OPRA: Optimal Relay Assignment for Capacity Maximization in Cooperative Networks

Transcription

1 OPRA: Optimal Relay Assignment fo Capacity Maximization in Coopeative Netwoks Dejun Yang, Xi Fang an Guoliang Xue Aizona State Univesity Tempe, AZ {ejun.yang, xi.fang, Abstact As pomising as it is, coopeative communication has been popose to incease the capacity of wieless netwoks though spatial ivesity. Without equiing multiple antennas on the same evice, spatial ivesity is achieve by exploiting the antennas on othe noes, i.e., elay noes, in the netwok. Theefoe, the selection of elay noes has a significant impact on the achieve total capacity. In this pape, we stuy the poblem of elay assignment in coopeative netwoks, whee multiple souceestination tansmission pais shae the same set of elay noes. Specifically, we popose a system moel whee a elay noe can be shae by multiple souce-estination pais an pesent a coesponing fomulation fo the capacity calculation. Ou objective is to fin a elay assignment to maximize the total capacity of the netwok. As the main contibution, we evelop an optimal elay assignment algoithm to solve this poblem in polynomial time. We also show that ou algoithm has seveal attactive popeties. 1. INTRODUCTION Though coopeative elaying fom othe evices (geneally calle elay noes), Coopeative Communication (CC) [7] has been shown to have the potential to incease the channel capacity between two wieless evices. The essence of CC is to exploit the natue of boacast an the elaying capability of othe noes to achieve spatial ivesity. Two pimay CC moes have been commonly use, Amplify-an-Fowa (AF) an Decoe-an-Fowa (DF), epening on how the elay noe pocesses the eceive signal an tansmits to the estination. In the AF moe, the elay noe amplifies the signal eceive fom the souce noe an fowas it to the estination noe. In the DF moe, the elay noe ecoes the signal eceive fom the souce noe an e-encoes it befoe fowaing it to the estination noe. Although CC pomises to incease the capacity, an impope selection of elay noe can esult in an even smalle capacity than that une iect tansmission. Theefoe, the assignment of elay noes plays a citical ole in the pefomance of CC [2, 3, 6, 13, 17]. We consie the following scenaio in this pape. In a wieless netwok, thee ae a numbe of souce-estination pais an many othe wieless evices functioning as elay noes. We ae inteeste in fining a elay assignment fo each souce-estination pai, such that the total capacity of all pais is maximize. suppote in pat by ARO gant W911NF , an NSF gants an The infomation epote hee oes not eflect the position o the policy of the feeal govenment. This poblem has many applications. Fo example, in WiMAX netwoks (base on the IEEE stana), elay stations have been intouce to elay taffic fo subscibe stations in oe to meet the gowing eman fo thoughput an capacity [1]. In this context, all the subscibe stations ae souce noes an they shae the same estination noe, i.e., the base station. In cellula netwoks, the emans fo banwithhungy multimeia an intenet-base sevices have pushe the caie companies to evelop innovative netwok solutions with low cost. To this en, multihop cellula netwok (MCN) [8, 11] has emege as an efficient an pomising solution. In multihop cellula netwoks, mobile stations can elay the packets fo the souce mobile station to the estination mobile station if the estination mobile station is within the same cell as the souce mobile station o to the base station othewise. Ou main contibutions can be summaize as follows: We stuy the elay assignment poblem in coopeative netwoks, which seeks fo a elay assignment fo each souce-estination pai so as to maximize the total capacity of all pais. We consie a system moel which allows a elay noe to be shae by multiple souce noes. It is moe geneal compae with the moel in [13], which esticts each elay to be assigne to only one souce-estination pai. We esign a polynomial time algoithm to optimally solve the elay assignment poblem. That is, ou algoithm can fin a elay assignment that gives the maximum total capacity among all the possible assignments. We show that ou algoithm woks egaless of which CC moe is use in the netwok. It is also inepenent of the elation between the numbe of souce-estination pais an that of the elay noes. In aition, ou algoithm can guaantee that the achieve capacity between each souce-estination pai une the assignment is no less than that une iect tansmission. The est of this pape is oganize as follows. In Section 2, we give a bief eview of the elate wok in the liteatue. In Section 3, we escibe the system moel fo the elay assignment poblem stuie in this pape. In Section 4, we then pesent a polynomial time optimal algoithm to solve the elay assignment poblem. We illustate the numeical esults in Section 5. Finally, we conclue this pape in Section 6.

2 2. RELATED WORK In this section, we give a bief eview of the elate wok on coopeative communication (CC), with the focus on elay assignment. As the pionee in the evelopment of CC, Van De Meulen [9] fist intouce a thee-teminal coopeative channel moel an stuie the capacity fo iffeent elaying stategies. Anothe funamental wok on CC was one by Cove an El Gammal in [5]. They gave an achievable lowe boun on the capacity of the geneal elay channel. In [2], Bletsas et al. popose a novel scheme to select the best elay noe fo a single souce-estination pai fom a set of available elays. Howeve, this can not be extene to a netwok consisting multiple souce-estination pais, which is the moel stuie in this pape. Some effots have been mae on the elay assignment poblem o the elay selection poblem in coopeative netwoks. In [3], Cai et al. stuie the poblem of elay selection an powe allocation fo AF wieless elay netwoks. They fist consiee the simple netwok with only one souceestination pai, an then extene it to the multiple-pai case. The popose algoithm is an effective heuistic, but offes no pefomance guaantee. Fom a iffeent pespective, Xu et al. [15] stuie a simila poblem but with a iffeent objective, which is to minimize the total powe consumption of the netwok. In [10], Ng an Yu jointly consiee the elay noe selection, coopeative communication an esouce allocation fo utility maximization in a cellula netwok. Howeve, the algoithm is heuistic an not polynomial, as pointe out by Shi et al. [13]. In [12], Shama et al. investigate a joint poblem of elay noe assignment an multi-hop flow outing, with the objective to maximize the minimum ate among a set of concuent sessions. They fomulate the poblem as a mixe intege linea pogamming an solve it using a banch-an-cut famewok, which pouces a (1 ε)- appoximation algoithm. The most closely elate wok was one by Shi et al. [13]. They stuie the elay assignment poblem in netwoks, such that the minimum capacity among all souce-estination pais is maximize. Following this wok, Zhang et al. [16] consiee the elay assignment poblem with intefeence mitigation. In both moels in [13] an [16], a elay noe is esticte to be assigne to at most one souce-estination pai. In contast, ou moel in this pape is moe geneal in the sense that it allows multiple souce noes to shae the same elay noe. In aition, iffeent fom [13], ou objective is to maximize the total capacity of all pais. Though Zhang et al. [16] ha the same objective as ous, they only povie a heuistic algoithm. 3. SYSTEM MODEL In this pape, we consie a static wieless netwok consisting of n souce-estination pais {s 1, 1 ; s 2, 2 ; ; s n, n } an a set R = { 1, 2,, m } of m elay noes. We use S = {s 1, s 2,, s n } to enote the set of souce noes an D = { 1, 2,, n } to enote the set of estination noes. As in [13], we assume that othogonal channels ae available in the netwok (e.g. using OFDMA) to mitigate intefeence. We assume that each noe is equippe with one single tansceive an can eithe tansmit o eceive at a time. Let Pi s enote the tansmission powe of souce noe s i an Pj enote the tansmission powe of elay noe j. We moel the channel popagation as follows. When noe u tansmits a signal to noe v with powe P u, the signal-to-noise atio (SNR) at noe v, enote as SNR uv, is SNR uv = P u, (1) N 0 u, v α whee N 0 is the abient noise, u, v is the Eucliean istance between noes u an v, an α is the path loss exponent which is between 2 an 4 in geneal, epening on the chaacteistics of the communication meium. Fo the tansmission moel, we assume that each souceestination pai has an option to use coopeative communication (CC) with the help of a elay noe. A ecent wok by Zhao et al. [17] showe that it is sufficient fo a souce-estination pai to choose the best elay noe even when multiple ae available to achieve full ivesity. Theefoe, it is easonable to assume that each souce-estination pai will eithe tansmit iectly o use CC with the help of only one elay noe. Next, we pesent both the iect tansmission moel an the coopeative communication moel in etails. Diect Tansmission: When souce noe s tansmits to estination noe iectly, the achievable capacity is C DT (s, ) = W log 2 (1 + SNR s ), (2) whee W is the banwith of the channel. We use a well-known thee-noe example in Fig. 1 to escibe the essence of CC. In this example, s is the souce noe that tansmits infomation, is the estination noe that eceives infomation an is the elay noe that elays infomation to enhance the communication between the souce an the estination. CC pocees in a fame-by-fame fashion. Each fame is ivie into two time slots. Souce noe s tansmits ata to estination noe in the fist time slot. Due to the boacast natue, elay noe can ovehea this tansmission. In the secon time slot, fowas the ata to using iffeent techniques epening on iffeent CC moes. Thee ae two iffeent CC moes, Amplify-an-Fowa (AF) an Decoe-an-Fowa (DF) [7]. s (a) s s slot 1 slot 2 slot 3 slot 4 fame 1 fame 2 (b) Fig. 1: A thee-noe example fo CC Amplify-an-Fowa (AF): In the amplify-an-fowa moe, the elay noe amplifies the signal eceive fom the

3 souce noe in the fist time slot an then tansmits the amplifie signal to the estination noe in the secon time slot. The achievable capacity fom s to is C AF (s,, )= W ( 2 log 2 1+SNR s + SNR ) s SNR. SNR s +SNR +1 Decoe-an-Fowa (DF): In the ecoe-an-fowa moe, the elay noe ecoes an estimates the signal eceive fom the souce noe in the fist time slot an then tansmits the estimate ata to the estination noe in the secon time slot. The achievable capacity fom s to is C DF (s,, ) = W 2 min{ log 2(1 + SNR s ), log 2 (1 + SNR s + SNR )}. Since both C AF an C DF ae functions of P, s, an,, it is unobvious whethe using CC can benefit the tansmission between a souce-estination pai, in the sense that C AF (s,, ) > C DT (s, ) o C DF (s,, ) > C DT (s, ). We use C R to enote the achievable capacity une the use CC moe, i.e., C R = C AF if AF is use an C R = C DF if DF is use. We say that elay noe j is assigne to souce noe s i if j helps s i to achieve coopeative communication fom s i to i. Let σ : S R {φ} be a elay assignment. Hee σ(s i ) = φ means that s i tansmits to i iectly. Note that it is possible to have σ(s i ) = σ(s j ) fo s i = s j. This is a majo iffeence fom the moel in [13], in which a elay noe can be assigne to only one souce noe. Since we o not have such constaints, ou moel is moe geneal than the moel in [13]. 1 s1 (a) 2 s2 1 s 1 2 s2 1 2 slot 1 slot 2 slot 3 slot 4 fame 1 fame 2 Fig. 2: Multi-souce coopeative communication. Now let us consie the case whee the same elay noe is assigne to multiple souce noes. We enote S( j ) as the set of souce noes, to which j is assigne, i.e., S( j ) = {s i σ(s i ) = j }. In this case, we assume that each elay noe equally povies sevice to all the souce noes employing that elay noe. This can be achieve fo example by using a esevation-base TDMA scheuling. The elay noe seves each souce noe in a oun-obin fashion. Each fame is eicate to a single souce noe fo CC. Each souce noe gets seve evey fames, whee = S( j ). Theefoe, the aveage achievable capacity fo each souce noe. A simple example is shown in Fig. 2. Fo notational simplicity, we use C(s i, σ(s i )) to enote the achievable capacity when σ(s i ) is assigne to s i. Heeafte we also omit i in the capacity expession because it is clea s i S( j ) is C R(s i,σ(s i), i) (b) that i an s i have a one-one mapping elation. Thus we have C(s i, σ(s i )) = { CR (s i,σ(s i)), if σ(s i ) = φ, C DT (s i ), if σ(s i ) = φ. Ou objective in this pape is to fin a elay assignment such that the total capacity is maximize. It is iffeent fom the poblem in [13], of which the objective is to maximize the minimum capacity among all souce-estination pais. Definition 3.1: (Relay Assignment Poblem (RAP)): Given a set (S, D) of souce-estination pais an a set R of elay noes, the Relay Assignment Poblem seeks fo a elay assignment σ such that the total capacity Csum σ = s C(s i S i, σ(s i )) is maximize among all the possible elay assignments. In the est of this pape, we use C sum to enote Csum σ when the context is clea. 4. AN OPTIMAL ALGORITHM FOR RAP Due to the possibility of shaing a common elay noe among multiple souce noes, it is not clea how to fomulate RAP as an intege linea pogamming poblem. Howeve, exploiting some special an specific popeties of the stuie poblem, we ae able to esign a polynomial time optimal algoithm to solve RAP. In this section, we fist stuy these popeties, which ae essential to the esign of ou algoithm. Then we pesent an optimal algoithm fo RAP. At the en of this section, we outline some nice popeties petaining to ou algoithm. A. Motivating Example We stat with an example consisting of 5 souce-estination pais an 2 elay noes. Each of the five subtables in Table I epesents a elay assignment. Moe specifically, the numbe in the cell of column s i an ow j is the achievable capacity fo souce noe s i, when elay noe j is exclusively assigne to it. The symbol φ epesents iect tansmission to the coesponing estination. Fo example, in Table I(a), the numbes in the fist column epesent C R (s 1, 1 ) = 10, C R (s 1, 2 ) = 4 an C DT (s 1 ) = 4. Each highlighte cell epesents the cuent assigne elay noe fo the coesponing souce noe. Fo example, in Table I(b), σ(s 1 ) = 1, σ(s 2 ) = σ(s 4 ) = σ(s 5 ) = 2 an σ(s 3 ) = φ. Fom Table I(a) to I(), we illustate an iteative poceue to impove the total capacity. The total capacity C sum is compute accoing to Definition 3.1. In each iteation, we change the elay assignment of the uneline souce noe fom its cuently assigne elay noe to tansmitting iectly. Fo example, in Table I(b), we change the elay assignment of s 3 fom 1 to φ an impove the total capacity fom 17 to 20. Note that uing this poceue, it seems that we can impove the total capacity by changing the assignment of the souce noe with minimum C R among all the souce noes shaing the same elay noe an letting it tansmit iectly to its estination. In section 4-B, we will pove that this is not a coincience but an inheent popety. (3)

4 (a) C sum = = (b) C sum = = (c) C sum = = 22.5() C sum = = (e) C sum = = 25 TABLE I: An example with 5 souce-estination pais an 2 elays B. Algoithm Details We fist pove the popety obseve fom the example in Section 4-A, which is fomally state in Lemma 4.1. Lemma 4.1: Let σ be a elay assignment, whee some elay noe j R is assigne to > 1 souce noes. Let s i S( j ) be the souce noe with the minimum C R, i.e., C R (s i, j ) = min sk S( j) C R (s k, j ). If we let s i tansmit to i iectly, instea of using j, an keep othe souce noes assignments the same, the total capacity will be incease. That is Csum σ > Csum, σ whee σ (s i ) = φ an σ (s k ) = σ(s i ) fo all s k = s i. Poof. Let S ( j ) = S( j ) {s i }. If s i tansmits to i iectly instea of employing j fo CC, we have socially optimal assignment is shown in Table I(e). Howeve, Lemma 4.1 implies a nice popety petaining to the optimal elay assignment fo RAP. Lemma 4.2: In the optimal solution σ to RAP, each elay noe is assigne to at most one souce noe, i.e., 1 fo j R. Poof. Assume to the contay that thee exists a elay noe j R that is assigne to moe than one souce noes, i.e. > 1. By Lemma 4.1, we can obtain a new elay assignment with stictly highe total capacity by changing one of the souce noes in S( j ) to tansmit to the estination noe iectly. This contaicts the optimality of the elay assignment σ. Theefoe, each elay noe is assigne to at most one souce noe in the optimal solution. Supisingly, although we allow multiple souce noes to shae a common elay noe in ou moel, an optimal elay assignment pefeably assigns a elay noe to at most one souce noe to achieve the maximum total capacity. On the othe han, we know that each souce noe will eithe employ a elay noe fo CC o tansmit to the estination iectly, but not both at the same time. This one-to-one matching elation in the optimal solution inicates that we can tansfom any instance of RAP into that of the Maximum Weighte Bipatite Matching (MWBM) poblem [14] an solve it using coesponing algoithms. Fo any instance (S, D, R) of the RAP poblem, we constuct an instance G = (U, V, w) of the MWBM poblem as follows. Let a set U of vetices epesent S. Let a set V of vetices epesent D R. We set w(s i, j ) = C R (s i, j ) fo all s i U, j R, an set w(s i, i ) = C DT (s i ) fo all 1 i n. The tansfome MWBM instance of the example in Section 4-A is shown in Fig 3. Fo claity pupose, we put no labels on the eges. s1 s1 s2 s2 s3 s3 s4 s4 s5 s5 C σ sum C σ sum = C(s i, φ) + = C(s i, φ) + s k S ( j) ( CR (s k, j ) C ) R(s k, j ) C R(s i, j ) 1 C R (s k, j ) ( 1) C R(s i, j ) s k S ( j) C(s i, φ) + C R (s i, j ) s k S ( j) ( = C(s i, φ) + C R (s i, j )( 1) = C(s i, φ) > 0. 1 ( 1) C R(s i, j ) 1 ( 1) C R(s i, j ) Theefoe, we complete the poof. Accoing to Lemma 4.1, we can always impove the total capacity if thee exists a elay noe shae by moe than one souce noe in the cuent elay assignment. Unfotunately, the example in Section 4-A shows that this poceue may lea to a local optimum, as shown in Table I(), wheeas a ) Fig. 3: RAP tansfome into MWBM poblem. Now we ae eay to pesent ou optimal algoithm fo RAP. The etaile pseuo-coe is illustate in Algoithm 1. Next we pove the coectness an analyze the computational complexity of Algoithm 1. Theoem 4.1: Algoithm 1 guaantees to fin an optimal elay assignment fo RAP in time boune by O(n 2 m). Poof. We pove the coectness an the unning time sepaately. Coectness Analysis: Fist, Lemma 4.2 assues that each elay noe is assigne to at most one souce noe in the optimal elay assignment. In othe wos, each souce noe eithe tansmits iectly to its estination o use coopeative communication with the help of a elay noe that is not shae with any othe souce noes. Theefoe, each optimal elay

5 Algoithm 1: Optimal Algoithm fo RAP Input : A set S of souce noes, a set D of estination noes, an a set R of elay noes. Output: A elay assignment σ. 1 Constuct a set U of n vetices coesponing to S; 2 Constuct a set V of n + m vetices coesponing to D R; 3 Constuct a set E of eges, whee (s i, v) E if v = i o v R; 4 fo i = 1 to n o 5 w(s i, i ) C DT (s i ); 6 en 7 fo s i U an j R o 8 w(s i, j ) C R (s i, j ); 9 en Apply an MWBM algoithm to fin a maximum weighte matching M in gaph G = (U, V, w); fo (s i, v) M o if v R then σ (s i ) = v; else σ (s i ) = φ; en etun σ assignment can be mappe to a matching in the gaph G constucte fom Line 1 to Line 9. Assume that thee exists anothe elay assignment σ esulting in a highe capacity than σ etune by Algoithm 1. If we map it back to a matching in gaph G, we obtain a matching M with highe weight than that of M coesponing to σ. It contaicts the fact that M is a maximum weighte matching in G. Hence, σ is an optimal elay assignment. Running Time: Note that the most time consuming component in Algoithm 1 is the MWBM algoithm in Line 10. Thus we focus ou analysis on this algoithm. The MWBM poblem can be solve using a moifie shotest path seach in augmenting path algoithm. If the Dijksta algoithm with Fibonacci heap is use, the unning time is O(min{ U, V } (( U + V ) log( U + V ) + E )) [4]. Since U = n, V = n + m an E = nm+n = O(nm), the unning time of Algoithm 1 is boune by O(n(n + m) log(n + m) + n 2 m) = O(n 2 m). Remak 1. Algoithm 1 woks egaless of the CC moe use in the netwok. Even fo a hybi netwok whee some noes use AF moe an some use DF moe, ou algoithm can still fin an optimal assignment. Remak 2. Fom the esciption of Algoithm 1, it is clea that ou algoithm is inepenent of the elation between the numbe of souce-estination pais an that of elay noes. Because of the way we constuct the bipatite gaph, we can always fin an assignment fo each souce noe. Remak 3. Algoithm 1 guaantees to fin a elay assignment such that the capacity fo each souce-estination pai is no less than that une iect tansmission. The eason is that if the final capacity of cetain souce-estination pai is less than that une iect tansmission, we can assign it to tansmit to the estination iectly. It is clea that this change woul not euce the capacities of othe souce-estination pais, but can incease the capacity of cuent souce-estination pai. Thus we can obtain a bette elay assignment, contaicting the optimality of Algoithm NUMERICAL RESULTS In this section, we evaluate the pefomance of ou algoithm though extensive expeiments. The pefomance metics inclue both the unning time an the total capacity. A. Expeiment Setup We consie a wieless netwok, whee wieless noes ae anomly istibute in a 1000m 1000m squae. We follow the same paamete settings as in [13]. We set the banwith W to be 22 MHz fo all channels. The tansmission powe is the same fo each noe, i.e., P s i = P j = 1 Watt fo all s i S an j R. Fo the tansmission moel, we assume that the path loss exponent α = 4 an the abient noise N 0 = In the expeiments, we have two paametes, the numbe of souce-estination pais n an the numbe of elay noes m. We vaie both n an m fom 50 to 400 with incement of 50. Fo each setting, we anomly geneate 10 instances an aveage the esults. All tests wee pefome on a 2.0GHz Linux PC with 1.5G bytes of memoy Since this pape is the fist wok on the poblem of elay assignment in coopeative netwoks with the objective to maximize the total capacity, we compae ou algoithm, enote as OPT, with the following algoithms. 1 Geey Assignment Algoithm (GAA): We assign a elay noe to each souce noe iteatively. In each iteation, we geeily assign a elay noe to the souce noe o let the souce noe tansmit iectly, such that the total capacity of the cuent assignment is maximize. Diect Tansmission Algoithm (DTA): We let each souce noe iectly tansmit to its estination. That is the total capacity etune by this algoithm is C sum = s i S C DT (s i, i ). DTA seves as a lowe boun of the total capacity of the netwok une any effective elay assignment algoithm. ORA [13]: The basic iea of ORA is to ajust the assignment iteatively, stating fom any abitay initial assignment. In each iteation, ORA ientifies the souce noe with cuently minimum capacity among all souce noes an seaches a bette elay noe fo it. Although ORA is not intentionally esigne fo the RAP poblem, we inclue it in the compaison fo the sake of completeness. B. Result Analysis 1) Running Time: Fig. 4 shows the unning time of ou algoithm applie to netwoks with iffeent size. To have a clea pictue about the impacts of the numbe of souceestination pais an the numbe of elay noes on the unning time, we show the esults in Fig. 4(b). Moe specifically, to see the impact of the numbe of souce-estination pais, we vaie the value fom 50 to 400 while keeping the numbe of elay noes fixe at 200, an vice vesa. Fig. 4(b) confims 1 We have iscusse the iffeence fom [13] in Section 2 an Section 3.

6 Running time (s) Numbe of elay noes(m) Numbe of souce noes(n) (a) Running time as a function of n an m C sum (Mbps) OPT GAA DTA ORA Numbe of elay noes (a) Vaying the numbe of elay noes Running time (s) Souce noes (n) Relay noes (m) C sum (Mbps) OPT GAA DTA ORA Numbe of noes (b) Running time as a function of n o m Fig. 4: Scalability Numbe of souce estination pais (b) Vaying the numbe of souce-estination pais Fig. 5: Results on total capacity ou theoetical analysis on the unning time of ou algoithm, which poves that the unning time is popotional to n 2 m. 2) Total Capacity: Fig. 5 shows the total capacity of the elay assignments achieve by iffeent algoithms. As expecte, OPT has the best pefomance while DTA has the wost. Supisingly, the pefomance of GAA is only slightly wose than that of OPT, especially when the numbe of elay noes is geate than the numbe of souce-estination pais. The eason is that some souce noes may not nee to compete with othe souce noes fo thei best elay noes. Theefoe, we may have the same assignment fo these souce noes in both OPT an GAA. 6. CONCLUSIONS In this pape, we stuie the poblem of elay assignment in coopeative netwoks such that the total capacity is maximize among all the possible assignments. Diffeent fom pevious wok, we allowe the elay noe to be shae by multiple souce-estination pais an popose a coesponing fomulation fo capacity calculation. Then we evelope a polynomial time algoithm to optimally solve this poblem. We also showe that ou algoithm has thee nice popeties: (i) it woks egaless of the CC moe use in the netwok; (ii) it is inepenent of the elation between the numbe of souce-estination pais an that of elay noes; an (iii) it guaantees fo each souce-estination pai to have capacity no less than that une iect tansmission. REFERENCES [1] IEEE Woking Goup, Pat 16: Ai Inteface fo fixe an mobile boaban wieless access systemscmultihop elay specification, IEEE Daft Stana, [2] A. Bletsas, A. Khisti, D. Ree, an A. Lippman; A simple coopeative ivesity metho base on netwok path selection; IEEE Jounal on Selecte Aeas in Communications vol. 24(2006), pp [3] J. Cai, S. Shen, J. W. Mak, an A. S. Alfa; Semi-istibute use elaying algoithm fo amplify-an-fowa wieless elay netwoks; IEEE Tans. on Wieless Communications, vol.7(2008), pp [4] W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, an A. Schijve; Combinatoial Optimization, John Wiley an Sons, [5] T. M. Cove an A. EL Gamal; Capacity theoems fo the elay channel; IEEE Tans. on Infomation Theoy, vol. 25(1979), pp [6] L. Ding, T. Meloia, S.N. Batalama, an J.D. Matyjas; Distibute outing, elay selection, an spectum allocation in cognitive an coopeative a hoc netwoks; IEEE Secon 10, pp [7] J.N. Laneman, D.N.C. Tse an G.W. Wonell; Coopeative ivesity in wieless netwoks: efficient potocols an outage behavio; IEEE Tans. Infom. Theoy, vol.50(2004), pp [8] Y.D. Lin an Y.C. Hsu; Multihop cellula: A new achitectue fo wieless communications; IEEE Infocom 00, pp [9] E.C. van e Meulen; Thee teminal communication channels; Avances in Applie Pobability, vol. 3(1971), pp [10] T. C.-Y. Ng an W. Yu; Joint optimization of elay stategies an esouce allocations in coopeative cellula netwoks; IEEE Jounal on Selecte Aeas in Communications, vol. 25(2007), pp [11] A. Rawan an H.S. Hassanein; Congestion elief in CDMA cellula netwoks using multihop inte-cell elay; IEEE Globecom 09, pp [12] S. Shama, Y. Shi, Y.T. Hou, H.D. Sheali, an S. Kompella; Coopeative communications in multi-hop wieless netwoks: Joint flow outing an elay noe assignment; IEEE Infocom 10, pp [13] Y. Shi, S. Shama, Y.T. Hou, an S. Kompella; Optimal elay assignment fo coopeative communications; ACM Mobihoc 08, pp [14] D.B. West; Intouction to Gaph Theoy; Pentice Hall, 2n Eition, [15] H. Xu, L. Huang, G. Wang, T. Xu an G. Liu; Joint elay assignment an powe allocation fo coopeative communications; Wieless Netwoks, pp. 1 11, [16] P. Zhang, Z. Xu, F. Wang, X. Xie an L. Tu; A elay assignment algoithm with intefeence mitigation fo coopeative communication; IEEE WCNC 09, pp [17] Y. Zhao, R.S. Ave, an T.J. Lim; Impoving amplify-an-fowa elay netwoks: optimal powe allocation vesus selection; IEEE Intenational Symposium on Infomation Theoy 06, pp