A Mapping Scheme of Users to SCMA Layers for D2D Communications

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1 A Mapping Scheme of Users to SCMA ayers for D2D Communications Yanping iu 1,XumingFang 1, Huali Yang 1,Xii 1,QiXiao 1, Shuangshuang An 1, Yan uo 1, Dageng Chen 2 1 Key ab of Information Coding & Transmission, Southwest Jiaotong University, Chengdu, China 2 Huawei Technologies, Co. td., Shanghai, China {liuyanping,hlyang,xiao,shuang,bk }@my.swjtu.edu.cn, {xmfang,lixi}@swjtu.edu.cn, chendageng@huawei.com Abstract Sparse code multiple access (SCMA) is a nonorthogonal multiple access scheme, which has been considered as one of the key 5G technologies to improve spectral efficiency. Moreover, device-to-device (D2D) communication is introduced as a vital technology component for 5G cellular communication system to improve spectral reuse. D2D communication combined with SCMA will be a significant part of 5G technology to support higher spectral efficiency. However, these benefits depend on efficiently allocating SCMA layers for cellular users and D2D pairs to share corresponding spectrum resources. In this paper, a mapping scheme of users to SCMA layers for D2D communication is proposed to maximize the system sum rate, in which after assigning SCMA layers to cellular users, a coalition game based scheme is proposed to obtain the solution for mapping of D2D pairs to SCMA layers. Simulation results validate the effectiveness of the proposed scheme and show that the proposed scheme outperforms other schemes, and the D2D communication combined with SCMA can obtain significant gain over the one in TE networks in terms of system sum rate. Index Terms sparse code multiple access (SCMA),device-todevice(D2D) communication, coalition game, spectral efficiency. I. INTRODUCTION In order to meet the requirements of massive connectivity, higher throughput, lower latency, better quality of service and so on, new waveform and multiple access technology should be designed [1]. Sparse code multiple access (SCMA)[2] is a multi-dimensional codebook-based non-orthogonal spreading technique, which can address the above requirements. In SCMA, the procedure of bit to QAM symbol mapping and spreading are combined together, and incoming bits are directly mapped to multi-dimensional codewords of SCMA codebook sets. Multiple access is achievable by generating multiple codebooks one for each user. In general, SCMA has the following features: i) binary domain data are directly mapped to multidimensional complex domain codewords selected from a predefined codebook set, ii)the system can be overloaded such that the number of multiplexed layers can be more than the spreading factor, iii)due to the sparse of the codewords, message passing algorithm (MPA) multi-user detection technique can be applicable to detect the multiplexed codewords with a moderate complexity, and iv) thanks to the insensitivity of codeword collision in SCMA, grant-free multiple access based on contention can be designed to decrease the access delay and overheads by utilizing blind detection technique, which is an important supplement of scheduling based access to improve the access performance of small packages and machine-type service. The current research on SCMA is very insufficient. Only a few related results are presented, which include the SCMA code book design, and the preliminary performance evaluation for uplink and downlink multiple accesses. SCMA is introduced in [2][3], where the details of the codebook design are presented. In [4], an uplink contention-based SCMA design is proposed, in which the SCMA parameters can be adjusted to provide different levels of overloading. In [5], a blind detection solution is introduced and analyzed to support massive connectivity in an SCMA-based uplink grant-free multiple access, which can blindly detect the active users or pilots with reasonable complexity and decode the active users data without the knowledge of active codebook sets. A technique is developed to enable multi-user SCMA(MU- SCMA) for downlink wireless access[6], in which user pairing, power sharing, and rate adjustment were designed to improve the downlink throughput. Inspired from [6], the performance of open-loop coordinated multipoint (CoMP) joint transmission techniques in downlink MU-SCMA is evaluated in [7]. The energy efficiency for SCMA is analyzed and a low complexity decoding algorithm is proposed in [8]. Device-to-device (D2D) communication is expected to be one of the key technologies for 5G to improve spectrum efficiency and energy-efficiency [9][10]. By introducing SC- MA, the time-frequency resources can be allocated to more cellular users and D2D pairs to improve the spectrum efficiency. Hence, D2D communication combined with SCMA is a significant part of 5G technology. However, when cellular users and D2D pairs employing the same SCMA layer share the same spectrum resource, there must be serous interference between them, if efficient interference management and resource management schemes are not available. Hence, it is necessary to develop a solution to reduce interference between the users sharing the same SCMA layers and maximize the system sum rate by reasonably mapping of cellular users and D2D pairs to SCMA layers. In this work, we formulate the optimal resource allocation problem SCMA-based D2D communication as a sum rate maximization problem. Firstly, the mapping of cellular users to SCMA layers is carried out applying greedy selection. Then, a coalitional game approach is used to assign the mapping of D2D pairs to SCMA layers. Finally, simulation results are provided to validate the effectiveness of the proposed scheme. The rest of this paper is organized as follows. Section II is devoted to introduce the system model and problem formulation of the proposed scheme. In Section III, the mapping /16/$ IEEE

2 scheme of users to SCMA layers is proposed. The simulation results and analysis are provided in Section IV. The paper finally concludes in Section V. BS CU1 II. SYSTEM MODE AND PROBEM FORMUATION A. System Model As shown in Fig. 1, a single-cell uplink cellular network with N cellular users (CUs) and D D2D pairs is considered. The base station (BS) is located at the center of the cell. The corresponding sets of cellular users and D2D pairs are denoted as Ω c = {1,..., N} and Ω d = {N +1,..., N + D}. Without loss of generality, we assume the BS and all the users are equipped with single antenna. We mainly focus on the D2D communications underlaying cellular networks where the cellular users and D2D pairs sharing the same SCMA layer will induce interference to each other. An SCMA encoder is defined as a mapping from log 2 (H) coded bits to a K-dimensional complex codebook of size H, and the elements of the selected K-dimensional complex codeword of each codebook will be further mapped into K orthogonal resources (e.g. OFDMA tones) for transmission [2]. The K- dimensional complex codewords of each codebook are sparse vectors with ( < K) non-zero entries. We assume there are M SCMA separate layers in the system, each of which is jointly determined by K orthogonal resources and the codebooks overlaid on them. That is, each SCMA layer is associated with a codebook and users data is transmitted using the codeword from the codebook over K OFDMA tones. Therefore, multiple access is achieved by sharing the same time-frequency resources among the SCMA layers. According to [2], the maximum number of codebooks J contained by an SCMA encoder is a function of the codeword length K and the number of non-zero elements in the codeword. The generation of codebooks in an SCMA is equivalent to selecting positions within K elements, that is, J = CK. The total SCMA layers of the system M = N E J, where N E is the number of SCMA encoders in the system. In Fig. 2, the mapping of users to SCMA layers is shown in the case with K =4, =2, and J =6. A cellular user or a D2D pair can be mapped to different SCMA layers to choose different codebooks for sharing the K orthogonal resources. However, users should be mapped to the SCMA layers which can minimize the interference experienced. Due to the sparsity of the SCMA codewords, multi-user detection based on message passing algorithm (MPA) can be implemented at the SCMA receiver with low complexity. Using ideal MPA receiver, codewords from different SCMA layers can be decoded without interfering with each other. Therefore, different SCMA layers can be considered as orthogonal resources. Then interference occurs only when the same SCMA layer is reused by more than one user. et h cu u,b,m,k represent the channel power gain of cellular u to the BS on OFDMA tone k of SCMA layer m, and hu,m,k d2d denote the channel power gain from the transmitting terminal of D2D pair u to its receiving terminal on OFDMA tone k of SCMA layer m. h dc u,b,m,k is the channel power gain from the transmitting terminal of D2D pair u to the BS on OFDMA tone k of SCMA layer m. h cd is the channel power gain from Fig. 1. Fig. 2. f D2DTx2 D2DRx2 System model. Tones of an SCMA layer CU n CU2 signal Mapping of users to SCMA layers. J codebooks overlaid on time-frequency resources D2DTx1 D2DRx1 interference t UEs mapping to SCMA layers celluar u to the receiving terminal of D2D pair u on OFDMA tone k of SCMA layer m. eth dd denote the channel power gain from the transmitting terminal of D2D pair u to the receiving terminal of D2D pairs u on OFDMA tone k of SCMA layer m, and σu,m 2 represents background noise power on SCMA layer m. eta u,m =1denote user u is mapped to SCMA layer m, otherwise a u,m =0. We assume each cellular user or D2D pair can only be assigned one SCMA layer, i.e., M m=1 a u,m =1 u, and the number of cellular users in an SCMA layer should not exceed one, i.e., N u=1 a u,m 1, m. Similar to [6], we assume the power of cellular u or D2D pair u is equally distributed to the effective OFDMA tones of the assigned SCMA layers. Then the interference of cellular user u at the BS is described as I cu u,m = σ 2 u,m + M u =N+1 m=1 k Θ m p u,m hdc u,b,m,k (1) where Θ m is the set of effective OFDMA tones in SCMA layer m. The interference experienced at D2D pair u which

3 reuses the SCMA layer m can be given as N M Iu,m d2d = σu,m 2 p u +,m hcd (2) + u =1 m=1 k Θ m M u =N+1,u =u m=1 k Θ m SINR cu u,m = p u,m hdd. The SINR of cellular user u at the BS is given by p u,m hcu u,b,m,k k Θ m SINR d2d u,m = I cu u,m The received SINR at D2D pair u is given by p u,m hd2d u,m,k k Θ m I d2d u,m. (3). (4) Based on Shannon s capacity formula, the achievable data rate of cellular user u in SCMA layer m can be given as Cu,m cu = B log 2 (1 + SINRu,m) cu (5) where B is the bandwidth of effective OFDMA tones in an SCMA layer. The achievable data rate of D2D pair u in SCMA layer m can be expressed as Cu,m d2d = B log 2 (1 + SINRu,m). d2d (6) B. Problem Formulation Our target is to maximize the total rate of cellular uses and D2D pairs. Thus, the corresponding problem can be formulated as max { M N M a u,m Cu,m cu + a u,m Cu,m} d2d (7) a m=1 u=1 m=1 u=n+1 s.t. C1 : N u=1 a u,m 1, m C2 : M m=1 a u,m =1 u C3 :a u,m = {0, 1}, u, m where constraint C1 represents that the number of cellular users in an SCMA layer should not exceed one. Constraint C2 and C3 are imposed to guarantee that each cellular user or D2D pair can only be assigned one SCMA layer. The above problem is a non-linear 0-1 programming problem. Therefore, it is difficult to derive the optimal solution even if a u,m is relaxed to take real value. In the following section, we will divide the problem into two subproblems to obtain the suboptimal solution and solve them one by one. III. A MAPPING SCHEME OF USERS TO SCMA AYERS FOR D2D COMMUNICATIONS To maximize the system sum rate, the cellular users and D2D pairs should be carefully grouped into the SCMA layers. In this section, the mapping of cellular users to SCMA layers is firstly presented. Then, the coalition game formulation for D2D pairs grouping into SCMA layers is proposed. Finally, we analyze the stability of the coalition game formation. A. Mapping of cellular users to SCMA layers Similar to [11], we assume the number of cellular users is less than the number of D2D pairs, i.e., N<D. In order to obtain better performance and lower complexity, the mapping of cellular users to SCMA layers is carried out firstly. et C tot be the total rate of the system. Cellular user u should be mapped to SCMA layer m to maximize the system sum rate, which is given by m = max { C tot } (8) m Ψ m where Ψ m is the set of SCMA layers in which there are no cellular users. B. Mapping of D2D pairs to SCMA layers based on coalitional game approach In this work, we formulate the mapping of D2D pairs to SCMA layers as a coalitional game with the transferable utilities, where the D2D pairs being the game players tend to form coalitions to share the SCMA layers with cellular users to improve the overall performance of the network. After the mapping of cellular users to SCMA layers, the D2D pairs choose to share the SCMA layers of the system with cellular users to improve the system sum rate. Therefore, because there are M SCMA layers in the system, D D2D pairs form M coalitions. et Ω d denote the set of D2D pairs. We denote the coalition structure as A = {A 1,A 2,..., A M }, where A m A m =, m = m, and M m=1a m =Ω d. Considering the coalition of A m A sharing the SCMA layer m with cellular user u, which has been mapped to SCMA layer m. The achievable rate of the cellular user and D2D pairs in SCMA layer m can be given by C m,c = Cu cu,m (9) C m,d = u,m (10) u A m C d2d respectively. Therefore, the sum rate of the cellular user and D2D pairs on SCMA layer m can be written as Φ(A m, A) =C m,c + C m,d. (11) We define the payoff of player u A m, which is the average data rate allocated to player u given the partition of the network is A, i.e., Φ(A m, A) Φ u (A m, A) = m A m m, u A m (12) where A m denotes the number of the cellular user and D2D pairs on SCMA layer m. For each player, it is able to leave its current coalition and join another coalition based on the received payoff. Each player must be able to compare and order its potential coalitions so that it can decide whether it should stay in its current coalition or join another coalition. Here, we introduce the concept of preference operator u for any D2D pair u Ω d as the following definition.

4 Algorithm1 Coalition formation algorithm for the mapping of D2D pairs to SCMA layers 1: Initialize the system by any random partition A ini; 2: Set the current partition as A cur A ini ; 3:repeat 4: Uniformly randomly select one D2D pair u Ω d,and denote its coalition as A m A cur; 5: Uniformly randomly select another coalition A m A cur; 6: Calculate the payoff of the selected D2D pair according to (12); 7: if A m u A m then 8: D2D pair u leaves its current coalition A m and joins the coalition A m; 9: Update the current coalition partition set as A cur (A cur {A m,a m }) {A m {u},a m {u}}; 10: endif 11: until a stable coalition partition is obtained. Definition 1: for each D2D pair u Ω d,the preference order u is defined as a complete, reflexive, and transitive binary relation over the set of all coalitions that D2D pairs u can possibly form, i.e., the set {A m Ω d,u A m }. In this coalition partitions for the mapping of D2D pairs to SCMA layers, the D2D pairs choose to leave or join in the coalitions according to their preference order. For any D2D pair u, A m u A m means that D2D pair u prefers being a member of coalition A m with u A m than A m with u A m. In this paper, for any D2D pair u A m,a m, and A m Ω d,a m Ω d, we define the preference A m u A m as follows A m u A m Φ u (A m, A) > Φ u (A m, A ). (13) This definition represents that D2D pair u prefers being a member of A m over A m when it gains an increase in its individual profit. Suppose given a coalitional structure or a partition A = {A 1,A 2,..., A m},m M of D2D pairs Ω d, we assume the current coalition of D2D pairs u is A m A. If a switch from A m to A m A { }, A m = A m is carried out, the current coalitional structure A of Ω d will be modified to a new coalitional structure A such that A =(A {A m,a m }) {A m {u},a m {u}}. Based on the coalitional structure and switch operation above, a stable coalitional structure is obtained after enough repeating switch operations, in which all the players have no incentives leave its current coalition. The detailed steps of the proposed coalition formation algorithm for the mapping of D2D pairs to SCMA layers are summarized in Algorithm1. C. Stability of the coalition formation algorithm In this subsection, we analyze the stability of the proposed coalition formation algorithm. First, the definition of Nashstable coalitional structure is given as follows. Definition 2(Nash-stable Structure): A coalitional structure A = {A 1,A 2,..., A M } is Nash-stable if u Ω d and u A m A, A m u A m {u}, A m A A m. Then, we have the following lemma. emma 1:Start from any initial coalition partition A ini,the proposed caolition formation algorithm will always converge to Nash-stable partition A fin with probability 1. Proof: In each switch operation in algorithm 1, it will either yield a new partition or stay in existing partition. The maximum number of coalitions is M because there are only M SCMA layers. Therefore, the number of partitions of a set is finite, i.e., the Bell number, and then, the sequence of switch operations will terminate with probability 1. Finally, the system will converge to a final partition A fin after finite transformations with probability 1. If the final partition A fin is not Nash-stable, there must be a D2D pair u Ω d whose coalition can be denoted as A m and another coalition A m A fin, satisfyinga m {u} u A m, then the D2D pair u isabletoperformaswitchfroma m to A m with probability 1,which contradicts the fact that A fin is the final partition. Therefore, we have proved that the final partition obtaining from algorithm 1 is Nash-stable. IV. PERFORMANCE EVAUATION In this section, simulations are conducted to evaluate the performance of the proposed scheme. We carry out the simulation in random networks, where the cellular users and D2D pairs are randomly distributed in a circle with radius of 500 m. The maximum distance between transmitting terminal of each D2D pair to its receiving terminal is 20 m. Both path loss model and shadow fading are considered, where the path loss model is log10(d[km]) and shadowing standard is 8dB. The codebooks of SCMA are designed based on the principles in [3]. The dimension of SCMA codewords is 4 with 2 non-zero elements in each codeword, and the number of SCMA layers is 6 in an SCMA encoder. The OFDMA tone is corresponding a specific subcarrier with bandwidth of 156 khz. Thermal noise spectral density is -174dBm/Hz. The transmit power of each D2D pair and cellular user are all set as 23 dbm. In Fig.3, we compare system sum rate of the proposed coalitional game (CG), greedy selection (GS) and randomly selection (RS) under various ratios of cellular user to D2D pairs, where the number of SCMA layers is 48 and the number of cellular users equals the number of SCMA layers. Randomly selection is the initial state of coalitional structure. It can be see that the sum rates of three algorithms all increase with the increasing of ratio of D2D pairs to cellular users. The reason is that the increase of the number of access users per SCMA layer resource improves the spectrum efficiency. We can also see that the proposed scheme outperforms the other two algorithms, and improves the system sum rate by about 5% compared to greedy selection and by about 45.8% compared to randomly selection in terms of the system sum rate when the ratio of the number of D2D pairs to the number of cellular users is 3. This is because the interference among the users decreases by the aid of the proposed coalitional game algorithm. Fig.4 shows the performance comparison of D2D communications in SCMA networks and in TE networks in terms of system sum rate, where the number of cellular users is equal to the number of SCMA layers in SCMA networks and the number of subcarriers in TE networks, respectively. To be fair, the ratio of the number of D2D pairs to the cellular users is the same in SCMA networks and TE networks, and here, this ratio is set as 3. We can find that the performance of D2D communications in SCMA networks outperforms the one in TE networks in terms of system sum rate by about 200%. The reason is that there are more orthogonal resources for users to access in SCMA networks than in TE networks, when there is the same number of subcarriers in the two networks.

5 System sum rate(bps) 10 x CG GS RS Ratio of the number of D2D pairs to the number of cellular users Fig. 3. System sum rate under different schemes with different ratio of the number of D2D pairs to the number of cellular users. System sum rate(bps) 2.5 x D2D communications combined with SCMA D2D communications in TE networks REFERENCES [1] Huawei Technologies Co., td. 5G: a technology vision, Shenzhen, China, Whitepaper Nov [Online]. en/download/hw [2] H.Nikopour, H.Baligh,, Sparse code multiple access, in. Proc. IEEE PIMRC, pp , Sept [3] M. Taherzadeh, H. Nikopour, A. Bayesteh, H.Baligh, SCMA codebook design, IEEE Veh. Technol. Conf.- Fall, pp.1-5, Sept [4] K. Au,. Zhang, H. Nikopour, and et al, Uplink contention based SCMA for 5G radio access, Proc.IEEE GOBECOM 2014,pp ,Dec [5] A. Bayesteh, E. Yi, H. Nikopour, H. Baligh, Blind detection of SCMA for uplink grant-free multiple-access, in.proc. IEEE ISWCS, pp , Aug [6] H. Nikopour, E. Yi, A. Bayesteh, and et al, SCMA for downlink multiple access of 5G wireless networks, Proc.IEEE GOBECOM 2014,pp , Dec [7] U. Vilaipornsawai, H. Nikopour, A. Bayesteh, et al, SCMA for Open- oop Joint Transmission CoMP, arxiv preprint arxiv: , [8] S. Zhang, X. Xu,. u, and et al, Sparse code multiple access: An energy efficient uplink approach for 5G wireless systems, Proc.IEEE GOBECOM 2014,pp , Dec [9] W. Chin, Z. Fan, R. Haines, Emerging technologies and research challenges for 5G wireless networks. IEEE Wireless Commun. Mag.,vol.21,no.2,pp , [10] S. Mumtaz, K. Huq, J. Rodriguez, Direct mobile-to-mobile communication: paradigm for 5G. IEEE Wireless Commun. Mag.,vol.21.no.5,pp.14-23, [11] Y. i, D. Jin, J. Yuan, and et al, Coalitional games for resource allocation in the device-to-device uplink underlaying cellular networks, IEEE Trans.Wireless,Commun.,vol.13,no.7,pp , Number of subcarriers in the system Fig. 4. System sum rate in SCMA and TE networks with different numbers of subcarriers. V. CONCUSION SCMA is a multi-dimensional codebook-based nonorthogonal spreading technique, which can address the requirements of massive connectivity, higher throughput, lower latency and better quality of service. The D2D communication has been proposed as a promising technology for future cellular communication systems due to its advantages in high spectrum efficiency, low energy consumption and enhanced system capacity. If efficient interference management is available, D2D communication combined with SCMA will obtain higher spectrum efficiency and higher throughput. In this paper, to maximize the system sum rate and minimize the interference between users, a mapping scheme of users to SCMA layers is proposed. Simulation results show that the proposed scheme outperforms other schemes in terms of system sum rate and the D2D communication in SCMA networks obtains higher sum rate than the D2D communication in TE networks. ACKNOWEDGMENT The work was partially supported by NSFC under Grant , and Huawei HIRP Flagship Plan under Grant YB