Distributed Resource Allocation for Relay-Aided Device-to-Device Communication: A Message Passing Approach

Transcription

1 Distributed Resource Aocation for Reay-Aided Device-to-Device Communication: A Message Passing Approach Monowar Hasan and Ekram Hossain arxiv: v [cs.ni] 2 Jun 204 Abstract Device-to-device D2D communication underaying ceuar wireess networks is a promising concept to improve user experience and resource utiization by aowing direct transmission between two ceuar devices. In this paper, performance of network-assisted D2D communication is investigated where D2D traffic is carried through reay nodes. Considering a mutiuser and muti-reay network, we propose a distributed soution for resource aocation with a view to maximizing network sumrate. An optimization probem is formuated for radio resource aocation at the reays. The objective is to maximize end-to-end rate as we as satisfy the data rate requirements for ceuar and D2D user equipments under tota power constraint. Due to intractabiity of the resource aocation probem, we propose a soution approach using message passing technique where each user equipment sends and receives information messages to/from the reay node in an iterative manner with the goa of achieving an optima aocation. Therefore, the computationa effort is distributed among a the user equipments and the corresponding reay node. The convergence and optimaity of the proposed scheme are proved and a possibe distributed impementation of the scheme in practica LTE-Advanced networks is outined. The numerica resuts show that there is a distance threshod beyond which reay-aided D2D communication significanty improves network performance with a sma increase in end-to-end deay when compared to direct communication between D2D peers. Index Terms Resource aocation, LTE-Advanced LTE-A networks, D2D communication, L3 reay, graphica mode, maxsum message passing, factor graph. I. INTRODUCTION In recent years, new appications such as content distribution and ocation-aware advertisement underaying ceuar networks have drawn much attention to end-users and network providers. The emergence of such new appications brings D2D communication under intensive discussions in academia, industry, and standardization bodies. The concept of D2D communication has been introduced to aow oca peer-topeer transmission among user equipments UEs bypassing the base station [e.g., enb in a Long Term Evoution Advanced LTE-A network] to cope with high data rate services i.e., video sharing, onine gaming, proximity-aware socia networking. D2D communication was first proposed in [] to enabe muti-hop reaying in ceuar networks. In addition to traditiona oca voice and data services, other potentia D2D use-cases have been introduced in the iterature such M. Hasan and E. Hossain are with the Department of Eectrica and Computer Engineering, University of Manitoba, Winnipeg, Canada emais: monowar hasan@umanitoba.ca, Ekram.Hossain@umanitoba.ca. as peer-to-peer communication, oca advertisement, mutipayer gaming, data fooding [2] [4], muticasting [5], [6], video dissemination [7] [9], and machine-to-machine M2M communication [0]. Using oca data transmissions, D2D communication offers the foowing advantages: i extended coverage; ii offoading users from ceuar networks []; iii increased throughput and spectrum efficiency as we as improved energy efficiency [2]. However, in a D2D-enabed network, a number of practica considerations may imit the advantages of D2D communication. In practice, setting up reiabe direct inks between the D2D UEs whie satisfying the quaity-of-service QoS requirements of both the traditiona ceuar UEs CUEs as we as the D2D UEs is chaenging due to the foowing reasons: i Large distance: the potentia D2D UEs may not be in near proximity; ii Poor propagation condition: the ink quaity between potentia D2D UEs may not be favorabe for direct communication; iii Interference to and from CUEs: in an underay system, without an efficient power contro mechanism, the D2D transmitters may cause severe interference to other receiving nodes. The D2D receivers may aso experience interference from CUEs and/or enb. One remedy to this probem is to partition the avaiabe spectrum i.e., use overay D2D communication. However, this can significanty reduce the spectrum utiization. Network-assisted transmissions through reays coud efficienty enhance the performance of D2D communication when the D2D UEs are too far away from each other or the quaity of the channe between the UEs is not good enough for direct communication. Unike the existing iterature on D2D communication, in this paper, we consider reay-assisted D2D communication underaying LTE-A ceuar networks where D2D UEs are served by the reay nodes. We utiize the sefbackhauing configuration of LTE-A Layer-3 L3 reay which enabes it to perform operations simiar to those of an enb. We consider scenarios in which the potentia D2D UEs are ocated in the same macroce i.e., office bocks or university areas, concert has etc.; however, the proximity and ink condition may not be favorabe for direct communication. Therefore, they communicate via reays. The radio resources e.g., resource bocks [RBs] and power at the reays are shared among the D2D communication inks and the two-hop ceuar

2 2 inks using these reays. The goa of this work is to design a practica resource aocation agorithm for network-assisted D2D communications. We show that the resource aocation probem can be converted to a max-sum message passing MP probem over a graphica mode. The MP agorithms have been recognized as powerfu toos that can be used to sove many probems in signa processing, coding theory, machine earning, natura anguage processing and computer vision. When MP is appied to sove a probem, the messages represent probabiities i.e., beiefs exchanged with the goa of achieving optima decisions. Anaogousy, in the context of the resource aocation probem for reay-aided D2D communication, the MP strategy can be appied to pass messages between UEs and reays unti a goba aocation is obtained. The advantage of appying MP strategy in resource aocation is that it provides a owcompexity distributed soution and reduces the computation burden at the controer node. Motivated by the above fact, in this work, we appy the max-sum variation of the message passing technique to represent the resource aocation probem by a factor graph. To this end, we propose a distributed soution approach with poynomia time-compexity and ow signaing overhead. The main contributions of this paper can be summarized as foows: We mode and anayze the performance of reay-assisted D2D communication. The probem of RB and power aocation at the reay nodes for the CUEs and D2D UEs is formuated. As opposed to most of the resource aocation schemes in the iterature where ony a singe D2D ink is considered, we consider mutipe D2D inks aong with mutipe ceuar inks that are supported by the reay nodes. We provide a nove soution technique using message passing. Utiizing message passing strategy, we provide a ow-compexity distributed soution by which resource bocks and transmission power can be aocated in a distributed fashion. We anayze the compexity and the optimaity of the soution. To this end, we compare the performance of our reay-based D2D communication scheme with a direct D2D communication method and observe that reaying improves network performance for distant D2D peers without increasing the end-to-end deay significanty. The remainder of this paper is organized as foows. A review of the existing work in the iterature and motivation behind this work are presented in Section II. Foowed by the system mode and reated assumptions in Section III, we formuate the resource aocation probem in Section IV. The message passing strategy to sove the resource aocation probem is introduced in Section V and a distributed soution is proposed in Section VI. The performance evauation resuts are presented in Section VII. We concude the paper in Section VIII. The key mathematica notations used in the paper are isted in Tabe I. II. RELATED WORK AND MOTIVATION Athough resource aocation for D2D communication in orthogona frequency-division mutipe access OFDMA-based Notation N = {, 2,..., N} L = {, 2,..., L} C = {, 2,..., C}, D = {, 2,..., D} U, U TABLE I MATHEMATICAL NOTATIONS Physica interpretation Set of avaiabe RBs Set of reays Set of CUEs and D2D UEs, respectivey Set of UEs and tota number of UEs served by reay, respectivey A UE served by reay,,, γn,,2 SINR for UE over RB n is first and second hop, respectivey R u n End-to-end data rate for over RB n Q u Data rate requirement for,, RB aocation indicator and actua transmit power for over RB n, respectivey x, P R n,, W u, δ Rn, δ Wu, x u n φ n ψ n n,, ψ, υ u j z\n τ n, κ u abs{y} D 2hop RB and power aocation vector Utiity functions in factor graph deaing with optimization constraints Message from function node R n, to variabe node Message from W u, function node to any variabe node Margina at variabe node in factor graph Normaize messages for UE over RB n z-th sorted eement of χ u without considering the term R u n n + ψ, Node margina for UE over RB n Required number RBs for to satisfy the rate requirement Q u Absoute vaue of variabe y End-to-end deay for two hop reay-aided communication wireess networks is one of the active areas of research, ony a very few work in the iterature consider reays for D2D communication. A summary of reated iterature and comparison with our proposed scheme is presented in Tabe II. In [3], a greedy heuristic-based resource aocation scheme is proposed for both upink and downink scenarios where a D2D pair shares the same resources with CUE ony if the achieved SINR is greater than a given SINR requirement. A new spectrum sharing protoco for D2D communication overaying a ceuar network is proposed in [4], which aows the D2D users to communicate bi-directionay whie assisting the two-way communications between the enb and the CUE. In [5], the mode seection and resource aocation probem for D2D communication underaying ceuar networks is investigated and the soution is obtained by partice swarm optimization. Through simuations, the authors show that the proposed scheme improves system performance compared to overay D2D communication. In [6], D2D communication is proposed to improve the performance of muticast transmission among the members of a muticast group. A graph-based resource aocation method for ceuar networks with underay D2D communication is proposed in [6]. Due to the intractabiity of

3 3 TABLE II SUMMARY OF RELATED WORK AND PROPOSED SCHEME Reference Probem focus Reay-aided Soution approach Soution type Optimaity [6] Theoretica anaysis, No Iterative custer partitioning Centraized Optima spectrum utiization [9] Resource aocation No Proposed heuristic Centraized Suboptima [3] Resource aocation No Proposed greedy heuristic Centraized Suboptima [4] Resource aocation No * Numerica optimization Semi-distributed Pareto optima [5] Resource aocation, No Partice swarm optimization Centraized Suboptima mode seection [6] Resource aocation No Interference graph cooring Centraized Suboptima [7] Resource aocation No Coumn generation based Centraized Suboptima greedy heuristic [8] Resource aocation No Two-phase heuristic Centraized Suboptima [9] Theoretica anaysis, Yes Statistica anaysis Centraized Optima performance evauation [20] Performance evauation Yes Heuristic, simuation Centraized N/A [2] Resource aocation Yes Numerica optimization Centraized Asymptoticay optima Proposed scheme Resource aocation Yes Max-sum message passing Distributed Asymptoticay optima * D2D UEs serve as reays to assist CUE-eNB communications. No information is avaiabe. resource aocation probem, the authors propose a sub-optima graph-based approach which accounts for interference and capacity of the network. A resource aocation scheme based on a coumn generation method is proposed in [7] to maximize the spectrum utiization by finding the minimum transmission ength i.e., time sots for D2D inks whie protecting the ceuar users from interference and guaranteeing QoS. A twophase resource aocation scheme for ceuar network with underaying D2D communication is proposed in [8]. Due to N P-hardness of the optima resource aocation probem, the author proposes a two-phase ow-compexity sub-optima soution where after performing optima resource aocation for ceuar users, a heuristic subchanne aocation scheme for D2D fows is appied which initiates the resource aocation from the fow with the minimum rate requirements. In [9], the authors propose an incrementa reay mode for D2D communication where D2D transmitters muticast to both the D2D receiver and BS. In case the D2D transmission fais, the BS retransmits the muticast message to the D2D receiver. Athough the base station receives a copy of the D2D message which is retransmitted in case of faiure, this incrementa reay mode of communication consumes part of the downink resources for retransmission and reduces spectrum utiization. In [9], [20], the maximum ergodic capacity and outage probabiity of cooperative reaying is investigated in reayassisted D2D communication considering power constraints at the enb. The numerica resuts show that muti-hop reaying owers the outage probabiity and improves ce edge capacity by reducing the effect of interference from the CUE. It is worth noting that most of the above cited works provide centraize soutions. Besides, in [6], [9], [3] [8], the effect of using reays in D2D communication is not studied. As a matter of fact, reaying mechanism expicity in context of D2D communication has not been studied comprehensivey in the iterature. Taking the advantage of L3 reays supported by the 3GPP standard, in our earier work [2], we studied the performance of network-assisted D2D communication and showed that reay-aided D2D communication provides significant performance gain for ong distance D2D inks. However, the proposed soution in [2] is obtained in a centraized manner by a centra controer i.e., L3 reay. In this work, we deveop a distributed soution technique utiizing the MP strategy on a factor graph. Factor graph and other graphica modes have been used as powerfu soution techniques to tacke a wide range of probems in various domains; however, they have not been commony used in the context of resource aocation in ceuar wireess networks. To the best of our knowedge, the MP scheme for resource aocation in wireess networks was first introduced in [22] to minimize the transmission power in the upink of a muticarrier system. A resource aocation scheme based on MP is proposed in [23] for DFT-Spread-OFDMA upink communication. In [24], the message passing approach is used to aocate resources to minimize the transmission power for both singe and mutipe transmission formats in an OFDMAbased ceuar network. In [25], a message passing agorithm is proposed for a cognitive radio network to find assignment of secondary users to detect primary users so that the best overa network performance is achieved in a computationay efficient manner. Different from the above works, to aocate radio resource efficienty in a reay-aided D2D communication scenario, we use the max-sum MP strategy in our probem domain and propose a distributed soution in order to maximize the spectrum utiization. To this end, we anayze the compexity of the proposed soution and prove its optimaity and convergence. We aso discuss the deay performance and present an approach for possibe impementation of our

4 4 proposed soution in the LTE-A network setup. III. SYSTEM MODEL AND ASSUMPTIONS A. Network Mode Let us consider a D2D-enabed ceuar network with mutipe reays as shown in Fig.. A reay node in LTE-A is connected to the radio access network RAN through a donor enb with a wireess connection and serves both the ceuar UEs and D2D UEs. Let L = {, 2,..., L} denote the set of fixed-ocation Layer 3 L3 reays in the network. The system bandwidth is divided into N RBs denoted by N = {, 2,..., N}. When the ink condition between two D2D UEs is too poor for direct communication, scheduing and resource aocation for the D2D UEs can be done in a reay node i.e., L3 reay and the D2D traffic can be transmitted through that reay. We refer to this as reayaided D2D communication which can be an efficient approach to provide a better QoS e.g., data rate for communication between distant D2D UEs. The CUEs and D2D UEs constitute set C = {, 2,..., C} and D = {, 2,..., D}, respectivey, where the pairs of D2D UEs are discovered during the D2D session setup. We assume that the CUEs are outside the coverage region of enb and/or having bad channe condition, and therefore, CUE-eNB communications need to be supported by the reays. Besides, the direct communication between two D2D UEs requires the assistance of a reay node. The UEs i.e., both ceuar and D2D UEs assisted by reay are denoted by. The set of UEs assisted by reay is U such that U {C D}, L, U = {C D}, and U =. In the second hop, there coud be mutipe reays transmitting to their associated D2D UEs. We assume that the reays transmit to the enb using orthogona channes and this scheduing of reays is done by the enb 2. According to our system mode, taking the advantage of L3 reays, scheduing and resource aocation for the UEs is performed in the reay node to reduce the computationa oad at the enb. B. Radio Propagation Mode For modeing the propagation channe, we consider distance-dependent path-oss and shadow fading; furthermore, the channe is assumed to experience Rayeigh fading. In particuar, we consider reaistic 3GPP propagation environment 3 presented in [27]. For exampe, UE-reay and reay-d2d ink foows the foowing path-oss equation: P L u, [db] = og + L su + 0 ogς where is the distance between UE and reay in kiometer, L su accounts for shadow fading and is modeed as a og-norma An L3 reay with sef-backhauing configuration performs the same operation as an enb except that it has a ower transmit power and a smaer ce size. It contros ces and each ce has its own ce identity. The reay transmits its own contro signas and the UEs receive scheduing information directy from the reay node [26]. 2 Scheduing of reay nodes by the enb is out of the scope of this paper. 3 Any other propagation mode for D2D communication can be used for the proposed resource aocation method. L3 reay L3 reay enb L3 reay Ceuar UE D2D UE Fig.. A singe ce with mutipe reay nodes. We assume that the CUEeNB inks are unfavorabe for direct communication and need the assistance of reays. The D2D UEs are aso supported by the reay nodes due to ong distance and/or poor ink condition between peers. random variabe, and ς is an exponentiay distributed random variabe which represents the Rayeigh fading channe power gain. Simiary, the path-oss equation for reay-enb ink is expressed as P L,eNB [db] = og + L sr + 0 ogς 2 where L sr is a og-norma random variabe accounting for shadow fading. Hence given the distance, the ink gain between any pair of network nodes i, j can be cacuated as 0 P L i,j 0. C. Achievabe Data Rate We denote by h n i,j the direct ink gain between node i and j over RB n. The interference ink gain between reay UE i and UE reay j over RB n is denoted by g n i,j where UE reay j is not associated with reay UE i. The unit power SINR for the ink between UE U and reay using RB n in the first hop is given by,, = u j U j, j,j L h n,. 3 u j,j gn u j, + σ2 The unit power SINR for the ink between reay and enb for CUE i.e., {C U } in the second hop is as foows:,,2 = u j {D U j}, j,j L h n,enb. 4 j,u j g n j,enb + σ2 Simiary, the unit power SINR for the ink between reay and receiving D2D UE for the D2D UEs i.e., {D U } in the second hop can be written as,,2 = u j U j, j,j L h n, j,u j g n j, + σ 2. 5

5 5 In 3 5, i,j is the transmit power in the ink between i and j over RB n, σ 2 = N 0 B RB, where B RB is bandwidth of an RB, and N 0 denotes therma noise. h n,enb is the gain in the reay-enb ink and h n, is the gain in the ink between reay and receiving D2D UE corresponding to the D2D transmitter UE. The achievabe data rate 4 for in the first hop can be expressed as r n, = B RB og 2 +, γn,,. Simiary, the achievabe data rate in the second hop is given by r n,2 = B RB og 2 +,,,2. Since we are considering a two hop communication approach, the end-to-end data rate for on RB n is the haf of minimum achievabe data rate over two hops, i.e., R u n = { } 2 min r n,, rn,2. 6 IV. FORMULATION OF THE RESOURCE ALLOCATION PROBLEM For each reay, the objective of resource i.e., RB and transmit power aocation probem RAP is to obtain the assignment of RB and power eve to the UEs that maximizes the system capacity, which is defined as the minimum achievabe data rate over two hops. The RB aocation indicator is denoted by a binary decision variabe {0, }, where = {, if RB n is assigned to UE 0, otherwise. Hence, the objective of RAP is to obtain the RB and power aocation [ vectors for each reay L, i.e., T x = x,..., xn,..., x U,..., xn U ] and P = [ T P,,..., P N,,..., P U,,..., P N U,] respectivey, which maximize the data rate. Let the maximum aowabe transmit power for UE reay is Pu max P max. Let the QoS i.e., data rate requirements for UE is denoted by Q u and R u = R u n denotes the achievabe sum-rate over aocated RBs. Considering that the same RBs wi be used by the reay in both the hops, the resource aocation probem 4 If there is no reay in the network, the achievabe data rate for the UE u over RB n can be expressed as r u n = B RB og 2 + P u n γ u n, where u = h n u,û j g n u,j j Ûu ink u C or the channe gain between D2D UEs u D and the set of UEs transmitting with same RBs as u. 7, hn u,û is the channe gain between CUE-eNB + σ2 Ûu denotes for each reay L can be stated as foows: P max R u n,, subject to U U U,P n, U U, n N 8a, P u max, U 8b, P max, gn u,, In th,, g n,u 8c, n N 8d,2 In th,2, n N 8e R u Q u, U 8f, 0,, 0, n N, U 8g where the rate of over RB n R n = 2 min { BRB og 2 +, γn,,, B RB og 2 +,u,,2 the unit power SINR for the first hop,,,2 =,, = h n, I n,, +, σ2 and the unit power SINR for the second hop, h n,enb I n,,2 +, {C U } σ2 } h n, I n,,2 + σ2, {D U }. In the above, I n,, and In,,2 denote the interference received by over RB n in the first and second hop, respectivey, and are given as foows: I n,, = u j u j,j gn u, j, I n,,2 = u j {D U j}, j,j L u j U j, j,j L u j U j, j,j L u j j,u j g n j,enb, {C U } u j j,u j g n j,, {D U }. With the constraint in 8a, each RB is assigned to ony one UE. With the constraints in 8b and 8c, the transmit power is imited by the maximum power budget. The constraints in 8d and 8e imit the amount of interference introduced to the other reays and receiving D2D UEs in the first and second hop, respectivey, to be ess than some threshod. The constraint in 8f ensures the minimum data rate requirements for the CUE and D2D UEs. The constraint in 8g is the nonnegativity condition for transmit power.,

6 6 Simiar to [28], we appy the concept of reference node. As an exampe, in the first hop, each UE associated with reay node chooses from among the neighbouring reays having the highest channe gain according to foowing equation: g n u,, = max g n u j,j, U, j, j L 9 and aocates the power eve considering the interference threshod. Simiary, in the second hop, for each reay, the transmit power wi be adjusted accordingy considering interference introduced to receiving D2D UEs associated with neighboring reays according to g n,u,2 = max g n u,u j, j, j L, u j {D U j }. 0 j From 6, the maximum rate for the UE over RB n is achieved when, γn,, =,,,2. Therefore, the power aocated to reay node for the UE can be expressed as a, function of power at UE as, = γn,,,,2 of over RB n is given by R u n = 2 B RB og 2 +, γn,, Hence the probem P can be written as P2 max,, U and the rate. 2 xn B RB og 2 +, γn,, subject to, n 2a U, P max, 2b U U U,,,,2, P max, gn u,, In th,,,, gn,u,,2 2 xn B RB og 2 +, γn,,,2 In th,2, n, 0, 2c, n 2d 2e Q u, 2f n,. 2g Remark. The RAP formuation is a mixed-integer noninear program MINLP. MINLP probems have the difficuties of both of their sub-casses, i.e., the combinatoria nature of mixed integer programs MIPs and the difficuty in soving noninear programs NLPs. Since MIPs and NLPs are N P- compete, the RAP P2 is strongy N P-hard. In order to obtain a tractabe soution for the RAP formuation, in the foowing, we utiize the MP strategy. V. MESSAGE PASSING APPROACH TO SOLVE THE RESOURCE ALLOCATION PROBLEM A. MP Strategy for the Max-sum Probem Given the RAP formuation P2, we focus on the maxsum variant [29] of MP paradigm. Let us consider a generic function fy, y 2,..., y J : D y R where each variabe y j corresponds to a finite aphabet a, i.e., D y = a J. We concentrate on maximizing the function f, i.e., Z = max y fy. 3 That is, Z represents the maximization over a possibe combinations of the vector y a J where y = [y, y 2,..., y J ] T. The margina of Z with respect to variabe y j is given by φ j y j = max fy 4 y j where max f denotes the maximization over a variabes in α f except variabe α. Let us decompose fy into the summation of K functions f k : Dŷk R, k {, 2,..., K}, K i.e., fy = f k ŷ k, where ŷ k is a subset of eements of y k= and Dŷk D y. Besides, et f = [f, f 2,..., f K ] T denote the vector of K functions and f j represent the subset of functions in f where the variabe y j appears. Hence, 4 can be rewritten as φ j y j = max y j K f k ŷ k. 5 k= Utiizing any MP agorithm, the computation of marginas invoves passing messages between nodes represented by a specific graphica mode. Among different graphica modes, in this work, we consider factor graph [30] to capture the structure of generic function f. The factor graph consists of two different types of nodes, namey, function or factor nodes and variabe nodes. A function node is connected with a variabe node if and ony if the variabe appears in the corresponding function. Consequenty, a factor graph contains two types of messages, i.e., message from factor nodes to variabe nodes and vice-versa. According to the max-sum MP strategy, the message passed by any variabe node y j, j {, 2,..., J}, to any generic function node f k, k {, 2,..., K}, is given as δ yj f k y j = i f j, i k δ fi y j y j. 6 Likewise, the message from factor node f k to variabe node y j is given as foows: δ fk y j y j = max f ky,..., y J + δ yi f k y i. y j i ŷ k, i j 7 When the factor graph is cyce free, it is represented as a tree i.e., there is a unique path connecting any two nodes; hence, a the variabe nodes can compute the marginas as φ j y j = K δ fk y j y j. 8 k=

7 7 x R, W, x N x u R N, W u, x u N Fig. 2. An arbitrary factor graph representing MP formuation of the RAP. For ease of representation, the variabes are denoted by circuar nodes whereas the functions are denoted by square nodes. A variabe node x u n is connected to the function nodes R n, and W u, if and ony if the variabe appears in the corresponding function. By invoking the genera distributive aw i.e., max = max [3], the maximization in 3 can be computed as B. Utiity Functions Z = J j= max y j φ j y j. 9 In the foowing, we deveop a joint RB and power aocation mechanism that everages the dynamics of MP strategy. Compared to centraized optimization soutions, MP aows to distribute the computationa burden of achieving a feasibe resource aocation by exchanging information among UEs and the corresponding reay. In order to sove RAP P2 using the MP scheme, we reformuate it as a utiity maximization i.e., cost minimization probem and define the utiity functions as in 20 and 2 where unfufied constraints resut in infinite cost. Per RB constraints [i.e., 2a, 2c, 2d, 2e] are incorporated in the utiity function R n, as foows: 0, if R n, =, U U U U,,,,2, max, gn u,, In th,,,, gn,u,,2,2 In th,2 otherwise 20 where max P = max N. On the other hand, per UE constraints are incorporated in the utiity function W u, which is the achievabe rate of each UE ony if the constraints in 2b and 2f are satisfied, i.e., W u, =, R u n, if otherwise., P u max R u n Q u 2 C. MP Formuation for the Resource Aocation Probem Using the utiity functions above, the RAP for each reay can be rewritten as N x = max R n, + W u,. 22 x U By expoiting the concept described in Section V-A, et us associate 22 with a factor graph as shown in Fig. 2. Foowing an MP strategy, the variabe and function nodes exchange messages aong their connecting edges unti the vaues of are determined for, n. Let φ n be the marginaization of 22 with respect to and given as N φ n = max R n, + W u,. x u n U 23 Let δ Rn, and δ n x R n, denote the message exchanged between function nodes R n, and the connected variabe nodes for, n. Simiary, δ Wu, x u n and δ n x W u u, denote the exchanged messages between function nodes W u, and variabe nodes for, n. Let us consider a generic RB n in the factor graph. The square node in Fig. 2 corresponding to R n, which is connected to a variabe nodes for U. Hence from 7, the message to be deivered to the particuar variabe node δ Rn, x u n = max subject to x u n U U U is obtained as foows: j U,j δ x n j R n, U,,,,2, max, gn u,, In th,,,, gn,u,,2 j,2 In th,2. 24 Let us consider a generic user. As iustrated in Fig. 2, the square nodes corresponding to function W u, in factor graph are connected to a variabe nodes x u n for n N. Using 7 and 2, the message from function node W u, to any variabe node is given by 25. From 24 and 25, the margina φ n x u n can be obtained as φ n = δ Rn, u + δ Wu, x u n. 26 Consequenty, the RB aocation indicator for UE over RB n is given by [ ] = argmax φ n. 27 x u n From 24 and 25, it can be noted that both the messages, i.e., δ Rn, x u n and δ Wu, sove a

8 8 δ Wu, subject to = R u n + max, P u max, j=, j n x j R u j + δ j x x j W u, x u n R u n Q u. 25 oca optimization probem with respect to the aocation variabe. It is worth noting that, in our system mode, each function node W u, and corresponding variabe nodes are ocated at the UE, whie a δ Rn, nodes are ocated at the reay. Hence, sending messages δ Rn, from variabe nodes to function nodes and vice-versa requires actua transmission on the radio channe. However, the message exchanges between variabe nodes and function nodes W u, are performed ocay at the UEs without actua transmission on the radio channe. D. An Effective Impementation of MP Strategy In a practica LTE-A system, since the exchange of messages actuay invoves effective transmissions over the channe, the MP scheme described in the preceding section might be imited by the signaing overhead due to transfer of messages between reay and UEs. In the foowing, we observe that the amount of message signaing can be significanty reduced by some agebraic manipuations. Note that, the message δ Wu carries information regarding the, use of RB n by UE with transmission power,, whie 0 carries information regarding the ack of δ Wu, transmission on RB n by UE, i.e.,, = 0. Hence, each UE eventuay deivers a rea-vaued vector of two eements, i.e., [ ] T Wu = δ, x u n Wu, δ, u Wu 0., Let κ u denote the required number of RBs 5 to satisfy the data rate requirement Q u for UE. Therefore, the constraint in 2f can be rewritten as κ u,. 28 Now, repacing the constraint in 25 with that in 28 and subtracting the constant term δ j x 0 from both W u, j=; j n sides of 25, we obtain 29. Let us introduce the normaized n messages ψ, = δ n x W u, δ W u, 0 = 0. It can be observed that the δ Rn, δ Rn, terms within the summation in 29 are either 0 or R n ψ n, + depending on whether the RB aocation indicator variabe is 0 or. 5 The cacuation of κ u is given in Appendix A. Given the above, the maximization is straightforward. For instance, consider the vector [ ] T χ u = R u + ψ,,..., Rj j + ψ,,..., RN N + ψ, and υ u j z\n be the z-th sorted eement of χ u without considering the term R u j + so that ψ j, υ j z\n υ j z\n υ j z+\n for j N, j n. Hence, for wi be achieved if [24] δ Wu, j=, j n =, the maximum rate δ x j W u, 0 κ u = R u n + υ u j z\n. 30 z= Simiary, for = 0, the maximum is given by [24] δ Wu, 0 Since by definition j=; j n κu W u, 0 = δ x j z= υ j ψ n, = δ δ W u, u Wu 0,, x u n z\n. 3 from 30 and 3, the normaized messages can be derived as foows: ψ n, = Rn υ u j κu \n = R n R j + ψ j, κ u \n 32 where j N and j n. Note that the messages sent from UE to RB n in factor graph is a scaar quantity. Simiary, the normaized messages from RB n to UE, i.e., ψn δ Rn, δ Rn, 0 becomes [24] ψ n, = max i U, i, = ψ n i,. 33 Note that, for any arbitrary graph, the aocation variabes may keep osciating and might not converge to any fixed point. In the context of oopy graphica modes, by introducing a suitabe weight, the messages in 32 and 33 perturb to a

9 9 δ Wu, u j=; j n δ x j W u, subject to 0 = xn R u n + max, P u max, j=, j n x j R u j + δ j x x j W u, δ j x W u, 0 κ u. 29 fixed point. Accordingy, 32 and 33 can be rewritten as [32] ψ n, = Rn ω R u j + ψ j, +ω R n n u κ u \n + ψ, ψ n, = ω max i U, i ψ n i, ωψ n,. 34a 34b Note that, when ω =, 34a and 34b reduce to the origina formuation, i.e., 32 and 33, respectivey. Thus the soution x u n can be easiy obtained by cacuating the node marginas for each UE-RB pair, i.e., for a U, n N pair as foows: τ n, = ψn n, + ψ,. 35 Hence, from 27, the optima RB aocation can be computed as { 0, if τ n =, < 0 36, otherwise. VI. DISTRIBUTED SOLUTION FOR THE RESOURCE A. Agorithm Deveopment ALLOCATION PROBLEM Once the optima RB aocation is obtained, the transmission power of the UEs on assigned RBs is obtained as foows. We coupe the cassica generaized distributed constrained power contro scheme GDCPC [33] with an autonomous power contro method [34] which considers the data rate requirements of UEs whie protecting other receiving nodes from interference. More specificay, at each iteration, the transmission power is updated using 38 where and P u n max P = max n ˆP, is obtained as ˆ, = min n P,, min P u n ma, ϖ,. 37 n In 37, P, is chosen arbitrariy within the range of 0, P u n ma and ϖ, is given by ϖ n, = min I n th,,,,2 I n th,2. 39 g n u,,,, g n,u,2 Each reay independenty performs the resource aocation and aocates resources to the associated UEs. For competeness, the distributed joint RB and power aocation agorithm is summarized in Agorithm. Since the L3 reays can perform the same operation as an enb, these reays can communicate using the X2 interface [35] defined in the LTE-A specification. Therefore, the reays can obtain the channe state information through inter-reay message passing without increasing the overhead of signaing at the enb. Remark 2. Since x satisfies the binary constraints, and the optima aocation x, P satisfies a the constraints in P2, for a sufficient number of avaiabe RBs, the soution obtained by Agorithm gives a ower bound on the soution of the origina RAP P2. B. Compexity Anaysis If the agorithm requires T iterations to converge, it is easy to verify that the time compexity at each reay L is of OT U N. Simiary, considering a standard sorting agorithm e.g., merge sort, heap sort to generate the outputs υ u j z\n for n with a worst-case compexity of ON og N, the overa time compexity at each UE is O T N 2 og N. C. Convergence of the Agorithm and Optimaity of the Soution Theorem. If the agorithm converges to a fixed point message, this point foows the sackness condition of P2, and hence it becomes the optima soution for the origina resource aocation probem. Proof: See Appendix B. Theorem 2. The message passing agorithm converges to a soution with zero duaity gap as the number of resource bocks goes to infinity, i.e., dua probem of P2 [e.g., D, given by B.4] has the same optima objective function vaue [23]. Proof: See Appendix C. D. End-to-End Deay for the Proposed Soution We measure the tota end-to-end deay due to reaying for the proposed framework as foows [36]: D 2hop = t schedue + t [] deivery + t decode + t [2] deivery 40 where t schedue is the time required to schedue the UEs and perform resource aocation, t decode is the decoding time at reay nodes before data packets are forwarded in second hop, and t [j] deivery = t[j] transmit + t[j] pd is the sum of packet transmission time and propagation deay for hop j {, 2}. Whie cacuating deay using 40, we assume that each schedued UE is ready to transmit data and the waiting time before transmission is zero i.e., there is no queuing deay.

10 0,t + = 2 Q 2 R t, t, if 2 Q 2 R t, n max t P ˆ,, otherwise 38 Agorithm Aocation of RB and transmission power using message passing : Estimate channe quaity indicator CQI matrices from previous time sot. 2: Initiaize t := 0, max P 0 := 3: repeat, N 4: Each UE sends messages ψ n, reay L for each RB n N. 5: The reay L sends messages, ψn n,0 := 0, ψ t + = Rn t ω n ψ,t + = ω max i U, i, 0 := 0 for U, n N. R j t + ψ j, t κ u \n + ω R n t + ψ n, t to the ψ n i, t ωψn, t to each associated UE U for n N. 6: Each UE computes the marginas as τ n n,t + = ψn,t + ψ,t for n N and reports to the corresponding reay. 7: Each reay cacuates the RB and power aocation vector for each UE according to 36 and 38, respectivey. 8: Cacuate the aggregated achievabe network rate as R t + := R u t +. U 9: Update t := t +. 0: unti t = T max or the convergence criterion met i.e., abs{r t+r t} < ε, where ε is the toerance for convergence. : Aocate resources i.e., RB and transmit power to the associated UEs for each reay. E. Impementation of Proposed Soution in a Practica LTE-A Scenario [ ] T Let ψ u = ψ u, ψ u 2,..., ψ u N and ψu = [ ] T ψ 2 N, ψ,..., ψ denote the message vectors for UE. These messages can be mapped into standard LTE-A scheduing contro messages as iustrated in Fig. 3. In an LTE-A system, UEs periodicay sense the physica upink contro channe PUCCH and transmit known sequences using sounding reference signa SRS. After reception of scheduing request SR from UEs, an L3 reay performs scheduing and resource aocation. After scheduing, the L3 reay aocates RBs and informs to the UEs by sending scheduing grant SG through physica downink contro channe PDCCH. Once the aocation of RBs is received, the UEs periodicay send the buffer status report BSR using PUCCH to the reay in order to update the resource requirement, and in response, the reay sends back an acknowedgment ACK in physica hybrid-arq indicator channe PHICH. Considering the above scenario, our proposed message passing approach can be impemented by incorporating ψ u messages in SR and BSR, and ψ u messages in SG and ACK contro signas, respectivey. A. Simuation Setup VII. PERFORMANCE EVALUATION In order to evauate the performance of the proposed resource aocation scheme, we deveop an event-driven simuator. A the simuations are performed in MATLAB environment. The simuator focuses on capturing the medium access contro MAC ayer behavior of the LTE-A network. We simuate a singe three-sectored ce in a rectanguar area Fig. 3. UE L3 Reay SRS SR, BSR,. ψ SG, ψ ~ BSR, ACK, ψ ~ ψ ψ Possibe impementation of the MP scheme in an LTE-A system. of 700 m 700 m, where the enb is ocated in the center of the ce and three reays are depoyed in the network, i.e., one reay in each sector. The CUEs are uniformy distributed within the reay ce. The D2D transmitters and receivers are uniformy distributed within a radius D r,d whie keeping a distance D d,d between peers as shown in Fig. 4. Both D r,d and D d,d are varied as simuation parameters. We consider a snapshot mode to obtain the network performance, where a the network parameters remain constant during a simuation run. n In our simuations, we assume ω =, P, is set to 0 dbm, and interference threshod is 70 dbm for a the RBs. The simuation parameters are isted in Tabe III. The simuation

11 3.5 4 x 06 Tota UE 2 C = 9, D = 3 Tota UE 8 C = 2, D = 6 Tota UE 24 C = 5, D = 9 Reay ce radius D r,d D d,d D r,d Average endtoend rate bps Fig. 4. D2D UEs are uniformy distributed within the radius D r,d whie keeping distance D d,d between peers. Parameter TABLE III SIMULATION PARAMETERS Vaues Ce ayout Hexagona grid, 3-sector sites Carrier frequency 2.35 GHz System bandwidth 2.5 MHz Tota number of avaiabe RBs 3 MAC frame duration 0 msec Scheduing time 0.0 msec Packet size 500 bytes Reay ce radius 200 meter Distance between enb and reays 25 meter Minimum distance between UE and reay 0 meter Tota power avaiabe at each reay 30 dbm Tota power avaiabe at UE 23 dbm Rate requirement for ceuar UEs 28 Kbps Rate requirement for D2D UEs 256 Kbps Standard deviation of shadow fading: for reay-enb inks 6 db for UE-reay inks 0 db Noise power spectra density 74 dbm/hz Number of iterations Fig. 5. Convergence behavior of the proposed agorithm with different number of UEs: D r,d = 80 meter, D d,d = 40 meter. Normaized average achievabe data rate Proposed scheme Reference scheme Maximum distance between D2D UEs m Fig. 6. Average achievabe data rate for both the proposed and reference schemes with varying distance between D2D UEs: number of CUE, C = 5 and number of D2D pairs, D = 9 i.e., 5 CUE and 3 D2D-pairs are assisted by each reay, and hence U = 8 for each reay. D r,d is considered 80 meter. resuts are averaged over different reaizations of UE ocations and channe gains. B. Resuts Convergence: In Fig. 5, we depict the convergence behavior of the proposed agorithm. In particuar, we show the average achievabe data rate versus the number of iterations. The averageachievabe rate R avg for UEs is cacuated as u {C D} C+D R ach u R avg = where Ru ach is the achievabe data rate for UE u. Note that the higher the number of users, the ower the average data rate. 2 Performance of reay-aided D2D communication: We compare the performance of the proposed scheme with the underay D2D communication scheme presented in [3]. In this reference scheme, an RB aocated to CUE can be shared with at most one D2D-ink. The D2D UEs share the same RBs aocated to CUE using Agorithm and communicate directy between peers without reay if the data rate requirements for both CUE and D2D UEs are satisfied; otherwise, the D2D UEs refrain from transmission on that particuar time sot. i Average achievabe data rate vs. distance between D2D UEs: The average achievabe data rate of D2D UEs for both the proposed and reference schemes is iustrated in Fig. 6. Athough the reference scheme outperforms when the distance between D2D UEs is sma i.e., d < 70 m, our proposed approach, which uses reays for D2D traffic, can greaty improve the data rate especiay when the distance increases. This is due to the fact that when the distance increases, the performance of direct communication deteriorates due to increased signa attenuation. Besides, when the D2D UEs share resources with ony one CUE, the spectrum may not be utiized efficienty, and therefore, the achievabe rate decreases. As a resut, the gap between the achievabe rate with our proposed agorithm and that with the reference scheme becomes wider when the distance increases. ii Gain in aggregated achievabe data vs. varying distance between D2D UEs: The gain in terms of aggregated achievabe data rate is shown in Fig. 7a. We cacuate

12 2 Gain in aggregated achievabe data rate % Gain in aggregated achievabe data rate % Asymptotic upper bound Proposed scheme Maximum distance between D2D UEs m a Maximum distance between D2D UEs m b Fig. 7. a Gain in aggregated achievabe data rate and b Comparing gain with asymptotic upper bound using the simiar setup of Fig. 6. There is a critica distance, beyond which reaying of D2D traffic provides significant performance gain. the rate gain as foows: R gain = R prop R ref R ref 00% 4 where R prop and R ref denote the aggregated data rate for the D2D UEs in the proposed scheme and the reference scheme, respectivey. In Fig. 7b, we compare the rate gain with the asymptotic upper bound 6. The figures show that, compared to direct communication, with the increasing distance between D2D UEs, reaying provides considerabe gain in terms of achievabe data rate and hence spectrum utiization. In addition, our proposed distributed soution performs neary cose to the upper bound. iii Effect of reay-ue distance and distance between D2D UEs on rate gain: The performance gain in terms of the achievabe aggregated data rate under different reay- D2D UE distance is shown in Fig. 8. It is cear from the figure that, even for reativey arge reay-d2d UE distances, e.g., D r,d 80 m, reaying D2D traffic provides considerabe rate gain for distant D2D UEs. iv Effect of number of D2D UEs and distance between D2D UEs on rate gain: We vary the number of D2D UEs and pot the rate gain in Fig. 9 to observe the performance of our proposed scheme in a dense network. The figure suggests that even in a moderatey dense situation e.g., C + D = 5+2 = 27 our proposed method provides a higher rate compared to direct communication between distant D2D UEs. v Impact of reaying on deay: In Fig. 0, we show resuts on the deay performance of the proposed reayaided D2D communication approach. In particuar, we observe the empirica compementary cumuative distri- 6 The asymptotic upper bound is obtained through reaxing the constraint that an RB is used by ony one UE by using the time-sharing factor [37]. Thus 0, ] represents the sharing factor where each x u n denotes the portion of time that RB n is assigned to UE and satisfies the constraint, n. For detais refer to [2]. U bution function CCDF 7 for both the proposed scheme which uses reay for D2D communication and reference scheme where D2D UEs communicate without reay. Note that in the reference scheme, the deay for one hop communication is given by D hop = t schedue + t deivery. The variation in end-to-end deay is experienced due to variation in achievabe data rate and propagation deay at different vaues of D r,d and D d,d. From this figure it can be observed that the reay-aided D2D communication increases the end-to-end deay. However, this increase e.g., = msec of deay woud be acceptabe for many D2D appications. Gain in aggregated data rate % Maximum distance between reay and D2D UEs m Maximum distance between D2D UEs m Fig. 8. Effect of reay distance on rate gain: C = 5, D = 9. For every D r,d, there is a distance threshod i.e., upper side of the ighty shaded surface beyond which reaying provides significant gain in terms of aggregated achievabe rate. η 7 The empirica CCDF of deay is defined as D ηt = I η [deayi >t] i= where η is the tota number of distance observations e.g., UE-reay distance for the proposed scheme and the distance between D2D UEs for the reference scheme, respectivey used in the simuation, deay i is the end-to-end deay at i-th distance observation, and t represents the x-axis vaues in Fig. 0. The indicator function I [ ] outputs if the condition [ ] is satisfied and 0 otherwise.

13 3 Gain in aggregated data rate % Tota number of D2D UEs Maximum distance between D2D UEs m Fig. 9. Effect of number of D2D UEs on rate gain: C = 5, D r,d = 80 meter. The upper position of ighty shaded surface iustrates the positive gain in terms of aggregated achievabe rate. Empirica CCDF Empirica CCDF Proposed scheme Deay ms Reference scheme Deay ms Fig. 0. End-to-end deay for the proposed and reference scheme where C = 5, D = 9. We vary the distances D r,d and D d,d from 60 to 40 meter with 5 meter interva. The decoding deay at a reay node is assumed to be 0.73 miisecond obtained from [36]. VIII. CONCLUSION We have presented a comprehensive resource aocation framework for reay-assisted D2D communication. Due to the N P-hardness of origina resource aocation probem, we have utiized the max-sum message passing strategy and presented a ow-compexity distributed soution based on the message passing approach. The convergence and optimaity of the proposed scheme have been proved. The performance of the proposed method has been evauated through simuations and we have observed that after a distance margin, reaying of D2D traffic improves system performance and provides a better data rate to the D2D UEs at the cost of a sma increase in end-to-end deay. In the context of D2D communication, most of the resource aocation probems are formuated under the assumption that the potentia D2D UEs have aready been discovered. However, to deveop a compete D2D communication framework, this work can be extended considering D2D discovery aong with resource aocation. In addition, due to time-varying and random nature of wireess channe, the ink gain uncertainties for resource aocation in such reay-aided D2D communication is worth investigating. APPENDIX A REQUIRED NUMBER OF RBS FOR A GIVEN QOS REQUIREMENT Let,, and γn,, denote the instantaneous and average SINR for the UE over RB n. In order to determine the required number of RBs for a given data rate requirement for any UE, we need to derive the probabiity distribution of γn,,,, [38]. Note that, the channe gain due to Rayeigh fading and og-norma shadowing can be approximated by a singe ognorma distribution [39], [40]. In addition, the sum of random variabes having og-norma distribution can be represented by a singe og-norma distribution [4]. Therefore, Γ n,, =,,,, can be approximated by a og-norma random variabe whose mean and standard deviation can be cacuated as shown in [40]. Hence the average rate achieved by UE over RB n can be written as A. where F n Γ ϑ and f n,, Γ ϑ are,, the probabiity density function and probabiity distribution function of Γ n,,, respectivey. Now, et R u, be the minimum rate achieved by UE. In order to maintain the data rate requirement, we can derive the foowing inequaity 8 : Q u κ u R u, U A.2 where by R u, U we expicity describe the dependence of the minimum achievabe rate R u, on the number of UEs U. Therefore, the minimum number of required RBs is given by κ u Q u R u, U APPENDIX B PROOF OF THEOREM. A.3 Let us rearrange the Lagrangian of P2 defined by B. as foows: L = 2 xn U bu U d n U ë n R n U U fu ä n, c,,,,2 2 xn, gn u,, U U, gn,u,2,,,,2, R u n + Õ. B.2 where Õ denote the eftover terms invoving Lagrange mutipiers, i.e., ä, b, c, d, ë, f. From above we can derive the foowing emma: 8 Simiar to [38], we assume that the ong-term channe gains on different RBs are same, and hence, the average rates achieved by a particuar UE on different RBs are the same.

14 r n, = 2 B RB 0 og 2 +, Γn u,, γn,, F Γ j U, j n j,, ϑ f Γ n,, ϑdϑ. A. 4 L = 2 xn U + c + P max ë n R n + ä n U I n th,2 U,,,,2,,,,2 U, +, gn,u,2 + U bu P max d n I n th, + U fu x u n U N 2 xn,, gn u,, R n Q u. B. Lemma B.. The sackness conditions for P2 are R u n n λ = max Rj j u j N λ n where λ, n. B.3 invoves the terms with Lagrange mutipiers for Proof: By Weierstrass theorem Appendix A.2, Proposition A.8 in [42] the dua function can be cacuated by B.4. Therefore, if P2 has an optima soution, its dua has an optima soution, i.e., Hence, max n N U Rn n N U D = Rn U n λ κ u + Õ = R u n. B.5 U R u n. Since x is an optima aocation, from B.6 we obtain n max λ κ u In addition, since U = Rn U = κ u, B.7 becomes R u n n λ max Rn u n N Now, if > 0, we have R n λ n B.6 n λ. B.7 = max Rj j u j N λ. n λ = 0. B.8 From 36, at each iteration, each UE can distinguish between two different subsets of RBs by sorting the marginas in an increasing order. Let us define the first subset N u N given by the first κ u N RBs in the ordered ist of marginas where the second subset Nu N is given by the ast N κ u of the ist. Accordingy, we can have the foowing emma: Lemma B.2. At convergence, Rṅ for, ṅ N u, n N u. + ψ ṅ, < R n + ψ n, Proof: See [32]. From Lemma B. and B.2, it can be noted that, the inequaity R ṅ λ u ṅ n < R λ n impies the sackness condition ṅ ṅ n n B.3 by imposing λ = ψ, and λ = ψ, ; hence, the proof of Theorem foows. APPENDIX C PROOF OF THEOREM 2 From [43] and Proposition 4 of [44], there must exist a non-overapping binary vaued feasibe aocation even after reaxation when the number of RBs tends to infinity. Since in our probem the number of RBs is sufficienty arge, the messages converge to a fixed point and we can concude that 0, ] achieves the same optima objective vaue. Thus, directy foowing the theorem of integer programming duaity i.e., if the prima probem has an optima soution, then the dua aso has an optima one for any finite N, the optima objective vaue of D ies between P2 and its LP reaxation. the LP reaxation of P2, i.e., REFERENCES [] Y.-D. Lin and Y.-C. Hsu, Mutihop ceuar: a new architecture for wireess communications, in Annua Joint Conference of the IEEE Computer and Communications Societies INFOCOM, vo. 3, 2000, pp [2] L. Lei, Z. Zhong, C. Lin, and X. Shen, Operator controed deviceto-device communications in LTE-advanced networks, IEEE Wireess Communications, vo. 9, no. 3, pp , 202. [3] M. Corson, R. Laroia, J. Li, V. Park, T. Richardson, and G. Tsirtsis, Toward proximity-aware internetworking, IEEE Wireess Communications, vo. 7, no. 6, pp , 200. [4] Technica specification group services and system aspects; Feasibiity study for proximity services ProSe, reease 2, 3rd Generation Partnership Project, Tech. Rep. 3GPP TR V2.2.0, June 203.

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16 6 [4] [42] [43] [44] scheduing in WCDMA networks, IEEE Transactions on Wireess Communications, vo. 5, no. 8, pp , N. Mehta, J. Wu, A. Moisch, and J. Zhang, Approximating a sum of random variabes with a ognorma, IEEE Transactions on Wireess Communications, vo. 6, no. 7, pp , D. P. Bertsekas, Noninear Programming, 2nd ed. Athena Scientific, 999. W. Yu and R. Lui, Dua methods for nonconvex spectrum optimization of muticarrier systems, IEEE Transactions on Communications, vo. 54, no. 7, pp , K. Yang, N. Prasad, and X. Wang, An auction approach to resource aocation in upink OFDMA systems, IEEE Transactions on Signa Processing, vo. 57, no., pp , Monowar Hasan S 3 received his B.Sc. degree in Computer Science and Engineering from Bangadesh University of Engineering and Technoogy BUET, Dhaka, in 202. He is currenty working toward his M.Sc. degree in the Department of Eectrica and Computer Engineering at the University of Manitoba, Winnipeg, Canada. He has been awarded the University of Manitoba Graduate Feowship. His current research interests incude internet of things, software defined networks and resource aocation in mobie coud computing. He serves as a reviewer for severa major IEEE journas and conferences. Ekram Hossain S 98-M 0-SM 06 is a Professor since March 200 in the Department of Eectrica and Computer Engineering at University of Manitoba, Winnipeg, Canada. He received his Ph.D. in Eectrica Engineering from University of Victoria, Canada, in 200. Dr. Hossain s current research interests incude design, anaysis, and optimization of wireess/mobie communications networks, cognitive radio systems, and network economics. He has authored/edited severa books in these areas hossaina. His research has been widey cited in the iterature more than 7000 citations in Googe Schoar with an h-index of 42 unti January 204. Dr. Hossain serves as the Editor-in-Chief for the IEEE Communications Surveys and Tutorias and an Editor for IEEE Journa on Seected Areas in Communications Cognitive Radio Series and IEEE Wireess Communications. Aso, he is a member of the IEEE Press Editoria Board. Previousy, he served as the Area Editor for the IEEE Transactions on Wireess Communications in the area of Resource Management and Mutipe Access from and an Editor for the IEEE Transactions on Mobie Computing from He is aso a member of the IEEE Press Editoria Board. Dr. Hossain has won severa research awards incuding the University of Manitoba Merit Award in 200 for Research and Schoary Activities, the 20 IEEE Communications Society Fred Eersick Prize Paper Award, and the IEEE Wireess Communications and Networking Conference 202 WCNC 2 Best Paper Award. He is a Distinguished Lecturer of the IEEE Communications Society Dr. Hossain is a registered Professiona Engineer in the province of Manitoba, Canada.