc etwork, or a wreless mesh etwork. I all these etworks, the chael qualty of a lk s ormally tme-varyg due to such factors as fadg, shadowg, ose, ad terferece. Moreover, dfferet lks usually experece depedet stataeous chael qualtes. Ths pheomeo s wdely referred to as the multuser dversty the lterature [7], [8], [9]. For example, as show Fg. 1a, ode 1 s terfered by ogog trasmsso of ode 5 ad the lk of! 2 suffers deep fadg or shadowg. The lk of! 4 has a stataeous qualty to support basc data rate trasmsso. The lk qualty of! 3 happes to be o-peak. Sce oly oe of these lks s allowed to commucate at a tme, t s better for ode to trasmt data to ode 3 or 4 rather tha ode 1 or 2 at the curret tme. We refer to ths as the mult-output lk dversty. Smlarly, the multput lk dversty ca be observed the example show Fg. 1b. By usg lk dversty va opportustc trasmssos, the Head-of-Le blockg problem [1] ca be allevated ad hgher throughput ca be acheved. 2.2 Localzed Opportustc Trasmsso Ideally, f there s a global scheduler whch kows the systemwde chael formato ad topology wth lttle cost, the effcecy wll be maxmally exploted by cosderg both lk qualty ad space reuse of all actve lks. Ufortuately, global multuser schedulg s mpossble multhop ad hoc etworks, where o cetralzed scheduler s avalable ad complete chael formato ad topology formato are hard to obta. Of course, t s stll terestg to utlze the multuser dversty locally. As show our prevous work [12], [13], multuser dversty ga ca be sgfcatly acheved wthout too may lks partcpato. I fact, eve two lks ca produce substatal dversty ga.

3 1766 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 12, DECEMBER 26 Based o the above observato, we lmt multuser schedulg to a set of lks wth the same sedg ode or the same recevg ode. Therefore, a ode satsfyg certa degree requremets ca locally coordate multuser schedulg amog ts ow put lks or output lks. We defe the set of lks wth the same sedg ode or the same recevg ode as a cluster ad defe the commo sedg ode or recevg ode as the clusterhead ad others as cluster members or users. Sce multple clusters may share the same medum, tercluster coteto resoluto s ecessary. I our protocol, the clusterhead represets the whole cluster to resolve tercluster chael coteto. If a clusterhead successfully captures the chael floor, t mmedately coordates the multuser dversty-based trasmsso wth the cluster for a certa perod. As llustrated Fg. 1, odes -4 form oe cluster ad odes 5-6 form aother cluster. Node coordates the opportustc trasmssos to (from) odes 1-4. Node 5 coordates the trasmsso to ode 6. We wll further detal the cluster formato ad mateace the ext secto. Note ths lk-layer dversty-drve clusterg s much dfferet from the etwork-layer clusterg [21], [22], [23]. The etwork-layer clusterg s desged to mprove routg scalablty ad smplfy etwork maagemet; the dmeso of etwork-layer cluster may be across several hops; the cost to establsh ad mata such etwork clusters s oe of the major desg ssues. The lk-layer clusterg s a logcal orgazato to utlze multuser dversty locally, uder whch each cluster member s drectly assocated wth clusterhead, ad eghborg clusters do ot eed to exchage formato betwee each other. Moreover, t s smple to establsh ad mata a cluster, whch s explaed later. 2.3 Desg Challeges The frst challege s the MAC desg for multuser dversty-based trasmssos wth a cluster. Oe straght approach s that the clusterhead schedules trasmssos based o the chael ad queue formato collected from all users. Although ths approach s feasble cellular etworks where dedcated cotrol chaels (oe for each user) are avalable, the cost of collectg chael ad queue formato ca be forbddely hgh sgle-chael ad hoc etworks, especally whe the umber of users s large. Aother approach s that each user dstrbutedly makes a trasmsso decso based o ts ow stataeous chael qualty (kow to each user by observato) ad past chael qualty dstrbuto. The user wth the hgher ormalzed chael qualty s grated hgher prorty, e.g., wth smaller IFS (terframe space) to access the medum. I our paper, we desg MAC based o the latter approach sce t does ot requre the collecto of chael formato from others so that the overhead ca be sgfcatly reduced. Uder ths dstrbuted approach, the challege wll be how we ca make the user wth the hghest ormalzed chael qualty w the chael a more effcet way. Our objectve utlzg multuser dversty s to mprove the system performace wthout sacrfcg socal faress. We use tracluster faress ad tercluster faress to characterze the faress wth ad across clusters, respectvely. Itracluster problem occurs whe lks a cluster have dfferet chael qualty dstrbutos. Opportustc medum access may easly lead to ufaress whe the chael states of dfferet users are statstcally heterogeeous. For example, the saturated scearo wth two users, the user wth a poor average SNR (sgal-to-ose-plus-terferece-rato) may be severely starved, whle the oe wth a good average SNR may occupy the medum for most of the tme. The tracluster problem becomes more complcated whe lks have dfferet weghts terms of traffc ad utlty. The tercluster faress problem always exsts sce tercluster chael cotetos are ormally locato-depedet ad clusters may carry dfferet weghts terms of aggregate traffc ad utlty. The tercluster faress problem s hard to solve because the traffc/topology/chael formato of a cluster s ormally ukow to aother cluster. I ths paper, we wll address both tracluster ad tercluster faress problem terms of socal optmalty wth ad across clusters. 3 FRAMEWORK OF CLUSTER-BASED MULTIUSER COMMUNICATIONS I ths secto, we frst preset the geeral dea of clusterg ad opportustc medum access. The, we clarfy some assumptos ad otatos to be used the later dscussos. 3.1 Multuser Dversty-Drve Clusterg The geeral dea of cluster formato ad mateace s descrbed as follows: Whe a ode has more tha oe output lk, t wll form a output cluster; each output lk jos the output cluster. Whe a ode has more tha oe put lk that s ot assocated wth a output cluster, t wll form a put cluster; each put lk that s ot assocated wth a output cluster jos the put cluster. Each cluster s desgated a uque Cluster ID to detfy the cluster. The Cluster ID s a tuple comprsed of the MAC address of the clusterhead, the drecto flag (1 dcates put, dcates output), ad a sequece umber. Meawhle, each cluster member s allocated a local user ID for detfcato the cluster. The, the Cluster ID ad the local user ID are set to the cluster member as a global detty. We call ths process the assocato process. After a cluster s created, the clusterhead may perodcally or reactvely check the coectvty of assocated lks. If a lk s dscoected, the clusterhead removes the lk from ts cluster ad returs the local user ID to the user ID pool. We call t the deassocato process. Smlarly, f a ew lk s establshed to be coected wth the clusterhead, the clusterhead wll allocate a ew local user ID from the user ID pool to the ew user ad coduct the assocato process. Depedg o the chage of out-degree at the seder sde ad -degree at the recever sde, a drected lk may leave a put cluster to jo a output cluster, ad vce versa, by followg the same rule as the cluster formato troduced earler ths secto. 3.2 Chael Aware Medum Access Now, we brefly troduce tracluster medum access ad collso resoluto. I each cycle of data trasmsso, the clusterhead tates medum access, whle cluster members

4 WANG ET AL.: OMAR: UTILIZING MULTIUSER DIVERSITY IN WIRELESS AD HOC NETWORKS 1767 Fg. 2. Format of multcast RTS ad RTR frame. dstrbutedly make medum access decsos based o the observed stataeous chael codtos. I the multoutput scearo, the clusterhead s the seder of data traffc, so seder-tated medum access cotrol (SI Mode) s appled. The hadshake before data trasmsso sedertated medum access cotrol cludes a RTS (requestto-sed) ad CTS (clear-to-sed) sequece. We exted the ucast RTS to the multcast RTS ad ehace CTS wth chael awareess capablty so that the hadshake ca probe the chael amog multple users as well as avodg or resolvg collsos wth ad outsde the cluster. I the mult-put scearo, the clusterhead s the recever of data traffc, so the recever-tated medum access cotrol (RI mode) [24], [25] s appled. The hadshake before data trasmsso the recever-tated medum access cotrol cludes RTR (ready-to-receve), RTS, ad CTS sequece. We propose multcast RTR ad chael-aware RTS (followed by CTS) to utlze mult-put lk dversty as well as collso avodace ad resoluto. For the recever-tated medum access, t s better for the clusterhead to kow the traffc formato. We assume the clusterhead kows ths formato ether by servce level agreemet o the flow level or the pggyback the users trasmtted/receved packets o the packet level. Related dscussos ca be foud [24], [25]. Whe the clusterhead has packets backlogged for several users ( the SI mode) or wats to receve packets from oe of the backlogged users ( the RI mode), t wll multcast RTS or RTR wth the cluster ID to the chose caddate users. Fg. 2 shows the formats of the multcast RTS frame ad the multcast RTR frame. To otfy a user of whether t s chose or ot, a array of bts s cluded the RTS or RTR, where s the total umber of cluster members. The th bt the array correspods to the user whose user ID s equal to. If a bt s marked as 1, t meas the correspodg user s chose to compete for data recepto or trasmsso; otherwse, t s ot wth the caddate lst the gve cycle. Whe all the users the cluster are caddates for data recepto or trasmsso, the clusterhead may sed RTS or RTR the maer of groupcast wthout usg the bt array to otfy dvdual users. The groupcast frames are smlar, but wthout the bt markg array. The ose power cluded the RTR frame dcates the ose plus terferece power level at the clusterhead. Recall that, the mult-put scearo, data traffc s trasmtted from users to the clusterhead. It s the receved SNR at the clusterhead that determes the achevable data rate. But, the medum access decsos are made a dstrbuted fasho at the users. So, t s desrable to let the users kow the ose power level at the clusterhead. Assumg that the stataeous chael gas betwee two odes are detcal ether drecto, a caddate user ca derve the chael ga. By the derved chael ga ad formed ose power level at the clusterhead, users ca estmate the receved SNR ad make the approprate medum-access decso. Sce a RTS (RTR) has to be set at the begg of each cycle of data trasmsso for collso avodace ad chael probg ad s ormally set at the basc rate multrate ad hoc etworks, the overhead of the RTS (RTR) s oe of the major factors affectg the chael utlzato rato. Wth the clusterg techque troduced above, the legth of the RTS (RTR) s qute small ad scalable to a very large group (oe addtoal bt wth oe addtoal member). I addto, a large group may be parttoed to several smaller groups so that the scalablty s stll mataed. Ayoe except the caddate recevers who receves the multcast RTS (RTR) should tetatvely keep slet to avod possble collsos before the clusterhead receves the collso-free CTS (RTS). After a qualfed user s selected ad the trasmsso durato s determed ad aouced by CTS, the seder wll clude the durato the subheader of DATA for the fal NAV settg. The subheader s referred to as the reservato subheader (RSH), whch has already bee employed the MAC header of data packets IEEE 82.11e, RBAR [5], ad OAR [6]. RSH s set at the basc rate so that all overhearg odes ca decode. Upo recevg a multcast RTS (RTR), each user checks the bt-markg array. If the correspodg bt s set to 1 ad the observed stataeous SNR s above the threshold dcated the RTS (RTR) message, t s allowed to compete for the chael. For groupcast RTS (RTR), every user eeds to evaluate the chael ad prepare to compete for the chael f the observed chael codto s good eough. If there s oly oe user who has the desred chael codto, the user captures the chael wthout a collso wth the cluster. If there s o qualfed user, the group head defers for a certa tme ad seds a multcast RTS (RTR) aga. I case there s more tha oe qualfed user, collsos may happe. Thus, a collso resoluto scheme s requred to fd a qualfed user. We provde a scheme termed the CDF-based K-ary opportustc splttg algorthm a later secto. Ths scheme ca quckly determe the user wth the best ormalzed chael qualty. We beg wth the basc CDF-based K-ary splttg algorthm to guaratee tmeshare faress amog users ad geeralze t to a weghted CDF-based K-ary opportustc splttg algorthm to optmze local system performace. The geeral dea ad ecessary procedures to utlze mult-put lk dversty are smlar to that of mult-output lk dversty. Thus, we wll focus o the mult-output lk dversty the followg dscusso. 3.3 Some Assumptos ad Notatos I each cycle of coteto resoluto plus data trasmsso, we assume that, oce a user captures the shared

5 1768 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 12, DECEMBER 26 medum, t s allowed to trasmt data up to TXOP. TXOP, a oto troduced IEEE 82.11e, s the trasmsso opportuty wth whch a user ca cosecutvely trasmt data wthout cotedg for the chael. TXOP ca be represeted as the total trasmsso tme T. We assume low moblty throughout ths paper. The chael s modeled as a block fadg chael whch the stataeous chael ga may vary radomly from oe cycle to aother, but s approxmately costat durg each cycle. Suppose the trasmsso power s fxed ad, thus, the recevg power s almost costat durg oe cycle, but may be varable betwee cycles. Smlarly, we assume that the ose plus terferece power does ot chage much durg oe cycle, although t may chage sgfcatly whe a user captures the chael aother cycle. So, the SNR s stable each cycle but may radomly chage from oe cycle to aother. Let h be the stataeous SNR of user, whch s cosdered to be depedet for dfferet users. If the large-scale path loss chages very slowly comparso wth the stataeous chael ga ad ose power, h ca be cosdered ergodc durg a suffcetly log system observato perod. We ote that, the multhop scearo, the terferece may partly deped o whch set of odes are actually trasmttg. I other words, the stataeous terferece each user gets s spatally correlated to some extet, eve though fadg effects make the terferece power radom. However, sce we avod ad resolve multhop tercluster collso based o carrer sesg, the terferece ca be kept low. Our smulato results valdate ths assumpto. Now, we assume h s a radom varable wth the probablty desty fucto f H ðhþ. I practce, each user may kow the dstrbuto of ts ow SNR but ot those of other odes. Smlarly, each user ca determe ts ow stataeous SNR just at the begg of each cycle of data trasmsso, but ot those of other odes. The stataeous chael state ca be measured durg the hadshake of the collso avodace process. The log-term SNR dstrbuto ca be derved va the teratve approach as follows: We deote SNRs requred to support the lowest rate ad the hghest rate (costraed by the physcal layer) as h m ad h max, respectvely, ad quatze the stataeous chael qualty as h m þ j M ð h max h m Þ ð j MÞ, where ðh max h m Þ=M represets the quatzato terval. Defe k as the terato dex ad P j as the PMF (probablty mass fucto) that the quatzed chael qualty equals h m þ j M ð h max h m Þ. P j ca be updated as P kþ1 j ¼ 1 k P k m þ k ; j ¼ m 1 k P k j ; j 6¼ m; where k ð k 1Þ s the step sze to update PMF. We ca choose a approprate step-sze sequece to balace the covergece speed ad smoothess. I our smulato, we set k 1 as mðk; 1;Þ. Rate adaptato s based o the stataeous SNR h evaluated at the begg of each cycle of data trasmsso. Oce the data rate s set, t wll ot be chaged durg the whole data trasmsso perod. Let RðhÞ be the rate at whch a user ca relably trasmt f the stataeous SNR evaluated at the begg of data trasmsso s h. ð1þ 4 OPPORTUNISTIC MEDIUM ACCESS WITH TIMESHARE FAIRNESS (OMAR-B) If chael qualty of each user follows..d dstrbuto, we ca drectly use the SNR value as the crtero for medum access each cycle of data trasmsso. Tmeshare faress s aturally preserved due to the statstcal propertes of the SNR. However, t fals to guaratee tmeshare faress f the SNRs are heterogeeously dstrbuted amog users. Oe smple way to guaratee tmeshare faress whle explotg multuser dversty s to use the ormalzed chael qualty as the threshold for medum access ad as the crtera to determe who wll w the chael access. We map the stataeous SNR of each user,.e., h, to ts ow R complemetary cumulatve probablty p ¼ F H ðh Þ¼ 1 h f H ðhþdh ( the dscrete case, p ¼ F H ðh Þ¼ X M j¼ M ð h h mþ ðhmax h m Þ where P j s PMF troduced above) ad take some pð < p 1Þ as the medum access threshold. I other words, users wth the stataeous SNR hgher tha FH 1 ðpþ are allowed medum access. Clearly, the lower p s, the hgher the chael qualty requred for medum access s, whch lmts the umber of users volved the competto for the chael. Takg F H ðh Þ as a radom varable, we easly fd that F H ðh Þ s..d across users wth the ormalzed uform dstrbuto. Ths meas that each user has the same probablty to access the medum for ay medumaccess threshold p. Furthermore, the polcy that the user wth the lowest stataeous F H ðh Þ ws the chael wll guaratee that each user has the same probablty of capturg the chael. We call ths scheme the basc opportustc medum access cotrol (OMAR-B). Now, the questo s how to desg a dstrbuted collso resoluto algorthm to fd the user wth the best ormalzed stataeous qualty. I the followg, we propose a fast carrer sesg-based splttg algorthm, amely, the K-ary opportustc splttg algorthm, to resolve the collsos amog the qualfed users. The K-ary opportustc splttg algorthm ca be cosdered the exteso of the bary-tree collso resoluto algorthm troduced [15]. 4.1 CDF-Based K-Ary Opportustc Splttg Algorthm After recevg a RTS, user wth chael qualty h > FH 1 ðpþ s allowed to compete for the chael ad trasmt a CTS at the begg of mslot m 1; f there s o trasmsso the prevous m 1; 1 mslots. The detecto of trasmsso of other users s based o carrer sesg wthout the eed to decode the trasmtted packet. The carrer sesg rage s ormally more tha twce the trasmsso rage [26]. Furthermore, CTS (as well as RTS) s appled wth suffcet chael error codg ad set at the basc data rate. So, eve wth fadg, a large carrer sesg rage stll allows users the same cluster to check f the chael s busy or ot. The mslot metoed ths paper s aslott me (2s 82.11b wth DSSS), as defed the stadard. The roud of competto just P j ;

6 WANG ET AL.: OMAR: UTILIZING MULTIUSER DIVERSITY IN WIRELESS AD HOC NETWORKS 1769 Fg. 3. A example of tracluster collso resoluto. followg the RTS s the frst roud of competto. If there are at least two users the above process that sed CTS smultaeously, t goes to the secod roud of competto. The users volved wth collsos ca detect collsos by observg that there s o data trasmsso oe mslot after the CTS. Let m j ð1 m j KÞ deote the umber of mslot at the begg of whch collsos occur the jth roud of competto. User wll partcpate the secod roud of competto f t partcpated the frst-roud competto,.e., had chael qualty better tha FH 1 ð m 1p K Þ. It wll trasmt CTS at the begg of mslot m 2; f there s o trasmsso the prevous m 2; 1 mslots after t detects collsos. I the jthðj 3Þ roud of competto, user volved wth the ðj 1Þth roud of competto,.e., user wth chael qualty better tha FH 1 ð P j 2 k¼1 ðm k 1Þp K k þ mj 1p K j 1 Þ, wll partcpate competto aga ad trasmt a CTS at the begg of mslot m j; f there s o data trasmsso the prevous m j; 1 mslots after t detects collsos, where 8 l >< 2 m j; ¼ >: 6 F H ðh Þ p=k F H ðh Þ Pj 1 m ; j ¼ 1 3 ðm k 1Þ p K k k¼1 p=k j ; j 2: 7 Fg. 3 shows a example of tracluster collso resoluto wth fve users, medum access threshold p ¼ :8, ad K ¼ 4. I the frst roud, those users wth chael qualty betwee ad.2 are expected to trasmt CTS at the tme SIFS after recevg RTS. Those users wth chael qualty betwee.2 ad.4 are expected to trasmt CTS at the tme SIFS þ aslott me after recevg RTS ad so o. Sce o user s wth chael qualty less tha.2, users 1 ad 2 take the opportuty to trasmt CTS at the tme SIFS þ aslott me after recevg RTS. User 3 ad user 4 may trasmt CTS at SIFS þ 2 aslottme ad SIFS þ 3 aslottme, respectvely, after recevg RTS, but observe that the chael s busy ad, thus, they yeld opportuty to user 1 ad user 2. User 5 s ot qualfed ad thus wll ot prepare to trasmt CTS. User 1 ad user 2 detect collso ad eter the secod ð2þ roud of chael coteto. Sce the chael qualty of user 1 falls betwee.2 ad.25, user 1 trasmts CTS at the begg of the frst mslot after detectg collso. User 2 may trasmt CTS at the begg of the secod mslot f t observes that chael stays dle after collso. Sce user 1 has better qualty ad takes the opportuty, user 2 gves up. Now, the clusterhead receves collso-free CTS ad starts DATA trasmsso. Whe two of the best qualty users, say user a ad user b, have very close SNRs, whch meas that jf Ha ðh a Þ F Hb ðh b Þj! ; t may take a large umber of competto rouds to resolve collsos. Wth the lmtato of quatzato SNR dstrbuto, t may be mpossble to tell whch oe s better tha the other. Besdes, t s ot worth fdg the best oe sce ot much SNR ga ca be acheved eve f the best oe s foud. We use the followg algorthm to resolve collsos after certa rouds, say, of competto. I the jthðj Þ roud of competto, user volved wth the ðj 1Þth roud of competto wll radomly select a mslot, say m j;, amog K mslots to trasmt a CTS aga after t detects collsos f there s o trasmsso the prevous m j; 1 mslots the jthðj Þ roud of competto. I practce, the maxmal umber of rouds to resolve collsos should ot be too large; otherwse, the chael codto may chage sgfcatly after a user ws out. We lmt the wdow sze of opportustc collso resoluto,.e., the total resoluto tme, to T c, whch s a system parameter set by the clusterhead accordg to the umber of backlogged users ad chael coherece tme. Fortuately, the average umber of rouds of competto eeded s very small, about Oðlog K ðþþ, where s the umber of qualfed users. Lemma 1 shows the expected tme requred to resolve a collso. Lemma 1. Let EX deote the expected tme requred to resolve a collso wth volved users seder tated medum access by the carrer sese opportustc splttg algorthm wth K dmesoal tree, we have

7 177 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 12, DECEMBER 26 TABLE 1 Parameter Settg ad Fg. 4. Average tme requred to resolve collso. EX T þ log k ðþt crf þ log k ðþþ K T d þ T crs 2 ð3þ P Rðp; ; Þ T ¼1 S B ðp; Þ T o ðp; ; KÞþT wth tme share faress, where ð6þ for ay K 2 ad 1, where T d ¼ aslott me; T ¼ RTS þ SIFS; T crs ¼ CTS þ SIFS; ad T crf ¼ CTS þ aslott me. Proof. See Appedx A. tu Fg. 4 shows the aalytcal boud ad smulato result. The parameter settg for the smulato s show Table 1. The lower boud of the expected tme, deoted by EX Q, requred to resolve a collso by Q ad Berry s algorthm [15], s EX Q T þ log 2 ðþt Q crf þ T crs for ay 1, where T Q crf deotes the roud-trp tme requred for a user to trasmt a small reservato packet ad detect f a collso occurs. T Q crf s o less tha T crf. Sce T crf s ormally tes of aslott me, we may easly fd that the K-ary carrer sesg splttg algorthm reduces a lot of collso-resoluto overhead whe K s larger tha Throughput Scalg Suppose a user trasmts data wth fxed T after successfully capturg the medum. I other words, TXOP s T. For smplcty of aalyss, we also cosder that the packet trasmtted T s pure DATA. The throughput uder the costrats of faress s gve Proposto 1, whch gves the lower boud we ca acheve the saturated case. Proposto 1. Let S B ðp; ; Þ ad S B ðp; Þ deote the achevable throughput of user ad the total achevable throughput, respectvely, wth depedet backlogged users ad the medum access threshold p for the pure output-lk scearo. Uder the basc opportustc medum access cotrol ad the K-ary splttg tree algorthm, we have S B ðp; ; Þ Rðp; ; Þ T T o ðp; ; KÞþT ð4þ ð5þ Rðp; ; Þ ¼ X Z p p k ð1 pþ k k R FH 1 k ðtþ k¼1 p 1 t k 1 dt!! ; p ð7þ T o ðp; ; KÞ ¼ð1 ð1 pþ Þ T þ log k log K þ p 1 ð1 pþ Þþ K 2 RðhÞ s the trasmsso rate whe SNR s h, p 1 ð1 pþ T d þ T crs ; T crf T d ¼ aslottme; T ¼ RTS þ SIFS; T crs ¼ CTS þ SIFS; ad T crf ¼ CTS þ aslott me. Proof. See Appedx B. tu 5 OPTIMAL OPPORTUNISTIC MEDIUM ACCESS WITH GENERAL OPTIMIZATION GOAL (OMAR-E) I the last secto, the opportustc medum access algorthm guaratees each user the same probablty of accessg the chael. I other words, each user gas the same tme fracto f TXOP s T. Now, we cosder a exteded verso (OMAR-E) so that each user ca get a dfferet proporto of servce tme. By adjustg the weght vector, we ca obta the desred rate vector whch optmzes the local system performace. 5.1 Weghted CDF-Based Opportustc Medum Access Let W ¼ fw 1 ;...;w k ;...;w g deote the weght vector, where <w < 1ð8Þ ad P ¼1; w ¼ 1. The geeral CDFbased opportustc medum access polcy s defed as o ¼ arg max ð1 F H ðhþþ ; ð9þ whereby user ca w the chael wth probablty w. ð8þ

8 WANG ET AL.: OMAR: UTILIZING MULTIUSER DIVERSITY IN WIRELESS AD HOC NETWORKS 1771 Proposto 2. The probablty that user s selected for trasmsso, gve that h ¼ h, s Prf ¼ jh ¼ h g ¼ ð1 F H ðhþ Þ ð1 wþ=w ð1þ ad the average probablty that user ca w the chael s w. Proof. Prf ¼ jh ¼ hg o 1=wj ¼ Pr 1 F Hj ðh j Þ ð1 F H ðhþþ 1=w ; 8j 6¼ ¼ Y ð11þ ð1 F H ðhþþ w j=w ð ¼ð1 F H ðhþþ 1 w Þ=w j6¼ ad Prf ¼ g ¼ ¼ Z 1 Z 1 ð1 F H ðhþ Prf ¼ jh ¼ hgf H ðhþdh ð Þ 1 w Þ=w dð1 F H ðhþþ ð12þ ¼ w : tu Here, we dscuss the exteded opportustc splttg algorthm. Now, we set the threshold p to 1, whch meas each user s allowed to compete for the chael regardless of ts stataeous chael codto. Smlarly to the basc K-ary splttg algorthm dscussed Secto 4.1, the frst roud of chael competto, user wll trasmt a CTS at the begg of mslot m 1; f there s o trasmsso the prevous m 1; 1 mslots after recevg RTS. User wll partcpate the jthðj 2Þ roud of competto f t partcpated the last roud of competto ad collded wth others. It wll trasmt a CTS at the begg of mslot m j; f there s o trasmsso the prevous m j; 1 mslots after t detects collsos. The algorthm to calculate m j; s as follows: m j; 8 l ¼ m K 1 ð1 FH ðhþ w >< Þ 1 ; j ¼ 1 K j w >: 1 ð1 F H ðh ÞÞ 1 Pj 1 ðm k 1Þ 1 ; j 2; K k k¼1 ð13þ where s the umber of backlogged users. We ote that, whe each user has equal weght,.e., w ¼ w j ð8 6¼ jþ, the exteded opportustc splttg algorthm s reduced to the basc oe (OMAR-B) gve medum access threshold p ¼ 1. Geerally speakg, the expected tme to resolve collso each cycle of data trasmsso wll deped o the weght vector W. But, t would be a good approxmato f we use the upper boud of EX show (1) to characterze the expected tme to resolve collso by the exteded opportustc splttg algorthm. Let EX þ deote the upper boud of EX. Suppose TXOP s T, the the servce rate of user s gve by T S E ð; ; w Þ¼ EX þ Z þ T T 1 ¼ EX þ þ T Z 1 RðhÞð1 F H ðhþ RðhÞ Prf ¼ jh ¼ hgf H ðhþdh ð Þ 1 w Þ=w f H ðhþdh; where RðhÞ s the trasmsso rate whe SNR s h. Proposto 3. S E ð; ; w Þ s cocave w. Proof. ð14þ S E ð; ; w Þ Z T 1 ¼ EX þ þ T Rh ð Þð1 F H ðhþþ ð1 wþ=w f H ðhþdh Z T 1 ¼ EX þ þ T w Rð1Þ w ð1 F H ðhþþ 1=w R ðhþdh : ð15þ tu Sce oegatve weghted sums ad tegrals preserve cocavty, t s suffcet to show that fðw Þ w a 1=w s cocave w, gve <w 1 ad a 1. Sce f ðw Þ¼ 1 a 1=w w 3 ðlog aþ 2, t completes the proof. 5.2 Determg the Optmal Weght Vector Next, we wat to optmze the system performace by choosg a approprate weght vector. Defe U ðxþ as the utlty fucto of user terms of average servce rate x. Suppose t s strctly creasg, cocave, dfferetable, ad addtve. The optmal weght vector ca be acheved by solvg the optmzato problem NLP : Maxmze s:t: z ¼ X X ¼1 ¼1 U ðs E ð; ; w ÞÞ w 1 ad w ; 8: ð16þ Proposto 4. Optmal weght vector W s the weght vector whch satsfes the K-T codtos of NLP. Proof. As show by Proposto 3, S E ð; ; w Þ s cocave w. We also otce t s odecreasg ad dfferetable. Sce U ðxþ s cocave, dfferetable, ad odecreasg x, U ðs E ð; ; w ÞÞ s also cocave, dfferetable. ad odecreasg w. Thus, z s a cocave fucto the weght vector W. The costrats fucto P ¼1 w s covex ad dfferetable. So, t completes the proof (please refer to [27] for detals). tu It may be dffcult to solve the K-T codto equatos practce. Fortuately, we ca use the well-kow waterfllg techque [28] to fd the optmal solutos ad apply the K-T codtos to valdate the optmalty. 6 CONTENTION RESOLUTION BETWEEN CLUSTERS Wth a cluster, as we propose the prevous sectos, we use opportustc splttg algorthms to resolve collsos

9 1772 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 12, DECEMBER 26 amog qualfed users. To deal wth collsos betwee clusters, the legacy expoetal backoff algorthm used IEEE ca stll be used but may ot provde systemwde faress. I order to optmze systemwde performace, we troduce a persstet-based coteto resoluto algorthm to resolve collso betwee clusters. Ths part of work exteds the work [29]. 6.1 Modelg Global Optmzato The systemwde optmzato problem ca be formulated as follows: Maxmze s:t: Z ¼ X j2a X j X j ¼1 w j 1; 8j 2 A ¼1 X r j 1; 8k 2 A j2a k w j ;r j ; 8; j; U r j S E ð j ;;w j Þ ð17þ where j; k are dces of clusters, A s the set of all clusters, A k s a subset of A whch cludes cluster k plus the clusters who share the chael wth cluster k, r j s the chael allocato rate (.e., tme fracto) for j, j s the umber of assocated users (actve drected lks) cluster j, ad w j s the weght for user cluster j. The optmzato problem ca be easly solved usg a covex optmzato techque smlar to that show Secto 5. However, our goal s to acheve fully dstrbuted chael allocato. Each cluster s supposed to cotrol ts chael allocato rate, whch s adjusted respose to the feedback of coteto wth eghborg clusters. The optmzato fucto of each cluster ca be modeled as follows: Maxmze s:t: Jðr j Þ¼ Xj X j ¼1 ¼1 w j 1 w j ; 8ð; jþ; U r j S E ð j ;;w j Þ ðj Þr j ð18þ where j s the perceved coteto loss probablty betwee cluster j ad ts eghborg clusters. The hgher r j s, the larger j s. Here, ð j Þ s the shadow prce terms of coteto loss probablty. The shadow prce fucto should be strctly creasg ad covex. The above optmzato problem ca also be represeted as Maxmze Jðr j Þ¼ Xj U ¼1 r j S E ð j ;;w j ðr jþþ ð j Þr j ; ð19þ where w j ðr jþ deotes the optmal w j gve a r j. Optmal weght vector Wj s acheved by solvg the followg optmzato problem: Maxmze s:t: z ¼ X j X j ¼1 ¼1 U r j S E ð j ;;w j Þ w j 1 w j ; 8ð; jþ: ð2þ Followg the same proof as [3], we ca show that P j2a Jðr jþ s maxmzed whe each dvdual cluster j maxmzes ts ow objectve fucto Jðr j Þ. Further, as the shadow prce becomes large wth the crease of coteto loss probablty, the fully dstrbuted soluto also coverges to a chael allocato scheme that maxmzes the aggregate utlty over all the clusters. 6.2 Dstrbuted Implemetato I ths secto, we frst propose a stochastc approxmato algorthm rug each clusterhead to teratvely update the chael allocato rate based o the feedback of the tercluster collso probablty. The, we detal the protocol to resolve tercluster collsos a persstet way by updatg the medum access probablty,.e., the chael allocato rate Iteratvely Derve Chael Allocato Rate Note that the cocave objectve fucto Jðr j Þ s maxmzed whe J ðr j Þ¼, X j U ¼1 r j S Eð j ;;w j ðr j ÞÞ j ¼ ; ð21þ where r j s the optmal chael allocato rate of cluster j ad j s the perceved coteto loss probablty whe cluster j ad ts eghborg clusters access the medum wth optmal chael allocato rate. Now, we use a tme-averagg stochastc approxmato algorthm wth feedback to update the chael allocato rate, r kþ1 j ¼ r k j þ k Þr k 1 X j U ¼1 r k j S Eð j ;;w j ðrk j ÞÞ! k j ; r k j ¼ ð 1 k j þ k r k j ( ; k j ¼ ð1 k Þ j k 1 þ k ; collso happes cycle k ð1 k Þ j k 1 ; o collso cycle k; ð22þ where, k, k, ad k are adjustg parameters. Followg the stadard proof [31], we ca show that r k j coverges to r j wth probablty 1. I our study, we take as 16 ad take k, k, ad k as 1 k ; our smulatos show that the covergece speed s quck Implemetato Detals The state dagram of a clusterhead s show Fg. 5. At the tal state, k, r j, ad j are, respectvely, set to 1, 1/6, ad. However, the settg of tal value for r j ad j s qute flexble. Wth r j optmzed teratvely, the statstcal approxmato algorthm guaratees r j coverges to r j wth ay tal state. The optmal weght vector Wj wll be

10 WANG ET AL.: OMAR: UTILIZING MULTIUSER DIVERSITY IN WIRELESS AD HOC NETWORKS 1773 Fg. 6. Chael effcecy wth tme-share faress. Fg. 5. State dagram of clusterhead. derved teratvely by (2) wth updated r j. K-DIFS (K-ary DCF Iter-Frame Space) s equal to ðk þ 1ÞaSlotT me. T c s defed Secto 4.1 ad deotes the wdow sze for tracluster opportustc collso resoluto. 7 PERFORMANCE EVALUATION Three sets of smulatos are preseted ths secto. We frst study the throughput scalg effect ad faress a solated cluster. The, we vestgate effcecy ad faress across several clusters whch are cotedg wth each other. Fally, we cosder the jo effects of the umber of users each cluster ad moblty o the effcecy, faress, ad stablty of our scheme. The parameter settg s show Table 1. The smulato tool we use s s2. We provde two sets of smulatos. The frst set s to exame sgle-cluster performace. The secod set s to vestgate the effcecy ad faress of tercluster collso resoluto. 7.1 Sgle-Cluster We cosder the saturated case a local area ad hoc etwork wth oly oe clusterhead. All the traffc s from the clusterhead to the users. The clusterhead ca mmedately tate a ew cycle of data trasmsso after the prevous oe completes. Wth the same assumpto as the theoretcal aalyss the prevous sectos, we assume that each packet ca be correctly receved oce t s trasmtted at the approprate data rate ad that ACK s ot used. We set the protocol operatos ths way to facltate the comparatve study o the chael effcecy of dfferet schemes. The chael s modeled as Raylegh fadg. Deote h as the stataeous SNR. The, we have f H ðhþ ¼e h=h =h, where h s the average SNR of user. We assume that the lk qualtes at dfferet odes are..d. The achevable data rate of each lk s formulated as a trucated Shao rate,.e., RðhÞ ¼B log 2 ð1 þ mðh; h max ÞÞ, where h max s the upper boud related to T (we set h max as 1 our performace evaluato) Tme-Share Faress We compare our scheme (OMAR-B) wth the roud-rob scheduler ad the deal scheduler. The deal scheduler has full kowledge of the chael formato pror to schedulg so that t ca target the best qualty user wthout overhead. For the aalytcal results, the formula to calculate the throughput of OMAR-B has bee troduced the prevous sectos. The formulae to calculate the throughput of the roud-rob scheduler ad the deal scheduler are smlar to that of OMAR-B ad are omtted here. We frst cosder the case wth homogeeous chael codto. h s equal to 1 for each user. Fg. 6 shows oe set of aalytcal ad smulato results whch the medum access threshold for OMAR-B s.9. The smulato results are qute close to the aalytcal results. The OMAR-B performs much better tha the roud-rob scheduler ad ca scale well wth the umber of backlogged users. The chael effcecy of the OMAR-B ca approach approxmately 9 percet of that for the dea scheduler whe TXOP s T. Whe the medum access thresholds for OMAR-B are set wth dfferet values, the performace s affected. However, the throughput scalg effects ad the relatoshp betwee the theoretcal results ad smulato results are also observed. Next, we cosder heterogeeous chael codtos. Table 2 shows the chael codto ad throughput result of each user. The smulato results match the aalytcal results very well. Almost every user of the OMAR scheme gets twce the throughput of the roud-rob scheme.

11 1774 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 12, DECEMBER 26 TABLE 2 Throughput wth Tme-Share Faress Heterogeeous Case TABLE 3 Case Study of Geeral Optmzato Geeral Optmzato We cosder two cases. I the frst case, the utlty fucto of user equals U ðx Þ¼v logðx Þ, where x s the achevable throughput (bt/s). I the secod case, the utlty fucto of user s equal to U ðx Þ¼v x =1;, where v s the assgg utlty weght. As show Table 3, the hgher the utlty weght v, the hgher the throughput ad the hgher the acheved utlty. I the frst case, eve wth logðþ effects, the aggregate utlty s stll mproved sgfcatly comparso wth the roud-rob scheme. For the secod case, sce the utlty fucto s lear, the aggregate utlty has bee sgfcatly mproved. 7.2 Multcluster wthout Moblty Here, we dscuss the tercluster collso resoluto. Global faress s acheved by dstrbutedly optmzg socal optmalty. Fg. 7 shows the smulated topology. There are three clusters wth fve, oe, ad three drected lk flows, respectvely. Suppose that the traffc o each lk flow s greedy. The utlty fucto of each flow s U ðx Þ¼v logðx Þ, where v s the utlty weght ad x s the throughput (bt/s). I the frst cluster, the clusterhead ode 6 coordates the recever-tated medum access to explot mult-put lk dversty. I cluster 3, ode 7 coordates the seder-tated medum access to explot the mult-output lk dversty. The chael model ad achevable rate fucto are formulated the same as the sgle-cluster case. We use the stochastc approxmato algorthm to dstrbutedly acheve the optmal chael allocato rate for each cluster. The shadow prce terms of perceved collso probablty s gve by ðþ ¼:1. Fg. 8 shows the covergece speed of the tme averaged stochastc Fg. 7. Multcluster topology.

12 WANG ET AL.: OMAR: UTILIZING MULTIUSER DIVERSITY IN WIRELESS AD HOC NETWORKS 1775 the mslot s relatvely short to the TXOP. Thus, the wasted tme for collso resoluto s small. We use throughput ad utlty to evaluate the performace ga comparso wth Show by Table 4, the aggregate utlty ad aggregate throughput have bee mproved by 6 percet ad 54 percet, respectvely. I 82.11, the throughput are equally shared. I OMAR, more tmeshares are gve to the user wth a hgher utlty fucto, thus the aggregate utlty s creased. Furthermore, OMAR explots multuser dversty, so the throughput of each user has bee creased. Fg. 8. Covergece speed of the chael allocato rate wth the stochastc approxmato algorthm. approxmato wth feedback. It takes oly about 2 cycles,.e., 1.5 sec, to reach stablty. We also fd the slope of the shadow prce fucto does ot affect the covergece speed much as log as t s suffcetly large. The chael allocato rate of each cluster decreases (proportoally wth each other) whe the shadow prce creases to a very large value. However, the throughput ad utlty are ot affected much. The reaso s that each clusterhead persstetly accesses medum wth the chael allocato rate mslot by mslot wheever a chael s free. Note that 7.3 Multcluster wth Moblty We cosder a heterogeeous ad hoc etwork wth moblty ths set of study. Fg. 9 presets a abstracto of the smulated heterogeeous ad hoc etwork. Each powerful ode forms a cluster ad fuctos as the clusterhead. Each commo ode assocates wth the earest powerful ode. I the begg, both powerful odes ad commo odes are evely dstrbuted over a 4m 6m area (but each commo ode s away from the earest powerful ode wth 7m). Later o, commo odes move radomly, followg the radom-way pot moblty model wth mmal speed larger tha.1 m/s. Each commo ode estmates ts SNR dstrbuto teratvely by (1). For smplcty, we cosder that all the traffc s from powerful odes to assocated commo odes. The traffc of each lk s saturated. The utlty fucto of each lk s U ðx Þ¼logðx Þ, where x s the throughput (bt/s). Uder ths utlty fucto, each user ca obta equal opportuty to access chael a cluster,.e., tme-share faress wth a cluster ca be acheved by OMAR. For 82.11, we use roud-rob schedulg to TABLE 4 Optmal Itercluster Collso Resoluto Fg. 9. A abstracto of the smulated heterogeeous ad hoc etwork.

13 1776 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 12, DECEMBER 26 Fg. 1. (a) Throughput versus ode desty. (b) Throughput versus ode moblty. (c) Throughput faress. guaratee the tme-share faress amog the output lks. The achevable data rate, terms of the dstace d, ad the fadg factor h, s! 25 4 mðh; h max Þ Rd;h ð Þ ¼ B log 2 1 þ ; ð23þ maxð25;dþ 156 where h follows the Raylegh dstrbuto wth expectato 1 ad h max equal to 1. The smulato tme of each scee s 2,s. The result of each scearo s averaged over 1 smulato results. We frst exame the effect of the ode desty o throughput. We vary the total umber of odes from sx to 6 such that the average umber of users each cluster s from oe to 1. Each commo ode moves at the average speed 1 m/s. As show Fg. 1a, the aggregate throughput ca be sgfcatly mproved by utlzg multuser dversty eve though the umber of users each cluster s small, e.g., two. The performace ga steadly creases as the umber of users crease. Whe the average umber of users each cluster s 1, the throughput by OMAR s about twce that uder The, we exame the effect of the ode moblty o throughput. The average umber of users each cluster s fve. As show Fg. 1b, both OMAR ad crease throughput as the average speed creases. Ths s reasoable. I the begg, we put each ode away from the earest powerful ode wth 7m. Later o, some odes get much closer to the assocated powerful ode eve though some odes get further. But, o matter how far away, each lk a cluster gets a smlar opportuty to access chael. Cosderg the achevable rate fucto, (23), ad the total smulato tme, the aggregate throughput wll crease as the speed creases from.5 m/s to 5 m/s. It s worthy to ote that the performace ga of OMAR over s affected whe speed creases, maly due to creasg clusterg overhead ad chael estmato error. However, the performace ga of OMAR over s stll substatal. OMAR acheves hgher aggregate throughput wthout sacrfce of dvdual faress. Fg. 1c shows the throughput of each user the scee wth 3 commo odes movg at 1 m/s o average. Users are sorted accordg to throughput. Each user by OMAR acheves much hgher throughput tha that uder The reaso that some odes get hgher throughput tha others uder the same scheme s maly because of ther shorter dstaces to assocated powerful odes after they radomly move. 8 CONCLUSION I ths paper, we propose the opportustc medum access ad auto rate protocol (OMAR) to mprove system performace wth the use of multuser dversty. A dversty drve clusterg techque s preseted to coordate multuser commucatos locally. We troduce the CDFbased K-ary opportustc splttg algorthm ad a dstrbuted stochastc schedulg algorthm to resolve tra ad tercluster collsos, respectvely. Faress s mataed, wth respect to socal optmalty, wth ad across clusters. To the best of our kowledge, ths s the frst paper that takes the cross-layer optmzato approach to explot multuser dversty the based ad hoc etworks. Theoretcal aalyss ad smulato results dcate that our scheme ca sgfcatly mprove throughput wthout sacrfce of faress. Other ce features of our proposed protocol are ts smplcty for dstrbuted mplemetato ad ts compatblty wth popular MAC stadard. APPENDIX A PROOF OF LEMMA 1 The proof of Lemma 1 s motvated by [15]. Proof. Whe there s oly oe user, EX 1 ¼ K 1 2 T d þ T crs. For ay 2;K 2, 8 EX ¼ EX ;K EX ; ¼ 1Tcrs þ P 1 j j¼2 j 1 1 j >< EX j þ T crf þ 1 1 ð24þ EX; 1 þ T d ; 2 K >: EX ;1 ¼ EX þ T crf : Let EC be the total umber of rouds to resolve a collso wth volved users, whch EC 1 rouds fal ad the last roud succeeds. Let EI be the total

14 WANG ET AL.: OMAR: UTILIZING MULTIUSER DIVERSITY IN WIRELESS AD HOC NETWORKS 1777 umber of dle mslots spet durg collso resoluto. The, we have EX ¼ðEC 1ÞT crf þ EI T d þ T crs : ð25þ To prove EX log K ðþt crf þ log K ðþþ K 2 Td þ T crs, we oly eed to prove EC log K ðþþ1 ad EI log K ðþþ K 2 whe 1 ad K 2. Frst, we exame EC. Sce EC 1 ¼ 1 ad EC 2 ¼ k k 1, EC log K ðþþ1 holds whe ¼ 1 ad ¼ 2 for ay K 2. Accordg to (24), we have EC ¼ 1 K 1 X K j 1 þ 1 1 K 1 ð EC þ 1Þ þ 1 X 1! ð26þ K 1 X j ðec K þ 1Þ; 1 ¼2.e., K 1 EC ¼ 1 K 1 X X 1 K EC þ 1 ¼2 whe 3 ad K 2. Usg the ducto hypothess, we have K 1 EC 1 K 1 X K Let c ¼ 1 K X K 1 X 1 ¼2 X 1 ¼2 j ¼ j ðlog k ðþþ1þþ1: K K 1 X j 1 : 1 K Usg Jese s equalty, for all 3, we have 1 K 1 X K ¼ c X 1 ¼2 1 K 1 X ck j log k ðþ X 1 ¼2 c log k 1 ck X K 1 ¼ c log k Kc! j log k ðþ X 1 ¼2 K 2! j : Substtutg (28) to (27), t yelds K 1 EC c log k Kc K 2 þ c þ 1 ¼ c log k c K 2 þ 1: We ca show that c log k c K þ 1 2 log k ðþþ1 K 1 ð27þ ð28þ ð29þ ð3þ holds for all K 2, 3. Thus, we get EC log K ðþþ1 as desred. Now, we wll prove EI log K ðþþ K 2. Sce EI 1 ¼ K 2 ad EI 2 ¼ 1 P K 1 KðK 1Þ j2, EI log K ðþþ K 2 holds whe ¼ 1 ad ¼ 2 for ay K 2. Accordg to (25), we have EI K 1 ¼ 1 K 1 X K X 1 ¼2 j EI þ 1 j K X K 1 ð31þ whe 3. Usg the ducto hypothess ad Jese s equalty, we have K 1 EI ¼ 1 K 1 X X 1 K ¼2 1 K 1 X X 1 K ¼2 c log k Kc j EI þ 1 K 1 X j K j log k ðþþ K 2 þ Kc 2 þ 1 K 2 þ 1 j K X K 1 K 1 X K j : ð32þ We ca show that c log k Kc K þ Kc 2 2 þ 1 P K 1 K j log k ðþþ K ð33þ 2 K 1 holds for all K 2, 3. So, EI log K ðþþ K 2 s satsfed as desred. So, EX log K ðþt crf þ log K ðþþ K 2 Td þ T crs satsfes for ay 1;K 2. tu APPENDIX B PROOF OF PROPOSITION 1 Proof. For ay trasformed SNR threshold p, each user has the same probablty of beg qualfed ad the qualfed users have..d SNR dstrbuto wth Y U½;pŠ. The probablty that there are k qualfed users (.e., those satsfyg h >FH 1 ðxþ) amog backlogged users s p k k ð1 pþ k. Let MX k;p mfy ; 1 kg. Its easy to get f MXk;p ðtþ ¼ k p 1 t k 1; p t p. To provde tme-share faress, each wg user s allowed to trasmt data wth durato T. The average achevable rate of user, gve t ws out of caddate users, s show to be Z Rp;; ð Þ ¼ X p p k ð1 pþ k R FH 1 k¼1 ðtþ f MXk;p ðtþdt Z ¼ X p k p k ð1 pþ k R FH 1 k¼1 ðtþ p 1 t k 1 dt!! : p ð34þ

15 1778 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 12, DECEMBER 26 The average cycle durato s T cyc ¼ X p k ð1 pþ k EX k þ T: k¼1 Accordg to Lemma 1, we have T cyc T þ X p k ð1 pþ k k¼1 T þ log k ðkþt crf þ log k ðkþþ K T d þ T crs : 2 Usg Jese s equalty, we have T cyc T þð1 ð1 pþ Þ T þ log k Let þ log k p 1 ð1 pþ p 1 ð1 pþ þ K 2 T o ðp; ; KÞ ¼ð1 ð1 pþ Þ T þ log k þ log k T crf p 1 ð1 pþ p 1 ð1 pþ þ K 2 the T cyc T o ðp; ; KÞþT. Sce we have S B ðp; ; Þ as desred. ACKNOWLEDGMENTS S B ðp; ; Þ ¼ Rðp; ; Þ T T cyc ; Rðp;;ÞT T o ðp;;kþþt T d þ T crs : T crf T d þ T crs ; ð35þ ð36þ ð37þ ð38þ wth tme-share faress tu Ths work was supported part by the US Offce of Naval Research Youg Ivestgator Award N , the US Natoal Scece Foudato uder Faculty Early Career Developmet Award ANI-93241, ad uder grat DBI REFERENCES [1] P. Bhagwat, P. Bhattacharya, A. Krsha, ad S.K. Trpath, Ehacg Throughput over Wreless LANs Usg Chael State Depedet Packet Schedulg, Proc. INFOCOM 96, [2] T.S. Eugee Ng, I. Stoca, ad H. Zhag, Packet Far Queueg Algorthms for Wreless Networks wth Locato-Depedet Errors, Proc. INFOCOM 98, [3] S. Lu, V. Bharghava, ad R. Srkat, Far Schedulg Wreless Packet Networks, IEEE/ACM Tras. Networkg, vol. 7, o. 4, Aug [4] Y. Cao ad V.O.K. L, Schedulg Algorthms Broad-Bad Wreless Networks, Proc. IEEE, vol. 89, o. 1, Ja. 21. [5] G. Hollad, N.H. Vadya, ad P. Bahl, A Rate-Adaptve MAC Protocol for Mult-Hop Wreless Networks, Proc. MobCom 1, 21. [6] B. Sadegh, V. Kaoda, A. Sabharwal, ad E. Kghtly, Opportustc Medum Access for Multrate Ad hoc Networks, Proc. MobCom 2, 22. [7] R. Kopp ad P.A. Humblet, Iformato Capacty ad Power Cotrol Sgle-Cell Multuser Commucatos, Proc. It l Cof. Comm., [8] D. Tse ad S. Haly, Mult-Access Fadg Chaels: Part I: Polymatrod Structure, Optmal Resource Allocato ad Throughput Capactes, IEEE Tras. Iformato Theory, vol. 44, o. 7, pp , Nov [9] P. Beder, P. Black, M. Grob, R. Padova, N. Sdhushayaa, ad A. 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Berry, Opportustc Splttg Algorthms for Wreless Networks, Proc. INFOCOM 4, 24. [16] P. Larsso, Selecto Dversty Forwardg a Multhop Packet Rado Network wth Fadg Chael ad Capture, Moble Computg ad Comm. Rev., vol. 5, o. 4, pp , 21. [17] S. Bswas ad R. Morrs, Opportustc Routg Mult-Hop Wreless Networks, Proc. Secod Workshop Hot Topcs Networks (HotNets II), Nov. 23. [18] R.R. Choudhury ad N.H. Vadya, MAC-Layer Aycastg Wreless Ad Hoc Networks, Proc. Secod Workshop Hot Topcs Networks (HotNets II), Nov. 23. [19] S. Ja, Y. Lv, ad S.R. Das, Explotg Path Dversty the Lk Layer Wreless Ad Hoc Networks, techcal report, WINGS Lab, July 23. [2] J. Wag, H. Zha, W. Lu, ad Y. Fag, Relable ad Effcet Packet Forwardg by Utlzg Path Dversty Wreless Ad Hoc Networks, Proc. IEEE Mltary Comm. Cof. (Mlcom 4), Nov. 24. [21] C.-C. Chag, G. Pe, M. Gerla, ad T.-W. Che, Scalable Routg Strateges for Ad Hoc Wreless Networks, IEEE J. Selected Areas Comm., vol. 17, pp , [22] A.B. McDoald ad T.F. Zat, A Moblty-Based Framework for Adaptve Clusterg Wreless Ad Hoc Networks, IEEE J. Selected Areas Comm., vol. 17, o. 8, Aug [23] T. Hou ad T. Tsa, A Access-Based Clusterg Protocol for Multhop Wreless Ad Hoc Networks, IEEE J. Selected Areas Comm., vol. 19, o. 7, July 21. [24] J.J. Garca-Lua-Aceves ad A. Tzamaloukas, Recever-Itated Collso-Avodace Wreless Networks, ACM Wreless Networks, specal ssue o selected papers from MobCom 99, vol. 8, os. 2/3, pp , 22. [25] Y. Wag ad J.J. Garca-Lua-Aceves, A New Hybrd Chael Access Scheme for Ad Hoc Networks, ACM Baltzer Wreless Networks J., vol. 1, o. 4, July 24. [26] Z. Fu, P. Zerfos, H. Luo, S. Lu, L. Zhag, ad M. Gerla, The Impact of Multhop Wreless Chael o TCP Throughput ad Loss, Proc. IEEE INFOCOM 3, Apr. 23. [27] M. Bazaraa ad C. Shetty, Nolear Programmg: Theory ad Algorthms. Wley, [28] R.G. Gallager, Iformato Theory ad Relable Commucato. Joh Wley ad Sos, [29] T. Nadagopal, T. Km, X. Gao, ad V. Bharghava, Achevg MAC Layer Faress Wreless Packet Networks, Proc. MobCom, 2. [3] S. Kuyur ad R. Srkat, Ed-to-Ed Cogesto Cotrol Schemes: Utlty Futos, Radom Losses ad ECN Marks, Proc. INFOCOM, Mar. 2. [31] H. Kusher ad G. Y, Stochastc Approxmato Algorthms ad Applcatos. Sprger-Verlag, 1997.

16 WANG ET AL.: OMAR: UTILIZING MULTIUSER DIVERSITY IN WIRELESS AD HOC NETWORKS 1779 Jafeg Wag (S 3) receved the BE ad ME degrees electrcal egeerg from the Huazhog Uversty of Scece ad Techology, Wuha, Cha, 1999 ad 22, respectvely. Now, he s workg toward the PhD degree the Departmet of Electrcal ad Computer Egeerg, Uversty of Florda. Hs curret research terests clude wreless MAC, wreless multmeda, IP QoS, seamless moblty, rado resource maagemet, ad system coexstece for 3G/4G cellular etworks, WLANs, WPANs, moble ad hoc etworks, wreless mesh etworks, ad wreless sesor etworks. He s a studet member of the IEEE. Hogqag Zha (S 3) receved the BE ad ME degrees electrcal egeerg from Tsghua Uversty, Bejg, Cha, July 1999 ad Jauary 22, respectvely. He worked as a research ter at Bell Labs Research Cha from Jue 21 to December 21 ad at Mcrosoft Research Asa from Jauary 22 to July 22. Curretly, he s pursug the PhD degree the Departmet of Electrcal ad Computer Egeerg, Uversty of Florda. He s a studet member of IEEE. Yuguag Fag (S 92-M 94-S 96-M 97-SM 99) receved the PhD degree systems ad cotrol egeerg from Case Wester Reserve Uversty Jauary 1994 ad the PhD degree electrcal egeerg from Bosto Uversty May From Jue 1997 to July 1998, he was a vstg assstat professor the Departmet of Electrcal Egeerg at the Uversty of Texas at Dallas. From July 1998 to May 2, he was a assstat professor the Departmet of Electrcal ad Computer Egeerg at the New Jersey Isttute of Techology. I May 2, he joed the Departmet of Electrcal ad Computer Egeerg at the Uversty of Florda, where he receved a early promoto wth teure August 23 ad became a full professor August 25. He has publshed more tha 18 papers refereed professoal jourals ad cofereces. He receved the US Natoal Scece Foudato Faculty Early Career Award 21 ad the US Offce of Naval Research Youg Ivestgator Award 22. He s curretly servg as a edtor for may jourals cludg IEEE Trasactos o Commucatos, IEEE Trasactos o Wreless Commucatos, IEEE Trasactos o Moble Computg, ad ACM Wreless Networks. He s also actvely partcpatg coferece orgazato such as servg as the program vce char for IEEE INFOCOM 5, as the program cochar for the Global Iteret ad Next Geerato Networks Symposum at IEEE Globecom 4, ad as the program vce char for the IEEE Wreless Commucatos ad Networkg Coferece (WCNC ). He s a seor member of the IEEE. Joh M. Shea (S 92-M 99) receved the BS degree (wth hghest hoors) computer egeerg from Clemso Uversty 1993 ad the MS ad PhD degrees electrcal egeerg from Clemso Uversty 1995 ad 1998, respectvely. Dr. Shea s curretly a assocate professor of electrcal ad computer egeerg at the Uversty of Florda. Pror to that, he was a assstat professor at the Uversty of Florda from July 1999 to August 25 ad a postdoctoral research fellow at Clemso Uversty from Jauary 1999 to August He was a research assstat the wreless commucatos program at Clemso Uversty from 1993 to He s curretly egaged research o wreless commucatos wth a emphass o error-cotrol codg, cross-layer protocol desg, cooperatve dversty techques, ad hybrd ARQ. Dr. Shea was selected as a falst for the 24 Eta Kappa Nu Outstadg Youg Electrcal Egeer Award. He receved the Ellersck Award from the IEEE Commucatos Socety He was a US Natoal Scece Foudato fellow from 1994 to He s a assocate edtor for the IEEE Trasactos o Vehcular Techology. He s a seor member of the IEEE. Dapeg Olver Wu (S 98 M 4 SM 6) receved the BE degree electrcal egeerg from the Huazhog Uversty of Scece ad Techology, Wuha, Cha, 199, the ME degree electrcal egeerg from the Bejg Uversty of Posts ad Telecommucatos, Bejg, Cha, 1997, ad the PhD degree electrcal ad computer egeerg from Carege Mello Uversty, Pttsburgh, Pesylvaa, 23. Sce August 23, he has bee wth the Electrcal ad Computer Egeerg Departmet at the Uversty of Florda, Gaesvlle, as a assstat professor. Hs research terests are the areas of etworkg, commucatos, multmeda, sgal processg, ad formato ad etwork securty. He receved the IEEE Crcuts ad Systems for Vdeo Techology (CSVT) Trasactos Best Paper Award for 21. Curretly, he s a assocate edtor for the IEEE Trasactos o Wreless Commucatos, IEEE Trasactos o Crcuts ad Systems for Vdeo Techology, IEEE Trasactos o Vehcular Techology, ad Iteratoal Joural of Ad Hoc ad Ubqutous Computg. He s also a guest-edtor for the IEEE Joural o Selected Areas Commucatos (JSAC) specal ssue o cross-layer optmzed wreless multmeda commucatos. He has served as program char for the IEEE/ACM Frst Iteratoal Workshop o Broadbad Wreless Servces ad Applcatos (Broad- WISE 4) ad as a techcal program commttee member of more tha 3 cofereces. He s vce char of the Moble ad Wreless Multmeda Iterest Group (MobIG), Techcal Commttee o Multmeda Commucatos, IEEE Commucatos Socety. He s a member of the Best Paper Award Commttee, Techcal Commttee o Multmeda Commucatos, IEEE Commucatos Socety. He s a seor member of the IEEE.. For more formato o ths or ay other computg topc, please vst our Dgtal Lbrary at