ROBUST RADIO RESOURCE ALLOCATION IN LTE NETWORKS BY CHANNEL AND RELAY ASSIGNMENT

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1 Joural of Egieerig Sciece ad Techology Vol. 12, No. 7 (2017) School of Egieerig, Taylor s Uiversity ROBUST RADIO RESOURCE ALLOCATION IN LTE NETWORKS BY CHANNEL AND RELAY ASSIGNMENT R. SANTHAKUMAR*, N. AMUTHA PRABHA School of Electrical Egieerig, VIT Uiversity, Vellore Campus, Vellore , Tamil Nadu, Idia *Correspodig Author: sathakumar@vit.ac.i Abstract The radio resource allocatio i wireless commuicatio is aalysed i this paper. Pair of users commuicates each other through multiple two way relays i orthogoal frequecy divisio multiplexig trasmissio systems. The total throughput is maximized by relay selectio, chael ad relay assigmet, subcarrier pairig ad subcarrier allocatio by prim s algorithm. The graphical theory approach has used to solve the problem optimally i polyomial time. The evaluatio of the etwork total throughput with respect to trasmit power ode ad the umber of relay odes are aalysed through simulatio. I this work, the improvemet i sum rate with optimum carrier assigmet usig proposed algorithm is demostrated agaist the classical work. Keywords:.Orthogoal frequecy divisio multiplexig (OFDM), Relay, Subcarrier pairig, Prim s algorithm, Graph theory, Throughput. 1. Itroductio The requiremet of ubiquitous etworks ad boomig volume of multimedia applicatio traffics demad eergy cosumptio ad optimal utilizatio of resources. To meet these demads, various wireless commuicatio techiques have bee developed. Oe of the promisig techiques is the cooperative relay etworks. Cooperative wireless relay etworks have the iheret ability, to exploit various diversity to reduce chael fadig ad they aturally exted coverage. For the users, the cooperative commuicatio is offerig wide rage of data services ad helps i achievig the required diversity gais. Cooperative commuicatio explores the wireless chael broadcastig ature ad users cooperatio to improve the system performace. 1845

2 1846 R. Sathakumar ad N. Amutha Prabha I a sigle relay cooperative etworks, joit optimizatio of chael pairig, chael user assigmet ad power allocatio maximizes the weighted sum-rate has bee discussed i detail i the past [1]. I a dual hop cooperative etwork, the capacity bouds with opportuistic sigle relay selectio is addressed [2]. The sub-carrier usage alog with bit loadig has bee aalysed with power cotrol for cooperative commuicatios [3]. Direct dual hop with gree resource allocatio schemes with reduced computatioal complexity has also bee proposed. I the gree resource allocatio, mixed dowlik (DL) ad uplik (UL) relayig schemes with block diagoalizatio to joitly allocate trasmissio power, subchael ad phase is studied [4]. The resource allocatio i two-way relay, especially i estimatio of dowliks trasmissio delay i power trasmissio usig etwork codig is also aalysed [5]. The etwork codig techique is also used i orthogoal frequecy divisio multiplexig (OFDM) based multiple access chaels for resource allocatio i a multi-dimesioal way [6]. I resource allocatio usig relays, to achieve a better performace sub-carrier pairig is a importat issue ad optimal utilizatio of sub-carrier is ecessary to reduce co-chael ad adjacet relay chael iterferece. The sub-carrier pairig with joit optimizatio of power, relay selectio, chael ad relay assigmet has bee doe i the past. I resource allocatio usig OFDM based etwork to maximize the overall throughput amog multiple pair of two users, optimal coordiatio betwee relay ad sub-carrier assigmet is also demostrated [7]. To maximize the throughput i OFDM based two hop relay, lot of research has already bee udertake. Oe such joit power costrait to maximize the lik relay rate is give i [8]. As said earlier, relayig schemes uses the chael state iformatio to maximize the performace. Sice the accurate chael state iformatio (CSI) is hardly available, the relay desig with chael state iformatio impacts the resource allocatio. Oe such a scheme i multi-relay Orthogoal Frequecy Multiple Access (OFDMA) systems, imperfect CSI to joitly optimize lik selectio ad power allocatio has bee aalysed [9]. If the CSI is ot perfect, the system suffers from various forms of iterferece. The sum-rate maximizatio i iterferece limited systems for optimal resource allocatio usig Decode ad Forward (DF) cooperatio strategies is also discussed [10]. Whether the CSI degrades the system performace or ot, the idea of cooperatio i resource allocatio usig relays used to reduce the computatioal complexity besides improvig sum-rate. With miimal computatioal complexity, the multi-relay systems i OFDM were studied usig joit power allocatio [11]. Time divisio duplex systems for OFDMA have bee proposed to optimize the subcarrier pairig [12]. A more heuristic method of sub-carrier pairig with separate power allocatio is aalysed with three - ode, two - way relayig i OFDM systems usig water fillig algorithm [13]. Combiatorial optimizatio problem of joit resource assigmet, relay selectio ad bidirectioal trasmissio scheme selectio to maximize the total product of backlog ad rate (back-pressure priciple) has bee formulated. A graph based framework is trasformed ito a maximum weighted clique problem (MWCP) ad also trasformed i to a 3-D assigmet problem (3DAP). A hybrid at coloy optimizatio (ACO) algorithm is used to solve 3DAP [14]. From the recet research, it has bee foud that the joit optimizig sub-carrier pairig ad Joural of Egieerig Sciece ad Techology July 2017, Vol. 12(7)

3 Robust Radio Resource Allocatio i LTE Networks by Chael ad umber of relays for sum-rate maximizatio is a importat issue ad our ituitio is to provide the solutio with Prim s algorithm. I this paper, the sum-rate is maximized by usig Prim s algorithm ad achieved the higher sum-rate tha the recet works. 2. System Model for Resource Allocatio Problem I this work, a OFDM-based wireless etwork is cosidered as i Fig. 1. This system has K umber of user pairs (source i set oe ad two) ad R umber of relays, where the sources exchage iformatio betwee them through the relays. Ad direct commuicatios betwee ay two sources are ot permitted to avoid shadowig effect. The source ad relay are commuicated i a half-duplex mode. The relay operates i two-way relayig with costat gai. We also postulate cetral processor to cotrol all the commuicatio i the etwork by otrasparet cetralized schedulig mode of relay allocatio method [15]. So, the relays are amplified ad forward the iformatio provided by the source. The wireless fadig eviromet with large scale path loss ad shadowig ad small scale frequecy selective fadig is modelled. We cosider the perfect chael estimatio i the etwork where, the lik have differet idepedet fadig chael ad the etwork operate i slow fadig eviromet. The circular symmetric complex Gaussia radom variables are cosidered as additive white oises for all odes idepedetly ad the trasmit power of the all subcarriers are uiformly distributed. Cosider N = {1, 2,,} as the set of subcarriers, R = {1, 2,,} as the set of relays, ad S = {1, 2,,} as the set of user pairs. S k,1 ad S k,2 are the pair of sources i the k th set user pair. I the etwork, half duplex commuicatio is cosidered betwee sources ad relay ode. The k pairs of user commuicate betwee them through r th relay (oe of the R relay) as show i Fig. 1. The commuicatio betwee pair of user happeed i two phases. Phase oe labelled as multiple access (MAC), where S k,1 user trasmitter will trasmit the sigal to relay r by ooverlappig subcarriers to avoid iter pair iterferece. The subcarrier i the phase oe is deoted as m. The itra-pair iterferece will be cosider as back-propagated self-iterferece ad cacelled after two-way relayig. Phase two termed as broadcast (BC) phase, relay r will broadcast the received sigal to 2K user after amplificatio of sigal. To avoid iter relay iterferece, each relay will use o overlappig subcarriers. The subcarrier i the phase two is deoted as. To avoid iter carrier iterferece, each pair of subcarrier assiged to oe relay ad each relay will use more tha oe pair of subcarrier. We assig subcarrier m with user S k,1 to trasmit the sigal to relay r ad subcarrier with r to trasmit the amplified sigal to user S k,2. So, the achievable sum rate of user pair k over subcarrier pair (m,) through relay r ca be writte as R 1 k 1, r, mr, k log k, r, m, 2 r, k, k, r, m k, r, m k2, r, mr, k1, log r, k, k, r, m k, r, m (1) Joural of Egieerig Sciece ad Techology July 2017, Vol. 12(7)

4 1848 R. Sathakumar ad N. Amutha Prabha where i, j, deotes the istataeous sigal-to-oise ratio (SNR) from i th ode to j th ode over th subcarrier. All the odes i the system are assumed to have the uit oise variace. For subcarrier assigmet, a set of biary variables itroduced for all user pair k, relay r, subcarrier m ad, where k, r, m, {0,1} ρ k,r,m, = 1 meas that subcarrier m i the first phase is paired with subcarrier ad i the secod phase assisted by relay r for user pair k, ad ρ k,r,m, = 0, otherwise. As assumed above, each subcarrier ca be assiged to oe user pair ad oe relay, i the first ad secod phases, respectively to avoid iterferece. Therefore, {ρ k,r,m, } must satisfy the followig costraits: kk rr N kk rr mn k, r, m, 1, k, r, m, 1, N m N The system total throughput will be maximized by optimally pairig subcarriers i the two phases ad selectig the best relays ad the best paired subcarriers for each user pair. From Eqs. (1), (2) ad (3) the mathematical formula for relay assigmet ad subcarrier pairig ca be writte as. (4) max Rk, r, m, k, r, m, kk rm mn N (2) (3) Fig. 1. System Model with S k,1 ad S k,2 are k th user pair ad R M the r th relay A graph-based optimal approach The above problem i Eq. (4) is a optimizatio algorithm to select relay ad subcarrier pair that fid the optimal solutio with log search operatio. Whe K, R ad N icrease, the complexity of the solutio also icreases expoetial ad it Joural of Egieerig Sciece ad Techology July 2017, Vol. 12(7)

5 Robust Radio Resource Allocatio i LTE Networks by Chael ad is ot fit to fid optimal solutio. So, we modify the objective fuctio i Eq. (4) to weighted sum of all user rates without chage i optimum solutio usig graph based algorithm. The proposed optimum path algorithm fids the maximum weighted subcarrier pair (m,) as follows. R m (, ) max Rk, r, m, kk, rr (5) The associated user pair ad relay ode ca take the maximum i Eq. (5) for each subcarrier pair (m,) are deoted as u ad v respectively. Cosequetly, we ca trasform the origial problem i Eq. (4) to the followig simplified problem i Eq. (6) without loss of optimality: max R( m, ) mn N u, v, m, u, v, m, u, v, m, s. t. 1, N, N mn m 1, N. As per the discussio stated above, it implies that the simplified equatio i Eq. (6) is equivalet to a maximum weighted bipartite matchig (MWBM) problem. (6) Bipartite Graph The odes i the bipartite graph are divided ito two disjoit sets. I a set of edges, coect correspodig ode of both the sets. The balaced bipartite graph has both sets with same cardiality. A matchig is a set of mutually disjoit edges, i.e., ay two edges do ot share a commo ode. A perfect matchig occurs whe t every ode i the graph is matched as i Fig. 2. Costruct a balaced bipartite graph G=(V1 V2,E,W), where the two set of vertices, V1=[X1,X2, Xm] ad V2=[Y1,Y2,.Y], are the set of subcarriers N i the MAC phase ad the BC phase, respectively, as i Fig. 2. E is the set of edges that coect all possible pairs of vertices i the two set. N is shared i each phase, thus V1 = V2 = N = N ad E = N 2, where. is cardiality of a set. W is the weightig fuctio such that W: E. Fig. 2. Bipartite graph, where X is set of MAC subcarrier ad Y is the set of BC subcarrier. More specifically, each edge is assiged a weight, represetig the maximum achievable rate over the matched two vertices, amely, Joural of Egieerig Sciece ad Techology July 2017, Vol. 12(7)

6 1850 R. Sathakumar ad N. Amutha Prabha W( m, ) R( m, ) (7) where R( m, ) is defied i Eq. (5). From Eq. (6) the total complexity is calculated as (KRN 2 ) ad weight of all edges are calculated. The followig equivaleces are foud accordig to the above graph method: (i) A subcarrier pair i the MAC ad BC phases are matched as a pair of vertices, (ii) a matchig implies o violatig the exclusive subcarrier assigmet i each phase defied i Eqs. (2) ad (3), ad (iii) the optimal user pair ad relay for each possible subcarrier pair has bee foud by weight of each edge i E. As a result, the modified Prim s algorithm of subcarrier-pairig based subcarrier assigmet ad relay selectio i multi-relay multi-pair two-way relayig etworks for the total throughput maximizatio is equivalet to fidig a perfect matchig F E i G to achieve maximum sum weights of F. This MWBM problem is stated i Eq. (8). max (8) ( m, ) W FE ( m, ) F which is NP-complete ad equivalet to problem i Eq. (5). The importat aspect of the Graph based algorithm is the mappig from the origial problem Eq. (4) to the simplified problem Eq. (6) ad the to the MWBM problem Eq. (8) without loss of optimality. After the mappig is doe, the classic Hugaria algorithm ca be adopted to solve Eq. (8) optimally with the computatioal complexity (N 3 ). By combiig the about metioed complexity of the weightig process, the total complexity of graph based greedy algorithm is (KRN 2 +N 3 ), which is polyomial. 3. Modified Prim s Algorithm Let G= (V,E) where V is the set of odes ad E is the set of edges (No. of subcarrier) V1, V 2 V, u V1 ad v V2 The edge cost e m E Step1. Choose a elemet u from set V1 Step2. Choose a elemet v from set V2 Step3. Choose miimum cost edge e m from set E, Step4. If the cost of edge e m is less tha miimum cost, the miimum cost is cost of edge e m, Repeat step 2 to step 4 till all odes i V2 are checked. Step5. Repeat step 1 to step 4 till all odes i V1 are checked. Step6. Assig ode v ad ode u which satisfy the miimum edge criterio defied i step 4. The modified prim s algorithm for the bipartite graph based optimizatio problem whose computatioal complexity decreases from greedy algorithm [7 ], it is easy to pair the subcarrier betwee sources to destiatio ad suitable relay. Joural of Egieerig Sciece ad Techology July 2017, Vol. 12(7)

7 Robust Radio Resource Allocatio i LTE Networks by Chael ad Simulatio ad Results Simulatio is carried out with uiform distributio for the selectio of source odes ad relay odes. The path loss model is adopted i [7], where the path loss expoet is set to 4 ad the stadard deviatio of log-ormal shadowig is set to 5.8 db. The small-scale fadig is modelled by multi-path Rayleigh fadig process, where the power delay profile is expoetially decayig with maximum delay spread of 5 µs ad maximum Doppler spread of 5 Hz. A total of 2000 idepedet chael realizatios were geerated, each associated with a differet ode locatios. The umber of subcarriers is N = 64. All sources have the same maximum power costraits, with all relays satisfyig the relay power ad user pair power Pr Pk 1 3dB Pk 2 3dB (per-subcarrier) for all r ad k. As a performace bechmark, the fixed subcarrier pairig scheme is cosidered. As i [7], sigals trasmitted by the user pair o oe subcarrier i the MAC phase is forwarded o the same subcarrier by a relay i the BC phase, i.e., m =, rather tha seekig the optimal subcarrier pairig. The the problem reduces i selectig the optimal user pair ad relay for each subcarrier to achieve throughput maximizatio, which ca be optimally solved by the Greedy algorithm ad proposed Prims algorithm. Each subcarrier m shall be assiged to the user pair ad the relay that satisfy (, v) arg max R. The the results of fixed subcarrier pairig, Greedy u k, r, m, kk, rm algorithm ad Prims algorithm are aalysed. The overall complexity of the fixed subcarrier parig scheme is (KRN) ad graph based Greedy algorithm has (KRN 2 + N 3 ). The simulatio result reveals that the complexity of the proposed graph-based scheme is (KRN 2 ), which is higher tha the bechmark scheme ad less as that of the Greedy algorithm. The source, destiatio ad relay odes are placed radomly but follow uiform distributio i two-dimesioal plae as show i Fig. 3. Figure 4 illustrates the total throughput with five user pairs ad four relays i the etwork. The graph idicates that the proposed optimal chael ad relay assigmet with optimal subcarrier pairig achieves 20% improvemet i total throughput over the scheme with fixed subcarrier pairig ad 10% over the classical work. Table.1 lists out the performace improvemet compariso of proposed Prim s algorithm with Greedy algorithm ad fixed subcarrier pairig algorithm. Fig. 3. Two dimesio plae of user ad relay Joural of Egieerig Sciece ad Techology July 2017, Vol. 12(7)

8 1852 R. Sathakumar ad N. Amutha Prabha Fig. 4. Performace compariso of the proposed Prim s algorithm with Greedy algorithm [7] ad bechmark. Table. 1. Performace of sum-rate Source Sumrate (bits/s/hz) S. power/sub Proposed Prim s Greedy Fixed Subcarrier No carrier Algorithm Algorithm Pairig Figure 5 shows the throughput performace versus the umber of relays with five user pairs ad P K1 = 10 db. It is foud that from proposed Prim s algorithm, relay selectio diversity icreases by multiple relays i the system. However, the gai variatio is sigificatly less as the umber of relays R icreases. This is attaied with respect to the capacity scalig of relay selectio which is log log R [2]. Figure 6 the umber of subcarrier pairig N=16, 32 ad 64 are cosidered with adaptive subcarrier pairig. The sum rate performace of the etwork is better whe the umber of subcarrier parig is lesser. Fig. 5. Effects of the umber of relays, where N = 64, K = 5, ad P k1 = 10 db. Joural of Egieerig Sciece ad Techology July 2017, Vol. 12(7)

9 Robust Radio Resource Allocatio i LTE Networks by Chael ad Fig. 6. Effects of umber of relays, where differet umber of subcarrier pairig. 5. Coclusios The work cocludes that the subcarrier-pairig based subcarrier assigmet ad relay selectio for LTE etworks usig Prim s algorithm was optimal. The problem was desiged as a combiatorial optimizatio problem ad NP-complete. We proposed a optimizatio algorithm for bipartite graph to solve the problem optimally i polyomial time. The work assumed the amplify-ad-forward based o-regeerative relay strategy. The work ca exted to 128 subcarriers ad more. The total throughput improves by 10 % from the covetioal method. Refereces 1. Hajiaghayi, M.; Dog, M.; ad Liag, B. (2012). Joitly optimal chael ad power assigmet for dual-hop multi-chael multi-user relayig. IEEE Joural o Selected Areas i Commuicatios, 30(9), Shi, E.H.; ad Kim, D. (2009). O the capacity growth of opportuistic sigle-relay selectio usig quality-based feedback i fixed-gai amplifyad-forward relayig. IEEE Commuicatio Letters, 13(11), Ha, Z.; Himsoo, T.; Siriwogpairat, W.P.; ad Ray Liu, K.J. (2009). Resource allocatio for multiuser cooperative OFDM etworks: Who helps whom ad how to cooperate. IEEE Trasactios o Vehicular Techology, 58(5), Chag, T.-S.; Feg, K.-T., Li, J.-S.; ad Wag, L.-C. (2013). Gree resource allocatio schemes for relay-ehaced MIMO-OFDM etworks. IEEE Trasactios o Vehicular techology, 62(9), Xiog, K.; Fa, P.; Be Letaief, K.; Yi, S.; ad Lei, M. (2012). Resource allocatio for miimal dowlik delay i two-way OFDM Relayig with etwork codig IEEE Iteratioal Coferece o Commuicatios (ICC), Ha, B.; Peg, M.; Zhao, Z.; ad Wag, W. (2013). A multidimesioal resource-allocatio optimizatio algorithm for the etwork-codig-based Joural of Egieerig Sciece ad Techology July 2017, Vol. 12(7)

10 1854 R. Sathakumar ad N. Amutha Prabha multiple-access relay chaels i OFDM systems. IEEE Trasactios o Vehicular Techology, 62(8), Liu, Y.; ad Tao, M. (2012). Optimal chael ad relay assigmet i OFDM-based multi-relay multi-pair two-way commuicatio etworks. IEEE Trasactios o commuicatios, 60(2), Li, Y.; Wag, W.; Kog, J.; ad Peg, M. (2009). Subcarrier pairig for amplify-ad-forward ad decode-ad-forward OFDM relay Liks. IEEE Commuicatios Letters, 13(4), Wag, J.-B.; Su, Q.; Wag, J.; Feg, M.; Che, M.; Jiag, B.; ad Wag, J.- Y. (2014). Imperfect CSI-based joit resource allocatio i multirelay OFDMA etworks. IEEE Trasactios o Vehicular Techology, 63(8), Adia, M.G.; Aghaeiia, H. (2013). Optimal resource allocatio for opportuistic spectrum access i multiple-iput multiple-output-orthogoal frequecy divisio multiplexig based cooperative cogitive radio etworks. IET Sigal Processig, 7(7), Dag, W.; Tao, M.; Mu, H.; ad Huag, J. (2010). Subcarrier-pair based resource allocatio for cooperative multi-relay OFDM systems. IEEE Trasactios o Wireless Commuicatio, 9(5), Liu, Y.; Tao, M.; Li, B.; ad She, H. (2010). Optimizatio framework ad graph-based approach for relay-assisted bidirectioal OFDMA cellular etworks. IEEE Trasactios o Wireless Commuicatios, 9(11), Ho, C.K.; Zhag, R.; ad Liag, Y.-C. (2008). Two-way relayig over OFDM: optimized toe permutatio ad power allocatio IEEE Iteratioal Coferece o Commuicatios, ICC '08, Zaialdi, A.; Halabia, H.; ad Lambadaris, I. (2016). Joit resource allocatio ad relay selectio i LTE-advaced etwork usig hybrid cooperative relayig ad etwork codig. IEEE Trasactios o Wireless Commuicatios, 15(6), Gec, V.; Murphy, S.; Yu, Y.; ad Murphy, J. (2008). IEEE J relaybased wireless access etworks: A overview. IEEE Wireless Commuicatios, 15(5), Joural of Egieerig Sciece ad Techology July 2017, Vol. 12(7)