IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER Powe Allocatio ad Goup Assigmet fo Reducig Netwo Codig Noise i Multi-Uicast Wieless Systems Zaha Mobii, Studet Membe, IEEE, Paastoo Sadeghi, Seio Membe, IEEE, Majid habbazia, Membe, IEEE, ad Saada Zoaei Abstact I this pape, we coside physical-laye etwo codig PNC) i a multi-uicast wieless coopeative etwo with a sigle elay. We aim to deal with the NC oise, i.e., a additioal oise tem due to applyig NC, with the objective of impovig the etwo data ate. Ou appoaches ae based o elay powe-allocatio ad goup-allocatio techiques. To this ed, we povide a mathematical famewo fo the achievable ifomatio ate of the system with the otio of powe assigmet at the elay. Based o this famewo, we peset a ovel powe-allocatio scheme to maximize the total ifomatio ate amog all the souce destiatio commuicatio sessios i the etwo. Futhe, we povide a closed-fom solutio fo the two-uicast case. Simulatio esults show that the poposed elay powe allocatio ca sigificatly help alleviate the advese effects of NC oise. Next, we popose a goup-allocatio scheme to assig sessios to diffeet goups fo pefomig PNC at the elay. We combie powe allocatio ad goup allocatio to futhe impove pefomace. The fomulated joit optimizatio poblem is NP-had. Theefoe, a suboptimal heuistic algoithm is poposed ad implemeted at the elay to solve this poblem. Fom the simulatio esults, the poposed joit goup assigmet ad powe-allocatio scheme achieves up to 64% oveall data ate gai fo the multi-uicast system compaed with a sigle-goup system with o elay powe assigmet. This obsevatio shows that PNC ca be efficietly haessed i a multi-uicast coopeative etwo by exploitig poposed appoaches. Idex Tems Coopeative commuicatios, goup assigmet, multi-uicast wieless systems, etwo codig NC), NC oise, powe allocatio. I. INTRODUCTION IT HAS bee show that etwo codig NC) ca sigificatly impove the thoughput ad obustess of both wied ad wieless etwos [1], [2]. The ey featue of eithe digital Mauscipt eceived Novembe 8, 2011; accepted Jue 11, Date of publicatio July 10, 2012; date of cuet vesio Octobe 12, This wo was suppoted i pat by the Austalia Reseach Coucil s Discovey Pojects fudig scheme ude Poject DP ad i pat by the Ia Telecommuicatio Reseach Cete. The eview of this pape was coodiated by D. C. Yue. Z. Mobii ad S. Zoaei ae with the Depatmet of Electical ad Compute Egieeig,.N. Toosi Uivesity of Techology, Teha, Ia z.mobii@ee.tu.ac.i; szoaei@eetd.tu.ac.i). P. Sadeghi is with the Reseach School of Egieeig, The Austalia Natioal Uivesity, Cabea, ACT 0200, Austalia paastoo.sadeghi@ au.edu.au). M. habbazia is with the Depatmet of Electical ad Compute Egieeig, Uivesity of Albeta, Edmoto, AB T6G 2E1, Caada mhabbazia@gmail.com). Colo vesios of oe o moe of the figues i this pape ae available olie at Digital Object Idetifie /TVT Fig. 1. Multi-uicast system with souce destiatio pais. NC [2] o physical-laye NC PNC [3], [4]) is to ecouage the itemediate odes i the etwo, which ae ow as elays, to fowad the combiatio of thei obsevatios. This, alog with the boadcast atue of adio popagatio, maes PNC a pomisig cadidate fo multiuse coopeative commuicatios, eablig high-data-ate ad hoc etwos. Successful applicatio of PNC, howeve, depeds o the commuicatio sceaio. Fo example, PNC has bee applied to multiway elayig, whee multiple tasceives with o diect li betwee them wish to commuicate with all othes usig the help of a sigle elay ode. I this case, itefeece cacelatio a impotat equiemet fo PNC) ca be successfully accomplished. I ecet wos [5] [10], it has bee show that PNC ca sigificatly ehace the thoughput pefomace i multiway elay etwos. Moeove, PNC has bee studied fo commuicatio sceaios, whee multiple souces ae commuicatig with a commo destiatio multiple-access elay chaels), ad has bee show to be effective to impove the sum of uses s ifomatio ates, o sum ate fo shot, ad outage pobability pefomaces [11], [12]. The advatage of usig PNC i coopeative commuicatio, which is efeed to as etwo-coded coopeative commuicatio NC-CC), is ot esticted to multiway o multiple-access elay chaels. Fo example, coside PNC i a multi-uicast coopeative etwo with souce destiatio pais as show i Fig. 1. I this etwo, afte each souce ode taes tu to tasmit its ifomatio to the coespodig destiatio, which is ovehead by othe destiatios ad the elay, the elay amplifies ad fowads the liea combiatio of all the ovehead sigals i the pevious time blocs i a sigle time bloc. This example shows that PNC ca povide a sigificat data-ate pefomace /$ IEEE

2 3616 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012 ehacemet i a multi-uicast sceaio by equiig + 1) time blocs to complete the tasmissio, i compaiso with covetioal coopeative commuicatio, e.g., amplifyad-fowad coopeative commuicatio AF-CC) [13], that equies 2 time blocs. Howeve, bigig the pomisig beefits of PNC to the multi-uicast sceaio is ot fee of cost. I [14] ad [15], it was show that eve with the pefect owledge of chael ifomatio, thee will be a oegligible oise itoduced duig the sigal extactio at destiatios, which was coied NC oise. The NC oise oigiates fom iheetly impefect o oisy cacelatio of othe uses sigals at a give destiatio. Moeove, the data ates of souce destiatio pais ae highly depedet o the NC oise ad ca eve be lowe tha the covetioal coopeative scheme [14] [16]. Accodigly, the advatages of usig PNC ca otably decease o eve disappea if the effect of NC oise is ot tae ito accout i the system aalysis ad desig. The desig of tasmissio schemes that deal with this oise is, theefoe, of paamout impotace ad is oe mai goal of this pape. To the best of ou owledge, this is lagely a uaddessed poblem. Powe allocatio has log bee egaded as a effective way of impovig the wieless coopeative system pefomace [17], [18]. Some effots have bee ecetly made to exploit powe allocatio with NC i coopeative etwos [5], [19] [22]. Optimal elay powe allocatio has show to impove the sum ate, the sum of uses bit eo ate BER) [5], ad the weighted sum ate [19] fo a multiuse sceaio i PNC two-way elayig. Most of the wo ivolvig powe allocatio i NC-CC system to date, howeve, is limited to two-way elayig schemes, ad powe allocatio fo multiway o multi-uicast elay-assisted systems has ot eceived much attetio. Theefoe, a iteestig questio would be whethe elay powe allocatio ca also help alleviate the detimetal effects of NC oise i the multi-uicast NC-CC system. This is oe of the questios that we will addess i this pape. The secod half of this pape ecogizes the fact that eve whe optimal powe allocatio is used, the pefomace of the multi-uicast NC-CC system is fudametally limited by iceasig the umbe of souce destiatio pais 1 that shae the same elay ode. This is due to the highe NC oise at the destiatio odes fo highe umbe of uses ad highe complexity fo powe allocatio ad sigal extactio, as will be idicated i Sectio III. To deal with this poblem, this pape itoduces a multigoup NC-CC tasmissio scheme i which souce destiatio pais ae gouped ito diffeet sets fo pefomig PNC at the elay. Goupig odes i collaboative sets, i.e., the so-called coopeative clustes, has bee poposed i covetioal coopeative etwos with o NC to educe the esouce maagemet complexity [23]. Moeove, coopeative goupig ad pate selectio have bee developed i [24] ad [25] to aswe the issue of who helps whom i coopeative esouce-allocatio poblems. I [24], pate ad subcaie allocatio was ivestigated i coopeative multiuse othogoal fequecy-divisio multiplexig OFDM) etwos. Nosatiia 1 I this pape, we use the tems sessio ad souce destiatio pai itechageably. ad Hute [25] have poposed a coopeative pate assigmet to miimize the aveage outage pobability ove all uses i a coopeative etwo. The udelyig etwos i [24] ad [25] ae covetioal coopeative etwos with o NC ad ae vey diffeet fom ous. To the best of ou owledge, [26] is the oly wo that studied goup assigmet ad elay selectio i the multiuicast NC-CC system. Shama et al. [26] poposed a olie goup-allocatio algoithm based o a iteative scheme whee souce odes select the best goup amog all offes fom the eighboig elays. This algoithm is suitable fo the case whee etwo dyamics ae uow apioi. I this pape, howeve, by popely fomulatig the assigmet poblem, we detemie goup allocatio at the elay ode fo a ow etwo topology. Moeove, we peset a joit goupig ad elay poweallocatio scheme, wheeas Shama et al. [26] do ot addess the poblem of elay powe allocatio. I this pape, we aim at developig a ovel multi-uicast NC- CC scheme that efficietly deals with NC oise while taig advatage of the iheet beefits of powe allocatio ad goup assigmet. The mai cotibutios of this pape ae as follows. We itoduce powe assigmet i a sigle-goup NC-CC system with NC oise ad deive achievable ifomatio ates. We fomulate the optimal elay powe-allocatio poblem with the objective of sum-ate maximizatio. A closedfom solutio fo the two-use case is deived, ad a effective umeical algoithm is poposed fo the multiuicast case. We ivestigate the effectiveess of the poposed powe allocatio ad show that it ca sigificatly help alleviate the advese effects of NC oise compaed with [14]. It is also show that the pefomace of the NC- CC system degades as the umbe of souce destiatio pais is iceased. To deal with this, we itoduce goup allocatio ito NC-CC ad the efomulate the deived achievable ates fo the multigoup NC-CC system. To futhe ehace the pefomace of the NC-CC system, we combie goup assigmet ad elay powe allocatio. The joit optimizatio poblem is NP-had. Theefoe, we devise a suboptimal geedy algoithm to solve the joit poblem. The poposed elay powe allocatio ad goupig schemes ae implemeted at the elay ad oly ely o log-tem chael statistics. Nevetheless, they ae show to be effective to alleviate the impact of NC oise ad to otably ehace data ates i the NC-CC system. Futhemoe, the elay ode eeds to otify oly the destiatio odes of the goupig ad powe allocatio, istead of feedig bac this ifomatio to all souces ad destiatios. II. SYSTEM MODEL The wieless multi-uicast NC-CC etwo of iteest hee compomises mobile souces commuicatig with mobile destiatios though oe fixed elay usig a AF potocol ad PNC i the pesece of the souce-to-destiatio lis, as i Fig. 1. Let S deote the th souce, D the coespodig

3 MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3617 destiatio, ad R deote elay ode. Note that we use small subscipts s, d, ad to efe to odes S, D, ad R, espectively. We coside fequecy-oselective Rayleigh bloc fadig chaels. That is, the ealizatio of the fadig chael i each li stays costat duig tasmissio of a bloc of symbols ad chages to a idepedet value i the ext bloc. We assume all odes opeate i half-duplex mode usig timedivisio multiplexig. Thus, tasmissios fom souces ad the elay occu i diffeet time blocs. I each bloc, N symbols ae tasmitted i N-symbol time slots of duatio T S each. Fo thee coopeative tasmissio stategies sigle-goup NC-CC, multigoup NC-CC, ad AF-CC) discussed i this pape, a coopeatio oud cosists of two phases: the boadcast phase whee each souce seds its ow data to the destiatio that is also ovehead by the elay ad all othe destiatios, ad the elay phase whee elay helps fowad a additioal copy of the data to destiatios. Detailed desciptio of the tasmissio sceaios i the sigle-goup NC-CC ad AF-CC systems ae povided as follows. System desciptio fo each goup i a multigoup NC-CC is simila to the sigle-goup NC-CC case ad is omitted fo bevity. A. Multi-uicast Sigle-Goup NC-CC I this scheme, the oveall tasmissio ca be divided ito + 1) blocs: blocs i the boadcast phase ad oe bloc i elay phase. I the fist blocs, each souce S l, whee l = 1,...,, seds its ow bloc of N symbols with tasmissio powe P sl, to the elay ad all destiatio odes i a peassiged time bloc. The coespodig eceived sigals by the destiatio ode D, whee = 1,...,, ad the elay at the th time slot ca be expessed, espectively, as 2 y sl d = h sl d x l + z sl d 1) y sl = h sl x l + z sl 2) whee x l is the tasmitted sigal such that E{ x l } = P sl E{ } is the statistical expectatio), ad z sl,d ad z sl, epeset zeo-mea complex-valued additive white Gaussia oise AWGN) with vaiaces σs 2 l,d ad σs 2 l, duig the S l tasmissio at destiatio D ad at elay R, espectively. I additio, h sl,d ad h sl, deote the coefficiets of the chaels betwee souce S l ad destiatio D ad betwee souce S l ad elay R, espectively. We assume that chael coefficiets h sl,d ad h sl, follow a zeo-mea complex Gaussia ZMCG) distibutio with vaiaces σh 2 sl = 1/d a,d s l,d ad σh 2 = 1/da sl, s l,, espectively, whee d sl,d ad d sl, ae the S l to D ad S l to R distaces, ad a is the path loss expoet [27]. This chael model icludes both log-tem path loss ad shot-tem fadig. Doppig the idices, the log-tem path loss σh 2 detemies the stegth of the shot-tem fadig, i.e., the vaiace of the fadig chael h o the mea of h. I the fial bloc, i.e., the + 1)th bloc, the elay pefoms PNC by mixig the aalog eceived sigals. I paticula, i cotast with [14] ad [15] i which the elay mixes the 2 Time idex is omitted i equatios to simplify otatios. eceived sigals without optimizatio of powe allocatio, ou aim is to use powe assigmet at the elay whee each eceived sigal fom a souce is weighted by a powe-allocatio coefficiet, such that the sum-ate pefomace citeio is optimized. The pocessed sigal at the elay ca be expessed as x = α sl y sl = α sl h sl x l + z sl ) 3) l=1 l=1 whee α sl is the elay powe-allocatio coefficiet fo S l such that 0 α sl 1, ad l=1 α2 s l = 1. The elay amplifies x with a amplificatio facto, i.e., P A = 4) l=1 α2 s Psl l h sl + σs 2 l,) to maitai a costat powe P at the elay output ad the boadcasts the esulted sigal to all destiatio odes. The eceived sigal at the destiatio D ca be witte as y,d = Ah,d x + z,d = Ah,d α s y s, + Ah,d [α sl h sl x l + z sl )] + z,d 5) whee z,d epesets AWGN with vaiace σ,d 2 at the destiatio D duig the tasmissio fom R, ad h,d is the fadig chael betwee elay R ad destiatio D with ZMCG distibutio ad vaiace σh 2,d = 1/d a,d, whee d,d is the distace fom R to D. Accodigly, destiatio ode D eceives oe copy of sigal x i the fist tasmissio phase. Futhe, it obtais aothe copy of x i the secod phase as follows. Usig the ovehead sigals fom S l, whee l, atd 1), we ca wite x l = y sl,d z sl,d )/h sl,d. Usig this otatio i the eceived sigal fom S l at the elay i 2), we ca ewite y,d i 5) as y,d = Ah,d α s y s, + Ah,d + Ah,d α sl h sl, h sl,d [y sl,d z sl,d ] α sl z sl, + z,d. 6) The multi-uicast NC-CC system equies that complete chael state ifomatio CSI), i.e., h sl,, h,d, ad h sl,d, whee l = 1,..., be available at the destiatio ode D to cacel the uwated tems [14], [15]. Moeove, the elay has to sed cotol bits to the destiatios to idicate powe-allocatio coefficiets. This ceates some ovehead fo sigalig. Hee, we assume that the mobility of the souce ad destiatio odes is low so that the chael coditios ae stable fo sufficietly log time; theefoe, the fequecy to update the chael ifomatio ad powe-allocatio coefficiets is low. Howeve, the mae i which the destiatio obtais this ifomatio

4 3618 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012 is beyod the scope of this pape. To emove y sl,d, whee l = 1,..., ad l, D multiplies sigal y sl,d by facto Ah,d α sl h sl,/h sl,d ) ad subtacts it fom 6). Note that the destiatio ode D eeds to epeat this cacelatio fo all the 1) ovehead sigals y sl,d. The esultig sigal at destiatio ode D, which is deoted by y,d, is obtaied as y,d α sl h sl, = y,d Ah,d y sl,d h sl,d = Ah,d α s y s, Ah,d + Ah,d α sl h sl, z sl,d h sl,d α sl z sl, + z,d. 7) Fom 7), it is obseved that istead of z,d,weowhaveaew oise tem i this costucted sigal as zd ew = zd NC + z,d, whee z NC d = Ah,d α sl h sl, z sl,d h sl,d + Ah,d α sl z sl, 8) is the NC oise at destiatio ode D. It ca be show that has a zeo mea ad vaiace z ew d σ 2 z ew d = A 2 h,d [α 2sl hsl, h sl,d σ2 s l,d + σ 2 s l, )] + σ 2,d. 9) B. Achievable Rate i Multi-uicast Sigle-Goup NC-CC Hee, we will aalyze the achievable ifomatio ate fo the multi-uicast sigle-goup NC-CC system employig elay powe assigmet. Let us deive the mutual ifomatio fo the S D pai, which is deoted by I s,d. By substitutig y s, fom 2) ito 7), we have y,d = Ah,d α s h s,x + z s,)+z ew d. 10) Now, 1) fo l = ) ad 10) peset the appopiate chael model fo a NC-CC scheme with AF elayig ad a diect path fom souce S. We ca ewite these equatios i vecto fom as Y = Hx + BZ 11) whee Y = [ B = [ ys,d y,d ] [ ] h, H = s,d Ah,d α s h s, ], Z = z s, z s,d. zd ew Ah,d α s 0 1 As it was discussed i [13], the AF coopeative potocol with a diect path poduces a equivalet oe-iput two-output complex Gaussia oise chael with diffeet oise levels i the outputs. Theefoe, it ca be easily show that fo the give chael, I s,d is give by I s,d = W log det + 1 I 2 2 +P s HH ) BE[ZZ ]B ) ) 1 12) whee W is the available badwidth, det ) is the detemiat fuctio, I 2 2 is the idetity matix of size 2, symbolizes the complex cojugate taspositio, ad E[ZZ ]= diagσs 2,,σs 2,d,σz 2 ) is the covaiace matix of oise. ew d Note that i 12), the facto 1/ + 1) sigifies that it taes + 1) time blocs to complete the S D sessio. Afte algebaic maipulatios o 12) ad substitutig σz 2 fom ew d 9), we have 13), show at the bottom of the page. Thee obsevatios ae woth metioig hee: 1) Fom 9), the ew oise vaiace is lage tha the oigial oise vaiace σ 2,d ad is a fuctio of powe-allocatio coefficiets α sl, whee l = 1,...,; 2) mutual ifomatio o each pai is depedet o all powe-allocatio coefficiets; ad 3) fom 9) ad 13), as the umbe of sessios is iceased, the NC oise vaiace will icease, ad the mutual ifomatio will decease. C. AF-CC Let us biefly go ove the AF-CC, agaist which NC-CC will be compaed. I the AF coopeative wieless etwo i Fig. 1, each souce S commuicates with destiatio D via a diect li ad though oe AF elay without pefomig PNC) i a pedetemied time bloc. I phase 2, the elay idividually amplifies ad fowads the sigal y s,, whee = 1,...,, eceived fom each souce i phase 1. Theefoe, commuicatio occus i 2 time blocs, ad the achievable ate of th sessio, i.e., Is AF,d, ca be obtaied as [13] Is AF,d = W 2 log 1 + P s h s,d σs 2,d + P s A 2 AF h s, h,d A 2 AF h,d σ 2 s, + σ 2,d ) 14) I s,d = W + 1 log 1 + P s h s,d σ 2 s,d + P s A 2 α 2 s h s, h,d A 2 h,d l=1 α2 s l σs 2 l, + ) l=1 αs 2 h sl, l l h sl,d σ 2 2 s l,d + σ,d 2 13)

5 MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3619 whee P A AF = P s h s, + σs 2, is the elay amplificatio gai i the AF-CC scheme. III. RELAY POWER ALLOCATION IN A SINGLE-GROUP NETWOR-CODED COOPERATIVE COMMUNICATION SYSTEM Hee, we ae iteested i employig elay powe allocatio i the NC-CC system with the mai pupose of alleviatig the advese effects of NC oise. Ou objective is to fid the optimal elay powe allocatio that leads to the maximizatio of the system total data ate. We fist aalyze the geeal multi-uicast NC-CC system while icopoatig the elay powe allocatio i ou desig cosideatios. We also povide the aalytical solutio fo the special case of two-uicast. Note that, hee, we focus o sigle-goup tasmissio. The goupig issue will be addessed i Sectio IV. A. Optimizatio of Powe-Allocatio Coefficiets i a Multi-uicast System Let us defie α =[α s1,...,α s ] as the elay poweallocatio vecto fo the multi-uicast NC-CC system. With the objective of maximizig the sum ate sum of ifomatio ates) of sessios, deoted by R sum, we fomulate the followig powe-allocatio optimizatio poblem: Maximize R sum α) = α =1 I s,d s.t. =1 α2 s = 1 15) s.t. 0 α s 1, fo = 1,..., whee the depedece of R sum o α is explicitly show. This poblem is complex to solve diectly because the objective fuctio is o-covex ad also had to be tasfomed ito a covex fom [28]; theefoe, classical covex optimizatio techiques caot be used to fid a closed-fom expessio fo the powe allocatio. Thee ae some stadad umeical methods fo oliea multivaiable optimizatio such as cojugategadiet, Powell, o simplex [29] that ca be used to solve this poblem. Howeve, these algoithms ca be easily tapped i local maxima. Theefoe, istead of usig adom iitial values, we will use a obust optimizatio method by iitial samplig of the paamete space with the help of Sobol quasiadom sequeces [29]. I paticula, we apply a impoved vaiatio of the Matlab fmico fuctio, which offes efficiet computatios withi a polyomial time, as will be discussed i moe detail i Sectio III-C. I a pactical NC-CC system, elay powe-allocatio coefficiets ca be calculated at the elay ad set via a lowate cotol chael to the destiatios assumig that bloc legths ae sufficietly lage). The destiatios the extact the eceived sigal fom the elay path based o the eceived powe coefficiets. Late, i Sectios III-C ad V, we discuss eplacig istataeous CSI with log-tem chael vaiaces fo powe allocatio, which will educe the commuicatio ovehead betwee the elay ad destiatios. B. Aalytical Solutio fo Optimal Powe Allocatio i a Two-Uicast System Based o the deived mutual ifomatio fo the multiuicast case, we ca eadily obtai the achievable ates fo the special case of two-uicast. If we substitute with two i 13), we ca fid the mutual ifomatio betwee S 1 ad D 1, i.e., I s1,d 1, i 16) show at the bottom of the page, whee A 2 is the elay amplificatio fo the two-uicast case, which is obtaied fom 4) by substitutig = 2. The mutual ifomatio betwee S 2 ad D 2, i.e., I s2,d 2, ca be easily deived with appopiate chages of idices. Usig I s1,d 1, I s2,d 2, ad αs αs 2 2 = 1, we wite R sum α s1,α s2 ) i tems of α s1 o α s2 )as [ R sum α s1 )= W log 3 2 C 7 + C 1αs 2 ) 1 C 2 αs C 3 +log 2 C 8 + C ))] 4 1 α 2 s1 C 5 αs 2 17) 1 + C 6 whee 0 α s1 1 ad C i, whee i = 1,...,8, ae defied i Appedix A. Now, the maximum poit of 17) ca be calculated by fidig the zeos of its deivative. If we diffeetiate 17) with espect to α s1 ad let it be equal to zeo, the we have the followig quadatic equatio to solve Aα 2 + Bα + C = 0 18) whee α = αs 2 1, ad A, B, ad C ae fuctios of chael gais, elay ad souce powe values, ad oise vaiaces, espectively, ad defied i Appedix A. Fotuately, by solvig 18), we obtai a closed-fom solutio fo powe allocatio. Let S deote the set of the squae oots of the eal oots of 18) that belog to the ope iteval 0, 1). The optimum value of α s1, deoted by α s1,opt, is foud amog the elemets of S o at the bouday poits 0 ad 1. Theefoe α s1,opt = agmax R sum α s1 )) 19) α s1 {0,1} S ad the, usig the coditio αs αs 2 2 = 1, we have α s2,opt = 1 αs 2 1,opt. Note that, i the case that S =, whee is the empty set, dr sum α s1 )/dα s1 0 ad is stictly positive o egative i the age α s1 0, 1). Hece, the ed poits of the age, i.e., α s1 = 0 ad α s1 = 1, should be tested. I s1,d 1 = W 3 log 1 + P s 1 h s1,d 1 P s1 A 2 σs 2 + 2αs 2 1 h s1, h,d1 ) 16) 1,d 1 A 2 2 h,d 1 αs 2 1 σs 2 1, + αs 2 2 σs 2 2, + h s 2, h s2,d 1 α 2 2 s 2 σs 2 2,d 1 + σ,d 2 1

6 3620 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012 Fig. 2. Two-uicast etwo topology. p 1 ad p 2 peset two elay positios. C. Simulatio Results Hee, we study the advese impact of NC oise o the NC- CC pefomace ad the the efficiecy of the poposed powe allocatio i alleviatig the effect of this oise. I what follows, the simulatio esults fo the two-uicast NC-CC system ae illustated fist, ad those fo the multi-uicast system ae peseted ext. Two tasmissio methods ae compaed: EPA SG-NC is a sigle-goup NC-CC scheme with equal elay powe allocatio EPA), i.e., the elay mixes the sigals with equal powe-allocatio coefficiets α s = 1/, whee = 1,...,; OPA SG-NC is a sigle-goup NC-CC scheme with optimal elay powe allocatio usig 19) ad 15) fo twouicast ad multi-uicast cases, espectively. 3 Fo all the simulatios i this pape, we assume that the path-loss expoet is a = 4, ad without loss of geeality, assume that all the AWGN vaiaces ae equal to W. 4 We coside a caie fequecy of 2.5 GHz ad a badwidth of W = 10 Hz, which is suitable fo mobile WiMAX, i.e., IEEE e [31]. I ou umeical esults, coelated mobileto-fixed chael coefficiets, i.e., souces-to-elay ad elayto-destiatios chaels, ae geeated accodig to Clae s model [32]. I additio, coelated mobile-to-mobile chael coefficiets, i.e., souce-to-destiatio chaels, ae geeated usig the method of exact Dopple spead [33]. We use omalized Dopple fequecy i.e., f D T S, whee f D is the Dopple fequecy shift ad whee T S is the symbol duatio) of coespodig to the mobile speed of 13 m/h. Note that i simulatio esults, we povide a mea sum ate, which is obtaied by aveagig the sum ate ove 10 5 chael ealizatios. 1) Two-Uicast NC-CC System: We ivestigate two sceaios based o vaious elay positios ad souce powe values fo the topology show i Fig. 2. Moeove, the AF-CC scheme ad diect tasmissio ae peseted fo compaiso; whee i the latte, a souce diectly tasmits its data to the coespodig destiatio without help fom the elay. Fig. 3 shows the aveage sum ate of the two-uicast system fo vayig 3 Stictly speaig, sice 15) is solved umeically, global optimality of the solutio caot be guaateed. Howeve, as will be show i Fig. 5, the umeically foud solutios ae almost idistiguishable fom the optimal solutios. Hece, we will use the tem OPA SG-NC to efe to ou poposed powe allocatio. 4 Although the fomulatio i this pape is deived fo distict oise vaiaces at each ode, i simulatio modelig, simila to [14] [16], [24] [26], ad [30], we assume fo the pupose of expositio that all the AWGN vaiaces ae the same. Fig. 3. Aveage sum ate of the two-uicast NC-CC system vesus elay positio. Diffeet tasmissio schemes with P s1 = P s2 = P = 0.4 W ae compaed. elay positios fom s 1 to s 2 o the dotted lie i Fig. 2). Thee mai obsevatios that follow fom this simulatio ae as follows. Fist, the EPA NC-CC scheme without cosideig the NC oise, which is epeseted by ideal NC-CC, has the best sum-ate pefomace fo most of the elay positios. Howeve, i eality, whe NC oise is peset, the pefomace of EPA SG-NC is seveely degaded i compaiso with ideal EPA NC-CC. Secod, the OPA SG-NC sigificatly mitigates the effect of NC oise. Thid, the sum-ate pefomace of the ideal NC-CC scheme simila to AF-CC is highly depedet o elay positio [based o 17)]. Whe the elay ode is ot positioed midway betwee the souce ad destiatio odes, the sum ate is oticeably lowe [15]. 5 Howeve, i this case, powe optimizatio offes moe gai. Fo example, OPA SG- NC ca eve pefom bette tha EPA ideal NC-CC whe the elay is close to oe of the souces. I Fig. 3, it is also otable that diect tasmissio povides geate aveage sum ate fo some egios. Fo example, whe the elay ode is close to the souce o destiatio ode, the pefomace of diect tasmissio is the best. Two ituitive easos behid this pheomea ae as follows. Fist, as afoemetioed, the pefomace of NC-CC geeally woses as the elay moves close to o fathe fom the souce. It is expected that this will taslate to pooe pefomace of OPA SG-NC compaed with diect tasmissio whe the elay is eally close to oe souce ode, eve whe oequal powe allocatio is used. Secod, diect tasmissio i a two-uicast system has a highe spectal efficiecy facto of 1/2 compaed with 1/4 i 14) ad 1/3 i 16) fo the AF-CC ad NC-CC tasmissios, espectively. Howeve, it is ow that diect tasmissio offes pooe outage pobability due to divesity ode of 1 compaed with 2 whe elay is used [17]. 5 As ca be see fom the figue, whe the elay is positioed midway betwee the souce ad destiatio, AF-CC ad ideal NC-CC achieve thei optimum pefomace, which woses as the elay moves close to o fathe fom the souce. This pheomeo is cosistet with pevious esults peseted i [34] ad [35], whee it was show that if the powe allocatio to the souce ad elay is equal, the optimum elay locatio is just i the middle with espect to the souce ad destiatio.

7 MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3621 Fig. 4. Aveage sum ate of the two-uicast NC-CC systems vesus souce s 1 powe. Diffeet tasmissio schemes with P s1 = P s2 = P ae compaed. Fig. 4 demostates the aveage sum ate fo diffeet powe values fo souce s 1. I this simulatio, we focus o the positio p 1 fo the elay which is peseted i Fig. 2). We see that the poposed OPA SG-NC outpefoms othe schemes fo all souce powe ages. Whe the ode powe values ae high, OPA SG-NC ca achieve, espectively, up to 7.92% ad 19.48% sum-ate gai i compaiso with EPA SG-NC ad AF-CC schemes. We ote that, i this setup, OPA SG-NC outpefoms ideal NC-CC, which uses a equal powe-allocatio scheme. 2) Multi-uicast NC-CC System: Hee, esults fo the multiuicast system with a geeal adom etwo topology ae peseted. We coside 100 adomly geeated etwo istaces. Fo each istace, souce ad destiatio odes ad oe elay ae distibuted i a 2-D ectagula egio of size 450 m 450 m. The elay is fixed at coodiate 225, 225), i.e., at the cete of the squae. The souce destiatio pais ae adomly located with a uifom distibutio i a squae egio such that the elay is placed i the egio betwee each pai. The closest distace betwee ay two odes is limited to 30 m. We also assume that all souces have equal powe ad P = 1W. Fo each plot show, the esults ae aveaged ove 100 etwo istaces. Note that the powe-allocatio poblem 15) depeds o the istataeous CSI. Theefoe, to avoid the eed fo chagig powe-allocatio coefficiets fo each bloc tasmissio, we eplace the squae of magitude of chaels, i.e., h, with thei meas σh 2. We will compae the diffeece i pefomace betwee usig h ad σh 2 i Sectio V. Moeove, to calculate the powe-allocatio coefficiets, we have solved 15) usig the impoved vaiatio of Matlab fmico, which is iitially give a budget, i tems of the umbe of objective fuctio R sum ) calls. Withi the iitial budget, fmico evaluates the objective fuctio usig the Sobol sequece ad iitializes a subspace, which is costucted fom poits with the maximum sum ate. The Sobol sequece esues that we ca pogessively sample the paamete space i a vitually uifom fashio. Ituitively, if the budget is lage eough, the subspace ca sufficietly close i o the global maximum to allow successful executio of the optimizatio algoithm [36]. Fig. 5. Relay powe-allocatio coefficiets foud by the poposed umeical method ad aalytical solutio 19) vesus elay positio. Fig. 6. powe. Aveage sum ate of the six-uicast NC-CC system vesus souce Ulie most optimizatio methods that stat with a sigle poit i space, usig the Sobol sequece allows us to stat fom a egio of space that ca be abitaily made close to the global maximum by iceasig the iitial budget. We set the iitial budget as 1000 objective fuctio calls fo the followig simulatios. The effectiveess of the poposed umeical method is show i Fig. 5 fo the multi-uicast NC-CC system with = 2, whee the simulatio settigs ae the same as those i Fig I paticula, the powe-allocatio coefficiets foud via the impoved vesio of fmico usig the Sobol sequece ae compaed with those obtaied usig 19) fo vayig elay positios. Oe ca see that the esults of the poposed umeical scheme ae almost idetical to the optimal powe-allocatio coefficiets. Fig. 6 compaes the aveage sum ate of the two schemes fo a six-uicast NC-CC system. Two emas follow fom this figue as follows. Fist, OPA SG-NC povides sigificat 6 Fo the sae of simplicity ad sice we have the aalytical solutio fo the optimum powe allocatio i two-uicast NC-CC [give i 19)], we examie the NC-CC system with = 2.

8 3622 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012 Fig. 8. Tasmissio scheme of the souces ad the elay. a) Diect scheme ad b) multigoup NC-CC scheme. Fig. 7. Ratio of the sum ate offeed by the OPA SG-NC to that offeed by AF-CC vesus sessio umbe fo ideal NC-CC ad NC-CC cosideig NC oise schemes. sum-ate impovemet ove the EPA SG-NC, e.g., at souce powe of 0.4 W, a gai of appoximately 1.43 bps equivalet to 18.21%) is achieved via the poposed powe allocatio. Secod, while multi-uicast NC-CC usig the poposed powe allocatio outpefoms AF-CC fo all souce powe values, EPA SG-NC has pooe pefomace tha AF-CC fo smallto-medium souce powe values. Howeve, this esult caot be see i the two-uicast case. This obsevatio aises a questio about how good the NC-CC ca pefom compaed with the AF-CC whe the umbe of sessios i the etwo is iceased. To aswe this questio, we plot the atio of the sum ate offeed by OPA SG-NC to that offeed by AF-CC as a fuctio of sessio umbe, i.e.,, ifig.7.theesult fo ideal NC-CC with the poposed elay powe allocatio is also show fo compaiso. Oe ca see that the atio fo the NC-CC system cosideig NC oise deceases as the umbe of sessios is iceased. Fo example, OPA SG-NC pefoms wose tha AF-CC whe thee ae moe tha ie sessios i the etwo. This is maily due to the accumulatio of high NC oise at the destiatio odes that is ot peset i ideal NC- CC scheme) fo iceasig the umbe of sessios accodig to 13). This esult is i accodace with the thid obsevatio i the pevious sectio: The highe the umbe of sessios i the NC-CC system, the highe the NC oise, ad theeby, the lowe the achievable ates. This motivates us to ivestigate the NC-CC pefomace i a multi-uicast sceaio with goup allocatio ad to aalyze the gais that goupig ca offe i cojuctio with the poposed elay powe allocatio. IV. GROUP ALLOCATION Hee, we itoduce goupig ito the multi-uicast NC-CC system with powe allocatio. Thee ae two easos that lead us to coside goupig, which ae summaized as follows. Based o the pevious esults, we obseved that eve whe usig elay powe allocatio, it may be bette to allocate sessios ito diffeet goups with a smalle umbe of sessios athe tha ito a sigle goup with sessios) to educe the impact of NC oise. O the othe had, efeig to the spectal efficiecy facto of 1/ + 1) i 13) fo the ifomatio ate of a sigle-goup NC-CC system compaed with 1/2) i 14) fo the o-etwo coded AF-CC, we obseve that NC-CC may offe highe ates compaed with AF-CC fo a iceasig umbe of sessios. Theefoe, it is essetial to fid the NC-CC sceaio with a optimal umbe of sessios i each goup. The goupig cocept has also bee used i degaded boadcast chaels [37] to educe the complexity due to successive itefeece cacelatio. The complexity is also a issue i the cosideed NC-CC system whee PNC is essetially a fom of liea itefeece cacelatio with the use of apioiifomatio, i.e., apioiifomatio that each destiatio diectly obtais fom othe souces. Thus, effective goupig of sessios may educe the complexity of the NC-CC system. Let us fist deote G as the umbe of available goups, whee it has the maximum value of, ad use G i to idicate the ith goup ith set of sessios), whee i = 1,...,G. We defie a assigmet matix A G, whose elemets ae deoted by a i {0, 1}, whee i = 1,...,Gad = 1,...,.Thevalue of a i has the followig itepetatio: a i = 1 meas that souce S is assiged to the ith goup, i.e., G i, ad a i = 0 meas that S is ot assiged to G i. Each sessio ca oly be ivolved i exactly oe goup. That is, G i=1 a i = 1. Theefoe, G i is the set of souce odes as G i = {S a i = 1, = 1,...,}. Note that, i case of A = I, evey sessio is assiged to a distict goup, ad the system is the same as a multi-uicast AF-CC. A. Multigoup Tasmissio Model Each goup G i is a G i -uicast NC-CC system ad has the same tasmissio details as a sigle-goup case i Sectio II with G i souce destiatio pais. A modificatio to the time bloc stuctue of the NC-CC system is eeded to eable such sessio goupig. Fig. 8 shows a example of the cosideed time bloc stuctue fo multiple goups. I this case, the tasmissio ca be pefomed i two phases as follows. I phase 1, time blocs ae used fo tasmissio by the souce odes i a pedetemied time bloc. I phase 2, G time blocs ae used by the elay fo tasmittig liea combiatio of souces ifomatio i G i, whee i = 1,...,G. Ideed, the

9 MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3623 elay mixes G i ovehead sigals that belog to the G i with ou poposed powe-allocatio coefficiets ad tasmits the combied sigal i the + i)th time bloc. As show i Fig. 8, ude this scheme, the size of the time bloc fo ay souce i G i,aswellasfoelayfog i tasmissio), will be G i / G i + 1))N.T s, whee N.T s is the size of each time bloc ude diect tasmissio. Ideed, the total available time fo G i is G i time blocs, i.e., G i.n.t s. As oe additioal time bloc is eeded fo the elay tasmissio, the legth of each time bloc i G i will be G i / G i + 1))N.T s.this time stuctue fo the multigoup scheme esults i a fai time allocatio amog sessios see [26] fo moe details). B. Achievable Rate i the Multigoup NC-CC System We ca geealize the obtaied achievable ate expessio of sigle-goup NC-CC i 13) to the multigoup NC-CC system as follows. Let us assume S is i goup G i. Ude this settig ad usig the method i Sectio II, the mutual ifomatio betwee S ad D assiged to G i, deoted by Is i,d, ca be obtaied with 20), show at the bottom of the page, ad whee A i is the elay amplificatio gai fo the ith goup as P A i = 21) l=1 α2 s Psl l h sl, + σs 2 l,) ail ad whee α sl is the elay powe-allocatio coefficiet such that l=1 α2 s l a il = 1 ad G i = l=1 a i l. We will coside how to assig a sessio to a goup i the followig. V. J OINT GROUP ASSIGNMENT AND POWER ALLOCATION As afoemetioed, fom the system optimizatio poit of view, the oveall ate of all sessios ca be maximized by allocatig the pope coefficiet of elay powe fo coopeatio ad NC. Moeove, it is essetial to allocate the sessios to optimal goups. Theefoe, to futhe ehace the pefomace of the NC-CC system, it is impeative to devise algoithms fo joit optimal goup assigmet ad elay powe allocatio acoss sessios. The joit optimizatio poblem with the objective of maximizig the oveall sum ate while satisfyig all the costaits ca be fomulated as Maximize G i=1 α,a Ri sumα, A) s.t. a i {0, 1}, foi=1,...,g, ad =1,..., s.t. G i=1 a i =1, fo =1,..., s.t. =1 α2 s a i =1, fo i=1,...,g s.t. 0 α s 1, fo =1,..., 22) whee R i sumα, A) is the sum ate of the ith goup ad is defied as R i sumα, A) = S G i I i s,d 23) whee Is i,d was give i 20). Fom 20), Rsum i is a fuctio of the assigmet matix A ad the elay powe allocatio coefficiet vecto α. Note that the poblem i 22) ca be viewed as a geealized assigmet poblem, which is a NPhad poblem [24], [26]. Howeve, some special cases of this poblem ca be efficietly solved. Fo example, if we estict G i to at most two, the poblem ca be educed to the maximum matchig poblem accodig to the followig lemma. Lemma 1: Fo the case whee the size of goups ae esticted to at most two, poblem 22) ca be educed to maximal matchig. Poof: Fist, let us give a bief desciptio of the maximal matchig poblem. Maximal weighted matchig, which is a gaph-theoetical poblem, selects a subset of edges such that each vetex is icidet with at most oe edge o with exactly oe edge i the case of the pefect matchig poblem), ad secod, the total weight of the selected edges is as lage as possible [38]. Coside a multi-uicast NC-CC system with sessios, i which the goup size is esticted to at most two. We costuct a weighted gaph GV,E), whee the set V cosists of 2 vetices epesetig physical souce odes, i.e., S 1,...,S, ad auxiliay odes Ŝ1,..., S ˆ. Each pai of distict vetices S l ad S fom the set {S 1,...,S } is joied by a edge with weight equal to Is i l,d l + Is i,d. This weight is equal to the mutual ifomatio betwee S l ad D l plus the mutual ifomatio betwee S ad D, whe S l ad S ae allocated to the goup i with o othe odes i that goup), ad the elay powe-allocatio coefficiets ae set usig the poposed scheme i Sectio III. Futhemoe, each pai of odes S ad Ŝ is joied by a edge with weight equal to Is AF,d,asgivei 14). The optimizatio poblem is the equivalet to fidig a maximal weight matchig i GV,E). Maximum matchig i a gaph ca be solved i polyomial time [38]; hece, this special case of poblem has a polyomial time solutio. This is a iteestig obsevatio because, i the followig Theoem 1, fo a NC-CC system with EPA, we ca achieve a appoximatio facto of at least f m = gmg 2 m + 2)/g m + 1) 3 by estictig the size of goups by some positive itege g m. Note that thee ae expoetially may ways to do goupigs eve whe we estict the size of goups to at most two i.e., g m = 2). Theoem 1: I a multigoup NC-CC system with EPA, ay optimal solutio to poblem 22) whe the size of goups is Is i,d = W G i G i +1 log 1+ P s h s,d σs 2 +,d P s A 2 i α2 s h s, h,d A 2 i h,d l=1 α2 s l σ 2 s l,a il + l=1,l h sl, h sl,d α 2 s l σ 2 s l,d a il )+σ 2,d 20)

10 3624 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012 esticted to a positive itege g m is at most a facto of f m = g2 mg m + 2) g m + 1) 3 24) smalle tha ay optimal solutio to poblem 22) with o estictio o the size of goups. Poof: See Appedix B. We will veify the tightess of the lowe boud 24) i Sectio V-B. To tacle the geeal poblem, we divide it ito two subpoblems. The fist subpoblem fids the elay powe-allocatio coefficiet fo a give A. This ca be solved usig the solutio peseted i Sectio III, by applyig it to each goup G i as follows: { Maximize α s.t. Rsumα, i A) S G i αs 2 = 1 ad 0 α s 1. 25) I the secod subpoblem, by utilizig the esults of the fist subpoblem, we attempt to fid A that esults i the optimum goup assigmet. The esultig goup-allocatio subpoblem is a NP-had poblem [24] sice ay elemet of A has a value of eithe 0 o 1, ad the seach dimesio of A is 2. Oe appoach to solvig this subpoblem is do a exhaustive seach. Fist, fo ay give A, we calculate powe-allocatio coefficiets fo each goup ad the the sum ate accodig to 25) ad 20), espectively. Next, we select the goupig that gives the maximum sum ate. Ufotuately, this appoach quicly becomes impactical as the umbe of uses i the etwo iceases. Theefoe, i the followig, we popose a suboptimal geedy algoithm. Note that geedy algoithms have also bee developed i [24] ad [25] to fom goups o subsets of odes fo the puposes of coopeatio. Howeve, they ae ot eadily applicable to ou NC-CC system ude cosideatio. I [24], a geedy algoithm has bee developed fo pate ad subcaie allocatio i a coopeative multiuse OFDM etwo. Usig a geedy algoithm, Nosatiia ad Hute [25] have poposed a coopeative pate assigmet to miimize the aveage outage pobability ove all uses i a coopeative etwo. The udelyig etwos i [24] ad [25] ae covetioal coopeative etwos with o NC ad ae vey diffeet fom ous. A. Suboptimal Algoithm fo Joit Goupig ad Relay Powe Allocatio i the NC-CC System Hee, we popose a suboptimal geedy algoithm to fid the assigmet matix A. I the poposed joit goupig ad powe assigmet algoithm, oly the destiatio odes ot the souce odes) have to be ifomed by the elay of the assigmet matix A ad the powe-allocatio coefficiet vecto α. The poposed algoithm is pefomed at the elay ode. The elay the coveys the goup assigmet ad the poweallocatio coefficiets to the destiatios though a low-ate cotol chael. I each iteatio, the algoithm assigs a sessio to a goup. The, cosideig the poposed elay powe allocatio, it calculates the ew sum ate accodig to 23). This causes a icease i the total sum ate. The objective is to fid the best sessio goup pai that maximizes the icease i oveall sum ate afte each iteatio. As a esult, thee ae iteatios to be pefomed, ad the complexity fo each iteatio of the poposed algoithm is O 2 ). Afte a iteatio, the assiged sessio i.e., the souce assiged to a goup) is emoved fom the set of uassiged sessios, which is deoted by B. Algoithm 1: Joit goup assigmet ad powe allocatio 1Set A = I ad calculate the AF-CC ate based o 14) fo all sessios i the etwo. 2 Select souce S with the maximal AF-CC ifomatio ate. Set G = 1 ad update A as a 1 = 1, a 1l = 0 fo l, i.e., assig S to G 1. B {S 1,...,S }\{S } 3 while B do 4 fo all elemets of B, S l, do 5 G G+1 = S l 6 Hypotheses amog G + 1 available goups: If ith goup G i icludes S l :seta il = 1. Solve 25) ad the fid the coespodig goup sum ate fom 23) fo the goup ude cosideatio. Amog all hypotheses, fid the maximal sum-ate impovemet. I othe wods, fid the goup fo S l that esults i the best goup sum ate; deote this goup by G S l ad the coespodig sum ate by R S l. ed 7 Fid the souce S i B that esults i the maximum R S obtaied i Step 6; deote this souce by S. 8 Update A based o G S assig S to its best goup). 9 Update B B\{S }. 10 If G G+1 was selected as the best goup the icease G by oe. ed Iitially, A is set to the idetity matix, i.e., the iitial scheme is the AF-CC. The souces ae soted accodig to the souce destiatio-pai idividual achievable ifomatio ate i 14). The souce S with the maximal ifomatio ate is selected, ad A is updated as a 1 = 1, a 1l = 0fol ad set G = 1 e.g., assig S to G 1 ). Next, fo each souce S l i B, amog the G available goups, the algoithm maes G hypotheses that G i, whee i = 1,G, cotais S l.italso maes the G + 1)th hypothesis that cotais S l belogs to a ew goup, i.e., G G+1. The, amog the G + 1) hypotheses, the algoithm selects oe that maximally iceases the sum ate. Fo each hypothesis, the elay powe allocatio is obtaied by solvig 25), ad the, the goup sum ate is obtaied by 23). Afte epeatig this pocess fo all souces i B, fom all selected hypotheses, the algoithm chooses oe hypothesis that maximally iceases the sum ate, emoves the coespodig souce fom B, ad updates A ad α accodigly. The, it goes bac to detemie the best sessio goup pai agai ad cotiues the iteatio. The algoithm stops whe all the sessios ae assiged to goups, i.e., B =, ad outputs A ad α as the aswes of the joit optimizatio poblem. Note that the poposed algoithm is suboptimal because of the geedy local seach. It is ow that geedy algoithms may poduce

11 MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3625 suboptimal esults because they may costuct esults based oly o local maxima withi the seach space [29]. I additio, the iteatio always coveges because the sum ate is odeceasig i each iteatio. Algoithm 1 summaizes the poposed joit goup assigmet ad powe allocatio. Istead of cotiually computig the powe allocatio ad goup assigmet based o istataeous CSI, heei efeed to as the exact scheme, we popose a pactical scheme that detemies elay powe allocatio ad goup assigmet i advace based o log-tem chael statistics. This scheme maitais elay powe-allocatio vecto ad goup assigmet matix thoughout multiple bloc tasmissios as log as chael statistics ad the etwo topology ae uchaged. Hece, the complexity of looig fo powe allocatio ad goup assigmet ad the equied ovehead to update this ifomatio i the etwo is educed. I the followig, we compae the exact ad pactical schemes. Fig. 9. powe. Aveage sum ate of the six-uicast NC-CC system vesus souce B. Simulatio Results Hee, we coside the pefomace of the fou methods EPA SG-NC, OPA SG-NC, EPA MG-NC, ad OPA MG-NC) based o the poposed solutios fo the multi-uicast sceaio. We discuss the impact of these methods o the NC-CC systems i two etwo topologies. The EPA MG-NC ad OPA MG-NC schemes ae outlied as follows. I the EPA MG-NC method, sessios ae assiged to diffeet goups. Howeve, the elay uses equal powe allocatio to mix the eceived sigals. The poblem fomulatio i this case is a simplified vesio of the fomulatio give i 22), i.e., evey α s coefficiet is set to 1/ G i fo S G i. The solutio fo this poblem oly cosists of goup assigmet fo each sessio. I the OPA MG-NC method, joit powe allocatio ad goup assigmet ae employed. The poposed suboptimal algoithm is used to deive the powe-allocatio coefficiet vecto ad the goup assigmet matix. Note that all the simulatio settigs ae the same as those i Sectio III. I Fig. 9, we compae the sum-ate pefomace of fou methods vesus souce powe fo a six-uicast NC-CC case. We also peset esults fo diect tasmissio ad AF-CC fo pefomace compaiso. I paticula, simulatio esults lead to the followig coclusios. 1) As expected, EPA SG-NC poduces a miimal sum ate, compaed with all othe NC-CC schemes, which is elated to the metioed tadeoff betwee badwidth efficiecy ad NC oise, ad equal elay powe-allocatio scheme, which is ot optimal whe the etwo topology is ot symmetic. We coside this case as a lowe boud fo pefomace compaiso. We ote that EPA SG-NC has bette pefomace tha AF-CC fo high souce powe values. 2) Compaed with the sigle-goup case, EPA MG-NC allows cosideable pefomace gai achieved though goupig. It is clea that EPA MG-NC outpefoms EPA SG-NC fo low-to-modeate souce powe values. Howeve, as the souce powe is iceased, the diffeece betwee two schemes becomes smalle. I othe wods, as the souce powe iceases, the goupig algoithm teds to locate sessios i a goup with lage size. This ca be explaied fom 13), which shows that the effect of NC oise o mutual ifomatio becomes less pomiet ude high souce powe coditio. 3) OPA MG-NC pesets the best sum-ate pefomace. It povides up to 64.1%, 14.88%, ad 10.2% ehacemets i the sum ate, as compaed with the EPA SG-NC, OPA SG-NC, ad EPA MG-NC, espectively. Theefoe, ou poposed geedy algoithm pefoms well, which ca be used i pactical cases. Cosideig the ovehead ad complexity of OPA MG-NC, howeve, oe ca esig to OPA SG-NC as the ext best method fo high souce powe values. 4) I Fig. 9, we also compae the suboptimal goup allocatio obtaied by ou poposed geedy algoithm ad those obtaied by exhaustive seach cosideig all possible goup allocatios. Specifically, we compae OPA MG- NC with OPA MG-NC, exhaustive, whee the poposed powe allocatio is beig used at the elay. We also compae EPA MG-NC with the EPA MG-NC, exhaustive scheme. I both cases, we obseve that the pefomace of the poposed suboptimal goup allocatio is highly competitive. I Table I, we ivestigate the effect of the umbe of sessios o the poposed methods. I paticula, we study the sumate pefomace of thee methods defied as the pecetage of sum-ate ehacemet of each method ove the EPA SG- NC method) vesus sessio umbe ad two souce powe values of 0.2 ad 0.6 W. The followig coclusios ae daw fom Table I. 1) The highe the sessio umbe is, the highe the sum-ate impovemets will be; howeve, EPA MG-NC ad OPA MG-NC allow moe pefomace ehacemet fo high sessio umbes. The ituitive easo is that iceasig the umbe of sessios iceases the NC oise of each sessio i 8). Accodigly, the methods utilizig goupig ae moe liely to impove the system pefomace. 2) The pefomace impovemets decease as the souce powe iceases.

12 3626 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012 TABLE I EFFECT OF SESSION NUMBER ON THE SUM-RATE PERFORMANCE PERCENTAGE OF SUM-RATE ENHANCEMENT OVER THE EPA SG-NC SCHEME) Fig. 11. Sum-ate eductio facto f due to estictig the size of goups to a positive itege g m, which is defied i 29), fo vayig g m. The lowe boud f m, which is deived i Theoem 1, is also peseted. size educes the sum-ate pefomace of the NC-CC system; howeve, as expected, this eductio deceases as g m iceases. We also otice that the tightess of the deived lowe boud f m impoves as g m iceases. VI. CONCLUSION Fig. 10. Aveage sum ate of a typical fou-uicast NC-CC system vesus souce powe. Results ae also compaed fo pactical ad exact schemes. It is iteestig to see how good the poposed methods ca pefom fo a typical etwo topology. To this ed, we select a typical istace of fou souce destiatio pais with locatios 135 m, 225 m) 405 m, 315 m), 105 m, 375 m) 15 m, 105 m), 45 m, 375 m) 105 m, 375 m), ad 195 m, 105 m) 435 m, 405 m), espectively. Fig. 10 eveals the aveage sum ate vesus souce powe fo this idividual settig. Sigificat impovemet ca be obtaied by the poposed methods. Fo example, fo low souce powe values, the sum-ate impovemet of OPA MG-NC is up to 107% compaed with EPA SG- NC. I this figue, we have also compaed the diffeece i sum-ate pefomace betwee usig the poposed pactical scheme usig aveage chael powe values) ad the exact scheme usig istataeous CSI) fo powe allocatio ad goup assigmet. The compaiso shows a diffeece of up to 1.31 ad 1 bps at high souce powe values fo OPA SG-NC ad EPA MG-NC, espectively. This diffeece is expected as the poposed pactical schemes oly use aveage chael powe values. Howeve, the decease i complexity ad ovehead ca be moe appealig tha the esultig pefomace degadatio. Fially, we ivestigate the effect of estictig the goup size o the sum-ate pefomace. We use f, which is defied i 29), as a facto to detemie the eductio of the sum ate due to estictig the size of goups to a positive itege g m. We also study the tightess of the lowe boud of f, i.e., f m, which is deived i Theoem 1. I Fig. 11, we plot f vesus g m fo a ie-uicast NC-CC system with EPA usig Mote Calo simulatio. It is obseved that estictig the goup We have addessed the poblem of NC oise eductio i a multi-uicast NC-CC system. Oe of ou cotibutios i dealig with NC oise was developig a optimum poweallocatio famewo at the elay. We povided a mathematical famewo fo the achievable ifomatio ates of the system with the otio of powe assigmet ad the peseted a ovel powe-allocatio scheme to maximize the total data ate amog all the sessios. We also povided a simple closed-fom powe allocatio fo a two-uicast case. Though simulatios, we showed the efficiecy of the poposed powe-allocatio techiques i helpig ovecome the advese effects of NC oise. We obseved that powe optimizatio offes moe gai fo a asymmetic etwo sceaio. The ate aalysis ad simulatio esults evealed the fact that, despite the poposed powe allocatio, the pefomace of the multi-uicast NC-CC is fudametally limited by iceasig the umbe of souce destiatio pais that shae the same elay ode. I paticula, siglegoup NC-CC with powe allocatio pefoms wose tha oetwo coded AF-CC whe thee ae moe tha ie sessios i the etwo. Aothe cotibutio of this pape to tacle this issue was developig a goup assigmet scheme to assig sessios to diffeet goups fo pefomig PNC at the elay. We also combied powe allocatio ad goup allocatio to futhe impove pefomace. Fo this pupose, we used a suboptimal geedy algoithm to solve the NP-had joit powe ad goup assigmet poblem ad veified the efficiecy of ou algoithm i impovig the system ifomatio ate compaed with a multi-uicast system with o powe o goup allocatio. It was show that, although poposed algoithms oly ely o logtem chael statistics, they ca effectively alleviate the impact of NC oise ad otably ehace data ates i the NC-CC etwo, paticulaly fo a high umbe of sessios.

13 MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3627 APPENDIX A DEFINITION OF THE CONSTANTS IN 17) AND 18) Hee, we defie the costats that wee used i Sectio III as C 1 = Ps1 P h,d1 h s1, C 2 = σ 2 s1, σs 2 ) 2, P h,d1 +σ,d 2 ) P h s2, h,d1 1 h s2,d 1 σ 2 s 2,d 1 + σ 2,d 1 Ps1 h s1, P s2 h s2,) C 3 = P h,d1 σs 2 2, + P h s2, h,d1 h s2,d 1 σs 2 2,d 1 + σ,d 2 Ps2 1 h s2, + σs 2 ) 2, C 4 = Ps2 P h,d2 h s2, C 5 = σ 2 s1, σs 2 ) 2, P h,d2 +σ,d 2 ) P h s1, h,d2 2 + h s1,d 2 σ 2 s 1,d 2 + σ 2,d 2 Ps1 h s1, P s2 h s2,) C 6 = P h,d2 σs 2 2, + σ,d 2 Ps2 2 h s2, + σs 2 ) 2, C 7 = 1 + h s1,d 1 P s1 σ 2 s 1,d 1, C 8 = 1 + h s2,d 2 P s2 σ 2 s 2,d 2 A = C 1 C 3 C 5 C 8 C 5 C 4 ) C 2 C 4 C 6 + C 5 )C 7 C 2 + C 1 ) B = C 1 C 3 [2C 8 C 5 C 6 + C 4 C 5 C 6 )] C 3 C 4 C 5 + C 6 )2C 7 C 2 + C 1 ) C = C 3 [C 1 C 6 C 8 C 6 + C 4 ) C 4 C 7 C 3 C 5 + C 6 )]. APPENDIX B PROOF OF THEOREM 1 Coside a multigoup NC-CC system with sessios ad equal elay powe-allocatio scheme. A solutio to poblem 22) is called a g-esticted solutio if the size of the goups i the solutio is at most g. Aoptimum g-esticted solutio is a g-esticted solutio that has the highest sum ate amog all g-esticted solutios. To pove the theoem, we show that ay -esticted solutio with sum ate R ca be coveted to a g m -esticted solutio with a sum ate of at least f m R. If the size of all the goups i the -esticted solutio is at most g m, the o covesio is eeded as the solutio is aleady a g m -esticted solutio. Othewise, thee is at least oe goup of size at least g m + 1. To covet this solutio to a g m -esticted solutio, we patitio evey goup G of size = q g m +, whee q 1 ad 1 <g m,itoq goups, i.e., Ĝ1,...Ĝq, ofsizeg m, ad oe goup, i.e., Ĝq+1, ofsize. I goup Ĝq+1, we put the i-smallest, whee 1 i, idividual achievable ifomatio ate [give i 14)] i goup G. We show that the sum of the sum ates of goups Ĝi, whee 1 i q + 1, efeed to as ˆR, is at least f m times the sum ate of goup G, R. Deote the achievable ifomatio ate of the th sessio assiged to Ĝi, whee i {1,...,q+ 1}, byîi s,d, which ca be eadily deived with appopiate chages i powe-allocatio coefficiets i 20) as whee Î i s,d = Ĝi Ĝi + 1 bi s ) b i 1 s = log 1 + P s h s,d σs 2 + P s h s, h,d,d ηs i ηs i = h,d S l S σs 2 h sl, l, + h sl,d σ2 s l,d + σ2,d P S l Ĝi S l Ĝi S l Ĝi Psl h sl, + σs 2 ) l,. 26) I additio, deote the ifomatio ate of the th sessio assiged to the goup G of size by Îs,d. Similaly, Îs,d ca be witte as whee Î s,d = + 1 b s 27) ) 1 b s = log 1 + P s h s,d σs 2 + P s h s, h,d,d η s ) S l S η s = h,d σs 2 h sl, l, + h sl,d S l G σ2 s l,d + σ2,d P S l G Now, let us defie the atio f = ˆR R = S l G Psl h sl, + σs 2 ) l,. 28) q+1 i=1 s Ĝi Îi s,d s G Îs,d 29) ad deote the lowe boud of f by f m. Substitutig Îi s,d ad Î s,d ito 29), we get f = g m q g m +1 i=1 s bi Ĝi s s bq+1 Ĝq+1 s s G b s. 30) Fo each S {Ĝ1,...,Ĝq, Ĝq+1}, fom 26) ad 28), we have ηs i <η s ; hece, b i s >b s. Theefoe, eplacig b i s with b s fo all S {Ĝ1,...,Ĝq, Ĝq+1}, wehave f g m q g m +1 i=1 s b s Ĝi s Ĝq+1 b s s G b s. 31)

14 3628 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012 By defiig x = q be witte as Note that i=1 f hx) = x qg m s Ĝi b s / s Ĝq+1 b s ), 31) ca g m +1 g m +1 x +. x + 1) +1 mi b s S {Ĝ1,...,Ĝq} max b s. S Ĝq+1 Sice Ĝq+1 cosists of odes with the smallest idividual achievable ifomatio ate i G, we get Theefoe mi b s max b s. S {Ĝ1,...,Ĝq} S Ĝq+1 x qg m. 32) The fuctio hx) is a stictly iceasig fuctio of x because dhx) dx = g m g m x + 1)2 > 0 ad g m /g m + 1)) > / + 1)). Theefoe, hx) gets its miimum value at x = qg m /. Cosequetly f h qgm ) = g m g m +1 qg m ) Let = q g m. Thus, = +. By 33), we have f h qgm ) = = = = g m g m gm g m +1 > gm g m + 1 gm g m + 1 which cocludes the poof. +1 ) ) + gm +1 g m ) ) ) ) 1 +1 gm )1 1 ) g m ) ) gm 1 1 g m + 1 g m + 1) 2 = g2 mg m + 2) g m + 1) 3 34) REFERENCES [1] R. Ahlswede, N. Cai, S. R. Li, ad R. W. Yeug, Netwo ifomatio flow, IEEE Tas. If. Theoy, vol. 46, o. 4, pp , Jul [2] S. atti, H. Rahul, W. Hu, D. atabi, M. Medad, ad J. Cowcoft, XORs i the ai: Pactical wieless etwo codig, IEEE/ACM Tas. Netw., vol. 16, o. 3, pp , Ju [3] S. Zhag, S. C. Liew, ad P. P. Lam, Hot topic: Physical-laye etwo codig, i Poc. 12th Au. It. Cof. MOBICOM, Los Ageles, CA, Sep. 2006, pp [4] S. atti, S. Gollaota, ad D. atabi, Embacig wieless itefeece: Aalog etwo codig, i Poc. ACM SIGCOMM, yoto, Japa, Aug. 2007, pp [5] R. H. Y. Louie, Y. Li, ad B. Vucetic, Pactical physical laye etwo codig fo two-way elay chaels: Pefomace aalysis ad compaiso, IEEE Tas. Wieless Commu., vol. 9, o. 2, pp , Feb [6] P. Popovsi ad H. Yomo, Wieless etwo codig by amplify-adfowad fo bi-diectioal taffic flows, IEEE Commu. Lett., vol. 11, o. 1, pp , Ja [7] Z. Dig, T. Wag, M. Peg, W. Wag, ad. Leug, O the desig of etwo codig fo multiple two-way elayig chaels, IEEE Tas. Wieless Commu., vol. 10, o. 6, pp , Ju [8] T. J. Oechteig ad H. Boche, Bidiectioal egeeative half-duplex elayig usig elay selectio, IEEE Tas. Wieless Commu., vol. 7, o. 5, pp , May [9] P. Lasso, N. Johasso, ad.-e. Suell, Coded bi-diectioal elayig, i Poc. IEEE Veh. Techol. Cof., VTC Spig, Melboue, Austalia, May 2006, pp [10] Z. Dig,.. Leug, D. L. Goecel, ad D. Towsley, O the study of etwo codig with divesity, IEEE Tas. Wieless Commu., vol. 8, o. 3, pp , Ma [11] Z. Dig, T. Rataajah, ad.. Leug, O the study of etwo coded AF tasmissio potocol fo wieless multiple access chaels, IEEE Tas. Wieless Commu., vol. 8, o. 1, pp , Ja [12] Y. Che, S. ishoe, ad J. Li, Wieless divesity though etwo codig, i Poc. IEEE WCNC, Las Vegas, NV, Ap. 2006, pp [13] J. N. Laema, D. N. C. Tse, ad G. W. Woell, Coopeative divesity i wieless etwos: Efficiet potocols ad outage behavio, IEEE Tas. If. Theoy, vol. 50, o. 12, pp , Dec [14] S. Shama, Y. Shi, J. Liu, Y. T. Hou, S. ompella, ad S. F. Midiff, Netwo codig i coopeative commuicatios: Fied o foe? IEEE Tas. Mobil. Comput., vol. 11, o. 7, pp , Jul [15] S. Shama, Y. Shi, J. Liu, Y. T. Hou, ad S. ompella, Is etwo codig always good fo coopeative commuicatios? i Poc. IEEE INFOCOM, Sa Diego, CA, Ma. 2010, pp [16] Z. Mobii, P. Sadeghi, ad S. Zoaei, Netwo codig oise eductio via elay powe allocatio i a two-uicast wieless system, i Poc. IEEE It. Symp. PIMRC, Tooto, ON, Caada, Sep. 2011, pp [17] Y. Zhao, R. Adve, ad T. J. Lim, Impovig amplify-ad-fowad elay etwos: Optimal powe allocatio vesus selectio, IEEE Tas. Wieless Commu., vol. 6, o. 8, pp , Aug [18] M. Hasa ad M.-S. Alouii, Optimal powe allocatio fo elayed tasmissios ove Rayleigh-fadig chaels, IEEE Tas. Wieless Commu., vol. 3, o. 6, pp , Nov [19] M. Che ad A. Yee, Powe allocatio fo F/TDMA multiuse two-way elay etwos, IEEE Tas. Wieless Commu., vol. 9, o. 2, pp , Feb [20] Z. Yi, M. Ju, ad I.-M. im, Outage pobability ad optimum powe allocatio fo aalog etwo codig, IEEE Tas. Wieless Commu., vol. 10, o. 2, pp , Feb [21] A. A. Zaidi, M. N. homuji, S. Yao, ad M. Soglud, Optimized aalog etwo codig stategies fo the white Gaussia multiple-access elay chael, i Poc. IEEE ITW, Stocholm, Swede, Oct. 2009, pp [22] V. Havay-Nassab, S. Shahbazpaahi, ad A. Gami, Optimal distibuted beamfomig fo two-way elay etwos, IEEE Tas. Sigal Pocess., vol. 58, o. 3, pp , Ma [23] A. D. Coso, U. Spagolii, ad C. Ibas, Coopeative distibuted MIMO chaels i wieless seso etwos, IEEE J. Select. Aeas Commu., vol. 25, o. 2, pp , Feb [24] Z. Ha, T. Himsoo, W. P. Siiwogpaiat, ad. J. R. Liu, Resouce allocatio fo multiuse coopeative OFDM etwos: Who helps whom ad how to coopeate, IEEE Tas. Veh. Techol., vol. 58, o. 5, pp , Ju [25] A. Nosatiia ad T. E. Hute, Goupig ad pate selectio i coopeative wieless etwos, IEEE J. Sel. Aeas Commu., vol. 25, o. 2, pp , Feb

15 MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3629 [26] S. Shama, Y. Shi, Y. T. Hou, H. D. Sheali, ad S. ompella, Optimizig etwo-coded coopeative commuicatios via joit sessio goupig ad elay ode selectio, i Poc. IEEE INFOCOM, Blacsbug, VA, Ap. 2011, pp [27] T. S. Rappapot, Wieless Commuicatios, Piciples ad Pactice, 2d ed. Uppe Saddle Rive, NJ: Petice-Hall, [28] S. Boyd ad L. Vadebeghe, Covex Optimizatio. Cambidge, U..: Cambidge Uiv. Pess, [29] W. H. Pess, S. A. Teuolsy, W. T. Vettelig, ad B. P. Flaey, Numeical Recipes: The At of Scietific Computig, 3d ed. Cambidge, U..: Cambidge Uiv. Pess, [30] F. Che, W. Su, S. Batalama, ad J. Matyjas, Joit powe optimizatio fo multi-souce multi-destiatio elay etwos, IEEE Tas. Sigal Pocess., vol. 59, o. 5, pp , May [31] IEEE Stadad fo Local ad Metopolita Aea Netwos, Pat 16: Ai Iteface fo Fixed ad Mobile Boadcast Wieless Access Systems, IEEE Std e-2005, Feb [32] R. H. Clae, A statistical theoy of mobile-adio eceptio, Bell Syst. Tech. J., vol. 47, o. 6, pp , [33] C. S. Patel, G. L. Stube, ad T. G. Patt, Simulatio of Rayleighfaded mobile-to-mobile commuicatio chaels, IEEE Tas. Commu., vol. 53, o. 11, pp , Nov [34] L. Fei, L. Qighua, L. Tao, ad Y. Guagxi, Impact of elay locatio accodig to SER fo amplify-ad-fowad coopeative commuicatios, i Poc. IEEE IWASID, Beijig, Chia, Ap. 2007, pp [35] Y. Li, Distibuted codig fo coopeative wieless etwos: A oveview ad ecet advaces, IEEE Commu. Mag., vol. 47, o. 8, pp , Aug [36] P. Sadeghi, P. O. Votobel, ad R. Shams, Optimizatio of ifomatio ate uppe ad lowe bouds fo chaels with memoy, IEEE Tas. If. Theoy, vol. 55, o. 2, pp , Feb [37] W. P. Tam ad T. M. Lo, Joit goupig ad schedulig i complexitycostaied boadcastig ad-hoc etwos, i Poc. IEEE ICUFN, Hog og, Ju. 2010, pp [38] R. Diestel, Gaph Theoy, 3d ed. New Yo: Spige-Velag, Zaha Mobii S 10) eceived the B.S. degee i electical egieeig fom Isfaha Uivesity of Techology, Isfaha, Ia, i 2006 ad the M.S. degee i electical egieeig fom M.A. Uivesity of Techology, Teha, i She is cuetly woig towad the Ph.D. degee with the Depatmet of Electical ad Compute Egieeig,. N. Toosi Uivesity of Techology, Teha. Fom Novembe 2010 to Novembe 2011, she was a Visitig Reseache with the Reseach School of Egieeig, Austalia Natioal Uivesity, Cabea, Austalia. Sice Septembe 2007, she has bee a Reseach Assistat with the Wieless Netwos Reseach Laboatoy, Depatmet of Electical ad Compute Egieeig,.N. Toosi Uivesity of Techology. He eseach iteests iclude commuicatio systems theoy, wieless commuicatios, coopeative etwos, ad etwo codig. Paastoo Sadeghi S 02 M 06 SM 07) eceived the B.E. ad M.E. degees i electical egieeig fom Shaif Uivesity of Techology, Teha, Ia, i 1995 ad 1997, espectively, ad the Ph.D. degee i electical egieeig fom The Uivesity of New South Wales, Sydey, Austalia, i Fom 1997 to 2002, she woed as a Reseach Egiee ad the as a Seio Reseach Egiee with Ia Commuicatio Idusties, Teha, ad with Deqx fomely ow as Claity Eq), Sydey, Austalia. She has visited vaious eseach istitutes, icludig the Istitute fo Commuicatios Egieeig, Techical Uivesity of Muich, Muich, Gemay, fom Apil to Jue 2008; ad the Massachusetts Istitute of Techology, Cambidge, fom Febuay to May She is cuetly a Fellow with the Reseach School of Egieeig, Austalia Natioal Uivesity, Cabea, Austalia. She is the autho o coautho of moe tha 80 efeeed joual o cofeece papes ad is a Chief Ivestigato fo a umbe of Austalia Reseach Coucil Discovey ad Liage Pojects. He eseach iteests iclude wieless commuicatios systems ad sigal pocessig. D. Sadeghi eceived IEEE Regio 10 Studet Pape Awads i 2003 ad 2005 fo he eseach o the ifomatio theoy of time-vayig fadig chaels. Majid habbazia M 11) eceived the udegaduate degee i compute egieeig fom the Shaif Uivesity of Techology, Teha, Ia; the Maste s degee i electical ad compute egieeig fom the Uivesity of Victoia, Victoia, BC, Caada; ad the Ph.D. degee fom the Uivesity of Bitish Columbia, Vacouve, BC, Caada, espectively. Fom 2009 to 2010, he was a Reseach Fellow with the Compute Sciece ad Atificial Itelligece Laboatoy, Massachusetts Istitute of Techology, Cambidge. He is cuetly a Assistat Pofesso with the Depatmet of Electical ad Compute Egieeig, Uivesity of Albeta, Edmoto, AB, Caada. His eseach iteests iclude wieless etwos, distibuted algoithms, applied cyptogaphy, ad etwo secuity. Saada Zoaei eceived the Maste s degee i electical egieeig fom the Uivesity of Teha, Teha, Ia, ad the Ph.D. degee i electical egieeig fom the Depatmet of Commuicatio ad Ifomatio Techology, Uivesity of Toyo, Toyo, Japa, i He is cuetly a Associate Pofesso with the Depatmet of Electical ad Compute Egieeig,. N. Toosi Uivesity of Techology, Teha. His eseach iteests iclude ifomatio secuity, wieless etwos, ad ext-geeatio etwos.