Throughput Maximization of Ad-hoc Wireless Networks Using Adaptive Cooperative Diversity and Truncated ARQ

Transcription

1 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 11, NOVEMBER Thoughput Maimization of Ad-hoc Wieless Netwoks Using Adaptive Coopeative Divesity and Tuncated ARQ Lin Dai, Membe, IEEE, and Khaled B. Letaief, Fellow, IEEE Abstact We popose a coss-laye design which combines tuncated ARQ at the link laye and coopeative divesity at the physical laye. In this scheme, both the souce node and the elay nodes utilize an othogonal space-time block code fo packet etansmission. In contast to pevious coopeative divesity potocols, hee coopeative divesity is invoked only if the destination node eceives an eoneous packet fom the souce node. In addition, the elay nodes ae not fied and ae selected accoding to the channel conditions using CRC. It will be shown that this combination of adaptive coopeative divesity and tuncated ARQ can geatly impove the system thoughput compaed to the conventional tuncated ARQ scheme and fied coopeative divesity potocols. We futhe maimize the thoughput by optimizing the packet length and modulation level and will show that substantial gains can be achieved by this joint optimization. Since both the packet length and modulation level ae usually discete in pactice, a computationally efficient algoithm is futhe poposed to obtain the discete optimal packet length and modulation level. Inde Tems Coopeative divesity, tuncated ARQ, cosslaye design, adaptive esouce allocation, MIMO, ad-hoc netwoks. I. INTRODUCTION THE use of multiple antennas at both the tansmitte and eceive can bing significant capacity gains [1]. Unfotunately, this could be impactical in an ad-hoc wieless netwok, due to the size of the node o the mobile unit. In ode to ovecome this limitation, a new fom of spatial divesity, wheeby divesity gains ae achieved via the coopeation of nodes, has been poposed. The main idea behind this appoach, which is called coopeative divesity, is to use othogonal elay tansmission to achieve divesity gain. In paticula, each node has one o seveal patnes. The node and its patnes) ae esponsible fo tansmitting not only thei own infomation, but also the infomation of thei patnes). Theefoe, a vitual antenna aay is obtained though the use of the elays antennas without complicated signal design o adding moe Pape appoved by G. S. Kuo, the Edito fo Communication Achitectues of the IEEE Communications Society. Manuscipt eceived Apil 8, 005; evised July 3, 006. This wok is suppoted in pat by the Hong Kong Reseach Gant Council Unde Gant No This pape was pesented in pat at Globecom 005, St. Louis, MO, USA, 005. L. Dai is with the Depatment of Electical Engineeing, City Univesity of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, China lindai@cityu.edu.hk). K. B. Letaief is with the Depatment of Electical and Compute Engineeing, The Hong Kong Univesity of Science and Technology, Clea Wate Bay, Hong Kong, China eekhaled@ee.ust.hk). Digital Object Identifie /TCOMM /08$5.00 c 008 IEEE antennas at the nodes. Sendonais et al poposed the idea of coopeative divesity and applied it into CDMA cellula systems. In [-3], they pesented an infomation-theoetic model, whee two nodes coopeate by tansmitting each bit ove two successive bit intevals. Thei esults showed that node coopeation inceases the sum-ate ove non-coopeative tansmission fo egodic fading links, given that the channel state infomation is available at the tansmitte. Laneman and Wonell futhe etended the above wok [4-5]. They thooughly investigated the pefomance gain of coopeative divesity in egodic and non-egodic scenaios and pesented seveal coopeative potocols, including amplify-and-fowad, decode-and-fowad, selection elaying and space-time-coded coopeation. Besides, Hunte et al intoduced coding RCPC codes [6-7] o tubo codes [8]) into the coopeation. This coded coopeative divesity has been shown to be able to achieve significant pefomance gains ove the amplify-andfowad and decode-and-fowad potocols [7]. Following a diffeent appoach, Stefanov and Ekip designed channel codes that can fully eploit the divesity gains of use coopeation [9]. Othe impotant wok includes coopeative egions analysis fo coded coopeative potocol [10], divesity-multipleing tadeoff analysis on coopeative potocols [11], space-time code design citeia fo amplify-and-fowad elay channels [1], capacity and symbol eo ate analysis [13-14] and coss-laye optimization fo enegy-constained coopeative netwoks [15]. In most of the pesent coopeative potocols, no estictions ae imposed on the selection of elays. Theefoe, when the channel between the souce node and the elay node s channel) is poo, coopeative divesity may esult in even wose pefomance than the non-coopeative case due to sevee eo popagation. In [4], a selection elaying potocol with two nodes coopeation was poposed, whee the elay fowads the souce node s infomation only if the s channel fading coefficient is above a given theshold. In othe wods, the node is selected to be a elay only when its coesponding s channel is good enough. Obviously, such selective potocol can achieve bette pefomance than the fied ones [4]. Howeve, it is usually not tivial to select a suitable theshold since it depends on the actual value of the channel fading coefficients. A highe theshold will educe the possible pefomance gain while a lowe one will allow moe eo popagation which also degades the pefomance. Automatic Repeat Request ARQ) potocol at the link

2 1908 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 11, NOVEMBER 008 laye is an effective means to ovecome the channel fading, whee Cyclic Redundancy Check CRC) is usually used fo eo check and etansmissions ae equested if the packet is eceived eoneously [16-17]. In pactice, the maimum numbe of etansmissions is usually limited so as to minimize the delay and buffe size and such vaiant ARQ is called tuncated ARQ potocol [16]. Despite the impoved eliability, the tuncated ARQ scheme equies moe tansmission time. It will be shown that the thoughput of the tuncated ARQ scheme is eactly the same as that of the diect tansmission. Actually as long as the channel statistics emains unchanged duing the diect tansmission and etansmissions, no thoughput gains can be achieved via ARQ. In this pape, we popose a coss-laye design which combines tuncated ARQ at the data link laye and coopeative divesity at the physical laye. We will show that though this combination, adaptive coopeative divesity gain can be achieved without any specific theshold and eo popagation is theefoe avoided. Besides, the channel quality is significantly impoved in the etansmissions by using elays so that substantial thoughput gains can be obtained. In paticula, in this new scheme, Q idle nodes aound the souce node ae defined as elay candidates. These nodes also eceive the packet tansmitted fom the souce node to the destination node and check the CRC esults. Only the ones who detect the coect CRC ae selected to be elays and involved in the possible etansmission, with both the souce node and the elays utilizing a suitable othogonal space-time block code STBC) to etansmit this packet. It can be seen that this new scheme is adaptive to the s channels by vitue of the CRC bits instead of some specific theshold and so no eo popagation will be incued by elaying. Besides, high efficiency can be achieved since node coopeation is adopted only when the destination node fails to detect the nodes coectly. As a esult, this scheme, which is efeed to as Selective Coopeative divesity with ARQ SCA), can be epected to bing significant pefomance gain ove the pevious ARQonly o fied coopeative divesity schemes. Anothe scheme which combines tuncated ARQ and fied node coopeation is also consideed in this pape. It will be shown that this scheme, which is efeed to as Fied Coopeative divesity with ARQ FCA), equies lowe compleity than SCA, while it may cause some pefomance loss due to eo popagation. Thoughput is defined as the data ate successfully eceived and egaded as a key measue of QoS fo wieless systems [18]. In this pape, we focus on the thoughput at the data link laye whee end-to-end delivey of the packet should be guaanteed. The loss due to etansmissions of the packet is also included hee. The thoughput epessions of SCA and FCA ae deived and compaed to that of the pue tuncated ARQ scheme. It will be shown that when the s channels ae pefect, both SCA and FCA can achieve substantial gains ove the tuncated ARQ scheme thanks to coopeative divesity. Howeve, with poo s channels, the pefomance of FCA will deteioate apidly and even become wose than the tuncated ARQ scheme due to eo popagation. On the othe hand, SCA will always achieve the highest thoughput among all the schemes because of its adaptability to the s channels. Thoughput is usually affected by many design paametes, including symbol ate, modulation level, packet length, the maimum numbe of etansmissions, and powe level. In this pape, we futhe maimize the thoughput by optimizing the packet length L and the modulation level b. Itisshownthat substantial gains can be obtained with the joint optimization of L and b. Besides, it is found that at low SNR we could only optimize the packet length to get an optimal thoughput, wheeas at high SNR, optimizing the modulation level can moe effectively maimize the thoughput. In pactice, the packet length L and the modulation level b should be discete and unde some constaints accoding to the specific tansmission schemes. Ehaustive seach ove the discete optimal L and b will esult in pohibitive compleity. In this pape, we futhe pesent a computationally efficient algoithm, low-compleity discete optimization algoithm L- DOA), by which the discete optimal values of L and b can be found with a athe low compleity. The compaison between the optimal thoughput with continuous optimal L and b and that of discete optimal L and b shows that in most cases, the esulting two thoughput cuves coincide vey well, which implies that the discetization of L and b esults in vey slight thoughput loss. This pape is oganized as follows. The channel model and the details of the poposed SCA and FCA ae povided in Section II. Section III pesents the thoughput compaison of SCA, FCA and the pue tuncated ARQ scheme. The thoughput is futhe maimized by optimizing the packet length L and the modulation level b in Section IV. Section V pesents the optimization pocess ove discete paametes. Finally, Section VI summaizes and concludes this pape. II. COOPERATIVE DIVERSITY WITH TRUNCATED ARQ In this section, we popose a new coss-laye design which combines tuncated ARQ at the link laye and coopeative divesity at the physical laye. A. Scheme Desciption We conside an ad-hoc netwok with K nodes and assume that each node is equipped with only one antenna. Q idle nodes ae assumed to be available as the possible elays fo the souce node duing the packet tansmission. Thoughout this pape, these Q nodes ae efeed to as elay candidates. 1 Paticulaly, the souce node tansmits a data packet with a C-bit CRC attached. The destination node detects CRC and then sends an acknowledgement that is eithe positive ACK) o negative NACK) back to the souce node. At the same time, all the Q elay candidates check the CRC and the ones who get positive esults ae selected to be elays. If the packet is coectly detected by the destination node with ACK feedback), the souce node continues to tansmit a new data packet and the above pocess is epeated. Othewise, etansmission will stat. Both the souce node and the elays will jointly etansmit the packet by utilizing a suitable othogonal STBC. The etansmission continues 1 The assumption that Q idle nodes ae available as elay candidates can be satisfied with a pope multiuse scheduling stategy. Howeve, a detailed study of the issues involved with the specific scheduling stategies is out of the scope of this pape.

3 DAI and LETAIEF: THROUGHPUT MAXIMIZATION OF AD-HOC WIRELESS NETWORKS USING ADAPTIVE COOPERATIVE DIVERSITY 1909 Fig. 1. Destination node sends ACK command Yes Souce node tansmits a new packet Q nodes check CRC. The ones who get the ight CRC become elays. Destination node eceives and checks CRC CRC is coect No Destination node sends NACK command Souce node and elay nodes etansmit the signals using STBC Flow chat of SCA. N N 1 Destination node eceives and checks CRC CRC is coect No N No N 0 N ma Destination node sends ACK command until the packet is successfully deliveed, o the numbe of etansmissions eceeds N ma which is a peset paamete indicating the maimum numbe of etansmissions allowed pe packet. The detailed flow chat of this new scheme is showninfig.1. It can be seen that this new scheme can adapt to the s channels thanks to the use of CRC bits. Only the elay candidates who coectly detect the packet ae selected to be elays. Adaptive coopeative divesity gain is actually achieved and eo popagation can be avoided. Besides, node coopeation is adopted only when the destination node fails to detect the packet coectly. Highe efficiency can theefoe be achieved compaed to the pevious coopeative Yes Yes divesity potocols. As a esult, it can be epected that this poposed SCA scheme can bing significant thoughput gains ove those ARQ-only o fied coopeative divesity schemes. Fo the sake of compaison, FCA, is also poposed in this pape, whee tuncated ARQ is combined with fied node coopeation. In contast to SCA, in FCA the elays ae peassigned and always fied duing the whole tansmission. In the etansmission, the elays send thei estimates instead of the oiginal signals. Theefoe, FCA equies lowe compleity than SCA, while it may cause some pefomance loss due to eo popagation, which will be shown in Section III. In SCA, the numbe of elays v may vay in each packet tansmission. In this pape, the STBC scheme is dependent on the value of v, i.e., we use v +1)-symbol STBC in the etansmission. It should be distinguished fom the space-time block coded potocol poposed in [5], whee a Q+1)-symbol STBC is adopted and fo each coopeative tansmission, v+1) columns ae selected fom the code mati. It can be checked that this space-time block coded potocol can achieve the same divesity gain as ous and the compleity is athe low since each elay candidate also the souce node) is allocated a fied othogonal coding patten egadless of v. Howeve, it may lead to low efficiency. Fo instance, assume that Q =and 1 elay is selected v =1). With the space-time block coded potocol in [5], the ate R is only 3/4. Instead, the Alamouti s scheme can be adopted in ou case so as to achieve the full ate R =1. It should be also noticed that in ou scheme, the elays should send a message to notify both the souce node and the destination node befoe each etansmission. The souce node then assigns the STBC columns to the elays. This node communication will esult in some additional delay and ovehead compaed to the conventional ARQ o pevious coopeative divesity potocols. Howeve, consideing that the tansmission is pefomed in the unit of packet ove one hunded symbols pe packet, fo eample), this ovehead can be neglected since it only equies seveal bits. B. Channel Model The communication between a souce and a destination node is assumed to be ove a flat Rayleigh fading channel and facilitated by v elays which ae selected fom Q elay candidates, as shown in Fig.. In addition, pefect channel knowledge is assumed to be available at the eceive side only, though the use of taining sequences. At time slots t 0 +1,..., t 0 + ς, the souce node sends a packet s t 0+1,...,s t 0+ς with tansmission powe P t pe symbol, whee s t 0+i is an M-QAM modulated symbol and ς = L/b is the numbe of symbols pe packet with a total packet length of L bits and a modulation level of b = log M bits. The signal eceived by the destination node at time slot t 0 + i, i =1,..., ς, is then given by y d t 0+i = h 0 s t 0+i + z 0 1) whee the channel gain h 0 is assumed to be a comple Gaussian andom vaiable with zeo-mean and vaiance σ0. Hee σ0 accounts fo the effect of lage-scale path loss Assume that the [3,4,3] STBC code given in [3] pp. 485, Eqn. 99)) is adopted. Fo a k-symbol-t -slot STBC, the ate R is equal to k/t.

4 1910 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 11, NOVEMBER 008 h sv z sv Relay v h v z v h s1 z s1... Relay 1 h 1 z 1 Souce Node h 0 z 0 Destination Node Fig.. System model. Q idle nodes ae assumed to be available as the elay candidates. and shadowing [5-6]. Also, z 0 epesents the additive white Gaussian noise with zeo-mean and vaiance N 0.Atthej-th elay candidate, j =1,...,Q, the eceived signal is given by y j t = h 0+i sj s t + z 0+i sj ) whee the noise z sj and the fading coefficient h sj ae comple Gaussian andom vaiables with zeo-mean and vaiance N 0 and σs j, espectively, j = 1,..., Q. In the following, the tansmission of the packet s t,..., 0+1 s t 0+ς is efeed to as diect tansmission. If the destination node fails to detect the packet coectly, etansmission will stat at time slot t L +1.LetN be the numbe of etansmissions, 1 N N ma. The eceived signal at the destination node at time slot t L + i is then given by y d t L+i = h 0 s t L+i + z 0 + v j=1 h j j t L+i + z j 3) fo i =1,..., N ς/r,wheer is the ate of STBC. s t and L+i j t L+i ae the space-time block coded symbols tansmitted by the souce node and the j-th elay node with the tansmission powe P t /v +1), espectively. The additive noise z j and the fading coefficient h j ae comple Gaussian andom vaiables with zeo-mean and vaiance N 0 and σ j, espectively, j = 1,..., v. In this pape, it is assumed that the lage scale fading of each d channel the channel between the elay and the destination node) is the same as that of the s d channel the channel between the souce node and the destination node), i.e., σ 1 = = σ v = σ0. 3 Thoughout the pape, the following symbols and notations will be used. γ sd : Aveage SNR pe symbol of the diect tansmission γ s : Aveage SNR pe symbol of the etansmission γss i : Aveage SNR pe symbol of the i-th s channel p pd : Aveage packet eo ate PER) of the diect tansmission p p : Aveage PER of the etansmission 3 The diffeence in the lage-scale fading among the d channels and the s d channel can be easily compensated fo by powe contol, i.e., diffeent tansmission powe levels can be allocated to each elay o the souce node accoding to its coesponding σ j o σ0. Fo simplicity, we assume that the lage scale fading effect is the same and so equal powe allocation is adopted in this pape. p i ps : Aveage PER of the i-th s channel p sd : Aveage symbol eo ate SER) of the diect tansmission p s : Aveage SER of the etansmission p i ss : Aveage SER of the i-th s channel III. THROUGHPUT ANALYSIS In this section, the thoughput of both SCA and FCA is analyzed. Fo the sake of compaison, the thoughput epession of the pue tuncated ARQ scheme is also povided. 4 A. Thoughput of the Tuncated ARQ Scheme Assume that the total length of a data packet is L, whee a C-bit CRC is attached and a squae M-QAM is adopted with b =log M bit/symbol. The symbol ate R s is assumed to be constant and thus omitted in the following. Fo a pointto-point single tansmission, the thoughput is then given by [18] T = L C L b1 p sd) L/b 4) whee p sd is the SER of the diect tansmission. With tuncated ARQ, etansmission will stat if the packet is detected eoneously and will continue until the packet is successfully deliveed o the numbe of etansmissions N eceeds N ma. In the etansmission, the data ate will be educed since the packet is epeated. Theefoe, the thoughput of the tuncated ARQ scheme can be obtained as whee T ARQ = L C L b P A/ N A 5) P A =1 p pd p p ) N ma 6) 4 In this section, we adopt a athe abstact system model. Fo eample, we only conside uncoded M-QAM and the additional ovehead in ARQ signaling such as ACK and NACK) is neglected. Nevetheless, the mathematical famewok is geneal and the thoughput analysis can be easily etended to the specific systems.

5 DAI and LETAIEF: THROUGHPUT MAXIMIZATION OF AD-HOC WIRELESS NETWORKS USING ADAPTIVE COOPERATIVE DIVERSITY 1911 is the packet successful ate. NA is the aveage numbe of tansmissions pe packet, which is given by N ma N A =1 1 p pd )+ i p pd p p ) i 1 p p ) +N ma +1) i= p pd p p ) N ma In 7), p pd and p p ae given by 1 1 p p )+p pd p p ) N ma p pd =1 1 p sd ) L/b andp p =1 1 p s ) L/b. 8) The channel statistics does not change in the etansmissions. Theefoe, the aveage SER of the etansmission p s should be equal to p sd. As a esult, we have p p = p pd and 5) can then be simplified as T ARQ = L C L b 1 p pd). 9) Fom 9) and 4), it can be seen that the tuncated ARQ scheme has eactly the same thoughput as the diect tansmission. Despite the impoved eliability fo each packet, the tuncated ARQ scheme equies moe tansmission time. As long as the channel statistics keeps constant in the etansmissions, no thoughput gain can be achieved. Nevetheless, we will show that by combining the tuncated ARQ scheme and coopeative divesity, the SER of the etansmission will be impoved geatly so that significant thoughput gains can be obtained. In this pape, it is assumed that the s d channel is a flat Rayleigh fading channel. As such, the closed-fom epession fo the aveage SER of M-QAM is given by [19] Eqn. 49), pp. 1331) p sd = 1 1 b 1 1 b ) ) 1 [ 4 π ) gγsd + 1+gγ sd 1+gγsd gγsd 1+gγ sd actan gγ sd ) 7) ) ] 1, 10) whee g = 3 b 1). γ sd is the aveage SNR pe symbol of the diect tansmission, which is given by γ sd = σ 0P t /N 0. Theefoe, by substituting 10) into 8) and 9), the thoughput of the pue tuncated ARQ scheme, T ARQ, can be computed. B. Thoughput of FCA In FCA, v pe-assigned elays and the souce node ae used in the etansmission and both utilize a v +1)-symbol othogonal STBC to send the packet togethe. Theefoe, the thoughput of FCA can be obtained as T FCA = L C L b P F / N F 11) whee P F is the packet successful ate which can be computed by 6). NF is the aveage numbe of tansmissions pe packet, which is given by N F =1 1 p pd )+p pd [ N ] ma i= 1 + i 1)/R) p p ) i 1 p p ) +1+N ma /R) p p ) N 1) ma 1 whee R is the ate of STBC fo a k-symbol-t -slot STBC, R = k T ). In this case, the aveage SER of the etansmission p s p sd since multiple antenna tansmission is adopted in the etansmission. In FCA, the etansmission can be egaded as v +1)-tansmit-1-eceive STBC with M-QAM symbols ove Rayleigh fading channels. Fom [0], we know that the aveage SER of m-tansmit-n-eceive STBC with M-QAM in Rayleigh fading channels is given by p s = qφ g) Γmn +1/) π Γmn +1) { F 1 mn; 1 } ; mn +1; 1 1+gγ { s q φ g) π mn +1 F 1 1,mn,1; mn + 3 ; 1+gγ s, 1 }, 1+gγ s 13) whee γ s is the aveage SNR pe symbol, q =1 1/ b, φ s) 1 + sγ s ) mn, and F 1 a, b; c; ) is the Gauss hypegeometic function defined as F 1 a, b; c; ) n=0 a) n b) n n. 14) c) n n! In the above equation, a) n = Γa + n)/γa) with Γ ) denoting the Gamma function. Likewise, F 1 a, b, b ; c;, y) is the Appell hypegeometic function defined as a) F 1 a, b, b n+k b) n b ) k ; c;, y) n y k. 15) c) n+k n!k! n=0 k=0 Theefoe, p s can be obtained by substituting m = v +1, n =1,andγ s = γ s into 13). The computation of γ s should include the effect of eo popagation since in FCA the elay nodes etansmit thei estimates instead of the oiginal signals. As a esult, γ s will γ not be given by sd v+1)r. Instead, the epession of γ s of FCA is given in Theoem 1. Theoem 1: The aveage SNR pe symbol of the etansmission in FCA, γ s, is given by γ sd γ s = aγ sd +v +1)R whee a = 4v b 1 1 b/ ) ) 1 gγss 1+gγ ss +1 b/ ) ) ) gγss π 1+gγ ss actan 1+gγss gγ ss 1 16), 17) assuming that the aveage SNR pe symbol of the i-th s channel γ i ss = γ ss = σ s P t/n 0 fo i =1,..., v. Poof: See the Appendi. By combining Theoem 1 and 11-1), the thoughput of FCA, T FCA, can be obtained. C. Thoughput of SCA In SCA, the numbe of elay nodes v is not fied. Only the candidates who detect the coect CRC esults ae involved

6 191 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 11, NOVEMBER 008 in the etansmission. Theefoe, the thoughput epession of SCA should be witten as T SCA = L C L b P S/ N S 18) whee P S and N S ae the packet successful ate and the aveage numbe of tansmissions pe packet, espectively. They ae given by and P S = Q j=0 ) 1 p pd p p j)) N ma P v = j) 19) N S = Q Nj) P v = j) 0) j=0 with Nj) given by Nj) =1 p pd + p pd [ N ] ma i= 1 + i 1)/Rj)) p p j) i 1 p p j)) +1+N ma /Rj)) p p j) N ma 1 1) fo j =0,...,Q. In 1), Rj) is the ate of a j +1)-symbol STBC let R0) = 1) andp p j) is the PER of the j-elay etansmission. 5 In SCA, no eo popagation is intoduced by elays. Theefoe, with a j-elay etansmission j >0), p s j) can be obtained via 13) by substituting m = j +1, n = 1, γ and γ s = γ s j) = sd j+1)rj).othewise,p sj) =p sd fo j =0). P v = j) is the pobability that j elay candidates detect the coect CRC esults and is given by P v =0)=p 1 ps p ps pq ps ) P v =1)=1 p 1 ps ) p ps p Q ps + p1 ps 1 p ps ) p Q ps + + p1 ps p ps 1 p Q ps ) 3).. whee p i ps is the PER of the i-th s channel, i =1,..., Q, and we have p i ps =1 1 p i ss ) L/b. p i ss is the SER of the i-th s channel and can be computed by p i ss = 1 1 ) ) gγ i ss 1 b 1+gγss i b [ ) ] 4 gγss i 1+gγss i π 1+gγss i actan gγss i 1 4) 3 whee g = b 1) and γi ss is the aveage SNR pe symbol of the i-th s channel which is given by γss i = σs i P t /N 0, i =1,...,Q. 5 Note that p pj) is now indeed by j since in SCA the PER of the etansmission is dependent on the numbe of nodes involved in the etansmission. ) When σs i = σs, i =1,..., Q, a geneal epession of P v = j) can be obtained as P v = j) =C j Q 1 pps ) j pps ) Q j 5) whee p ps = p i ps,foalli =1,..., Q, andj =0,..., Q. Finally, by combining 18-5), the thoughput of SCA, T SCA, can be obtained. D. Thoughput Compaison Assume that Q =idle nodes ae available as the elay candidates. C =16bit CRC is assumed to be adopted with a cyclic geneato polynomial of g CRC16 D) =D 16 + D 1 + D Assume that the packet length L is 10 bits and QPSK is adopted i.e., b =bits). The maimum numbe of etansmissions N ma is assumed to be 3. Fo simplicity, σs i isassumedtobeequaltoσs,foi =1,...,Q. Theefoe, we have γ ss = γss, i i =1,...,Q. Fig. 3 pesents the numeical and simulation esults on the thoughput of the pue tuncated ARQ, FCA with 1 elay, FCA with elays and SCA when the aveage SNR pe symbol of the s channels γ ss is 0dB. The -ais SNR is efeed to the aveage SNR pe symbol of the diect tansmission γ sd. A good match can be obseved between the simulation and numeical cuves, despite slight discepancy in the case of FCA. Fom Fig. 3 it can be also seen that both FCA and SCA pefom much bette than the tuncated ARQ scheme. Hee γ ss is assumed to be 0dB, which indicates athe good s channels. In this case, coopeative divesity gain can be fully eploited to impove the SER of the etansmission and so substantial thoughput gains can be epected to be achieved by SCA and FCA ove the tuncated ARQ scheme. As Fig. 3 shows, SCA always achieves the highest thoughput, which is due to its adaptability to the s channels. It should be noticed that at high SNR, FCA with 1 elay gets bette pefomance than the elay case. This is because with 3 nodes coopeation, the STBC is not full ate. 6 When the SNR of the s d channel also the d channels) is high enough which implies a good divesity gain), ate loss will significantly influence the thoughput. Theefoe, although in the low SNR egime FCA with elays can achieve a bette thoughput, this thoughput will become less than that of the 1 elay case when SNR is high enough. Fig. 4 shows the case when γ ss deceases to 15dB. Hee the s channels ae not good enough and theefoe the pefomance of FCA deteioates apidly due to the effect of eo popagation. When SNR is high which indicates a good s d channel, FCA even gets a wose thoughput than the tuncated ARQ scheme. In contast, SCA still achieves the highest thoughput among all the schemes and a significant gain can be obseved. We futhe conside the case of γ ss = 10 db, which indicates even wose s channels. In this case, FCA cannot wok since coopeative divesity gain is ovewhelmed by the effect of sevee eo popagation. Its SER of etansmission is always wose than that of the tuncated ARQ scheme. Theefoe, as Fig. 5 shows, the thoughput of FCA is much 6 In this pape, we take the [3,4,3] STBC code given in [3] pp. 485, Eqn. 99)). Theefoe, the ate R is 3/4.

7 DAI and LETAIEF: THROUGHPUT MAXIMIZATION OF AD-HOC WIRELESS NETWORKS USING ADAPTIVE COOPERATIVE DIVERSITY Thoughput bit/s/hz) Tuncated ARQ scheme, Numeical Tuncated ARQ scheme, Simulation FCA with 1 elay, Numeical FCA with 1 elay, Simulation FCA with elays, Numeical FCA with elays, Simulation SCA, Numeical SCA, Simulation Thoughput bit/s/hz) SNR db) Fig. 3. Thoughput of the tuncated ARQ scheme, FCA with 1 elay, FCA with elays and SCA when γ ss =0dB with L =10and b =. Fig. 5. Thoughput of the tuncated ARQ scheme, FCA with 1 elay, FCA with elays and SCA with Gaussian s channels and Rayleigh s channels when γ ss =10dB with L = 10 and b =. Thoughput bit/s/hz) Fig. 4. Thoughput of the tuncated ARQ scheme, FCA with 1 elay, FCA with elays and SCA when γ ss =15dB with L =10and b =. lowe than that of the tuncated ARQ scheme. SCA again has the best pefomance. Howeve, due to the bad quality of s channels, SCA seldom uses elays and theefoe it has nealy the same thoughput as the pue tuncated ARQ scheme. Fom the above discussion, we can conclude that SCA can always achieve a significant thoughput gain iespective of whethe the s channels ae good o not. In contast, the pefomance of FCA highly depends on the quality of the s channels. With poo s channels, the pefomance will deteioate apidly due to eo popagation and may be even wose than the pue tuncated ARQ scheme. This can be moe clealy seen in Fig. 6, whee the aveage SNR pe symbol of the s d channel γ sd is fied to be 15dB. Hee the -ais is given by ρ = γ ss /γ sd. It can be seen that FCA can achieve a highe thoughput than the tuncated ARQ scheme only when ρ is lage than 1.5. This can give us some insights on the selection of coopeation egion when fied coopeative divesity is adopted. SCA again achieves the highest thoughput and substantial gains can be obseved fo all the values of ρ. Fom Fig. 6, it can be also seen that a highe ρ indicates a bette pefomance gain of SCA o FCA ove the tuncated ARQ. In othe wods, moe coopeative divesity gain can be achieved with a lage atio of σs to σ 0. Neglecting the effect of shadowing, this implies that the elays should be located close to the souce node. Futhemoe, it is found that the pefomance gain will be even moe significant if fewe scattes eist between the souce node and the elays. As shown in Fig. 5, with the assumption of Gaussian s channels, substantial gains can be achieved by both SCA and FCA although γ ss is only 10dB. In contast, in Rayleigh fading s channels, no pefomance gain can be obtained by SCA and FCA with the same γ ss. Theefoe, we conclude that Q elay candidates should be selected fom those located aound the souce node so as to achieve bette pefomance. It should be noticed that in Gaussian s channels, FCA with 1 elay pefoms the best among all the schemes at high SNR. A close obsevation shows that in this case SCA is vey likely to choose Q =elays since the s channels ae with good quality. Theefoe, it has vey slight pefomance gain ove FCA with elays and both of them suffe fom the ate loss of 3-symbols STBC. IV. THROUGHPUT OPTIMIZATION USING ADAPTIVE TECHNIQUES The thoughput epessions of the tuncated ARQ scheme, FCA and SCA have been given by 9), 11) and 18), espectively. These epessions clealy depend on two impotant paametes: the packet length L and the modulation level b. As we know, a small packet length indicates that most packets aive without eos but at the cost of a lage packet ovehead. AlageL implies highe efficiency while the packet is moe susceptible to eos which cause moe etansmissions. As fo the modulation level b, a packet with a low modulation level

8 1914 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 11, NOVEMBER 008 Thoughput b Fig. 7. Thoughput plane of SCA vesus L and b with γ sd =15dB and γ ss =0dB Fig. 6. Thoughput of the tuncated ARQ scheme, FCA with 1 elay, FCA with elays and SCA when γ sd =15dB with L =10and b =. is moe obust but may esult in inefficient use of the channel. On the othe hand, a packet with a high modulation level is moe liable to eo but caies moe infomation pe symbol. Theefoe, an appopiate L o b isdesiedsoastoimpove the thoughput. In this section, we will futhe maimize the thoughput by optimizing L and b. Since the thoughput epessions ae neithe concave no conve, an analytical solution fo the optimal packet length L and modulation level b is had to be obtained. Theefoe, we esot to simulations to obseve how thoughput vaies with L and b fist. In this section, we always assume that both L and b take continuous values. Fig. 7 shows the selected sample when SCA is adopted with γ ss =0dB and γ sd =15dB. It can be seen that the thoughput plane is athe smooth, which indicates a good match between the local maimum and the global maimum. Actually, we have conducted etensive simulations of these thee schemes, i.e., the tuncated ARQ scheme, FCA and SCA, and found that the thoughput plane is always smooth. Theefoe, based on the above obsevation, we esot to the Method of Hooke and Jeeves [] to obtain the optimal L and b as well as the maimum thoughput. Fig. 8 shows the optimized thoughput cuves of the tuncated ARQ scheme, FCA with 1 elay, FCA with elays and SCA when γ ss is 0dB. It can be seen that with the joint optimization of L and b, the thoughput can be impoved geatly whicheve scheme is adopted. SCA again achieves the best thoughput and substantial gains can be obseved ove all the othe schemes. The thoughput of FCA with 1 elay and elays ae also significantly impoved by the joint optimization. Howeve, in contast to the case with a fied L of 10 and a fied b of, FCA with elays obtains a lowe optimal thoughput than that of the tuncated ARQ scheme at high SNR. A close obsevation shows that in this case the optimal packet length L of these schemes is aound 50, which is much lowe than 10. At high SNR, the communication link povided by the s d channel is eliable enough fo such a shot packet. Theefoe, although bette Thoughput bit/s/hz) Optimal thoughput with L and b optimized Thoughput with L=10 and b= Tuncated ARQ scheme FCA with 1 elay FCA with elays SCA SNR db) Fig. 8. Optimal thoughput vs. thoughput with fied L and b of the tuncated ARQ scheme, FCA with 1 elay, FCA with elays and SCA when γ ss =0dB divesity gain can be achieved by node coopeation, the ate loss plays a moe impotant ole hee. On the othe hand, this also indicates that ρ = γ ss /γ sd should be lage so as to assue that pefomance gain can be achieved by FCA. SCA always obtains the best pefomance egadless of the quality of s channels. The esults with a lowe γ ss ae simila and so we omit them hee. We take the eample of the tuncated ARQ scheme to futhe show the thoughput gains bought by the joint optimization of L and b. As Fig. 9 shows, the optimal thoughput cuve with both L and b optimized coincides with the suboptimal one with only L optimized b is fiedtobe)inthelow SNR egime. At high SNR, the suboptimal thoughput cuve with only b optimized appoaches that of the optimal one. This implies that at low SNR we could only optimize L to get an optimal thoughput, wheeas at high SNR, optimizing b can moe effectively optimize the thoughput. Besides, we compae the optimal packet length L with b fied and that

9 DAI and LETAIEF: THROUGHPUT MAXIMIZATION OF AD-HOC WIRELESS NETWORKS USING ADAPTIVE COOPERATIVE DIVERSITY 1915 thoughput begins to fall. This is based on the obsevation that the local thoughput and the global thoughput always pefectly match when b vaies and L is fied o L vaies and b is fied. This new algoithm shall be efeed to as lowcompleity discete optimization algoithm L-DOA) and is descibed below. Fig. 9. Thoughput optimization of the tuncated ARQ scheme TABLE I OPTIMAL L AND b SEARCHED BY L-DOA FOR THE TRUNCATED ARQ, FCA AND SCA γ ss =0DB) SNR γ sd ) 0dB 5dB 10dB 15dB 0dB Tuncated ARQ Scheme L u = i) b 4 FCA with v =1elay L u =i) b FCA with v =elay L u =3i) b SCA with Q =elay L u =6i) b 4 with b optimized. It is found that with b optimized, the optimal packet length L can be geatly deceased in the high SNR egime since in this case, we can use a highe modulation instead of inceasing the packet length. On the othe hand, the compaison of the optimal modulation level b with L fied and that with L optimized shows that with L optimized, even highe modulation can be adopted so as to impove the thoughput. We do not pesent the figues due to limited space. V. OPTIMIZATION OVER DISCRETE PARAMETERS In the above analysis, L and b ae always assumed to be continuous. Howeve, since squae M-QAM is adopted, b should actually be even, i.e. b =k, k =1,, 3,. Besides, L should be lage than C and be an intege multiple of b, i.e. L>Cand L = ub, wheeu is an intege. Fo SCA and FCA, thee ae even moe constaints on L due to the adoption of STBC. Fo eample, fo FCA with 1 elay, u should be an intege multiple of since a -symbol STBC is adopted in the etansmission. Fo SCA with Q =, u should futhe be an intege multiple of 6 since both -symbol and 3-symbol STBC may be adopted. Ehaustive seach ove the discete optimal L and b will esult in pohibitive compleity. In this section, we pesent a computationally efficient algoithm to find the discete optimal L and b. Paticulaly, in the new algoithm, we stat seaching the optimal packet length L with a fied b= and fo each incemental b, we compute the maimum thoughput by optimizing L. The whole pocess will teminate when the Algoithm 1 Low-compleity discete optimization algoithm L-DOA)) 1: Let L = ub whee u takes on diffeent values fo diffeent schemes. u = i, i =1,, 3,..., fo the tuncated ARQ scheme, u =i fo FCA with 1 elay, u =3i fo FCA with elays, and u =6i fo SCA with Q =. T [l, b] epesents the thoughput with a packet length l and a modulation level b. : Initialization: k =1, T =0; 3: loop 4: b k =k. Find the optimal packet length l unde the given b k. 5: Let a = l /ub k ). 6: Let L 1 = a ub k and L =a +1) ub k. 7: Compae T [L 1,b k ] and T [L,b k ]. 8: if T [L 1,b k ] T [L,b k ] then 9: L k = L 1, T k = T [L 1,b k ]; 10: else 11: L k = L, T k = T [L,b k ]; 1: end if 13: 14: if T k >T then 15: T = T k, L = L k, b = b k ; 16: else 17: stop; 18: end if 19: k = k +1 0: end loop It can be seen that with L-DOA, the joint optimization of L and b is decoupled so that the compleity can be educed damatically. Table 1 lists the discete optimal values of L and b fo the tuncated ARQ scheme, FCA with 1 elay, FCA with elays and SCA with Q = unde a γ ss of 0dB. The coesponding thoughput cuves ae plotted in Fig. 10. Fo compaison, the optimal thoughput cuves with continuous optimal L and b ae also shown. It can be seen that a good match between the thoughput cuves with continuous optimal L and b and that with discete optimal L and b can be achieved whicheve scheme is adopted, indicating that the discetization of L and b esults in vey slight thoughput loss. It also indicates the supeio pefomance of L-DOA. A close obsevation shows that a slight thoughput loss will be incued in the cases of SCA with γ sd =15dB and FCA and the tuncated ARQ scheme with γ sd =0dB. Actually, this is because the optimal b is aound 3 in these cases. By esticting b to be even, a thoughput loss will be incued. Nevetheless, the two coesponding thoughput cuves pefom a pefect match in most cases. The coesponding esults with the othe values of γ ss ae simila and so we omit them hee due to limited space.

10 1916 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 11, NOVEMBER Thoughput with continuous optimal L* and b* Thoughput with discete optimal L* and b* Tuncated ARQ scheme FCA with 1 elay FCA with elays SCA SNR db) Fig. 10. Thoughput with continuous optimal L and b and with discete optimal L and b of the tuncated ARQ scheme, FCA with 1 elay, FCA with elays and SCA when γ ss =0dB. VI. CONCLUSIONS In this pape, we poposed a coss-laye design combining tuncated ARQ at the link laye and coopeative divesity at the physical laye, which has been shown to be able to geatly impove the system thoughput. The thoughput epessions of the poposed SCA scheme, FCA scheme and the pue tuncated ARQ scheme ae deived and veified by simulation esults. The compaison of these thee schemes showed that the poposed SCA scheme can always achieve the highest thoughput and effectively avoid eo popagation. The thoughput is futhe maimized by optimizing the packet length L and the modulation level b and it was found that substantial gains can be achieved by this joint optimization. Besides, since both L and b ae usually discete and unde some constaints in pactice, we poposed a low-compleity discete optimization algoithm L-DOA) to seach the discete optimal L and b. It was then shown that the discetization of L and b esults in vey slight thoughput loss. It must be noted that the above pefomance analysis did not take into consideation some impotant effects such as the Dopple spead and fequency selectivity. Hence, etending this wok to conside these effects is of potential inteest. Anothe inteesting etension of this wok is to analyze the pefomance in multiuse scenaios with specific scheduling stategies. APPENDIX A PROOF OF THEOREM 1 Let X denote an m-antenna-t -time-slot-k-symbol STBC. It can be then epesented as X =[A 1 s + B 1 s, A s + B s,..., A T s + B T s ] 6) whee s is a k 1 comple vaiable vecto and A i, B i ae constant coefficient matices in R m k. Assume n antennas at the eceive side. Then, the n T eceive signal mati Y can be witten as SNR Y = HX + N 7) m whee SNR = σ0 P t/n 0, H and N ae the n m channel gain mati and n T noise mati, espectively. All h ij, i = 1,...,n, j =1,...,mand n ij, i =1,...,n, j =1,...,T ae i.i.d. comple-valued Gaussian andom vaiables with zeomean and unit vaiance. Afte a seies of linea tansfomation, we have SNR = H s + z 8) m whee HA 1 + H B 1 H =. 9) HA T + H B T Fom the popety of {A j } j=1,...,t and {B j } j=1,...,t,wehave H + H= taceh + H) I k 30) Theefoe, SNR = α s + z 31) m whee z i N c 0,α), i =1,..., k, andα = taceh + H). Obviously, is a cental chi-squae distibuted vaiable with mn degees of feedom. Fom 31), it can be seen that othogonal space-time block decoding tansfoms a MIMO channel into multiple equivalent SISO channels. Theefoe, s can be easily detected using a one-dimension MLD. In FCA, v elay nodes and the souce node use a v +1 symbol STBC to send the signals togethe. Theefoe, hee we have m = k = v +1 and n =1. Note that in FCA, the elay nodes ae pe-assigned and CRC will not be checked to assue eliable infomation fowading. As a esult, in the etansmission only the souce node tansmits the oiginal signal vecto s. At each elay, the estimate ŝ instead of the oiginal signal vecto s is tansmitted, whee ŝ =[ŝ 0,ŝ 1,..., ŝ v ].Afte decoding, the equivalent SISO channel model becomes = μα s+ z 3) whee μ = γ sd /v +1) and α is a cental chi-squae distibuted vaiable with v +1) degees of feedom. We have ŝ 0 s 0 z = μh + ŝ 1 s 1 H + z 33). ŝ v s v and HA 1 + H B 1 H =. 34) HA T + H B T whee A i B i ) is obtained by eplacing the fist ow of A i B i ) with zeos, i =1,..., T. Hee the new equivalent noise z includes both the additive white noise z and the effect of eo estimates. It can be futhe obtained that va z )=vaŝ i s i )I v+1 H + H H + H + αi v+1 αi v+1 vaŝ i s i )ψ +1) 35)

11 DAI and LETAIEF: THROUGHPUT MAXIMIZATION OF AD-HOC WIRELESS NETWORKS USING ADAPTIVE COOPERATIVE DIVERSITY 1917 whee ψ is a cental chi-squae distibuted vaiable with v degees of feedom. Let D s i ŝ i ) denote the distance between s i and ŝ i,then we have va ŝ i s i )=D s i ŝ i ) P s i ŝ i ). 36) Hee we assume that eos always happen between two neighbos. Theefoe, the minimum distance D min s i ŝ i ) is used instead of D s i ŝ i ).LetE s denote the aveage enegy of the constellation. Fom [1], it follows that fo M-QAM symbols D min s i ŝ i )= 6E s b 1. 37) Besides, we have assumed that the s channel is flat Rayleigh fading. Accoding to [1], P s i ŝ i )= 1 1 ) ) gγss 1 b 1+gγ ss ) b [ ) ] 4 gγss 1+gγ actan ss 1, π 1+gγ ss gγ ss 38) whee γ ss is the aveage SNR pe symbol of the s channel and is given by γ ss = σs P t/n 0. Theefoe, by combining 3-38), the instantaneous SNR pe symbol of the etansmission, γ s, should be given by whee w = ψ [ γ s = π b αγ sd 6 b 1 wγ sd +v +1)R ) gγss ) 1 1+gγ + ss gγss 1+gγ ss actan ) 1 1 b ] 1+gγ ss gγ ss ) 1 39). It can be easily checked that with a lage v, vaw)/ew) 0, implying that the fluctuation aound the mean of w can be neglected. Theefoe, w is eplaced by αγ sd aγ sd +v+1)r, Ew) and γ s can be futhe witten as γ s = whee a is given by 17). Finally, fom [0] the aveage SNR pe symbol of the etansmission γ s can be obtained, as shownin16). REFERENCES [1] R. D. Much and K. B. Letaief, Antenna systems fo boadband wieless access, IEEE Commun. Mag., vol. 40, no. 4, pp , Ap. 00. [] A. Sendonais, E. Ekip, and B. Aazhang, Use coopeation divesity pat I: system desciption, IEEE Tans. Commun., vol. 51, no. 11, pp , Nov [3] A. Sendonais, E. Ekip, and B. Aazhang, Use coopeation divesity pat II: implementation aspects and pefomance analysis, IEEE Tans. Commun., vol. 51, no. 11, pp , Nov [4] J. N. Laneman, G. W. Wonell, and D. N. C. Tse, Coopeative divesity in wieless netwoks: efficient potocols and outage behavio, IEEE Tans. Infom. Theoy, vol. 50, no. 1, pp , Dec [5] J. N. Laneman and G. W. Wonell, Distibuted space-time-coded potocols fo eploiting coopeative divesity in wieless netwoks, IEEE Tans. Infom. Theoy, vol. 49, no. 10, pp , Oct [6] T. E. Hunte and A. Nostatinia, Coopeation divesity though coding, in Poc. ISIT 0, pp. 0, placecitylausanne, July 00. [7] T. E. Hunte and A. Nostatinia, Pefomance analysis of coded coopeation divesity, in Poc. ICC 03, pp , May 003. [8] M. Janani, A. Hedayat, T. E. Hunte, and A. Nostatinia, Coded coopeation in wieless communications: space-time tansmission and iteative decoding, IEEE Tans. Signal Pocessing, vol. 5, no., pp , Feb [9] A. Stefanov and E. Ekip, Coopeative coding fo wieless netwoks, IEEE Tans. Commun., vol. 5, pp , Sept [10] Z. Lin, E. Ekip, and A. Stefanov, Coopeative egions fo coded coopeative systems, in Poc. Globecom 04, pp. 1-5, Dallas, TX, Nov [11] N. Pasad and M. K. Vaanasi, Divesity and multipleing tadeoff bounds fo coopeative divesity potocols, in Poc. ISIT 04, pp. 68, July 004. [1] R. U. Naba and H. B lcskei, Space-time signal design fo fading elay channels, in Poc. Globecom 03, pp , San Fancisco, Nov [13] P. A. Anghel and M. Kaveh, Eact symbol eo pobability of a coopeative netwok in a Rayleigh-fading envionment, IEEE Tans. Wieless Commun., vol. 3, no. 5, pp , Sept [14] A. Host-Madsen, Capacity bounds fo coopeative divesity, IEEE Tans. Infom. Theoy, vol. 5, no. 4, pp , Ap [15] W. Chen, L. Dai, K. B. Letaief, and Z. Cao, A unified coss-laye famewok fo esouce allocation in coopeative netwoks, IEEE Tans. Wieless Commun., vol. 7, no. 8, pp , Aug [16] E. Malkamaki and H. Leib, Pefomance of tuncated type-ii hybid ARQ schemes with noisy feedback ove block fading channels, IEEE Tans. Commun., vol. 48, no. 9, pp , Sept [17] Q. Liu, S. Zhou, and G. B. Giannakis, Coss-laye combining of adaptive modulation and coding with tuncated ARQ ove wieless links, IEEE Tans. Wieless Commun., vo. 3, no. 5, pp , Sept [18] R. J. Lavey, Thoughput optimization fo wieless data tansmission, M. S. Thesis, Polytechnic Univesity, June 001, [19] M.-S. Alouini and A. Goldsmith, A unified appoach fo calculating eo ates of linealy modulated signals ove genealized fading channels, IEEE Tans. Commun., no. 9, pp , Sept [0] H. Shin and J. H. Lee, Eact symbol eo pobability of othogonal space-time block codes, in Poc. Globecom 0, pp , Nov. 00. [1] F. Xiong, Digital Modulation Techniques. Atech House, 000. [] M. S. Bazaaa, Nonlinea Pogamming: Theoy and Algoithms. Wiley, [3] X. Liang, Othogonal designs with maimum ates, IEEE Tans. Infom. Theoy, vol. 49, no. 10, pp , Oct Lin Dai S 00-M 03) eceived the B.S. in electonic engineeing fom Huazhong Univesity of Science and Technology, Wuhan, China, in 1998 and the M.S. and Ph. D. degees in electical and electonic engineeing fom Tsinghua Univesity, Beijing, China, in 000 and 00, espectively. She was a postdoctoal fellow at the Hong Kong Univesity of Science and Technology and Univesity of Delawae. Since 007, she has been with City Univesity of Hong Kong, whee she is an assistant pofesso. He eseach inteests include wieless communications, infomation and communication theoy. She eceived the Best Pape Awad at IEEE WCNC 007.

12 1918 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 11, NOVEMBER 008 Khaled B. Letaief S 85-M 86-SM 97-F 03) eceived the BS degee with distinction in Electical Engineeing fom Pudue Univesity at West Lafayette, Indiana, USA, in Decembe He eceived the MS and Ph.D. Degees in Electical Engineeing fom Pudue Univesity, in August 1986, and May 1990, espectively. Fom Januay 1985 and as a Gaduate Instucto in the School of Electical Engineeing at Pudue Univesity, he has taught couses in communications and electonics. Fom 1990 to 1993, he was a faculty membe at the Univesity of Melboune, Austalia. Since 1993, he has been with the Hong Kong Univesity of Science and Technology whee he is cuently Chai Pofesso and Head of the Electonic and Compute Engineeing Depatment. He is also the Diecto of the Hong Kong Telecom Institute of Infomation Technology. His cuent eseach inteests include wieless and mobile netwoks, Boadband wieless access, OFDM, Coopeative netwoks, Cognitive adio, MIMO, and Beyond 3G systems. In these aeas, he has published ove 300 jounal and confeence papes and given invited keynote talks as well as couses all ove the wold. D. Letaief seved as consultants fo diffeent oganizations and is the founding Edito-in-Chief of the IEEE TRANSACTIONS ON WIRELESS COM- MUNICATIONS. He has seved on the editoial boad of othe pestigious jounals including the IEEE JOURNAL ON SELECTED AREAS IN COMMU- NICATIONS - WIRELESS SERIES as Edito-in-Chief). He has been involved in oganizing a numbe of majo intenational confeences and events. These include seving as the Co-Technical Pogam Chai of the 004 IEEE Intenational Confeence on Communications, Cicuits and Systems, ICCCS 04; Geneal Chai of the 007 IEEE Wieless Communications and Netwoking Confeence, WCNC 07; as well as the Technical Pogam Co-Chai of the 008 IEEE Intenational Confeence on Communication, ICC 08. In addition to his active eseach and pofessional activities, Pofesso Letaief has been a dedicated teache committed to ecellence in teaching and scholaship. He eceived the Mangoon Teaching Awad fom Pudue Univesity in 1990; the Teaching Ecellence Appeciation Awad by the School of Engineeing at HKUST 4 times); and the Michael G. Gale Medal fo Distinguished Teaching Highest univesity-wide teaching awad and only one ecipient/yea is honoed fo his/he contibutions). He is a Fellow of IEEE, an elected membe of the IEEE Communications Society Boad of Govenos, and an IEEE Distinguished lectue of the IEEE Communications Society. He also seved as the Chai of the IEEE Communications Society Technical Committee on Pesonal Communications and is cuently seving as the Chai of the Steeing Committee of the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. He is the ecipient of the 007 IEEE Communications Society Publications Eemplay Awad.