Cooperative Routing with Relay Assignment in Multi-radio Multi-hop Wireless Networks

Transcription

1 1 Coopeative Routing with Relay Aignment in Multi-aio Multi-hop Wiele Netwok Kun Xie 1,2,3, Xin Wang 3, Jigang Wen 4, an Jiannong Cao 5 1 College of Compute Science an Electonic Engineeing, Hunan Univeity, Changha, China 2 State key Laboatoy of Netwoking an Switching Technology, Beijing Univ. of Pot an Telecomm., China 3 Depatment of Electical an Compute Engineeing, State Univeity of New Yok at Stony Book, USA 4 Intitute of Computing Technology, Chinee Acaemy of Science, China 5 Depatment of computing, The Hong Kong Polytechnic Univeity, Hong Kong xiekun@hnu.eu.cn, xwang@ece.unyb.eu, wenjigang@ict.ac.cn, cjcao@comp.polyu.eu.hk Abtact Coopeative communication (CC) fo wiele netwok ha gaine a lot of ecent inteet. It ha been hown that CC ha the potential to ignificantly inceae the capacity of wiele netwok, with it ability of mitigating faing by exploiting patial iveity. Howeve, mot of the wok on CC ae limite to ingle aio wiele netwok. To emontate the benefit of CC in multi-aio multi-hop wiele netwok, thi pape tuie a joint poblem of multi-aio coopeative outing an elay aignment to maximize the minimum ate among a et of concuent communication eion. We fit moel thi poblem a a mixe intege pogamming (MIP) poblem an pove it to be NP-ha. Then we popoe a centalize algoithm an a itibute algoithm to olve the poblem. The centalize algoithm i eigne within a banch-an-boun famewok by uing the elaxation of the fomulate MIP, which can fin a global (1 + ε)-optimal olution. Ou itibute algoithm inclue two ub-algoithm: a coopeative oute election ubalgoithm an a faine-awae oute ajutment ub-algoithm. Ou imulation eult emontate the effectivene of the popoe algoithm an the ignificant ate gain that can be achieve by incopoating CC in multi-aio multi-hop netwok. I. INTRODUCTION In ecent yea, we have een ignificant eeach inteet in exploiting coopeative communication (CC) ove itibute antenna to impove the tanmiion pefomance [1]. Taking avantage of the boacat natue of wiele channel, one o moe neighboing noe can eve a elay an fowa ovehea packet fom a ene to it taget eceive, which can combine multiple copie of the packet to ecoe the oiginal one. Theefoe, by exploiting the inheent patial an multiue iveitie, the coopeative communication technique can efficiently impove the netwok pefomance. Thi make coopeative communication an emeging technique fo futue wiele netwok. Exiting tuie on CC ae motly bae on the ingle aio netwok [2] [14]. With the contant euction of hawae cot an the availability of cheap, off-the-helf commoity hawae equippe with multiple aio, moe an moe wiele evice ae equippe with multi-aio communication inteface. Thi not only bing in the exta capacity gain fo a ingle evice an a wiele netwok fome with multi-aio noe, but alo ceate moe oppotunitie fo coopeative communication. Although pomiing, thee ae vey limite tuie on exploiting the multi-aio capabilitie fo flexible coopeative communication to impove the multi-aio multihop wiele netwok pefomance. Thi pape inten to povie ome eign guieline an emontate the benefit of CC in multi-aio multi-hop wiele netwok. The exitence of multi-aio evice in the netwok allow fo moe tanmiion oppotunitie an flexibilitie, but alo lea to moe challenge in netwok eign, epecially the enabling of coopeative communication in multi-aio multi-hop netwok. With moe aio inteface, a noe in the netwok can act not only a a coopeative elay fo CC but alo a tanmiion elay fo multi-hop packet fowaing. The fit challenging iue i how to aign elay noe (eithe fo CC o a a multi-hop elay) fo each eion. Fig. 1 how example of coopeative communication with each noe equippe with two aio, whee the ahe line epeent coopeative tanmiion. In Fig. 1, the noe coul ue one aio a coopeative elay fo eion 1 1, an the othe aio a coopeative elay fo eion 2 2. In Fig. 1, the noe coul ue one aio a coopeative elay fo eion 2 2, an the othe aio a a multi-hop elay fo eion 1 1. The capability fo a noe o a aio inteface to eve a two iffeent type of elay make multi-aio coopeative outing an elay noe aignment inte-epenent. The econ challenging iue i how to olve the couple multi-aio outing poblem an elay aignment poblem optimally togethe while taking into account the wiele intefeence aien fom both iect tanmiion an coopeative communication. 1 2 Fig CC in multi-aio multi-hop wiele netwok. 1 2

2 To ae the above challenging iue, the aim of thi wok i to olve a joint poblem of multi-aio coopeative outing an elay aignment to unetan the benefit of applying CC in multi-aio multi-hop wiele netwok. Compae to conventional ingle-aio CC tuie, the intouction of multi-aio noe ignificantly inceae the flexibility in elay election thu the pefomance gain a emontate in ou pefomance evaluation. Howeve, thi alo make the poblem much hae to olve. The objective of ou wok i to maximize the minimum ate among a et of concuent communication eion to inceae the tanmiion faine by conieing the oppotunitie bought by coopeative communication an the limitation of the numbe of aio at netwok noe. Ou contibution can be ummaize a follow: We fit moel the poblem a a mixe intege pogamming (MIP) poblem an pove it to be an NP-ha poblem. To efficiently olve the poblem, we popoe a itibute algoithm with two tep. In the fit tep, an intefeenceawae coopeative oute election algoithm i popoe to elect an optimal outing path with the maximum capacity fo each newly aival eion. In the econ tep, a faine-awae algoithm i popoe to ajut the path locally aoun the link oveloae with tanmiion fom multiple eion. Fo pefomance efeence, bae on the elaxation of the fomulate MIP, we popoe a centalize algoithm within a banch-an-boun famewok to povie an effective global (1 + ε)-optimal olution whee ε i a eie appoximation eo boun. We have caie out extenive imulation to evaluate the pefomance of ou popoe algoithm. The imulation eult emontate the effectivene of ou algoithm an the ignificant ate gain that can be achieve by incopoating CC in multi-aio multi-hop netwok. The et of thi pape i oganize a follow: Section II peent elate wok. Section III ecibe the ytem moel. In Section IV, we moel thi poblem a a mixe intege pogamming (MIP) poblem an pove it to be a NP-ha poblem. We popoe a itibute algoithm an a centalize algoithm to olve the poblem in Section VI an Section V, epectively. Section VII peent imulation eult to emontate the ate gain that can be achieve by exploiting CC in multi-aio multi-hop wiele netwok. We conclue thi pape in Section VIII. II. RELATED WORK We ae not awae of any othe wok that concuently conie intefeence awae coopeative outing an elay aignment fo pefomance enhancement in multi-aio multihop wiele netwok. Following we eview ome liteatue wok that ha cetain pat elevant to ou wok. A. Coopeative Communication Coopeative communication i a phyical laye technique. Built upon the wok at the phyical laye [15] [19], application an netwok potocol have muhoome in ingleaio wiele netwok ecently, eithe ingle-aio ingle-hop netwok [2] [7] o ingle-aio multi-hop netwok [8] [14]. The eeach focu of CC in ingle-aio ingle-hop wiele netwok i on the election of the elay fo a ouceetination pai an eouce allocation fo the electe elay. In [2], Cai et al. tuy the poblem of elay election an powe allocation, fit ove a imple netwok with only one ouce noe, an then extening to the multiple-ouce cae. In [3], the autho popoe a itibute buye/elle game theoetic famewok ove multiue CC netwok to timulate coopeation an impove the ytem pefomance. In [4], Shi et al. tuy the elay aignment poblem uch that the minimum capacity among all ouce noe i maximize. They popoe an optimal polynomial time algoithm to olve the poblem. Following thi wok, the autho in [5] tuy the elay aignment poblem with intefeence mitigation. Aiming at maximizing netwok thoughput with popotional faine, the autho in [6] have invetigate the joint elay election an link cheuling poblem in a elay-aite wiele cellula netwok. The wok in [7] taget to olve the elay aignment poblem fo maximizing the total capacity of all pai in a moe geneal ene whee multiple ouce noe can hae ame elay noe. Howeve, the above tuie fo ingle-aio ingle-hop wiele netwok cannot be eaily extene to a multi-hop wiele netwok. Thee ae ome tuie of CC in ingle-aio multi-hop wiele netwok. In [8], Khanani et al. tuy a minimum enegy outing poblem in a tatic wiele netwok an evelop a ynamic-pogamming-bae algoithm fo fining the optimal oute in an abitay netwok. Howeve, thei appoach i limite to ingle eion a oppoe to multiple eion that we have coniee in thi pape. In [9], Emun et al. conie coopeative elay netwok with multiple tochatically vaying eion, which may be queue within the netwok. Thoughput optimal netwok contol policie ae tuie that take into account queue ynamic to jointly optimize outing, cheuling an eouce allocation, with the olution containe to the pecial cae of paallel elay netwok. The pape [1] [12] popoe heuitic cheme that fit evelop outing olution to fin a pimay path, an then conie elay noe aignment fo CC accoing to the pimay path. Howeve, thee olution ecouple outing an elay aignment, which make the path foun fa fom the optimal one. In [13], the autho popoe a itibute coopeative outing algoithm to contuct a minimum-powe oute to guaantee cetain thoughput. In [], the autho efine a banwith an powe awae coopeative multi-path outing poblem ove wiele multimeia eno netwok, an popoe a polynomial-time heuitic algoithm to olve the poblem. In [14], to illutate the benefit of CC in multi-hop wiele netwok, the autho olve a joint optimization poblem of elay noe aignment an flow outing fo concuent eion. The above eult ae eticte to a ingle-aio netwok. The peence of multi-aio noe povie moe oppotunitie fo netwok capacity enhancement, with the aio poibly 2

3 fowaing packet in the nomal outing path o eving a elay fo coopeative communication. The etemination of the optimal function fo the aio i a challenging poblem an ha vey limite wok. Only the wok in [21] tuie CC in multi-aio multi-hop netwok. It popoe a channel-oneman mathematical moel to maximize the capacity, an povie an optimal inteface aignment algoithm fo ealtime flow. Diffeent fom ou wok in thi pape, howeve, the appoach popoe i un with the aumption that the outing path i given. Theefoe, cuent wok on coopeative communication fo multi-aio multi-hop wiele communication i vey limite, which i the main focu of thi pape. Depite the wie inteet, coopeative communication can lea to inceae intefeence, which eult in tanmiion conflict an ata etanmiion an conequently netwok pefomance egaation [22]. The intefeence poblem have been notice an tuie by only a limite numbe of eeache [7], [23], [24]. Yang et al. [7] point out that the cochannel intefeence ha become a pominent iue to apply coopeative communication technique in wiele netwok. Zhang et al. [24] futhe how that the pefomance egaation a a eult of co-channel intefeence lagely impact the pefomance of multi-hop wiele netwok. Li et al. [25] tuy an enegy an pectum efficient coopeative communication poblem in a one-hop multi-channel wiele netwok. The objective of the wok i to fin the optimal tanmiion powe, elay aignment, an channel allocation uch that the ate equiement of all ue ae atifie an the total enegy conumption i minimize. Although the netwok ha multiple channel, each noe i aume to have only a ingle aio an can only acce one channel at a time. Conieing only a imple netwok moel, the olution of [7], [22] [25] ae ifficult to be extene to multi-aio multihop wiele netwok to achieve the coopeative iveity gain in the peence of wiele intefeence. B. Multi-aio Technique Many tuie [26] [3] have been mae to exploit multiaio an multi-channel (MRMC) technique to combat the inceae co-channel intefeence fo highe netwok capacity. With multiple wiele aio (i.e., netwok inteface ca (NIC)), noe within a neighbohoo can en ata though othogonal channel without tanmiion conflict, which lea to efficient pectum utilization an inceae the actual banwith available to the netwok. Diffeent fom the above wok which only conie conventional one-to-one iect tanmiion, coopeative communication can potentially impove the netwok pefomance by exploiting many-to-one tanmiion to mitigate faing. The technique popoe fo iect tanmiion can not be eaily applie in coopeative wiele netwok to achieve the coopeative iveity gain. A a multi-aio technique, MIMO can achieve patial iveity by employing multiple tanmitte-eceive aio inteface, which ha attacte lot of inteet ecently [31] [34]. The wok in [31], [32] exploit the ue of coopeative elay tanmiion in a MIMO-bae a hoc netwok to cope with hah channel conition, while autho in [33] popoe to eploy MIMO noe a elay to ait weak link in wiele netwok with the aim of eucing the numbe of elay noe an poviing pefomance poviioning. Thee effot taget to olution at MAC laye cheuling an fo eployment epectively without conieing the outing. A noe equippe with multiple aio oe not enue the noe to fom MIMO aay an enjoy the MIMO benefit. Theefoe, multi-aio communication an MIMO communication have been iffeent eeach thut in the community. To the bet of ou knowlege, thi i the fit wok to emontate the benefit of CC in multi-aio multi-hop wiele netwok. Thi pape conie a joint poblem of intefeenceawae coopeative outing an elay noe aignment, an popoe both centalize an itibute algoithm to olve the poblem. A. Netwok Scenaio III. SYSTEMS MODEL We conie a multi-aio multi-channel multi-hop wiele netwok with n noe containe in a et N, whee each noe i equippe with one o multiple wiele aio. Thee ae multiple concuent eion in the netwok, enote by a et F = {f 1, f 2...f J } of J. A eion f i ( i i ) goe though the ouce noe i an the etination noe i, an the ata fo each eion may tavee multiple hop in the netwok. We aume that thee ae a total of l othogonal channel in the netwok, enote by C={ch 1, ch 2,..., ch l }, an thee i no inte-channel intefeence. The et of woking channel aigne to noe i i enote a C i. Due to the intefeence containt, thee i no capacity benefit to aign two aio of a noe with the ame channel. Thee ae two type of elay noe on a path fom the ouce to the etination of a eion. The fit type i Coopeative Relay (CR) which i ue fo CC pupoe (i.e., noe 7 of eion 2 in Fig. 2). The econ type i multi-hop Relay (MR) which opeate at the netwok laye to elay the packet fom a ouce ove multiple hop to it etination (i.e., 6 of eion 2 in Fig. 2). A noe with multiple aio can eve a both CR an MR fo multiple eion. Similaly, a ouce noe (o a etination noe) can eve a a CR o MR fo othe eion, an a ingle CR noe can eve moe than one eion. In the example of Fig. 2, thee ae thee communication eion. The ahe line epeent a elay path though a CR elay noe which eve fo the pupoe of coopeative communication while the oli line epeent the nomal ata tanmiion path, an a noe on the path eve a an MR. A elay no with multiple aio can eve fo multiple eion an act in iffeent ole (CR o MR) in iffeent eion. Fo example, noe 3 i the CR of both eion 1 an eion 2, while noe 4 i the CR of eion 3 an i alo ue a an MR fo the eion 2. The noe 5 i ue a MR to cay taffic fo both eion 1 an 3. 3

4 Fig Coopeative elay 3 Multi-hop elay A multi-aio multi-hop netwok coniting of multiple eion. B. Two Kin of Tanmiion Moe Thee ae two tanmiion moe between any two noe in the netwok coniee, iect tanmiion (DT) an coopeative tanmiion. A iect tanmiion i caie iectly between two neighboing noe i an j ove one link, whee noe i i the ene an noe j i the eceive (i.e., 1 2 in Fig. 2). The coopeative tanmiion between two noe x an z involve thee link (x, y), (x, z), an (y, z), whee the elay noe y act a a CR elay fo the tanmiion between x an z (i.e., 2 5 ( 3 ) in Fig. 2, whee 3 i the CR elay). Fig. 3. A thee-noe CC moel. Fig. 3 how a thee-noe CC moel. In the coopeative tanmiion, a collaboative neighbo ovehea the ignal fom the ouce to the etination an fowa it to. combine two ignal team, an into a ingle team that ha a highe eitance to channel faing an noie an hence a highe pobability of being uccefully ecoe. A ecent tuy [35] how that the iveity gain achieve by exploiting multiple elay noe i maginally highe than the iveity gain achieve by electing the bet elay. Theefoe, we conie each hop of a eion can elect at mot one elay noe fo CC a one in othe elate wok [13], [14], [25]. The mechanim to accomplih CC i not unique. Between an une CC, thee ae two typical coopeative tanmiion moe incluing amplify-an-fowa (AF) an ecoe-anfowa (DF) moe [36]. In [37], autho ecibe an compae the capacity of iffeent coopeative tanmiion potocol an how that the AF-RAKE-bae coopeative tanmiion potocol can achieve the maximum capacity. In AF-RAKE, afte eceiving ignal fom, amplifie an fowa them to without emoulation o ecoing. ue a RAKE eceive to combine both ignal team of an. The achievable ate une AF-RAKE moe between an with a the elay [37] i given by C(,,, CC) = W I AF (,, ), (1) whee I AF (,, ) = log 2 (1 + SNR + SNR SNR SNR + SNR + 1 ) (2) SNR = P h σ 2 2, SNR = P h σ 2 2, SNR = P h σ 2 2. (3) W i the available banwith of channel at noe an, h, h, h epeent the effect of path-lo, haowing, an faing within it epective channel between noe an, an, a well a an, epectively. σ 2 an σ2 enote vaiance of the zeo-mean backgoun noie at noe an, while P an P enote the tanmiion powe at noe an epectively. Fo the iect tanmiion moe, the achievable ate between an i expee a C(,, DT ) = W log 2 (1 + SNR ) (4) IV. PROBLEM DESCRIPTION In multi-flow multi-aio multi-hop wiele netwok, a elay noe with multiple aio can be hae an eve fo multiple eion, a hown in Fig.1. A challenging poblem i how to efficiently aign elay noe fo each eion while taking account of wiele intefeence fom both iect tanmiion an coopeative communication. In ou poblem fomulation, we will jointly conie coopeative outing an elay aignment une thee type of containt: the containt on elay noe, the containt on flow outing, an the containt on link capacity. Following we fit intouce the containt. Let a binay vaiable A k uv enote whethe thee i a link u v though the channel ch k. Fo iect communication, the eceive v nee to be within the communication ange of the ene u, with u an v haing a common channel: { A k 1 v N(u) an k Cu C uv = v, u v (5) othewie whee N(u) enote the one-hop neighbo et of noe u. We conie the thee link fo coopeative communication (i.e., fom the ene to the eceive, fom the ene to the elay, an fom the elay to the eceive) a a vitual coopeative link, with the ene, elay, an the eceive aigne with a common channel. A binay vaiable Buv wk enote whethe thee i a vitual coopeative link u v(w) though the channel ch k an the elay w: Buv wk = v N(u) an w N(u) N(v) 1 an k C u C v C w, w u, w v othewie We futhe efine a binay vaiable yj:uv k to enote whethe o not a iect link u v ch k i electe by the eion j: { yj:uv k 1 link u v chk i electe by eion j = othewie (7) (6) 4

5 Similaly, we efine a binay vaiable x wk j:uv to inicate whethe o not a vitual coopeative link u v(w) ch k i electe by eion j: x wk j:uv = { 1 link u v(w) chk i electe by eion j othewie (8) A. Containt on Relay Noe Fo each hop (u, v), noe u can tanmit ata to noe v though eithe iect tanmiion o coopeative tanmiion: w N xwk j:uv + yj:uv k 1 (j F, k C) (9) B. Containt on Flow Routing Given a eion, a iect link i fome between only one tanmitte an one eceive: u v k C u C v u N v u k C u C v v N y k j:uv 1 (j F, v j) (1) y k j:uv 1 (j F, u j ) (11) Similaly, a vitual coopeative link i alo fome between one tanmitte an one eceive: k C u C v k C u C v u v,u w u N v u,v w v N x wk j:uv 1 (j F, v j ) (12) x wk j:uv 1 (j F, u j ) (13) Denote fj:uv k wk an fj:uv a a eion j flow ate on the iect link u v ch k an vitual coopeative link u v(w) ch k, epectively. Fo an intemeiate noe, the outgoing flow ate houl be equal to the incoming flow ate: k C u C w = k C w C v u w,u j ( yj:uwf k j:uw k + t u,t w ( yj:wvf k j:wv k + t v,t w u N v w,v j v N (j F, w N, w j, w j ) ) x tk j:uwfj:uw tk x tk j:wvf tk j:wv ) (14) Each hop (u, v) can tanmit ata uing eithe iect tanmiion o coopeative tanmiion, thu a eion outgoing link an incoming link can be eithe a iect link o a vitual coopeative link. Theefoe, the two ie of (14) can have at mot one non-zeo tem. On the left ie of Eq.(14), becaue of the containt in Eq(9), if the incomming link exploit iect tanmiion, then yj:uw k = 1 an the tem yk j:uw f j:uw k i non-zeo an the tem t u,t w x tk j:uw f j:uw tk i zeo. Othewie if the incomming link exploit the coopeative tanmiion, t u,t w x tk t u,t w j:uw = 1 an the tem x tk j:uw f j:uw tk i nonzeo an yj:uw k = an the tem yk j:uw f j:uw k i zeo. Similaly, on the ight ie of Eq.(14), if the outgoing link exploit iect tanmiion, then yj:wv k = 1 an the tem yj:wv k f j:wv k i non-zeo. Othewie if the outgoing link exploit coopeative tanmiion, then t v,t w x tk j:wv f j:wv tk i non-zeo. C. Containt on Link Capacity x tk j:wv = 1 an the tem We enote by R I the intefeence ange, which i q R T whee q 1 an R T i the communication ange. A communication between u an v may block othe tanmiion within the R I ange of eithe u o v. In paticula, we have the following two pinciple to ientify whethe two link in a coopeative wiele netwok intefee with each othe o not. Pinciple 1. Fo iect tanmiion, we conie a link A B to be the intefeence link of anothe link C D if A an B wok on the ame channel of C an D, an at leat one of the noe pai, pai(a, C), pai(a, D), pai(b, C), an pai(b, D) i within R I. Pinciple 2. If noe A tanmit ata to noe B with the help of a coopeative elay R, we conie the coopeative link A B (R) to intefee with anothe link C D if A, B, an R wok on the ame channel of C an D, an at leat one of the noe pai, pai(a, C), pai(a, D), pai(b, C), pai(b, D), pai(r, C), an pai(r, D) i within R I. Accoing to the TDMA cheule aopte in the MAC laye, if a channel i equally hae among competing link, the available capacity of a iect tanmiion link u v ch k can be calculate a C k (u, v, DT ) = C (u, v, DT ) I k (u, v) + 1 (15) whee C (u, v, DT ) (calculate by (4)) i the link capacity of a iect link, I k (u, v) enote the link et that intefee with the link u v ch k, I k (u, v) enote the ize of I k (u, v). The available capacity of a vitual coopeative link u v(w) ch k can be calculate a C k (u, v, w, CC) = C (u, v, w, CC) I k (u, v, w) + 1 (16) whee C (u, w, v, CC) (calculate by (1)) i the link capacity of a vitual coopeative link, I k (u, v, w) enote the link et that intefee with thi vitual coopeative link. Depening on whethe a link being iect o coopeative, the capacity containt fo the aggegate flow taveing the link though ch k mut not excee the link capacity a follow: fj:uv k C k (u, v, DT ) (17) j F j F D. Poblem Fomulation f wk j:uv C k (u, v, w, CT ) (18) The objective of thi pape i to maximize the minimum flow ate among all active flow via intefeence-awae coopeative outing an elay aignment. Following the flow containt in (14), although a eion may tavee multiple hop, the flow ate of evey hop in the eion i the ame. Theefoe, we ue the ate of the fit hop to enote the flow 5

6 ate. Moe fomally, fo a given eion ( j, j ), enote the en-to-en flow ate (o thoughput) a R j, whee R j = v j t v,t j yj: k j vfj: k j v + x tk j: j vfj: tk j v (19) k C j C v v N Let R min emote the minimum flow ate among all flow, i.e., Fig. 4. l i j k Example of coopeative oute. m R min = min j F Rj () Ou objective i to maximize R min a follow: Max R min.t. (9)(11)(1)(13)(12)(14)(17)(18) R min, fj:uv, k fj:uv wk (j F, k C, u, v, w N, w u, w v) x wk j:uv, yj:uv k {, 1} (j F, k C, u, v, w N, w u, w v) (21) whee R min, fj:uv k, f j:uv wk, xwk j:uv an yk j:uv ae optimization vaiable. Theoem 1: The max-min coopeative outing poblem in coopeative wiele netwok efine in (21) i NP-ha. Poof: Although a coopeative tanmiion conit of thee link, a mentione ealie, we teat them a a vitual coopeative link. Multiple eion can be tanmitte concuently ove iffeent channel. Afte thee implification, the max-min coopeative outing poblem can be tanlate to an un-plittable max-min banwith allocation poblem, which i a known NP-ha poblem [38]. V. DISTRIBUTED ALGORITHM Fo pactical implementation of coopeative communication in multi-aio multi-channel multi-hop wiele netwok, we popoe a Ditibute joint Flow Routing an Relay noe Aignment algoithm (DFRRA), which inclue two tep. In the fit tep, an intefeence-awae Coopeative Route Selection algoithm (CRS) i popoe to elect an optimal coopeative outing path. In the econ tep, a Faine Awae Routing Ajutment algoithm (FARA) i popoe to aapt the oute locally by conieing the link competition among multiple eion. A. Ditibute Coopeative Route Selection Algoithm Fo each active eion, ou popoe CRS will each fo a outing path with the maximum en-to-en capacity taking into account the wiele intefeence. In a coopeative netwok, a coopeative path coul be fome with a combination of coopeative tanmiion an iect tanmiion, a hown in Fig.4. Thi make the path fining ifficult. Fo each tanmiion hop, CRS not only nee to elect the fowaing noe an the woking channel of each hop but alo to etemine the tanmiion moe a well a the elay noe in cae that a coopeative tanmiion moe i the option. 1) Routing Metic To facilitate path election, we efine a outing metic of a hop (x, y) a the maximum available capacity among all poible channel though two poible tanmiion moe CMetic(x, y) = max {C(x, y, ch k, moe)}, ch k C x C y,moe DT,CC (22) whee C(.) i the available link capacity an C x C y i the feaible et of channel both noe x an y ae aigne with, an the tanmiion between noe x an y can be eithe iect when moe = DT o coopeative when moe = CT. If a link i faily hae by multiple eion, the outing metic in Eq.(22) can be futhe expee a: CMetic(x, { y) = max ch k C x C y C k (x,y,dt ) NSS(x,y,DT )+1, max R { C k (x,y,,ct ) NSS(x,y,,CT )+1 }} (23) whee R = N(x) N(y) i the caniate elay et fo hop (x, y) on channel ch k. C k (x, y, DT ) an C k (x, y,, CT ) can be calculate by (15) an (16). NSS k (x, y, DT ) an NSS k (x, y,, CT ) enote the numbe of eion electing the coeponing link x y ch k o the vitual coopeative link x y() ch k, epectively. Theefoe, C k (x,y,,ct ) C k (x,y,dt ) NSS(x,y,DT )+1 an NSS(x,y,,CT )+1 ae the available link capacity fo a new flow to elect the coeponing iect link o vitual coopeative link. Accoing to the outing metic in (22), a ene noe x can etemine if it will take iect tanmiion o coopeative tanmiion, an the channel to ue fo tanmiion. In the cae that a coopeative tanmiion i neee, the electe elay noe will be infome. Fig.5 how an example on outing metic calculation fo the hop (x, y) whee thee ae two feaible channel ch 1 an ch 2. In cae that ch 1 i ue, the available link capacity une the iect tanmiion i 18, while the capacity une the coopeative tanmiion going though caniate elay 1, 2, 3 i, 23, 21 epectively. Among thee option, the capacity fo the coopeative tanmiion though 2 i the maximum an ha the value 23 a hown in Fig.5. If x tanmit ata to y though ch 2, the maximum capacity i 24, which i achieve when chooing the coopeative tanmiion with 1 a the elay noe, a hown in Fig.5(). Thu, accoing to (22), the outing metic of hop (x, y) i 24 which i the maximum available capacity between ch 1 an ch 2, a hown in Fig.5(e). A a eult, ch 2 i the electe woking channel an 2 i the electe coopeative elay fo hop (x, y). 2) Routing Algoithm The outing path election can be ealize though ou popoe CRS, a itibute Coopeative Route Selection algoithm which i moifie fom AODV an bae on the outing metic CM etic. Cuent AODV-bae outing potocol ae eigne only fo one-to-one iect tanmiion intea of coopeative communication. In thi pape, we popoe a novel outing metic CMetic. To facilitate fining the coopeative path with maximum capacity, iffeent fom AODV, in ou CRS eign, 6

7 ch 1 x ch 2 x Fig y y ch 1 x ch 2 x 23( 2 ) 24( 1 ) Example of outing metic calculation. y y ch 2 x 24( 1 ) the RREQ meage caie the infomation of the capacity of the path egment fom the ouce to the peviou hop an the outing metic CMetic of the lat hop. CRS conit of thee majo pat, incluing ouce noe behavio, the behavio of an intemeiate noe when eceiving RREQ (Route Requet) an the behavio when eceiving RREP (Route Reply). Souce Noe Behavio Algoithm 1 how the behavio of the ouce noe in CRS. Fo a new aiving eion, when a ouce inten to en packet to a etination, fit check it outing table to ee whethe it ha a vali path. If o, begin to en packet to the next hop towa the etination; othewie, it eache fo the path by boacating a RREQ meage to it one-hop neighbo, which eboacat the meage until it eache the etination noe. Algoithm 1 Behavio of Souce Noe 1: if ha a vali path to in it outing table then 2: begin to en packet to the next hop towa the etination 3: ele 4: fo noe z in N() o 5: accoing to (22), noe calculate the outing metic of the outgoing link(, z) (enote a P z), which ientifie the optimal tanmiion moe, the woking channel, an the optimal elay if coopeative tanmiion i electe. 6: inet the calculate outing metic infomation P z into RREQ. 7: en fo 8: inet P = + into RREQ, whee P enote the maximum en-to-en capacity fom to, an boacat the RREQ. 9: en if Intemeiate Noe Behavio When Receiving RREQ In oe to euce the outing ovehea, in ou CRS, an RREQ meage can be tanmitte an fowae by an intemeiate noe only when it i fowae along a path with bette capacity fom the ouce noe to the intemeiate noe. Aume the capacity of the path egment fom the ouce to x i P x, which i et to initially an kept at noe x. A hown in Algoithm 2 (in tep 2 an tep 3), when an intemeiate noe x in the netwok eceive an RREQ fom it upteam noe z, if the RREQ meage i eceive in uplication an the cuent capacity of the path egment y Algoithm 2 Behavio of an Intemeiate Noe x When Receiving RREQ 1: Once RREQ meage i eceive fom noe z, noe x obtain P z (the maximum capacity of path egment fom to z), an P zx (the outing metic of link(z, x)). Noe x calculate the maximum capacity of path egment fom to x following P x= min(p zx,p z ). 2: if noe x ha eve eceive anothe RREQ of ouce an P x P x, whee P x i the latet maximum capacity of path egment fom to x kept in noe x, then 3: noe x op the RREQ. 4: ele if noe x i the etination an x wait fo ome time inteval afte it eceive an RREQ meage at the fit time then 5: noe x chooe the optimal path which i the one with the maximum en-to-en capacity fom all the RREQ meage eceive within the inteval. 6: noe x geneate an en an RREP meage to the ouce. 7: ele 8: noe x upate the maximum capacity of path egment fom to x by uing P x = P x. 9: noe x eco noe z, which will lea a evee path to the ouce. 1: noe x ceate a new RREQ meage. 11: fo noe y in N(x) o 12: accoing to (22), noe x calculate it outgoing link(x, y) outing metic CMetic(x, y) (enote a P xy), which ientifie the optimal tanmiion moe, the woking channel, an the optimal elay if the electe tanmiion moe = CC; inet the newly calculate infomation P xy into RREQ. 13: en fo 14: inet the maximum capacity of path egment fom to x, P x into RREQ an boacat it. 15: en if fom the ouce to noe x, enote a P x, i malle than the ecoe one P x, noe x will ica the RRE- Q an top fowaing, whee P x i the latet maximum capacity of the path egment fom to x kept in noe x an P x = min(p zx, P z ) (whee P z an P zx ae caie by the eceive RREQ). Compae to taitional AODV-elate potocol, uch a eign can not only pevent tanmiion loop but alo euce the RREQ meage by avoiing fowaing meage fom infeio upteam path, which lagely euce the outing ovehea. If noe x i the etination, it can wait fo ome time inteval. It then chooe the path which ha the maximum en-to-en capacity fom all the RREQ eceive within the inteval, an en a RREP back to the ouce. Othewie, noe x fit upate the capacity fom ouce to noe x a P x = P x, an then eco a evee oute to noe z, which will allow the fining of a evee path to the ouce that oiginate the RREQ. Finally, noe x ceate an eboacat a new RREQ meage by ineting P x an the hop metic between itelf an all it neighbo. Intemeiate Noe Behavio When Receiving RREP Let NSS (Numbe of Shae Seion) enote the numbe of eion that a link i electe to eve uing the CRS poceue, which i et to initially. A hown in (23), NSS ha been utilize to calculate the outing metic of a link, an it will be ue in the next ubection to guie the local ajutment of path egment. 7

8 Once a link x i electe in the outing path, when the ene of x eceive the RREP meage, it fit inceae the link NSS by 1, i.e. NSS x = NSS x + 1. If the coopeative communication moe i exploite by the link, the ene of x alo let the electe vitual coopeative link to inceae it NSS by 1. Then the link ene will fowa the RREP meage back to the upteam noe on the evee path to the ouce. Afte eceiving the RREP meage, the ouce fowa it ata packet along the electe path to the etination with the tanmiion moe an the woking channel on each hop et to the one etemine uing the path fining poce. B. Faine Awae Route Ajutment Algoithm The popoe CRS can elect goo coopeative outing path fo each eion when the eion aive. Howeve, the ol eion en-to-en capacity may eceae when the netwok ha newly aival eion becaue the newly aival eion may in tun bing eiou tanmiion competition on wiele channel an impact the pefomance of the ol eion. To ae thi iue, we popoe a Faine Awae Route Ajutment (FARA) algoithm. Ou eign inten to inceae the minimum tanmiion capacity of all the eion. 1) Notation an Definition If multiple path electe by iffeent eion go though ome common link, it woul eult in the eouce competition at thee link, an aitional poceue nee to be taken. Altenatively, we can change the eion to a caniate path which oen t inclue the competition link to obtain a bette en-to-en capacity. To euce the ie effect aociate with a path change, we etict the path ajutment an elay aignment to be local aoun the competition link to maximize the minimum ate of iffeent eion. Let R j (i, k) enote the et of feaible path egment between the noe pai (i, k) fo eion j. If one path egment in R j (i, k) i electe by the popoe CRS, then obviouly it ha the maximum capacity between the noe pai (i, k) fo eion j when thi eion aive, an we enote the coeponing path egment a O pj (i, k). The caniate path egment between a noe pai (i, k) fo eion j, enote a Can j (i, k), i a feaible path egment which ha the laget capacity among the one in R j (i, k) O pj (i, k) an the NSS of each link on the path egment i not lage than NASS (the Numbe of Allowable Shae Seion) of a link. NASS can be calculate with Eq.(26). Aume that a link i j ch k (o a vitual coopeative link i j(w) ch k ) i oveloae with a lage NSS value an the link i electe by flow f. Let m an n be the upteam noe an ownteam noe of thi link. Bae on the CRS algoithm popoe in Section V-A, we eign a caniate path egment fining algoithm which inclue the following two tep: Step 1. Mak the oveloae link i j ch k (o i j(w) ch k ) uneachable. Step 2. Apply the CRS algoithm popoe in Section V-A to look fo a coopeative outing path egment fom m to n that all link on the path egment have thei NSS malle than thei NASS; Retun the path egment a the caniate one fo m n fo tanmiion of flow f. The algoithm i eigne bae on the CRS algoithm in Section V-A, an the ovehea in thi poceue mainly inclue the contol meage to apply the CRS algoithm to look fo the local path egment, which i geneally mall. A hown in the Fig. 6, the maximum capacity of the path egment 1 4 i Aume the oveloae link i 6 7. A caniate path egment i the one that ha the maximum capacity among all othe feaible path egment (See Fig. 6) between 1 an 4 except the oiginal one electe by the eion. A hown in the Fig. 6(c), the caniate path egment fo 1 4 i j 3 i 28.5n m f=26 Fig. 7. f=26 Fig Example of U-path. m i n Example of L-path i 28.5n 26 f=26 29 Fig. 9. m 2 1 Example of B-path. j j j 27 m f=26 f=26 3 i 28.5n m 3 i n m i 28.5n 26 f= j j U-Path L-Path B-Path Bae on the efinition of caniate path egment, we have the following efinition. U-Path: Given O pj (i, k), if the capacity of it Can j (i, k) i lage than the en-to-en capacity of eion j, then we call O pj (i, k) a U-Path. L-Path: Given O pj (i, k), if the capacity of it Can j (i, k) i malle than the en-to-en capacity of eion j, then we call O pj (i, k) a L-Path. B-path: Given O pj (i, k), if the capacity of it Can j (i, k) i equal to the en-to-en capacity of eion j, then we call O pj (i, k) a B-path. Fig.7, Fig.8 an Fig.9 how the example of U-path, L- Path an B-Path, epectively. The path egment of m i j ( 2 ) n in Fig.7, the path egment of m i j n in Fig.8, an the path egment of m i j ( 2 ) n in Fig.8 ae the caniate path egment. The capacitie of thee caniate path egment ae 27.8, 25, 26, which ae epectively lage, lowe an equal to the en-to-en capacity of the coeponing eion. Accoing to the efinition, the oiginal path egment of m i k ( 1 ) n in Fig.7, Fig.8 an Fig.9 ae U-path, L-Path an B-Path, epectively. 8

9 2 3 f= f= (c) Fig. 6. Example of Caniate link. 2) Algoithm eign Given any path egment p R j (i, k), the path egment mut be one type of U-Path, L-Path an B-path. Among the NSS path egment belonging to iffeent eion, auming thee ae n 1 U-path, n 2 L-Path an n 3 B-Path, we have NSS = n 1 + n 2 + n 3. Given a link x that i electe by NSS x eion, the ento-en capacity of thee eion ae P 1, P 2,, P NSSx, (the en-to-en capacity i calculate bae on all link along the path except the competition link x), the available capacity of thi link i C(x) (C(x) calculate with Eq.(15) o Eq.(16) epening on the tanmiion moe of the link, then the elationhip of NASS of thi link an the en-to-en path capacity of thee eion can be expee a that i C(x) NASS x min {P 1, P 2,, P NSSx }, (24) NASS x C(x) min {P 1, P 2,, P NSSx }. (25) Futhemoe, becaue NASS x i an intege, we have C(x) NASS x =, (26) min {P 1, P 2,, P NSSx } whee i floo function an y i the laget intege not lage than y. Given a link x, if NSS x > NASS x, we nee to ajut the outing path election an elay aignment aoun the competition link. A a baic pinciple of ou Faine Awae Routing Ajutment (FARA) algoithm, in oe not to euce the capacity of the eion that go though the L-Path, the competition link will fit witch ome o all U-Path an B- Path to thei caniate path egment. Among the L-Path, we give eouce pefeence to the one with lowe capacity. We conie two cae in ou algoithm: Cae A: n 2 NASS x. The competition link x keep all L-Path, a well a NASS x n 2 U-Path o B-Path the ame, an anomly witche NSS x NASS x path-egment among n 1 + n 3 (U-Path an B-Path) to thei caniate path egment fo the coeponing eion. Cae B: n 2 > NASS x. The competition link x fit witche all the U-Path an B-Path to thei caniate path egment. Then it ot the capacity of n 2 caniate path, an witche the top n 2 NASS x one to go though thei caniate path egment. One example of Cae B i hown in Fig.1. In the example, thee ae thee eion uing link 9 1 though thee path egment, , , an , a hown in Fig. 1. The en-toen capacitie of thee thee eion ae 25.3, 23.8 an 23, epectively. We aume that NASS = 2 fo link 9 1. Theefoe, we nee to witch one path egment among the thee one to it caniate path egment. Fig. 1 how the thee coeponing caniate path egment, 1 2 ( 7 ), 3 5 ( 8 ) 6 4, 5 6, with the capacity 24.1, 21.5 an 22 epectively. Among all thee thee eion, the capacity of the caniate path egment in eion 1 ha the highet value. Accoing to ou algoithm, we witch fo eion 1 to 1 2 ( 7 ) a hown in Fig. 1(c). Afte the witch, the capacity of the thee path coeponing to iffeent eion ae 24.1, 23.8 an 23. Anothe example of Cae A i hown in Fig.11. In thi example, the en-to-en capacitie of the thee eion ae 25.3, 25 an 24, epectively. Fig. 11 how the thee caniate path egment of the coeponing thee eion which o not involve the competition link 9 1, 1 2 ( 7 ), 3 5 ( 8 ) 6 ( 9 ) 4, 5 6 ( 9 ), with the capacity 27, 25.5 an 25.6 epectively. Accoing to ou algoithm, becaue all the capacitie of caniate path egment of the thee eion ae lage than the capacity of thei en-to-en path, we can anomly witch one path to it caniate path, a hown in Fig.11(c). Afte the witch, the capacity of the thee eion emain the ame a that befoe witch. 3) Ripple Effect Reuction It i woth pointing out that we follow an impotant pinciple to ientify the caniate path egment: the caniate path egment houl not inclue the link whoe NSS i not malle than NASS. The pupoe of intoucing thi ule i to avoi netwok intability a a eult of tiggeing FARA to un in the witche caniate path egment thu ubequent oun of oute ajutment. If any link on the caniate path egment ha NSS lage than NASS, it may nee to etat anothe FARA algoithm afte aitional eion ae witche to thi path egment. Thi will lea to intability. Ieally, fo each caniate path egment, we houl check it impact on netwok tability befoe activating the caniate path egment to oute taffic fo a eion. Checking tability of netwok, howeve, i a time conuming tak. Intea, we popoe the imple ule. We call the eult of tiggeing FARA to un aoun ome oveloae link on the caniate path a Ripple Effect. We call Ripple Effect link a the one on the caniate path whoe NSS i not malle than NASS. To euce the ipple 9

10 7 f 1 = f 2= f 3 = f 1 = f 2= C 1 '= C 2 '= f 3 = f 1 = f 2= f 3 = (c) Fig. 1. Example of FARA poceue with n 2 > NASS. 7 f 1 = f 2= f 3 = f 1 = C 1 '=27 f 2= C 1 2 '= f 3 3 = C 11 3 '= f 1 = f 2= f = (c) Fig. 11. Example of FARA poceue with n 2 NASS. effect, in thi pape, we imply avoi electing caniate path containing ipple effect link. In cae thee oe not exit a caniate path egment without intoucing the ipple effect, multiple eion may hae a link, an iffeent eion can be cooinate in tanmiion uing the MAC laye cheme uch a CSMA o TDMA Fig Example of ipple effect icuion We illutate thi cenaio by an example in Fig. 12. Link 3 5 i hae by thee eion an link 1 2 ( 4 ) i hae by two eion. The NASS of link 3 5 an link 1 2 ( 4 ) ae 2. We aume that link 3 5 will invoke FARA algoithm an elect to change eion 1 to go though link 1 2 ( 4 ). A a eult of path witching, link 1 2 ( 4 ) woul have thee eion going though it, an then woul have to invoke anothe FARA algoithm. Thi effect may be popagate along a chain of uch neighboing link with NSS lage than thei NASS. If eion 1 oe not elect to go though link 1 2 ( 4 ) fo it ata tanmiion, link 1 2 ( 4 ) may not have to invoke anothe FARA algoithm. Theefoe, in the above example, link 7 6 intea 1 2 ( 4 ) houl be electe fo eion 1, a hown in Fig ) Avoiance of Route Ajutment Conflict If each link inepenently make a local oute ajutment eciion, multiple oute ajutment equet may be eceive imultaneouly by a link, which may lea to a oute ajutment colliion an eciion conflict at the link. Thi will futhe make the link be a Ripple Effect link, an invoke anothe FARA algoithm again Fig Example of oute ajutment conflict We illutate oute ajutment conflict poblem by an example in Fig. 13. In Fig.13, link 2 1 an 5 6 ae all hae by thee eion, but the NASS of thee two link ae 2. If link 2 1 an 5 6 invoke FARA algoithm inepenently, link 3 4 may be electe in eion 3 ( 3 3 ) an eion 5 ( 5 5 ) afte oute ajutment, a hown in Fig.13. A a eult of path witching, link 3 4 woul have thee eion going though, an then woul have to invoke anothe FARA algoithm. To mitigate thi poblem, we intouce a anom elay befoe a link w invoke FARA algoithm when the link etect

11 that itelf i hae by multiple eion with the NSS w lage than it NASS w, an the time can be et a follow: T ime w = 1 NSS w NASS w + anom (, g), (27) whee the anom numbe within (, g) i ae to euce colliion an eciion conflict fom multiple equet of oute ajutment. The link with a highe loa, i.e., a lage gap of NSS w NASS w, ha a lowe aveage time value thu an ealie chance of ajuting it local oute. C. Convegence Analyi In [39], the autho give the fomal analyi of convegence of AODV potocol. Ou coopeative outing algoithm (CRS) i eigne bae on AODV, an it i clea that the poce of ou CRS convege. Theefoe, we only nee to how that the poce of oute ajutment can convege an each a table tate. Theoem 2: If evey oveloae link invoke FARA algoithm to ajut it local path egment following the poceue in Section V-B, within a finite numbe of path egment witche, the netwok will each a table tate whee all link top the oute ajutment. Poof: Conie that a link i invoke FARA algoithm when etecting that it i oveloae (NSS i > NASS i ) an begin to witch ome of it eion on link i to thei caniate path egment at time t, an complete the path egment witche at time t ( t > t). Accoing to the poceue in Section V-B, NSS i NASS i eion houl witch thei tanmiion to the caniate path egment. Let P i enote the link et on the caniate path egment. In Section V-B4, we have the oute ajutment time et following the Eq.(27). Thi make the chance fo any othe link j to tigge it local oute ajutment imultaneouly with link i vey mall. Theefoe, at the time t, only link in P i woul be the new link (beie the link oiginally involve in eion) that may tigge a oute ajutment. Accoing to the pinciple in caniate-path-egment election in Section V-B3, the caniate path egment houl not inclue a link whoe NSS i not malle than it NASS. Theefoe, thee oute witche will not make the link in P i tigge anothe oute ajutment. Theefoe, although ou oute ajutment epen only on the infomation available within a local omain an i eigne to be itibute, the oute ajutment poce can elf-tabilize an help the netwok to each the table tate. VI. CENTRALIZED ALGORITHM Fo pefomance efeence, we futhe popoe a centalize algoithm. A one of the appoache to olving Intege Pogamming (IP) poblem [4], banch-an-boun metho fin the optimal olution to an IP by efficiently enumeating the point in the feaible egion. Bae on banch-an-boun famewok, we popoe a Centalize joint Flow Routing an Relay Aignment algoithm (CFRRA) to olve the MIP poblem in (21), a hown in algoithm 3. The baic iea of CFRRA i a follow. By uing the elaxation in tep 3, we can efficiently compute a global uppe boun, U B, fo poblem in (21). Thi elaxation olution eithe yiel a feaible olution to the poblem o, if not feaible, it can be ue a a tating point fo a local each to fin a feaible olution. Thi feaible olution then eve to povie a global lowe boun, LB, an an incumbent olution to the poblem. The banch-an-boun poce pocee by tightening LB an UB though a eie of patition ove the poblem omain, an teminate when UB (1 + ε)lb i atifie, whee ε > i ome eie appoximation eo. Algoithm 3 Centalize Joint Flow Routing an Relay Aignment Algoithm (CFRRA) 1: Let the optimal olution φ = ϕ an the initial lowe boun LB =. 2: Let the initial poblem lit contain only the oiginal poblem in (21), enote by P 1. 3: Contuct the elaxation fo P 1 by elaxing the containt x wk j:uv, yj:uv k {, 1} to x wk j:uv, yj:uv k [, 1], an olve it. Denote the olution to thi elaxation a φ 1 an it objective value a the uppe boun UB 1. 4: Select a poblem P z that ha the highet uppe boun (eignate a UB) among all the poblem in the poblem lit. 5: Fin, if neceay, a feaible olution φ z via a local each algoithm fo P z. Denote the objective value of φ z by LBz. 6: If LBz > LB, then let φ = φ z an LB = LBz. If UB (1 + ε)lb, then top with the (1 + ε)-optimal olution φ ; ele, emove all poblem P z having UB z (1 + ε)lb fom the poblem lit. 7: Select a binay x wk j:uv o yj:uv k an banch on the ichotomy of it value being o 1. 8: Remove the electe poblem P z fom the poblem lit, contuct two new poblem P z1 an P z2 bae on the foegoing banching tep. 9: Compute two new uppe boun UB z1 an UB z2 by olving the pogamming elaxation of P z1 an P z2, epectively. 1: If UB z1 > (1 + ε)lb then a Poblem P z1 to the poblem lit. If UB z2 > (1+ε)LB then a Poblem P z2 to the poblem lit. 11: If the poblem lit i empty, top with the (1 + ε) optimal olution φ. Othewie, go to Step 4. VII. SIMULATION RESULTS We peent ome imulation eult to emontate the ate gain by jointly applying intefeence-awae coopeative outing an elay aignment in multi-flow multi-aio multichannel wiele netwok. In thi ection, we fit ecibe the imulation etup, an then peent the imulation eult. A. Simulation Setup We evaluate the pefomance of ou popoe algoithm though extenive imulation uing MATLAB. Thee ae 12 othogonal channel in the netwok in total, an the efault numbe of eion in the netwok i et to 4. Following the paamete etting in [14], we et the banwith W of each channel to 22 MHz, the maximum tanmiion powe at evey noe to 1 W. The channel gain contain the path lo an the Rayleigh faing coefficient. White Gauian noie with the vaiance 1 1 W i ae to inclue envionment noie impact. In the imulation, 6 noe ae geneate anomly in a 1m 1m aea. Each noe i equippe with 3 aio, 11

12 an the maximum communication ange i et to 25 mete. The intefeence ange i et to twice the communication ange an will change with the communication ange vaie. Thee i no exiting wok tuying coopeative communication with multi-flow outing in multi-aio multi-channel netwok. We implement eight outing algoithm in iffeent netwok cenaio fo pefomance compaion, which ae intouce a follow. 1) Fo pefomance compaion, we implement ou popoe centalize algoithm CFRRA in Algoithm 3 in a multi-aio multi-channel coopeative netwok with ε =.1 in the algoithm, enote a CFRRA-MRMC- CC. 2) We implement ou popoe multi-flow multi-aio multi-channel coopeative outing algoithm DFRRA in Section V which inclue two ub-algoithm: the coopeative outing ub-algoithm in Section V-A an the faine-awae oute ajutment in Section V-B, enote a. 3) The CRS algoithm in Section V-A i applie to fin the maximum en-to-en coopeative path which ha the maximum capacity fo each new eion. We implement the CRS cheme in a multi-aio multi-channel coopeative wiele netwok, enote a CSC-MRMC-CC. 4) Diffeent fom the thi cheme, we implement the CRS in a ingle-aio ingle-channel coopeative wiele netwok whee each noe i aigne with the ame channel, enote a CSC-SRSC-CC. 5) Diffeent fom the thi cheme, we implement CRS in a ingle-aio multi-channel coopeative wiele netwok whee each noe i aigne with a channel anomly electe fom the et of othogonal channel, enote a CSC-SRMC-CC. 6) We implement a non-coopeative outing algoithm in which the Bellman-Fo path algoithm i applie to each fo the maximum en-to-en capacity path fo each new eion in multi-aio multi-channel wiele netwok, enote a. 7) Diffeent fom the ixth cheme, we implement the non-coopeative outing algoithm in ingle-aio inglechannel wiele netwok, enote a Bellman-SRSC- NC. 8) Diffeent fom the ixth cheme, we implement the non-coopeative outing algoithm in ingle-aio multichannel wiele netwok, enote a Bellman-SRMC- NC. Note that the lat thee algoithm,, an conie a noncoopeative wiele netwok which only conit of flow outing fo each eion. In the lat ix algoithm, if multiple eion elect the ame link, TDMA type cheuling can be applie at the MAC laye to allocate time lot to iffeent active eion bae on cetain faine ule. We evaluate the pefomance of ou itibute algoithm DFRRA-MR-CC une iffeent noe enity, numbe of eion, numbe of aio inteface on a noe, an the communication ange. Unle othewie pecifie, the efault numbe of noe in the netwok i 6, the numbe of eion i 4, each noe i equippe with 3 aio, an the communication ange i 25 mete. A imulation eult i obtaine by aveaging ove un of imulation. B. Simulation Reult 1) Impact of noe enity In Fig.14, the aggegate ate an minimum ate (in tem of kbp) une all outing algoithm inceae a the numbe of noe inceae, a thee ae moe caniate elay noe. Compae with the aggegate ate of ingle-aio netwok, the ate of the multi-aio netwok i about 6-8 time. The intouction of multi-aio noe with multi-channel ignificantly inceae the flexibility in elay election an eceae the wiele intefeence thu achieving highe pefomance gain. Compae to,, CRS-SRMC- CC,,, an Bellman- SRMC-NC, we fin that ou two multi-aio multi-channel coopeative outing algoithm, the centalize CFRRA-MRMC- CC an the itibute, have the laget aggegate ate an minimum ate. Compae to Bellman- MRMC-NC, can inceae up to 78% the aggegate tanmiion ate. Thi emontate the ignificant pefomance gain achieve by incopoating CC in multi-aio multi-channel multi-hop wiele netwok. In a multi-channel wiele netwok, two noe can communicate only if they ae aigne a common channel. Fo a ingle aio wiele netwok, a noe can be aigne at mot one channel. If the channel aigne to the noe i anomly electe, noe in the ingle-aio multi-channel netwok ha a limite numbe of neighbo. Thu thee ae limite numbe of link in the netwok, an the cuve of an ae cloe to x axi a hown in Fig.14. Moeove, compae to, ou DFRRA- MRMC-CC can obtain up to 4% an 41% highe aggegate ate an minimum ate, epectively. Thi inicate that the Faine-Awae Route Ajutment algoithm (FARA) popoe in Section V-B an inclue in can effectively eolve the eouce competition among iffeent eion an enue highe minimum thoughput aco eion. imply cooinate tanmiion though TDMA when multiple eion hae link, which will compomie the pefomance. When the numbe of elay noe i mall, thee may be moe elay competition among iffeent eion. Ou FARA algoithm can moe effectively aapt the elay election on competitive outing egment to inceae the aggegate ate. 2) Impact of the numbe of eion In Fig 15, a the numbe of eion inceae, the aggegate ate inceae, while the minimum ate eceae. Thi i a expecte. The lage numbe of eion bing highe competition on the elay noe an channel eouce in the netwok, which eult in lage intefeence thu the euction of the minimum thoughput. The two multi-aio coopeative outing algoithm, an, have much bette pefomance compae to othe outing algoithm. Compae with, ou 12

13 Aggegate Rate No.Noe aggegate ate Minimum Rate No.Noe minimum ate Aggegate Rate No.Raio Pe Noe aggegate ate Minimum Rate No.Raio Pe Noe minimum ate Fig. 14. Impact of noe enity. Fig. 16. Impact of numbe of aio. Aggegate Rate Fig No.Seion aggegate ate Minimum Rate Impact of numbe of eion No.Seion minimum ate Aggegate Rate Fig Communication Range aggegate ate Minimum Rate Impact of the communication ange Communication Range minimum ate achieve the ame pefomance when the numbe of eion i 2, an achieve highe aggegate ate an minimum ate when the numbe of eion i lage than 2. When the numbe of eion i mall, the elay noe an channel ae ufficient to eve all eion. In Fig.15, compae with CRS-MRMC- CC, a the numbe of eion inceae, the gain of ou i een to inceae initially an then euce. Ou FARA algoithm can effectively mitigate link competition initially, but the pefomance of DFRRA-MRMC- CC uffe when the numbe of eion i vey lage an thee ae vey few caniate elay to exploit. 3) Impact of the numbe of aio When vaying the numbe of aio fom 2 to 1 in Fig. 16, the aggegate ate an minimum ate achieve by,,, an inceae, a thee ae moe elay an tanmiion channel option. A an ae ingle-aio outing algoithm, the numbe of aio on t have impact on thei pefomance a in Fig. 16. Simila to the eaon of Fig 15, ue to limite link in ingle-aio multi-channel netwok, the cuve of CRS- SRMC-CC an ae cloe to x axi. The pefomance of outpefom CRS- MRMC-CC when thee ae competition in elay an link acce, which emontate that ou can make ue of elay an channel eouce moe efficiently. Compae to, ou DFRRA-MRMC- CC can obtain up to 3% an 37% highe aggegate ate an minimum ate epectively, which emontate that coopeative tanmiion outpefom iect tanmiion in multiaio multi-channel multi-hop wiele netwok. 4) Impact of the communication ange In oe to obeve the effect bought by the tanmiion itance, we vay the communication ange fom 1 to 4 mete in the netwok. A hown in Fig.17, when the commu- nication ange i vey mall, the aggegate ate an minimum ate fo all the outing cheme ae zeo becaue noe have limite numbe of neighbo an thee ae limite link in the wiele netwok. The aggegate ate an minimum ate fo all the outing cheme inceae initially. Howeve, with the futhe inceae of the communication ange, the thoughput euce until the communication ange eache a cetain value, then maintain a table thoughput. On the one han, the inceae of the communication ange lea to highe numbe of link thu moe option to elect elay an next-hop noe. The initial inceae of communication ange alo help to inceae the netwok connectivity an fin a bette tanmiion path. On the othe han, a lage communication ange alo ceate highe intefeence an hence euce the outing pefomance. Theefoe, it i not helpful to ue too high tanmiion powe to inceae the communication ange. Simila to the eult in Fig.14, Fig.15, an Fig.16, ou cheme an DFRRA- MRMC-CC how bette pefomance compae with othe cheme in Fig.17. In ummay, all the imulation eult emontate that, ou itibute algoithm i een to achieve the pefomance cloe to the boun povie by the centalize algoithm while unning much moe efficiently. VIII. CONCLUSION Thi pape tuie a joint poblem of coopeative outing an elay aignment in multi-hop an multi-aio netwok to maximize the minimum ate among a et of concuent communication eion. We fit moel thi poblem a a mixe intege pogamming (MIP) poblem an pove it to be NP-ha. Then we popoe a centalize algoithm an a itibute algoithm to olve the poblem. The centalize 13

14 algoithm can guaantee the fining of a global (1+ε)-optimal olution. The itibute algoithm can be applie to fin an efficient coopeative oute with polynomial complexity. We have one extenive imulation to evaluate the pefomance, an ou eult emontate the effectivene of the popoe algoithm an the ignificant ate gain that can be achieve by incopoating CC in multi-aio multi-hop netwok. Although we ue AF a the CC moe in thi pape, it i woth pointing out that ou algoithm o not epen on pecific CC moe to function. ACKNOWLEDGMENT The wok i uppote by the open Founation of State key Laboatoy of Netwoking an Switching Technology (Beijing Univeity of Pot an Telecommunication) une Gant No. SKLNST , the Popective Reeach Poject on Futue Netwok (Jiangu Futue Netwok Innovation Intitute) une Gant No. BY , the National Natual Science Founation of China une Gant No , an , U.S. National Science Founation une Gant No. ECCS an CNS REFERENCES [1] Q. Zhang, J. Jia, an J. Zhang, Coopeative elay to impove iveity in cognitive aio netwok, IEEE Communication Magazine, vol. 47, no. 2, pp , 9. [2] J. Cai, X. Shen, J. W. Mak, an A. S. Alfa, Semi-itibute ue elaying algoithm fo amplify-an-fowa wiele elay netwok, IEEE Tanaction on Wiele Communication, vol. 7, no. 4, pp , 8. [3] B. Wang, Z. Han, an K. Liu, Ditibute elay election an powe contol fo multiue coopeative communication netwok uing buye/elle game, in INFOCOM 7. [4] Y. Shi, S. Shama, Y. T. Hou, an S. Kompella, Optimal elay aignment fo coopeative communication, in MobiHoc 8. [5] P. Zhang, Z. Xu, F. Wang, X. Xie, an L. Tu, A elay aignment algoithm with intefeence mitigation fo coopeative communication, in WCNC 9. [6] Z. Yang, Q. Zhang, an Z. Niu, Thoughput impovement by joint elay election an link cheuling in elay-aite cellula netwok, IEEE Tanaction on Vehicula Technology, vol. 61, no. 6, pp , 12. [7] D. Yang, X. Fang, an G. Xue, Hea: An optimal elay aignment cheme fo coopeative netwok, IEEE Jounal on Selecte Aea in Communication, vol. 3, no. 2, pp , 12. [8] A. Khanani, J. Abounai, E. Moiano, an L. Zheng, Coopeative outing in tatic wiele netwok, IEEE Tanaction on Communication, vol. 55, no. 11, pp , 7. [9] E. Yeh an R. Bey, Thoughput optimal contol of coopeative elay netwok, IEEE Tanaction on Infomation Theoy, vol. 53, no. 1, pp , 7. [1] G. Jakllai, S. V. Kihnamuthy, M. Falouto, P. V. Kihnamuthy, an O. Ecetin, A co-laye famewok fo exploiting vitual mio link in mobile a hoc netwok, IEEE Tanaction on Mobile Computing, vol. 6, no. 6, pp , 7. [11] S. Lakhmanan an R. Sivakuma, Diveity outing fo multi-hop wiele netwok with coopeative tanmiion, in SECON 9. [12] M. Elhaway an Z. Haa, Enegy-efficient potocol fo coopeative netwok, IEEE/ACM Tanaction on Netwoking, vol. 19, no. 2, pp , 11. [13] A. Ibahim, Z. Han, an K. Liu, Ditibute enegy-efficient coopeative outing in wiele netwok, IEEE Tanaction on Wiele Communication, vol. 7, no. 1, pp , 8. [14] S. Shama, Y. Shi, Y. Hou, H. Sheali, an S. Kompella, Coopeative communication in multi-hop wiele netwok: Joint flow outing an elay noe aignment, in INFOCOM 1. [15] D. Gunuz an E. Ekip, Oppotunitic coopeation by ynamic eouce allocation, IEEE Tanaction on Wiele Communication, vol. 6, no. 4, pp , 7. [16] O. Guewitz, A. e Baynat, an E. Knightly, Coopeative tategie an achievable ate fo tee netwok with optimal patial eue, IEEE Tanaction on Infomation Theoy, vol. 53, no. 1, pp , 7. [17] T. Hunte an A. Noatinia, Diveity though coe coopeation, IEEE Tanaction on Wiele Communication, vol. 5, no. 2, pp , 6. [18] S. Savazzi an U. Spagnolini, Enegy awae powe allocation tategie fo multihop-coopeative tanmiion cheme, IEEE Jounal on Selecte Aea in Communication, vol. 25, no. 2, pp , 7. [19] A. Senonai, E. Ekip, an B. Aazhang, Ue coopeation iveity. pat i. ytem eciption, IEEE Tanaction on Communication, vol. 51, no. 11, pp , 3. [] H. Xu, L. Huang, C. Qiao, Y. Zhang, an Q. Sun, Banwith-powe awae coopeative multipath outing fo wiele multimeia eno netwok, IEEE Tanaction on Wiele Communication, vol. 11, no. 4, pp , 12. [21] X. Li an J. Wu, Channel on eman: Optimal capacity fo coopeative multi-channel multi-inteface wiele meh netwok, in MASS 1. [22] F. Yang, M. Huang, M. Zhao, S. Zhang, an W. Zhou, Coopeative tategie fo wiele elay netwok with cochannel intefeence ove time-coelate faing channel, IEEE Tanaction on Vehicula Technology, vol. 62, no. 7, pp , 13. [23] Z. Guan, T. Meloia, D. Yuan, an D. A. Pao, Ditibute pectum management an elay election in intefeence-limite coopeative wiele netwok, in Poceeing of the 17th ACM annual intenational confeence on Mobile computing an netwoking, pp , 11. [24] J. Zhang an Q. Zhang, Coopeative outing in multi-ouce multietination multi-hop wiele netwok, in Poceeing IEEE INFO- COM, pp , 8. [25] P. Li, S. Guo, an J. Hu, Enegy-efficient coopeative communication fo multimeia application in multi-channel wiele netwok, IEEE Tanaction on Compute, 14, DOI 1.119/TC [26] M. Alichey, R. Bhatia, an L. E. Li, Joint channel aignment an outing fo thoughput optimization in multi-aio wiele meh netwok, in Poceeing of the 11th annual intenational confeence on Mobile computing an netwoking, MobiCom 5, (New Yok, NY, USA), pp , ACM, 5. [27] H. Li, Y. Cheng, C. Zhou, an P. Wan, Multi-imenional conflict gaph bae computing fo optimal capacity in m-mc wiele netwok, in Ditibute Computing Sytem (ICDCS), 1 IEEE 3th Intenational Confeence on, pp , June 1. [28] H. Li, Y. Cheng, C. Zhou, an W. Zhuang, Routing metic fo minimizing en-to-en elay in multiaio multichannel wiele netwok, Paallel an Ditibute Sytem, IEEE Tanaction on, vol. 24, pp , Nov 13. [29] P.-J. Wan, Z. Wang, L. Wang, Z. Wan, an S. Ji, Fom leat intefeencecot path to maximum (concuent) multiflow in MC-MR wiele netwok, in INFOCOM, 14 Poceeing IEEE, pp , Apil 14. [3] J. Zhu, X. Wang, an D. Xu, A unifie mac an outing famewok fo multichannel multi-inteface a hoc netwok, IEEE Tanaction on Vehicula Technology, vol. 59, pp , Nov 1. [31] S. Chu, X. Wang, an Y. Yang, Aaptive cheuling in mimo-bae heteogeneou a hoc netwok, IEEE Tanaction on Mobile Computing, vol. 13, pp , May 14. [32] S. Chu, X. Wang, an Y. Yang, Exploiting coopeative elay fo high pefomance communication in mimo a hoc netwok, IEEE Tanaction on Compute, vol. 62, pp , Apil 13. [33] S. Chu, X. Wang, an M. Li, Enfocing high-pefomance opeation of multi-hop wiele netwok with MIMO elay, in IEEE Intenational Confeence on Ditibute Computing Sytem (ICDCS), (Macau), 12. [34] S. Chu an X. Wang, Oppotunitic an coopeative patial multiplexing in mimo a hoc netwok, IEEE/ACM Tanaction on Netwoking, vol. 18, pp , Oct 1. [35] Y. Zhao, R. Ave, an L. Teng Joon, Impoving amplify-an-fowa elay netwok: Optimal powe allocation veu election, in ISIT 6. [36] F. Li, K. Wu, an A. Lippman, Enegy-efficient coopeative outing in multi-hop wiele a hoc netwok, in IPCCC 6. [37] Y. Zhu an H. Zheng, Unetaning the impact of intefeence on collaboative elay, IEEE Tanaction on Mobile Computing, vol. 7, no. 6, pp , 8. [38] P. Nilon an M. Pioo, Unplittable max-min eman allocationa outing poblem, in HET-NET 5 Thi Intenational woking confeence, 5. [39] D. Obaovic, Fomal analyi of convegence of outing potocol. PhD thei, univeity of pennylvania,. 14

15 [4] W. L. A. Pochet, Yve, Pouction Planning by Mixe Intege Pogamming. 6. Kun Xie eceive B.S. egee in communication engineeing, M.S., PhD egee in compute application fom Hunan Univeity, Changha, China, in 1, 4, an 7 epectively. She woke a a potoctoal fellow in the epatment of computing in Hong Kong Polytechnic Univeity fom 7.12 to 1.2. She woke a a viiting eeache in the epatment of electical an compute engineeing in tate univeity of New Yok at Stony Book fom 12.9 to She i cuently an aociate pofeo in Hunan Univeity. He eeach inteet inclue wiele netwok an mobile computing, netwok management an contol, clou computing an mobile clou, an big ata. She ha publihe about 6 pape an applie patent in he eeach aea. Jiannong Cao (M 93-SM 5-FM 14) D. Cao i cuently a chai pofeo an hea of the Depatment of Computing at Hong Kong Polytechnic Univeity, Hung Hom, Hong Kong. He i alo the iecto of the Intenet an Mobile Computing Lab in the epatment. D. Cao eeach inteet inclue paallel an itibute computing, compute netwok, mobile an pevaive computing, fault toleance, an milewae. He ha co-authoe a book in Mobile Computing, co-eite 9 book, an publihe ove 3 pape in majo intenational jounal an confeence poceeing. He ha iecte an paticipate in numeou eeach an evelopment poject an, a a pincipal invetigato, obtaine ove HK$25 million gant fom govenment funing agencie an inutie. D. Cao ha won numeou pize an awa, an i vey active in pofeional activitie locally an intenationally. He i a enio membe of China Compute Feeation, a enio membe of IEEE, an a membe of ACM. He wa the Cooinato in Aia an now the Chai of the Technical Committee on Ditibute Computing of IEEE Compute Society. D. Cao ha eve a an aociate eito an a membe of the eitoial boa of many intenational jounal, incluing IEEE Tanaction on Paallel an Ditibute Sytem, IEEE Tanaction on Compute, IEEE Netwok, Pevaive an Mobile Computing Pee-to-Pee Netwoking an Application, an Jounal of Compute Science an Technology. He ha alo eve a a chai an membe of oganizing / pogam committee fo many intenational confeence, incluing PERCOM, INFOCOM, ICDCS, IPDPS, ICPP, RTSS, DSN, ICNP, SRDS, MASS, PRDC, ICC, GLOBECOM, an WCNC. D. Cao eceive the BSc egee in compute cience fom Nanjing Univeity, Nanjing, China, an the MSc an the Ph.D egee in compute cience fom Wahington State Univeity, Pullman, WA, USA. Xin Wang (M 1 / ACM 4) eceive the B.S. an M.S. egee in telecommunication engineeing an wiele communication engineeing epectively fom Beijing Univeity of Pot an Telecommunication, Beijing, China, an the Ph.D. egee in electical an compute engineeing fom Columbia Univeity, New Yok, NY. She i cuently an Aociate Pofeo in the Depatment of Electical an Compute Engineeing of the State Univeity of New Yok at Stony Book, Stony Book, NY. Befoe joining Stony Book, he wa a Membe of Technical Staff in the aea of mobile an wiele netwoking at Bell Lab Reeach, Lucent Technologie, New Jeey, an an Aitant Pofeo in the Depatment of Compute Science an Engineeing of the State Univeity of New Yok at Buffalo, Buffalo, NY. He eeach inteet inclue algoithm an potocol eign in wiele netwok an communication, mobile an itibute computing, a well a netwoke ening an etection. She ha eve in executive committee an technical committee of numeou confeence an funing eview panel, an i the efeee fo many technical jounal. D. Wang achieve the NSF caee awa in 5, an ONR challenge awa in 1. Jigang Wen eceive PhD egee in compute application fom Hunan Univeity, China, in 11. He woke a a eeach aitant in the epatment of computing in Hong Kong Polytechnic Univeity fom 8 to 1. Hi eeach inteet inclue wiele netwok an mobile computing, high pee netwok meauement an management. 15