OFDMA Based Two-hop Cooperative Relay Network Resources Allocation

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1 This full text paper was peer reviewed at the directio of IEEE Commuicatios Society subject matter experts for publicatio i the ICC 008 proceedigs. OFDMA Based Two-hop Cooperative Relay Network Resources Allocatio Mohamad Khattar Awad, Studet Member, IEEE, ad Xuemi (Sherma) She, Seior Member, IEEE Departmet of Electrical & Computer Egieerig, Uiversity of Waterloo, Waterloo, Otario, NL G, Caada mohamad@ieee.org, xshe@bbcr.uwaterloo.ca Abstract I this paper, we focus o the resources allocatio for the OFDMA based two-hop relay etwork which cosists of a sigle base statio, dedicated fixed relay statios ad subscriber statios. Subscriber statios are allocated the subcarriers ad relay statios that are required to satisfy their miimum rate requiremets i either o-cooperative mode (i.e., direct commuicatio with the base statio) or i cooperative mode with oe of the available relay statios. The cooperatio is limited to oe relay statio to reduce the complexity icurred by the eed for sychroizatio with multiple relays ad with the base statio at the PHY layer. The subcarriers ad relay statios allocatio problem is formulated as a Biary Iteger Programmig (BIP) problem with QoS costraits (miimum rate) ad a practical sychroizatio costrait (cooperatio with a sigle relay). Sice the formulated problem is NP-complete, a simple sub-optimal algorithm is proposed to maage the multi-service etwork resources. Simulatios ad complexity aalysis show that the preseted algorithm achieves a etwork ear optimal resources allocatio with low computatioal complexity. I. INTRODUCTION AND RELATED WORK The broadbad wireless access (BWA) etworks is emergig to replace the wirelie DSL ad T lie etworks []. I spite of their low deploymet cost compared to wirelie etworks, wireless wireless chael impairmets. I particular, the chael suffers from frequecy selective fadig ad distace depedet fadig (i.e., large-scale fadig). While frequecy selective fadig results i iter-symbol-iterferece (ISI), large-scale fadig atteuates the trasmitted sigal below a level at which it ca be correctly decoded. The advaced PHY layer techology, Orthogoal Frequecy Divisio Multiple Access (OFDMA), elimiates the frequecy selectivity effect by trasmittig the wide-bad sigal o multiple orthogoal subcarriers as arrow-bad sigals. Hece, the chael frequecy selectivity (frequecy ulls) affects oly selected arrow-bad sigals. OFDMA exploits multi-user diversity i frequecy selective chaels by exclusively assigig a subset of subcarriers to the subscriber statio with the highest chael gai []. I the Amplify-ad-Forward scheme (AF), relayig overcomes large-scale fadig by amplifyig the received sigal the re-trasmittig it to the receiver which traslates to higher trasmissio rates ad spectral efficiecy []. To further exploit the wireless chael capacity, a relay statio ca cooperate with a subscriber statio i the Time Divisio Duplex (TDD) scheme. For this scheme, the receiver receives the direct sigal from the trasmitter i the first half of the time slot ad receives the same sigal but amplified by the relay statio i the secod half of the time slot [], [5]. The OFDMA essetial property i elimiatig frequecy selective fadig ad the relayig effectiveess i compactig largescale fadig i additio to cooperative relayig effectiveess i ehacig trasmissio rates motivate the itegratio of these techologies ito oe etwork architecture. Wireless etworks of such architecture are expected to provide highspeed broadbad service that provides QoS guaratees o the data, voice ad video traffic. Oe direct implemetatio of this architecture is the multihop relay BWA etworks curretly uder stadardizatio by the IEEE 80.6j task group [6]. Similar to the origial stadard IEEE 80.6 [7], the amedmet IEEE 80.6j is expected to adopt OFDMA with adaptive modulatio ad codig (AMC) at the PHY layer. The problem of resource allocatio i this etwork is NP- Complete, ad a optimal resource allocatio ca ot be obtaied i a short time comparable to the chael coherece time. Further, the computatio burde icreases as the umber of subscriber statios, relay statios ad subcarriers icrease especially whe QoS costraits ad practical sychroizatio costrait are imposed. A efficiet ad low complexity resource allocatio algorithm is eeded. A resource allocatio protocol that allocates subcarriers to cooperatig subscriber ad relay statios was proposed i [8]. The QoS costrait is cosidered to be the fair utilizatio of the relayig odes (i.e., each relay statio relays sigals o a limited umber of subcarriers), a importat assumptio i sesor etworks where relayig odes are very limited i power, but ot the system model uder cosideratio. [9] presets a cetralized heuristic algorithm to allocate power ad subcarriers to user odes ad relays i a etwork where the ode ca establish a coectio either through a direct coectio or through the oe relay but ot i cooperative mode. Research activities i [8], [9] ted to focus o maximizig the total etwork throughput rather tha satisfyig each user s required rate. I this paper, we propose a low complexity resource allocatio protocol for OFDMA based two-hop relay etworks uder the followig costraits: (i) Each subscriber statio commuicates with the base statio either i o-cooperative mode or i cooperative mode with oly oe of the available relay statios; (ii) Users are allocated a sufficiet umber of subcarriers to guaratee their miimum rate requiremets; (iii) Each subcarrier is exclusively allocated to oe subscriber ad relay statio pair. The proposed algorithm is efficiet i /08/$ IEEE

2 This full text paper was peer reviewed at the directio of IEEE Commuicatios Society subject matter experts for publicatio i the ICC 008 proceedigs. utilizig the available subcarriers ad relay statios ad robust i terms of computatioal complexity. The remider of the paper is orgaized as follows. Sectio II itroduces a system model of the OFDMA relay etwork uder cosideratio. Problem formulatio is preseted i sectio III. The resource allocatio algorithm as well as the complexity aalysis are preseted i sectio IV. Performace of the algorithm is aalyzed via simulatios i sectio V, followed by the coclusios i sectio VI. II. SYSTEM MODEL Cosider a sigle cell sceario with oe base statio at the ceter of the cell, multiple fixed relay statios, ad multiple subscriber statios. Full chael state iformatio (CSI) is assumed to be available to the statios usig literature available chael estimatio methods, e.g., [0]. Subscriber statios ad relay statios report their CSI to the base statio. I additio, subscriber statios report their miimum rate requiremets to the base statio. The cetral resource allocatio uit at the base statio performs the resource allocatio, the reports the subcarriers assigmets ad relay statios assigmets to each subscriber statio ad relay statio. The relay statios are assumed to be fixed o a circle with a radius equal to half of the cell radius i order to elimiate the effect of relay statios placemets. I other words, the cell coverage is equally supported by the available relay statios (Fig. ). The relay statio forwards the received sigal to the subscriber statio by employig the Amplify-ad-Forward (AF) forwardig scheme o the same subcarrier [5], []. We cosider a TDD trasmissio patter that is half-duplex i a sese that the subscriber statio trasmits while the relay statio ad base statio receive i the first half of the time slot. I the secod half of the slot, the relay statio trasmits to the base statio. Fig. illustrates both cooperative ad ocooperative TDD trasmissio patters. Fig.. No-cooperative mode Trasmitter Reciever Trasmitter Cooperative mode (c) Slot legth T 0.5 T 0.5 T (d) Base Statio Relay Statio Subscriber Statio Reciever The TDD scheme i both cooperative ad o-cooperative modes. The maximum allowable trasmissio power is assumed to be uiformly distributed amog the source ad relay statios [5]. Adaptive modulatio ad codig is employed to facilitate the higher chael gai achieved by OFDMA via exploitig multi-user diversity. Because subscriber statios ad relay statios are fixed ad their chaels experiece slow fadig, the chael is assumed to be static over the resource allocatio duratio [8], [], ad is assumed to be frequecy selective with a coherece badwidth greater tha the trasmitted arrow-bad sigals badwidth. III. PROBLEM FORMULATION Fig. depicts the etwork uder cosideratio. There are A subscriber statios formig the set A = {s,,s a,,s A }. The available B relay statios forms the set B = {r,,r b,,r B }. The destiatio base statio is symbolized by d. A subscriber statios share a total of N sc subcarriers available to the cell. The set of subcarriers is deoted by N = {,,,,N sc }. As metioed i the system model, the subscriber statios ca establish a coectio with d either i o-cooperative mode or i cooperative mode (i.e., with the cooperatio of oe relay statio r b B) by employig the AF scheme. The achievable rate of the cooperative AF protocol, show i Fig. -(c) ad (d) is aalyzed i []. The maximum achievable rate i (bits/sec/hz) by s a o subcarrier with the cooperatio of r b is give by: I ab = log (+ γad + βb γ ab γ bd ) N 0 ( β b γ bd. () +)N 0 where γ ad, γ ab ad γ bd, respectively, are the th subcarrier SNR from s a to d, s a to r b ad r b to d. β b is the relay r b s amplifyig gai. The direct trasmissio maximum achievable rate i (bits/sec/hz) over both time slots as illustrated i Fig. - ad is give by the well kow result: I ad = log ( + γad N 0 ). () We formulate the resources allocatio problem as a BIP to maximize the etwork achievable rate while satisfyig subscribers miimum rate requiremets c a ad limitig cooperatio to oe relay statio. Let y ab {0, }, where y ab = meas that s a is cooperatig with r b, whereas y ab =0meas s a is ot cooperatig with r b. Also, let {0, } where =meas that the subcarrier is allocated to the pair s a r b ad =0otherwise. Because both the subscriber statio ad relay statio trasmit o the same frequecy, but i differet time slots, ad the resource allocatio is time idepedet, the base statio d ca be represeted by a virtual relay r. Addig a virtual relay statio elarges the set B to B +. To use a uiform cost fuctio i the optimizatio problem, we combie equatios () ad () i the followig: c ab =[ δ(b (B + ))]I ab + δ(b (B + ))Iab () where δ( ) is the Dirac delta fuctio, β () =0ad d = 5

3 This full text paper was peer reviewed at the directio of IEEE Commuicatios Society subject matter experts for publicatio i the ICC 008 proceedigs. B +. Mathematically, The optimizatio problem is A N sc max c ab (),yab s.t. a= b= = y ab = a (5) b= y ab a b (6) A (7) a= b= N sc = b= c ab c a a (8), y ab {0, } (9) Costraits (5) ad (6) are limitatios o the umber of relay statios cooperatig with each subscriber statio to be oe. Costrait (7) satisfies the defiitio of OFDMA that each subcarrier is allocated to oe s a r b pair []. The costrait (8) guaratees that subscriber statios miimum rate requiremets c a are met. A admissio cotroller is assumed to be i place such that the problem is feasible ad costrait (8) ca be satisfied. The resources maagemet problem is a BIP problem which is prove NP-complete [], thus, it is itractable. However, a optimum solutio ca be obtaied usig optimizatio tools (e.g., CPLEX ) which suffer log ruig time that makes it impractical. I additio, optimizatio tools ca oly solve a problem of limited size, thereby motivatio the developmet of a resource allocatio algorithm that obtais ear optimum solutio i a cosiderably shorter time, less tha the chael coherece time. N sc Oce a subscriber is cooperatig with oe relay statio, it is allocated the subcarrier(s) with maximum achievable rate o the same relay statio util its rate requiremet is satisfied. I frequecy selective chaels, if the subscriber experieces high gai o a subcarrier, it is possible that there are other subcarriers with a high gai. I other words, i a closely packed spectrum, eighborig subcarriers experiece similar gai. After all subscriber statios achieve their required rates, the remaiig subcarriers are allocated to subscribers that achieve the maximum rate o them. N a is the set of subcarriers assiged to subscriber s a. (a, b) is a pair of cooperatig subscriber statio ad relay statio. The pairs (a, b) form the set P. The total achievable rate by subscriber s a is deoted by c a. The proposed greedy algorithm is outlied below: Algorithm Greedy Algorithm Satisfy subscribers rate requiremets while A = do radom (N ) (a,b ) = arg max c ab a A b B + N a N a {} N N \{} c a c a + c a b while c a < c a do = arg max c a b N a N a { } N N \{ } c a c a + c a b P P {(a,b )} ed while N N\N a A A\{a } ed while Allocate remaiig subcarriers while N = do (a,b ) = arg max c ab (a,b) P N a N a {} N N \{} ed while Fig.. A B Base Statio Relay Statio Subscriber Statio The OFDMA based two hop relay etwork. IV. PROPOSED ALGORITHM AND COMPLEXITY ANALYSIS The proposed algorithm is greedy i a sese that a subcarrier is allocated to the subscriber statio that achieves the maximum rate o it either with the cooperatio of oe of the available relays or directly i the curret iteratio without cosiderig the future impact of the assigmet decisio [5]. A Mathematical Programmig Optimizer, To aalyze the computatioal complexity, we study its complexity i terms of the umber subscriber statios A, relay statios B + ad subcarriers N sc. To satisfy the subscribers rate requiremets, the outer loop iterates A times. For a radomly selected subcarrier, fidig the subscriber-relay statios pair that achieves the maximum rate requires O(AB) comparisos. The ier while loop iterates N, i the worst case ad each iteratio requires N comparisos; hece, it is O(N ). Allocatig the remaiig subcarriers requires, at most, O(N sc A) iteratios ad O(A) comparisos. Hece, the total algorithm complexity is O(A B + AN sc). The proposed algorithm is low i computatioal complexity compared to the complexity required for the complete search over the problem space that is ABN sc. V. PERFORMANCE EVALUATION Performace evaluatios focus o the followig questios: () How does the proposed algorithm allocatio compare to the 6

4 This full text paper was peer reviewed at the directio of IEEE Commuicatios Society subject matter experts for publicatio i the ICC 008 proceedigs. optimal allocatio obtaied by the optimizatio tool i terms of achievig the total etwork rate ad ruig time? () Does the algorithm guaratee the subscribers rate requiremets? () How does the algorithm perform as subscribers traffic itesity icreases? The simulated etwork cosists of a base statio located at the ceter of a cell with a 00m radius. Relay statios are placed o a circle with a 50m radius at equal agular distaces. Subscriber statios are uiformly distributed i the cell coverage area. Fig. shows a sapshot of the simulated etwork for A =50ad B =6. I this sceario, the cell coverage area is equally shared by the available relay statios. The wireless chaels are simulated to experiece both frequecy selective ad large-scale fadig. The subscriber statios ad relay statios receive three Rayleigh distributed sigals. The received sigals real ad imagiary compoets for differet subscribers are geerated from a ucorrelated multidimesioal Gaussia distributio with zero mea ad the idetity covariace matrix. Ucorrelated multi-path compoets lead to ucorrelated subscribers frequecy resposes i the frequecy domai. Thus, full multiuser diversity ca be exploited. However, eighborig subcarriers gais withi each subscriber frequecy respose are correlated. The large-scale fadig is distace depedat ad follows the iverse-power law: γ = D κ α. (0) where D is the distace betwee the trasmitter ad receiver i meters, κ is the path loss expoet, ad α is the th subcarrier chael gai at the trasmitter. I our simulatio, the path loss expoet is set to, κ =. Subscriber Statios Relay Statios 0 Base Statio (Greedy / Optimum ) Network Rate % Relay Statios 5 Relay Statios Subscriber Statios Subscriber Statios Fig.. The ratio of the proposed algorithm etwork maximum achievable rate to optimal achievable rate. The ratio of the proposed algorithm ruig time to optimizatio tool ruig time. For a etwork with N sc =6. to 90% of the optimum. However, the required ruig time is i the rage of oly % to % of the optimizatio tool ruig time. A etwork with 6 subcarriers (N sc = 6) ca support up to 5 subscriber statios (A = 5) assumig that each subscriber statio eeds subcarriers at most (N a ) to satisfy its miimum rate requiremets. I the worst case where the umber of subscriber statios is as large as possible, the proposed algorithm achieves 70% of the optimum i oly % of the ruig time required by the optimizatio tool (Fig. ). For a smaller problem size that cosists of A =0,B =ad N sc =6, the optimizatio tool requires a additioal 78% ruig time to achieve a optimal solutio that is oly % larger tha the sub-optimal solutio. Therefore, the proposed algorithm achieves a ear optimal solutio i a relatively short time Trial Trial Trial Trial Trial 5 Trial 6 Fig.. A represetative cell with 50 subscribers ad 6 relays. c a / c a (%) Fig.- shows the ratio of the etwork maximum achievable rate obtaied by the proposed algorithm to the optimal etwork achievable rate obtaied by the optimizatio package. The optimizatio package used i the simulatio is CPLEX that solves for the optimal solutio by employig brach-adboud techiques [6]. To evaluate the algorithm performace for various sizes of the problem, we vary the umber of available relay statios from to 5 ad the umber of subscriber statios from 0 to 0 i a cell with 6 subcarriers (N sc =6). It is clearly observed that the proposed algorithm achieves 70% Fig Subscriber Statios The ratio of the allocated rate to miimum required rate. I multi-service etworks, miimum rate requiremets are user specific. The proposed algorithm performace i satisfy- 7

5 This full text paper was peer reviewed at the directio of IEEE Commuicatios Society subject matter experts for publicatio i the ICC 008 proceedigs. ig subscriber statios miimum rate c a is evaluated i Fig. 5. Subscribers c a are radomly geerated i each trial. Fig. 5, represets the ratio of each subscriber statio s average assiged rate to the miimum required rate (c a /c a ) over six radomly geerated subscriber statios rate requiremets (i.e., c a /c a 00%). The aalysis shows that all subscriber statios s rates are satisfied. Some subscriber statios are allocated more rates tha their requiremets, i order to maximize the total etwork throughput. Subscriber statios close to relay statios or the base statio may experiece higher chael gai from others. Thus, allocatig the remaiig subcarriers to these subscriber statios maximizes the etwork achievable rate. Whereas the previously metioed simulatios evaluate the proposed algorithm efficiecy ad robustess i achievig a ear optimal allocatio, we further demostrate the subscriber statios trasmissio performace. Cosider a etwork of 5 subscriber statios (A =5), relay statios (B =) ad 6 subcarriers (N sc =6). Subscriber statios packet arrival follows the Poisso process with a equal ormalized average arrival rate of 0. packet/sec. The Droppig rate is defied as the ratio of dropped packets to arrived packets i a time slot. Packets are dropped whe the buffer size reaches the threshold. Throughput is defied as the umber of successfully trasmitted packets i a time uit. The ormalized throughput ad ormalized droppig rate average performace are achieved over 000 simulatio rus. Fig. 6 shows that the proposed algorithm satisfies subscriber statios ormalized rates. It is observed from Fig. 6- that, o average, the ormalized droppig rate is zero for arrival rates less tha c a = 0.. Similarly, Fig. 6- shows that the proposed algorithm guaratees throughput greater tha or equal the required rate. However, as the arrival rate icreases, subscriber statios share the available etwork resources. Normalized Average Droppig Rate (Packets/Sec) Normalized Average Throughput (Packets/Sec) Normalized Arrival Rate (Packets/Sec) Subscriber Statio s miimum rate Subscriber Statio s miimum rate Normalized Arrival Rate (Packets/Sec) Fig. 6. The average per user ormalized average droppig rate. The average per user ormalized average throughput. VI. CONCLUSIONS I this paper, the resource allocatio for the two-hop OFDMA cooperative relay etworks has bee addressed. Give the full chael state iformatio amog commuicatig statios, the algorithm at the base statio allocates subcarriers ad relay statios to the subscriber statios while satisfyig their miimum rate requiremets. Numerical ad complexity aalysis demostrate that the proposed algorithm achieves ear optimal allocatio i relatively short ruig time. I particular, the algorithm achieves about 70% to 90% of the optimum i oly % to % of the optimizatio tool ruig time. Sice the proposed algorithm is low i complexity give the chael state iformatio, our future wok is to develop a chael estimatio error resiliet resource allocatio algorithm. VII. ACKNOWLEDGMENTS The authors would like to thak Professor Joche Köema from the Departmet of Combiatorics ad Optimizatio at the Uiversity of Waterloo for his helpful commets ad suggestios. REFERENCES [] Z. Abichar, Y. Peg, ad J. Chag, Wimax: The emergece of wireless broadbad, IEEE IT Professioal, vol. 8, o., pp. 8, 005. [] H. Liu ad G. Li, OFDM-Based Broadbad Wireless Networks: Desig ad Optimizatio. Hobke, New Jersey: Wiley-Itersciece, 005. [] R. Pabst, B. Walke, D. Schultz, P. Herhold, H. Yaikomeroglu, S. Mukherjee, H. Viswaatha, M. Lott, W. Zirwas, M. Dohler, H. 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