IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX 21 1 Cross-layer Routng and Dynamc Spectrum Allocaton n Cogntve Rado Ad Hoc Networks Le Dng, Tommaso Meloda, Stella N. Batalama, John D. Matyjas, and Mchael J. Medley Abstract Throughput maxmzaton s one of the man challenges n cogntve rado ad hoc networks, where the avalablty of local spectrum resources may change from tme to tme and hop-by-hop. For ths reason, a cross-layer opportunstc spectrum access and dynamc routng algorthm for cogntve rado networks s proposed, called ROSA (ROutng and Spectrum Allocaton algorthm). Through local control actons, ROSA ams at maxmzng the network throughput by performng jont routng, dynamc spectrum allocaton, schedulng, and transmt power control. Specfcally, the algorthm dynamcally allocates spectrum resources to maxmze the capacty of lnks wthout generatng harmful nterference to other users whle guaranteeng bounded bt error rate (BER) for the recever. In addton, the algorthm ams at maxmzng the weghted sum of dfferental backlogs to stablze the system by gvng prorty to hgher-capacty lnks wth hgh dfferental backlog. The proposed algorthm s dstrbuted, computatonally effcent, and wth bounded BER guarantees. ROSA s shown through numercal model-based evaluaton and dscrete-event packet-level smulatons to outperform baselne solutons leadng to a hgh throughput, low delay, and far bandwdth allocaton. Index Terms Cogntve rado networks, routng, dynamc spectrum allocaton, cross-layer desgn, ad hoc networks. I. INTRODUCTION COGNITIVE 1 rado networks [2] have recently emerged as a promsng technology to mprove the utlzaton effcency of the exstng rado spectrum. In a cogntve rado network, users access the exstng wreless spectrum opportunstcally, wthout nterferng wth exstng users. A key challenge n the desgn of cogntve rado networks s dynamc spectrum allocaton, whch enables wreless devces to opportunstcally access portons of the spectrum as they become avalable. Consequently, technques for dynamc spectrum access have receved sgnfcant attenton n the last few years, e.g., [3] [4] [5] [6] [7]. In addton to ths, n cogntve rado networks wth multhop communcaton requrements (.e., cogntve rado ad Copyrght (c) 21 IEEE. Personal use of ths materal s permtted. However, permsson to use ths materal for any other purposes must be obtaned from the IEEE by sendng a request to pubs-permssons@eee.org. L. Dng, T. Meloda and S. Batalama are wth the Department of Electrcal Engneerng, The State Unversty of New York at Buffalo, Buffalo, NY 1426, USA. e-mal: {ledng,tmeloda,batalama}@buffalo.edu. J. Matyjas and M. Medley are wth the U.S. Ar Force Research Laboratory, RIGF, Rome, NY 13441, USA. e-mal: {john.matyjas,mchael.medley}@rl.af.ml. 1 Ths materal s based upon work supported by the US Ar Force Research Laboratory under Award No Approved for Publc Release; Dstrbuton Unlmted: 88ABW date 3 March 21. A prelmnary shorter verson of ths work [1] appeared n the Proc. of ACM Intl. Conf. on Modelng, Analyss and Smulaton of Wreless and Moble Systems (MSWM) 29. hoc networks), the dynamc nature of the rado spectrum calls for the development of novel spectrum-aware routng algorthms. In fact, spectrum occupancy s locaton-dependent, and therefore n a mult-hop path the avalable spectrum bands may be dfferent at each relay node. Hence, controllng the nteracton between the routng and the spectrum management functonaltes s of fundamental mportance. Whle crosslayer desgn prncples have been extensvely studed by the wreless networkng research communty n the recent past, the avalablty of cogntve and frequency agle devces motvates research on new algorthms and models to study cross-layer nteractons that nvolve spectrum management-related functonaltes. For the reasons above, n ths paper we consder nteractons between spectrum management and dynamc routng functonaltes. Wth ths respect, we propose a dstrbuted algorthm that jontly addresses the routng, dynamc spectrum assgnment, schedulng and power allocaton functonaltes for cogntve rado ad hoc networks. The objectve of the proposed algorthm s to allocate resources effcently, dstrbutvely, and n a cross-layer fashon. We further show how our algorthm can be nterpreted as a dstrbuted soluton to a centralzed cross-layer optmzaton problem. Whle the optmzaton problem s centralzed and hard to solve, our algorthm s practcally and dstrbutvely mplementable. We show how a cross-layer soluton that solves routng and spectrum allocaton jontly at each hop outperforms approaches where routes are selected ndependently of the spectrum assgnment, wth moderate computatonal complexty. Our man contrbutons can be outlned as follows: We derve a dstrbuted and localzed algorthm for jont dynamc routng and spectrum allocaton for mult-hop cogntve rado networks. The proposed algorthm jontly addresses routng and spectrum assgnment wth power control under the so-called physcal nterference model, whch computes the nterference among secondary users usng a SINR-based model. The proposed algorthm consders and leverages the unque characterstcs of cogntve rado ncludng the avalablty of spectrum holes at a partcular geographc locaton and ther possble varablty wth tme; In the proposed algorthm each cogntve rado makes real-tme decsons on spectrum and power allocaton based on locally collected nformaton. Nodes can adjust ther transmsson power to maxmze the lnk capacty on the selected spectrum porton; We ntroduce a noton of spectrum hole that consders nterference from neghborng secondary as well

2 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX 21 2 as prmary users, and leverage t to optmze resource utlzaton at a low computatonal cost; We dscuss a practcal mplementaton of the proposed algorthm that reles on a dual rado wth a common control channel and a frequency-agle data channel; We show how the proposed algorthm can be nterpreted as a dstrbuted and practcal soluton to a cross-layer optmal resource allocaton problem, whose performance s close to the optmum. The remander of ths paper s organzed as follows. In Secton II, we revew related work. In Secton III, we ntroduce the system model. In Secton IV we propose ROSA, our dstrbuted algorthm for jont routng and dynamc spectrum allocaton. Secton V addresses mplementaton detals. In Secton VI we show how ROSA can be nterpreted as a dstrbuted soluton to a centralzed cross-layer network utlty maxmzaton problem for cogntve rado ad hoc networks. Secton VII evaluates the performance of the algorthm. Fnally, Secton VIII concludes the paper. II. RELATED WORK Recent work has nvestgated algorthms and protocols for dynamc spectrum allocaton n cogntve rado networks. Proposed approaches to assgn spectrum can be broadly classfed nto centralzed and dstrbuted schemes. For example, the Dynamc Spectrum Access Protocol (DSAP) [8] s centralzed, and thus requres a central controller to allocate spectrum. In [7], a dstrbuted spectrum assgnment algorthm s proposed, whch ams at solvng the spectrum allocaton problem: whch node should use how wde a spectrum-band at what centerfrequency and for how long. Our work dffers sgnfcantly from [7], whch assumes mutually exclusve transmssons wth zero nterference tolerance. Spectrum band auctons [9][1] have been proposed to allocate wreless spectrum resources, n whch bdders obtan dfferent spectrum channels to mnmze the nterference. In contrast, our proposed soluton jontly consders spectrum allocaton and routng n a cross-layer fashon, snce the avalable spectrum bands may be dfferent at each hop. Some recent work has made ntal steps n the drecton of leveragng nteractons between routng and spectrum allocaton. In [11], each source node fnds canddate paths based on Dynamc Source Routng (DSR) [12] and collects nformaton on lnk connectvty and qualty. For each canddate route, the algorthm fnds all feasble spectrum assgnment combnatons and estmates the end-to-end throughput performance for each combnaton. Based on ths, t selects the route and spectrum assgnment wth maxmal throughput and schedules a conflctfree channel for ths route. In [13], a connectvty-based routng scheme for cogntve rado ad hoc networks s proposed, where the connectvty of dfferent paths s evaluated by takng nto account prmary user actvtes. The authors n [14] propose a layered graph model, where each layer corresponds to a channel, and fnd shortest paths based on the layered graph. Both [11] and [14] are channel-based solutons,.e., the avalable spectrum s dvded nto predefned channels, and devces are assgned opportuntes to transmt on channels on a relatvely long tme scale. However, cogntve rado networks requre spectrum allocaton on a short tme scale snce the avalable spectrum bands wll vary contnuously based on the actvtes of prmary and secondary users. In addton, the algorthms n [11] and [14] are based on the so-called protocol model [15], n whch two lnks ether nterfere destructvely or do not nterfere at all. Although smple, ths model fals to capture the cumulatve effect of nterference. Conversely, our work assumes a rcher nterference model, whch accounts for the fact that advanced transmsson technques, ncludng codedvson multple access (CDMA) [3] [16], allow concurrent co-located communcatons so that a message from node to node j can be correctly receved even f there s a concurrent transmsson close to j. Recent work has started nvestgatng cross-layer optmzatons for cogntve rado networks. In [17], Hou et al. formulate a cross-layer optmzaton problem for a network wth cogntve rados, whose objectve s to mnmze the requred network-wde rado spectrum resource needed to support traffc for a gven set of user sessons. The problem s formulated as a mxed nteger non-lnear problem, and a sequental fxng algorthm s developed where the nteger varables are determned teratvely va a sequence of lnear programs. Sh et al. studed the jont optmzaton of power control, schedulng, and routng for a mult-hop cogntve rado network va a centralzed approach [18] and a dstrbuted approach [19]. In [19] the authors developed a dstrbuted optmzaton algorthm wth the objectve of maxmzng data rates for a set of sessons. The performance of the algorthm s shown to be n average wthn 88% of the performance of the optmal (centralzed) algorthm. III. SYSTEM MODEL We consder a cogntve rado network consstng of M prmary users and N secondary users. Prmary users hold lcenses for specfc spectrum bands, and can only occupy ther assgned porton of the spectrum. Secondary users do not have any lcensed spectrum and opportunstcally send ther data by utlzng dle portons of the prmary spectrum. Let the mult-hop wreless network be modeled by a drected connectvty graph G(V, E), where V = {v 1,..., v N+M } s a fnte set of nodes, wth V = N + M, and (, j) E represent a undrectonal wreless lnk from node v to node v j (referred to also as node and node j, respectvely, for smplcty). Nodes from the subset PU = {v 1,..., v M } are desgnated as prmary users, and nodes from subset SU = {v M+1,..., v M+N } are desgnated as secondary users. We assume that all secondary users are equpped wth cogntve rados that consst of a reconfgurable transcever and a scanner, smlar for example to the KNOWS prototype from Mcrosoft [2]. The transcever can tune to a set of contguous frequency bands [f, f + B], where B represents the maxmum bandwdth of the cogntve rado. We keep the physcal layer model general. However, we assume that multple transmssons can concurrently occur n a frequency band, e.g., wth dfferent spreadng codes. Among others, our physcal layer model could represent orthogonal frequency dvson multplexng (OFDM)-based transmsson, whch s based on a flexble subcarrers pool, and s thus a promsng

3 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX 21 3 canddate technology for cogntve rado networks. Alternatvely, the consdered abstracton could model a mult-channel tme-hoppng mpulse rado ultra wde band system [21]. The avalable spectrum s assumed to be organzed n two separate channels. A common control channel (CCC) s used by all secondary users for spectrum access negotaton, and s assumed to be tme slotted. A data channel (DC) s used for data communcaton. The data channel conssts of a set of dscrete mnbands {f mn, f mn+1,, f max 1, f max }, each of bandwdth w and dentfed by a dscrete ndex. For example, the nterval [f, f + f ] represents the (dscrete) set of mnbands selected by secondary user between f and f + f, wth bandwdth w f. If we let w f B denote the maxmum bandwdth of the cogntve rado, where f B denotes the maxmum number of mnbands, we have f f B representng the constrant of maxmum bandwdth of the cogntve rado. Each backlogged secondary user contends for spectrum access on the control channel f cc, where f cc / [f mn, f max ]. All secondary users exchange local nformaton on the common control channel. Traffc flows are, n general, carred over mult-hop routes. Let the traffc demands consst of a set S = 1, 2,, S, where S = S, of uncast sessons. Each sesson s S s characterzed by a fxed source-destnaton node par. We ndcate the arrval rate of sesson s at node as λ s (t), and wth Λ the vector of arrval rates. Each node mantans a separate queue for each sesson s for whch t s ether a source or an ntermedate relay. At tme slot t, defne Q s (t) as the number of queued packets of sesson s watng for transmsson at secondary user. Defne rj s (t) as the transmsson rate on lnk (, j) for sesson s durng tme slot t, and R as the vector of rates. For SU, the queue s updated as follows: Q s (t+1) = Q s (t) + k SU,k r s k(t) l SU,l rl(t) s + λ s (t) IV. JOINT ROUTING AND DYNAMIC SPECTRUM ALLOCATION In ths secton, we present the dstrbuted jont ROutng and dynamc Spectrum Allocaton (ROSA) algorthm. We start by ntroducng the notons of spectrum hole and spectrum utlty n Sectons IV-A and IV-B, respectvely. Opportuntes to transmt are assgned based on the concept of spectrum utlty, and routes are explored based on the presence of spectrum holes wth the objectve of maxmzng the spectrum utlty. Then, n Secton IV-C we outlne the algorthm for spectrum and power allocaton executed n a dstrbuted fashon at each secondary user. Fnally, we present the core ROSA algorthm n Secton IV-D. A. Spectrum Holes For frequency f, secondary user needs to () satsfy the BER requrement when t transmts to secondary user j, and () avod nterferng wth ongong recevers. Denote SINRP th U and SINRSU th as the SINR thresholds to acheve a target + (1) bt error rate BER P U for prmary users and BER SU for secondary users, respectvely. The frst constrant can be expressed as. P (f) L j (f) G N j (f) + k V,k P k(f)l kj (f) SINRth SU (BER SU ), (2) where G s the processng gan, e.g., length of the spreadng code. P (f) represents the transmt power of on frequency f. L j (f) represents the the transmsson loss from node to j. The expresson k V,k P k(f)l kj (f) represents nterference at node j. Fnally, N j (f) s the recever nose on frequency f. The second constrant models the condton that recever l s not mpared by s transmsson. We can also ndcate nterference at node l V, l j as NI l (f)+ I l (f), where NI l (f) represents nose plus nterference at l before s transmsson, and I l (f) represents the addtonal nterference at l caused by s transmsson,.e., P (f)l l (f). Ths s expressed as (f) NI l (f) + I l (f) SINRth (BER ), l V, l j, (3) P R l where Pl R (f) represents the sgnal power beng receved at recever l. Snce ths has to be true for all ongong transmssons, the constrant can be wrtten as Il max max P (f) mn P (f) (4) l V L l (f) where I max l (f) = { P R l (f) SINR th P U (BER P U ) NI l(f), P R l (f) SINR th l PU, SU (BER SU ) NI l(f), l SU. (5) The constrant n (2) states that the SINR at recever j needs to be above a pre-defned threshold, whch means that the power receved at recever j on frequency f needs be suffcently hgh to allow recever j to successfully decode the sgnal gven ts current nose and nterferences. The constrant n (4) states that the nterference generated by s transmsson on each frequency should not exceed the threshold value that represents the maxmum nterference that can be tolerated by the most vulnerable of s neghbors l V, l j. Hence, s transmt power needs to be bounded on each frequency. The constrant n (2) represents a lower bound and the constrant n (4) represents an upper bound on the transmt power for each frequency. By combng constrants (2) and (4), we can defne for lnk (, j) and frequency f S j (f) = P max (f) P mn (f), (6) where P max (f) s defned n (4) and P mn (f) s the value of P (f) for whch equalty n (2) holds. Let vectors P max = [P max (f mn ), P max (f mn+1 ),, P max (f max )] and P mn = [P mn (f mn ), P mn (f mn+1 ),, P mn (f max )] denote the maxmum and mnmum transmt power constrants for lnk (, j). Hence, we ntroduce the followng defnton. Defnton 1: A spectrum hole for lnk (, j) s a set of contguous mnbands where S j (f). Fgure 1 llustrates the noton of spectrum hole. As shown n the fgure, the spectrum porton [f, f + f ] s a possble spectrum hole for lnk (, j).

4 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX 21 4 Fg. 1. Illustraton of a Spectrum Hole. B. Spectrum Utlty The control channel s assumed to be tme slotted. At each tme slot for whch node s backlogged and not already transmttng, node can evaluate the spectrum utlty for lnk (, j), defned as U j (t) = c j (t) + [Q s (t) Q s j (t)], (7) where s s the sesson wth maxmal dfferental backlog on lnk (, j). The spectrum utlty functon s defned based on the prncple of dynamc back-pressure, frst ntroduced n [22], where the authors showed that a polcy that jontly assgns resources at the physcal/lnk layers and routes to maxmze the weghted sum of dfferental backlogs (wth weghts gven by the achevable data rates on the lnk) s throughput-optmal, n the sense that t s able to keep all network queues fnte for any level of offered traffc that s wthn the network capacty regon. As wll be dscussed n Secton VI, the same result can be derved from a crosslayer network utlty maxmzaton problem, whch can be decomposed nto two subproblems. After the decomposton, the soluton of the routng and schedulng subproblem requres maxmzaton of a weghted sum of dfferental backlogs. Note that, for the sake of smplcty, we wll drop all tme dependences n the followng. Note also that the noton of spectrum utlty s defned for a specfc lnk (, j). In (7), c j (t) represents the achevable capacty for lnk (, j) gven the current spectrum condton, and s defned as [ c j (F, P ) w log P ] (f)l j (f)g, N j (f) + I j (f) f F =[f,f + f ] (8) where I j (f) represents the nterference at j on f. The achevable values of c j depend on the dynamc spectrum allocaton polcy,.e., spectrum selecton vector F = [f, f + f ], and power allocaton vector P = [P (f)], SU, f F. The noton of spectrum utlty can be thought of as a dfferental backlog, nspred by dynamc resource allocaton polces that react to the dfference (Q s Qs j ) of queue backlogs for a gven sesson [23][24], weghted wth dynamc spectrum avalablty nformaton. Routng wth consderaton of dfferental backlog can reduce the probablty of relayng data through a congested relay node. A large queue sze at an ntermedate node s nterpreted as an ndcator that the path gong through that node s congested and should be avoded, whle a small queue sze at an ntermedate node ndcates low congeston on the path gong through that node. Therefore, n ROSA nodes wth a smaller queue sze have a hgher probablty of beng selected as next hop. We let A ndcate actve lnks of secondary users on the data channel,.e., a j = 1 ndcates that lnk (, j) s actve, whle a j = ndcates that the lnk s not actve. Smlarly, we denote A P as the lnk status of prmary users,.e., a P j = 1 ndcates that lnk between prmary users and j s actve (nput to the problem). Thus, at each tme slot the global objectve s to fnd global vectors P = [P 1, P 2,, P N ], F = [F 1, F 2,, F N ], A (and, mplctly, C) that maxmze the sum of spectrum utltes over the actvated lnks, under gven BER and power constrants. Ths s expressed by the problem below. P1 : Gven : BERSU, G(V, E), P Bgt, Q, A P F nd : Maxmze : Subject to : SU P, F, A j SU,j U j a j (9) SINR f kl SINRth P U (BERP U ) a P kl, k, l PU, f F k (1) SINR f j SINRth SU (BERSU ) a j,, j SU, f F (11) P (f) P Bgt, SU, (12) f F f f B, SU. (13) In the problem above, we denote SINR j as the SINR for lnk (, j). Constrant (1) ndcates that prmary user transmssons should not be mpared. Constrant (11) mposes that secondary user transmssons should also satsfy a gven BER performance, whle sharng the spectrum wth other secondary users. In (12), P Bgt represents the nstantaneous power avalable at the cogntve rado. Constrant (13) mposes a lmt on the bandwdth of cogntve rados. In addton, SU (a j + a j ) 1, j SU must hold. Solvng the problem above requres global knowledge of feasble rates, s centralzed and ts complexty s worst-case exponental. Ths provdes the motvaton for our dstrbuted algorthm, whose objectve s to maxmze (9) under the constrants ntroduced by cogntve rado networks n a dstrbuted fashon. In addton, we show how the dstrbuted algorthm can be mplemented n a practcal protocol. C. Spectrum and Power Allocaton In ths secton we present the spectrum and power allocaton algorthm executed n a dstrbuted fashon at each secondary user to maxmze the lnk capacty gven the current spectrum condton. Maxmzng the capacty of lnk (, j) means selectng spectrum F = [f, f + f ] and correspondng transmt power P (f) on each frequency to maxmze the Shannon capacty.

5 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX 21 5 P2 : Gven : (, j), I j, N j, L j, P mn, P max, P Bgt F nd : [f, f + f ], P Maxmze : c j (14) Subject to : P mn (f) P (f) P max (f), f [f, f + f ]; (15) f [f,f + f ] P (f) P Bgt, SU; (16) f f B, SU, (17) where I j = [I j (f mn ), I j (f mn+1 ),, I j (f max )], N j = [N j (f mn ), N j (f mn+1 ),, N j (f max )], and L j = [L j (f mn ), L j (f mn+1 ),, L j (f max )] wth, j SU. The objectve of the problem above s to fnd the spectrum hole wth maxmal capacty, gven spectrum condton and hardware lmtatons of the cogntve rado. Note that constrant (15) mposes the presence of a spectrum hole, and constrants (16) and (17) ndcate the hardware restrctons. For a fxed contguous set of mnbands [f, f + f ], we can obtan a soluton to the problem above by relaxng constrants (15) and (16). Hence, we can express the dual objectve functon as [ g(p, Υ) = w log P ] (f)l j (f)g + N j (f) + I j (f) f [f,f + f ] f [f,f + f ] mn (P [υ f mn +υ Bgt ( where Υ = [υ f mn υf +1 (f) P (f))+υmax(p f (f) P max (f))] f [f,f + f ] mn υf + f mn P (f) P Bgt ), (18) υ f maxυ f+1 max υ f + f max υ Bgt ] (19) s the vector of Lagrange multplers, Υ. Algorthm 1 Spectrum and Power Allocaton. Inputs: (, j), I j, N j, L j, P mn, P max, P Bgt. 1: [f, f ] =, P = 2: for f [, f B ] do 3: m = 1, =, c j = 4: for f [f mn,, f max f ] do 5: whle > th do 6: m = m + 1 7: for f [f,, f + f ] do 8: Assgn P m (f) as n (2) 9: end for 1: Update Lagrange Multplers Υ(m) = [Υ(m 1) ɛ m + ɛ Γ(m)]+ (21) 11: = Υ(m) Υ(m 1) 2 12: end whle 13: Calculate c temp as n (8) 14: f c temp > c j then 15: c j = c temp 16: [f, f, P ] = [f, f, P ] 17: end f 18: end for 19: end for 2: Return soluton as [f, f, P, c j ] A soluton to problem P2 s obtaned as descrbed n Algorthm 1, whch provdes a dual-based teratve soluton to the problem. Specfcally, for a gven spectrum wndow between frequency f and f + f, at each teraton m the algorthm assgns power P m (f) sequentally for each frequency as n (2). Equaton (2) s obtaned by settng dg(p,υ) dp (f) =. Then, Lagrange multplers are updated followng a gradent descent algorthm. In Algorthm 1, th represents a target precson, whle ɛ s a small constant used n the gradent stepsze 1+ɛ m+ɛ. Fnally, Γ(m) represents a sutable gradent at step m,.e., Γ(m) = [(P mn ( P max (f ) P m 1 (f ))...(P mn (f + f ) P m 1 (f + f )) (f ) + P m 1 (f ))...( P max (f + f ) + P m 1 (f + f )) ( P m 1 (f) P Bgt )]. (22) f=[f,f + f ] D. Routng and Dynamc Spectrum Allocaton Algorthm We now present the cross-layer ROutng and dynamc Spectrum Allocaton algorthm (ROSA), whch ams at maxmzng throughput through jont opportunstc routng, dynamc spectrum allocaton and transmt power control, whle performng schedulng n a dstrbuted way. Every backlogged node, once t senses an dle common control channel, performs the followng jont routng and schedulng algorthm: 1) Fnd the set of feasble next hops {n s 1, n s 2,..., n s k } for the backlogged sesson s, whch are neghbors wth postve advance towards the destnaton of s. Node n has postve advance wth respect to ff n s closer to the destnaton than. Calculate c j for each lnk (, j), where j {n s 1, n s 2,..., n s k }, usng Algorthm 1. 2) Schedule s wth next hop j such that (s, j ) = arg max(u s j). (23) Note that Uj s depends on both the capacty and the dfferental backlog of lnk (, j). Hence, routng s performed n such a way that lghtly backlogged queues wth more spectrum resource receve most of the traffc. 3) Once spectrum selecton, power allocaton and next hop have been determned, the probablty of accessng the medum s calculated based on the value of Uj s. Nodes wth hgher Uj s wll get a hgher probablty of accessng the medum and transmt. Note that Uj s defned n (7) s an ncreasng functon of (Q s Qs j ),.e., lnks wth hgher dfferental backlog may have hgher spectrum utlty, thus have hgher probablty of beng scheduled for transmsson. Ths probablty s mplemented by varyng the sze of the contenton wndow at the MAC layer. The transmtter generates a backoff counter BC chosen unformly from the range [, 2 CW 1 ], where CW s the contenton wndow of transmtter, whose value s a decreasng functon Φ() of the optmal spectrum utlty U s j as below CW = α U s j k SU,(k,l) E U s kl + β, α >, β > (24) where k SU,(k,l) E U kl s represents the total spectrum utlty of the competng nodes. Note that sender col-

6 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX 21 6 P m (f) = wl j(f)glog 2 e (N j (f) + I j (f))(υ f,m mn + υf,m max υ Bgt,m ) L j (f)g(υ f,m mn + υf,m max υ Bgt,m ) (2) lects the spectrum utltes of ts neghbors by overhearng the control packets on the common control channel as dscussed n Secton V. Nodes wth smaller values of the backoff counter wll have hgher prorty n allocatng resources for transmsson than nodes wth larger value of the backoff counter. Wth ths mechansm, heavly backlogged queues wth more spectrum resources are gven hgher probablty of transmttng. Algorthm 2 ROSA Algorthm. 1: At backlogged node 2: U =, [f, f ] =, P = 3: for each backlogged sesson s do 4: for j {n s 1, n s 2,..., n s k} do 5: Calculate c j, [f, f ] and P usng Algorthm 1 6: U temp = c j (Q s Q s j) 7: f U temp > U then 8: U = U temp 9: [s, j, Uj s, f, f, P ] = [s, j, U, f, f, P ] 1: a j = 1 11: end f 12: end for 13: end for 14: Set contenton wndow CW = Φ(Uj s ) 15: Generate backoff counter BC [, 2 CW 1 ] 16: Return [s, j, BC, Uj s, f, f, P, a j ] The detals are shown n Algorthm 2. ROSA calculates the next hop opportunstcally dependng on queueng and spectrum dynamcs, accordng to the spectrum utlty functon n (7). Hence, each packet wll potentally follow a dfferent path dependng on queueng and spectrum dynamcs. Hence, packets from the same sesson may follow dfferent paths. At every backlogged node, the next hop s selected wth the objectve of maxmzng the spectrum utlty. The combnaton of next hops leads to a mult-hop path. The mult-hop path dscovery termnates when the destnaton s selected as the next hop. If the destnaton s n the transmsson range of the transmtter (ether a source or an ntermedate relay node for that sesson), the dfferental backlog between the transmtter and the destnaton s no less than the dfferental backlogs between the transmtter and any other nodes, because the queue length of the destnaton s zero. Hence, the destnaton has a hgher probablty of beng selected as next hop than any other neghborng node of the transmtter. Note that the transmtter may stll select a node other than the destnaton as the next hop even f the destnaton s n the transmsson range. Ths can happen, for example, f there s no avalable mnband (low nterference) between the transmtter and destnaton, or f the nterference on all mnbands at that tme s hgh, whch results n low lnk capacty between the transmtter and the destnaton. V. COLLABORATIVE VIRTUAL SENSING IN ROSA As dscussed earler, we assume that each node s equpped wth two transcevers, one of whch s a reconfgurable transcever that can dynamcally adjust ts waveform and Fg. 2. ROSA s Medum Access Control. bandwdth for data transmsson 2. The other s a conventonal transcever employed on the common control channel. Handshakes on the CCC are conducted n parallel wth data transmssons on the data channel. We propose a new scheme called Collaboratve Vrtual Sensng (CVS), whch ams at provdng nodes wth accurate spectrum nformaton based on a combnaton of physcal sensng and of local exchange of nformaton. Scanner-equpped cogntve rados can detect prmary users transmssons by sensng the data channel. In addton, collaboratve vrtual sensng s acheved by combnng scannng results and nformaton from control packets exchanged on the control channel that contan nformaton about transmssons and power used on dfferent mnbands. ROSA s medum access control logc s llustrated n Fg. 2. Smlar to the IEEE two-way RTS (request-to-send) and CTS (clear-to-send) handshake, backlogged nodes contend for spectrum access on the CCC. In partcular, backlogged nodes must frst sense an dle control channel for a tme perod of Dstrbuted Inter-Frame Spacng (DIFS), and then generate a backoff counter. The values of backoff counter are determned under the objectve that nodes wth hgher spectrum utlty should have a hgher channel access probablty. The sender nforms the recever of the selected frequency nterval [f, f + f ] usng an RTS packet. On recevng the RTS packet, the recever responds by usng a CTS packet after the Short Inter-Frame Space (SIFS) and tunes ts transcever for data transmsson on the frequency specfed n the RTS packet. As n [7], an addtonal control packet, DTS (Data Transmsson reservaton), s needed for the transmtter to announce the spectrum reservaton and transmt power to ts neghbors. Here, we modfy the RTS/CTS/DTS packets and nclude channel allocaton nformaton to allow the nodes to make adaptve decsons. The control packets carry address felds of the sender and the recever, the spectrum reservaton 2 Implementatons of ROSA that rely on a sngle transcever are also possble, for example by lettng the reconfgurable transcevers perodcally tune to the common control channel to exchange control nformaton. Ths s the subject of ongong research.

7 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX 21 7 [f, f + f ], reservaton duraton feld (t, t + t), nformaton on queue length Q, and power constrans P max, P mn, all of whch are nput parameters of ROSA. Based on the collected nformaton, each node learns the spectrum envronment and queue length nformaton from ts neghborhood. Each backlogged node performs ROSA to adaptvely select the porton of the spectrum to be used and the next hop. Note that t s the reservaton tme for the data channel, and ncludes the tme needed for transmttng all the remanng data n the scheduled queue Q s /c j, plus the tme needed to ACK packets. By actvely collectng RTS, CTS, and DTS packets transmtted on the CCC, each node learns spectrum and queue nformaton of ts neghborhood. Once RTS/CTS/DTS are successfully exchanged, sender and recever tune ther transcevers to the selected spectrum porton. Before transmttng, they sense the selected spectrum and, f t s dle, the sender begns data transmsson wthout further delay. Note that t s possble that the sender or the recever fnd the selected spectrum busy just before data transmsson. Ths can be caused by the presence of prmary users, or by conflctng reservatons caused by losses of control packets. In ths case, the node gves up the selected spectrum, and goes back to the control channel for further negotaton. Durng the RTS/CTS/DTS exchange, f the sender-selected spectrum can not be entrely used,.e., the recever just sensed prmary user presence, the recever wll not send a CTS. The sender wll go back to the control channel for further negotaton once the watng-for-cts tmer expres and the RTS retransmsson lmt s acheved. When data are successfully receved, an ACK wll be sent by the recever. The transacton s consdered completed after the ACK s successfully receved. VI. INTERPRETATION OF ROSA AS A NUM SOLVER In ths secton, we show how ROSA can be nterpreted as a dstrbuted dual-based soluton to a cross-layer network utlty maxmzaton problem for cogntve rado ad hoc networks under the system model descrbed n the prevous sectons. A jont congeston control, routng, and dynamc spectrum allocaton problem for cogntve rado networks can be formulated as follows. P3 : Gven : BERSU, BER P U, G(V, E), P Bgt, A P F nd : Maxmze : Subject to : λ s + k SU,k r s k = SU l SU,l Λ, R, C s S U (λ s ); (25) r s l, SU, s S (26) rj s c j, SU, j SU \. (27) s S Note that f C s the feasble set of the physcal rates, values of c j Co(C),.e., they are constraned to be wthn the convex hull of the feasble rate regon [24][25]. The feasble set of the physcal rates s expressed by [ c j w log P ] (f)l j (f)g (28) N j (f) + I j (f) f [f,f + f ] SINR f kl SINRth P U (BERP U ) a P kl, k, l PU, f [f k, f k+ fk ] (29) SINR f j SINRth SU (BERSU ),, j SUs.t. rj s, f F s S f [f,f + f ] (3) P (f) P Bgt, SU, (31) f f B, SU. (32) In the problem above, the objectve s to maxmze a sum of utlty functons U (λ s ), whch are assumed to be smooth, ncreasng, concave, and dependent on local rate at node only [26]. Constrant (26) expresses conservaton of flows through the routng varables rj s, whch represent the traffc from sesson s that s beng transported on lnk (, j). Fnally, constrant (27) mposes that the total amount of traffc transported on lnk (, j) s lower than the capacty of the physcal lnk. By takng a dualty approach, the Lagrange dual functon of P3 can be obtaned by relaxng constrant (26) through Lagrange multplers Q = [Q s ], wth SU and s S. { } L(Q) = max (U (λ s ) Q s λ s ) + Λ SU s S + max r s ( j Q s R,C Q s j), (33) SU j SU,j s S where varables ndcatng data rates are stll constraned to be c j Co(C), and C s defned by constrants (28)- (32). In the above decomposton, the frst term of (33) represents the congeston control functonalty (whch can be carred out ndependently), whle the second term represents routng, schedulng, and physcal rate allocaton. Let Λ (Q), R (Q), C (Q) be the vectors of optmum values for a gven set of Lagrange multplers Q. Whle λ s, (Q) can be computed locally at each source of sesson s, R (Q), C (Q) requre global knowledge and centralzed algorthms. To solve the above problem, the followng actons need to be performed at each tme slot t: Update the congeston control varables. For each sesson s and for each source node : λ s (t) = sup {U (λ s ) Q s λ s } (34) λ s Schedulng and Routng. For each lnk (, j), choose the sesson that maxmzes the dfferental backlog between transmtter and recever: s j = arg max s { Q s Q s j} (35) Then, set r s j j (t) = c j(t). Assgn lnk rates c j (t) to maxmze the weghted sum of the lnk rates of the network, where the weghts correspond to dfferental backlogs: C(t) = arg max C SU j SU,j c j ( Q s j ) Q s j j (36) Note that the maxmzaton above s analogous to the

8 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX 21 8 dynamc backpressure algorthm n [24][22]. Update Lagrange multplers (queues) as Q s (t) + ɛ k SU,k Q s (t + 1) = r s k(t) l SU,l rl(t) s + λ s (t) (37) Note that the Lagrange functon s always convex, and thus the multplers can be computed usng a subgradent algorthm. Clearly, the bottleneck of the above soluton les n the routng and schedulng component n (36). Solvng (36) requres global knowledge of feasble rates and centralzed algorthm. It has been shown that the complexty of ths famly of schedule problems s worst-case exponental [22][27]. Exact dstrbuted soluton of (36) s thus nfeasble. However, t can be shown that the closer a polcy gets to maxmzng (36), the closer the polcy gets to the capacty regon of the network [24]. Ths provdes the ratonale for our dstrbuted algorthm, whose objectve s to maxmze (36) under the constrants expressed by (3) and (31), together wth (32) for cogntve rado ad hoc networks. VII. SIMULATION RESULTS To evaluate ROSA, we have developed an object-orented packet-level dscrete-event smulator, whch models n detal all layers of the communcaton protocol stack as descrbed n ths paper. We frst concentrate on evaluatng the network throughput, delay, and farness. Then, we compare the performance of the proposed dstrbuted algorthm and the centralzed algorthm. In all smulaton scenaros, we consdered a common set of parameters. A grd topology of 49 nodes s deployed, n a 6 m x 6 m area. We ntate sessons between randomly selected but dsjont source-destnaton pars. Sessons are CBR sources wth a data rate of 2 Mbt/s each. We set the avalable spectrum to be 54 MHz - 72 MHz, a porton of the TV band that secondary users are allowed to use when there s no lcensed (prmary) user operatng on t. We restrct the bandwdth usable by cogntve rados to be 2, 4 and 6 MHz. The bandwdth of the CCC s 2 MHz. The duraton of a tme slot s set to 2 mcroseconds. Parameters α and β n (24) are set to 1 and 1 respectvely. A Larger CW can reduce the collson rate but may lead to lower utlzaton of the control channel caused by backoff. These values are mplctly optmzed based on the network sze n the paper. The SU SINR threshold s 9 db, and the PU SINR threshold s 19 db n the smulaton. We average over multple trals to obtan a small relatve error (wthn 1% of the average value). The data rate s a stepwse approxmaton of (8), whch can model, among others, dfferent modulaton schemes avalable for dfferent SIN R values. Fg. 3(a) llustrates the network throughput acheved by ROSA wth tme as the number of actve sessons vares. Wth a hgher number of actve sessons, ROSA acheves hgher overall network throughput by adaptvely adjustng bandwdth to enable concurrent parallel transmssons. We compare the performance of ROSA wth two alternatve schemes, both of whch rely on the same knowledge of the + envronment as ROSA. In partcular, we consder Routng wth Fxed Allocaton (RFA) as the soluton where routng s based on dfferental backlog (as n Secton IV) wth pre-defned channel and transmt power, and to Routng wth Dynamc Allocaton (RDA) as the soluton where routng s based on shortest path wth dynamc channel selecton and transmt power allocaton wthout consderng dfferental backlog. We compare aganst the three solutons by varyng the number of sessons njected nto the network and plot the network throughput (sum of ndvdual sesson throughput) n Fg. 4(a), whch shows that ROSA outperforms RFA and RDA. When there are a few actve sessons, e.g., 2 or 4, ROSA, RDA and RFA obtan smlar throughput performance. However, wth more actve sessons, ROSA and RDA perform much better than RFA snce they use the best among possble spectrum allocatons and routes adaptvely. RDA restrcts packets forwardng to the recever that s closest to the destnaton, even f the lnk capacty s very low or the recever s heavly congested. In contrast, ROSA, by consderng both the lnk capacty and the dfferental backlog, s more flexble and may route packets along paths that temporarly take them farther from the destnaton, especally f these paths eventually lead to lnks that have hgher capacty and/or that are not as heavly utlzed by other traffc. The mprovement obtaned by ROSA s more vsble when the number of actve sessons ncreases. Fg. 4(b) shows the delay performance for the three solutons. RFA, on average, delvers a larger delay than the other two solutons. The above delay performance gap grows as the number of sessons ncreases. As shown n Fg. 4(b), ROSA provdes very low and stable delay performance as the number of sessons ncreases. ROSA and RDA yeld almost the same delay performance. Fg. 4(c) shows the mpact of source data rate per sesson on the performance of throughput and delay. We evaluate the throughput and delay performance as the traffc load per sesson ncreases from 1 Kbt/s to 8 Mbt/s. As shown n Fg. 4(c), the throughput acheved by ROSA ncreases lnearly as the load per sesson ncreases. As the load ncreases, ROSA obtans a sgnfcant throughput gan. Fg. 3(b) shows Jan s farness ndex, calculated as ( r s ) 2 /S (r s ) 2, where r s s the throughput of sesson s, and S s the total number of actve sessons. As shown n the fgure, the overall farness among competng sessons s mproved by ROSA usng prortzed channel access scheme. When the sessons are dynamc, the protocol s supposed to be stable snce the algorthm adaptvely adjusts channel selecton and power allocaton accordng to the current transmssons. We compare the performance n terms of network spectrum utlty defned n (9) of P1 between our dstrbuted algorthm and the centralzed algorthm. We consder a cogntve rado network wth 1 nodes. We assume that there are 7 secondary users and 3 prmary users assocated wth 3 dfferent mnbands. Every prmary user holds a lcense for one specfc mnband, and can only occupy ts assgned mnband. We actvate sessons between randomly selected but dsjont source-destnaton pars among the 7 secondary users. Fg. 3(c) shows that even though ROSA uses only local nformaton and has low complexty, the performance

9 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX Throughput vs Tme, Farness ndex RFA RDA ROSA 18 x Performance Comparson Between ROSA and Centralzed Algorthm 118 Centralzed Algorthm ROSA Throughput [Mbt/s] Farness ndex Network Spectrum Utlty actve sessons 4 actve sessons 6 actve sessons 8 actve sessons Tme [s] Number of Actve Sessons Normalzed Traffc Load Fg. 3. (a) (b) (c) (a): Throughput for Dfferent Number of Actve Sessons; (b): Farness Index; (c): Performance Comparson Between ROSA and Centralzed Algorthm 3 Average throughput vs Number of Actve Sessons ROSA RFA RDA 45 4 Average Delay vs Number of Actve Sessons ROSA RFA RDA 35 3 ROSA RFA RDA Impact of the sesson load Average throughput [Mbt/s] Average Delay [s] Average throughput [Mbt/s] Number of Actve Sessons Number of Actve Sessons Load per sesson [Mbt/s] Fg. 4. (a) (b) (c) (a): Throughput vs Number of Actve Sessons; (b): Delay vs Number of Actve Sessons; (c): Impact of Source Data Rate per Sesson on Throughput s wthn 75% of the optmal (centralzed) soluton. However, the centralzed soluton s obtaned wth global nformaton and has exponental computatonal complexty. VIII. CONCLUSIONS We proposed, dscussed and analyzed ROSA, a dstrbuted algorthm for jont opportunstc routng and dynamc spectrum access n mult-hop cogntve rado networks. ROSA was derved by decomposng a cross-layer network utlty maxmzaton problem formulated under the constrants of cogntve rado networks. Through dscrete-event smulaton, ROSA was shown to outperform smpler solutons for nelastc traffc. Future work wll am at dervng a theoretcal lower bound on the performance of ROSA. In addton, we are currently mplementng ROSA on a software defned rado platform based on an open source platform bult on GNU rado and USRP2. REFERENCES [1] L. Dng, T. Meloda, S. Batalama, and M. Medley, ROSA: Dstrbuted Jont Routng and Dynamc Spectrum Allocaton n Cogntve Rado Ad Hoc Networks, n Proc. of ACM Intl. Conf. on Modelng, Analyss and Smulaton of Wreless and Moble Systems (MSWM), Tenerfe, Canary Islands, Span, October 29. [2] J. Mtola, Cogntve Rado Archtecture Evoluton, Proceedngs of the IEEE, pp , Aprl 29. [3] A. Attar, O. Holland, M. Nakha, and A. Aghvam, Interference-lmted Resource Allocaton for Cogntve Rado n Orthogonal Frequency- Dvson Multplexng Networks, IET Communcatons, vol. 2, pp , July 28. [4] L. Cao and H. Zheng, SPARTA: Stable and Effcent Spectrum Access n Next Generaton Dynamc Spectrum Networks, n Proc. of IEEE Intl. Conf. on Computer Communcatons (INFOCOM), Phoenx, AZ, USA, Aprl 28, pp [5] O. Holland, A. Attar, N. Olazreg, N. Sattar, and A. Aghvam, A Unversal Resource Awareness Channel for Cogntve Rado, n Proc. of IEEE PIMRC, Helsnk, Fnland, September 26. [6] K. Lu and Q. Zhao, A Restless Bandt Formulaton of Opportunstc Access: Indexablty and Index Polcy, n Proc. of the 5th IEEE Conf. on Sensor, Mesh and Ad Hoc Communcatons and Networks (SECON) Workshops, Crowne Plaza, CA, USA, June 28. [7] Y. Yuan, P. Bahl, R. Chandra, T. Moscbroda, and Y. Wu, Allocatng dynamc tme-spectrum blocks n cogntve rado networks, n Proc. of ACM Intl. Symp. on Moble Ad Hoc Networkng and Computng (MobHoc), 27. [8] V. Brk, E. Rozner, S. Banerjee, and P. Bahl, DSAP: A Protocol for Coordnated Spectrum Access, n IEEE Intl. Symp on New Fronters n Dynamc Spectrum Access Networks (DySPAN), Baltmore, Maryland, USA, November 25. [9] S. Gandh, C. Buragohan, L. Cao, H. Zheng, and S. Sur, A General Framework for Wreless Spectrum Auctons, n IEEE Intl. Symp on New Fronters n Dynamc Spectrum Access Networks (DySPAN), Dubln, Ireland, Aprl 27. [1] X. Zhou, S. Gand, S. Sur, and H. Zheng, ebay n the Sky: Strategy- Proof Wreless Spectrum Auctons, n Proc. of ACM Intl. Conf. on Moble Computng and Networkng (MobCom), San Francsco, CA, USA, September 28. [11] Q. Wang and H. Zheng, Route and Spectrum Selecton n Dynamc Spectrum Networks, n IEEE Consumer Communcatons and Networkng Conference (CNCC), January 26. [12] D. B. Johnson and D. A. Maltz, Dynamc Source Routng n Ad Hoc Wreless Networks, n Moble Computng, T. Imelnsk and H. Korth, Eds. Kluwer Academc Publshers, 1996, pp [13] A. Abbagnale and F. Cuomo, Gymkhana: A connectvty based routng scheme for cogntve rado ad-hoc networks, n Proc. of IEEE Intl. Conf. on Computer Communcatons (INFOCOM), Work-n-progress sesson, San Dego, CA, USA, March 21. [14] C. Xn, B. Xe, and C.-C. Shen, A novel layered graph model for topology formaton and routng n dynamc spectrum access networks, n IEEE Intl. Symp on New Fronters n Dynamc Spectrum Access Networks (DySPAN), November 25, pp [15] P. Gupta and P. Kumar, The capacty of wreless networks, IEEE Transactons on Informaton Theory, vol. 46, no. 2, pp , March 2. [16] I. N. Psaromlgkos, S. N. Batalama, and M. J. Medley, Rapd Combned Synchronzaton/Demodulaton Structures for DS-CDMA Systems - Part I: Algorthmc developments, IEEE Transactons on Communcatons, vol. 51, pp , June 23. [17] Y. T. Hou, Y. Sh, and H. D. Sheral, Optmal spectrum sharng for

10 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. X, XXXX 21 1 mult-hop software defned rado networks, n Proc. of IEEE Intl. Conf. on Computer Communcatons (INFOCOM), Anchorage, Alaska, USA, May 27. [18] Y. Sh and Y. T. Hou, Optmal power control for mult-hop software defned rado networks, n Proc. of IEEE Intl. Conf. on Computer Communcatons (INFOCOM), Anchorage, Alaska, USA, May 27. [19], A dstrbuted optmzaton algorthm for multhop cogntve rado networks, n Proc. of IEEE Intl. Conf. on Computer Communcatons (INFOCOM), Phoenx, AZ, USA, Aprl 28. [2] Y. Yuan, P. Bahl, R. Chandra, P. A. Chou, J. I. Ferrell, T. Moscbroda, S. Narlanka, and Y. Wu, KNOWS: Kogntv Networkng Over Whte Spaces, n IEEE Intl. Symp on New Fronters n Dynamc Spectrum Access Networks (DySPAN), Dubln, Ireland, Aprl 27. [21] T. Meloda and I. F. Akyldz, Cross-layer Qualty of Servce Support for UWB Wreless Multmeda Sensor Networks, n Proc. of IEEE Intl. Conf. on Computer Communcatons (INFOCOM), Mn-Conference, Phoenx, AZ, USA, Aprl 28. [22] L. Tassulas and A. Ephremdes, Stablty Propertes of Constraned Queueng Systems and Schedulng Polces for Maxmum Throughput n Multhop Rado Networks, IEEE Transactons on Automatc Control, vol. 37, no. 12, pp , January [23] A. Erylmaz and R. Srkant, Jont Congeston Control, Routng, and MAC for Stablty and Farness n Wreless Networks, IEEE Journal on Seclected Areas n Communcatons, vol. 24, no. 8, pp , Aug. 26. [24] L. Georgads, M. J. Neely, and L. Tassulas, Resource Allocaton and Cross-layer Control n Wreless Networks, Found. Trends Netw., vol. 1, no. 1, pp , 26. [25] X. Ln, N. Shroff, and R. Srkant, A tutoral on cross-layer optmzaton n wreless networks, IEEE Journal on Selected Areas n Communcatons, vol. 24, no. 8, pp , Aug. 26. [26] M. Chang, S. Low, A. Calderbank, and J. Doyle, Layerng as Optmzaton Decomposton: A Mathematcal Theory of Network Archtectures, Proceedngs of the IEEE, vol. 95, no. 1, pp , January 27. [27] G. Sharma, N. B. Shroff, and R. R. Mazumdar, On the complexty of schedulng n wreless networks, n Proc. of ACM Intl. Conf. on Moble Computng and Networkng (MobCom), Los Angeles, CA, USA, September 26. Le Dng receved the B.S. degree from Schuan Unversty, Chengdu, Chna, n 23, and the M.S. degree Bejng Insttute of Technology, Bejng, Chna n 26, both n Electrcal Engneerng. From 26 to 27, she was an engneer wth the R&D group of Motorola GTSS (Global Telecom Solutons Sector) Chna Desgn Center, Bejng, Chna. Currently, she s a Ph.D. student under the supervson of Dr. Tommaso Meloda wth the Wreless Networks and Embedded Systems Laboratory, Department of Electrcal Engneerng, State Unversty of New York at Buffalo. She was the recpent of the State Unversty of New York at Buffalo Dean s Scholarshp n 28. Stella N. Batalama (S 91, M 94) receved the Dploma degree n computer engneerng and scence (5-year program) from the Unversty of Patras, Greece n 1989 and the Ph.D. degree n electrcal engneerng from the Unversty of Vrgna, Charlottesvlle, VA, n From 1989 to 199 she was wth the Computer Technology Insttute, Patras, Greece. In 1995 she joned the Department of Electrcal Engneerng, State Unversty of New York at Buffalo, Buffalo, NY, where she s presently a Professor. Snce 29, she s servng as the Assocate Dean for Research of the School of Engneerng and Appled Scences. Durng the summers of she was Vstng Faculty n the U.S. Ar Force Research Laboratory (AFRL), Rome, NY. From Aug. 23 to July 24 she served as the Actng Drector of the AFRL Center for Integrated Transmsson and Explotaton (CITE), Rome NY. Her research nterests nclude small-sample-support adaptve flterng and recever desgn, adaptve multuser detecton, robust spread-spectrum communcatons, supervsed and unsupervsed optmzaton, dstrbuted detecton, sensor networks, covert communcatons and steganography. Dr. Batalama was an assocate edtor for the IEEE Communcatons Letters (2-25) and the IEEE Transactons on Communcatons (22-28). John D. Matyjas receved the A.S. degree n preengneerng from Nagara Unversty n 1996 and the B.S., M.S., and Ph.D. degrees n electrcal engneerng from the State Unversty of New York at Buffalo n 1998, 2, and 24, respectvely. He was a Teachng Assstant ( ) and a Research Assstant ( ) wth the Communcatons and Sgnals Laboratory, Department of Electrcal Engneerng, State Unversty of New York at Buffalo. Currently, he s employed snce 24 by the Ar Force Research Laboratory n Rome, NY, performng R&D n the nformaton connectvty branch. Hs research nterests are n the areas of wreless multple-access communcatons and networkng, statstcal sgnal processng and optmzaton, and neural networks. Addtonally, he serves as an adjunct faculty n the Department of Electrcal Engneerng at the State Unversty of New York Insttute of Technology at Utca/Rome. Dr. Matyjas s the recpent of the 29 Mohawk Valley Engneerng Executve Councl Engneer of the Year Award and the 29 Fred I. Damond Basc Research Award for best techncal paper. He also was the recpent of the State Unversty of New York at Buffalo Presdental Fellowshp and the SUNY Excellence n Teachng Award for Graduate Assstants. He s a member of the IEEE Communcatons, Informaton Theory, Computatonal Intellgence, and Sgnal Processng Socetes; char of the IEEE Mohawk Valley Chapter Sgnal Processng Socety; and a member of the Tau Beta P and Eta Kappa Nu engneerng honor socetes. Tommaso Meloda (M 27) s an Assstant Professor wth the Department of Electrcal Engneerng at the Unversty at Buffalo, The State Unversty of New York (SUNY), where he drects the Wreless Networks and Embedded Systems Laboratory. He receved hs Ph.D. n Electrcal and Computer Engneerng from the Georga Insttute of Technology n 27. He had prevously receved hs Laurea (ntegrated B.S. and M.S.) and Doctorate degrees n Telecommuncatons Engneerng from the Unversty of Rome La Sapenza, Rome, Italy, n 21 and 25, respectvely. He s the recpent of the BWN-Lab Researcher of the Year award for 24. He coauthored a paper that was was recognzed as the Fast Breakng Paper n the feld of Computer Scence for February 29 by Thomson ISI Essental Scence Indcators. He s an Assocate Edtor for the Computer Networks (Elsever) Journal, Transactons on Moble Computng and Applcatons (ICST) and for the Journal of Sensors (Hndaw). He was the techncal co-char of the Ad Hoc and Sensor Networks Symposum for IEEE ICC 29. Hs current research nterests are n modelng and optmzaton of mult-hop wreless networks, cross-layer desgn and optmzaton, cogntve rado networks, multmeda sensor networks, and underwater acoustc networks. Mchael J. Medley (S 91-M 95-SM 2) receved the B.S., M.S. and Ph.D. degrees n electrcal engneerng from Rensselaer Polytechnc Insttute, Troy, NY, n 199, 1991 and 1995, respectvely. Snce 1991, he has been a research engneer for the Unted States Ar Force at the Ar Force Research Laboratory, Rome, NY, where he has been nvolved n communcatons and sgnal processng research related to adaptve nterference suppresson, spread spectrum waveform desgn, covert messagng, and arborne networkng and communcatons lnks. In 22, he joned the State Unversty of New York Insttute of Technology n Utca, NY where he currently serves as an Assocate Professor and Coordnator of the Electrcal Engneerng program.