SCMA Spectral and Energy Efficiency With

SCMA Spectral and Energy Efﬁciency with QoS

Samira Jaber, and Wen Chen, Shanghai Institute of Advanced Communications and Data Sciences Department of Elecronic Engineering, Shanghai Jiao Tong University, China Email: {samira; wenchen}sjtu.edu.cn Kunlun Wang Shool of Information Sciences and Technology, ShanghaiTech University, China Email: wangkl2shanghaitech.edu.cn Qingqing Wu Department of Electrical and Computer Engineering, University of Macau, China Email: [email protected]

Abstract—Sparse code multiple access (SCMA) is one of the has sparsity in spreading sequences, which allows to use promising candidates for new radio access interface. The new a near optimal message passing algorithm (MPA) algorithm generation communication system is expected to support massive to decode. A systematic approach to optimize the SCMA user access with high capacity. However, there are numerous problems and barriers to achieve optimal performance, e.g., the codebooks has been proposed in [14] based on the design multiuser interference and high power consumption. In this pa- principles of lattice constellations. Futhermore, a resource per, we present optimization methods to enhance the spectral and allocation scheme for SCMA has been proposed in [15]. energy efficiency for SCMA with individual rate requirements. [16] evaluated the SCMA average spectral efficiency (SE) The proposed method has shown a better network mapping with adaptive codebooks based on star-QAM signaling con- matrix based on power allocation and codebook assignment. Moreover, the proposed method is compared with orthogonal stellations, while [17] tested the spectral efficiency improve- frequency division multiple access (OFDMA) and code division ment for three 5G key performance index. [18] compared the multiple access (CDMA) in terms of spectral efficiency (SE) and spectral-efficiency in SCMA system with three operational energy efficiency (EE) respectively. Simulation results show that scenarios to evaluate their SE performance. Besides, [19] SCMA performs better than OFDMA and CDMA both in SE presented 5G radio access technologies for very large number and EE. Index Terms—Spectral Efficiency, Energy Efficiency, SCMA, of links which was achieved by SCMA based on optimized QoS, Dual Method. sequence design. In addition to analysis and optimization of spectral efficiency studies, SCMA is also compared with the existing techniques [20] for the practical performances. I.INTRODUCTION It is shown that SCMA outperforms OFDMA in terms of N the history of mobile communication network devel- throughput and coverage in practical scenarios. The SCMA I opment [1], multiple access technique has evolved from area spectral efficiency for cellular network is analyzed via frequency division multiple access (FDMA), time division stochastic geometry in [21] and [22], which shows that SCMA multiple access (TDMA) and code division multiple access is a competitive technique for 5G massive access. (CDMA) to orthogonal frequency division multiple access On the other hand, the SCMA energy efficiency (EE) is (OFDMA) [2]–[4], where a fundamental cornerstone is the also extensively investigated in literatures such as [23]–[28]. orthogonality of resource block (RB). However, in the next An attempt was taken in [29] which maximize the SCMA generation of mobile communication system, the demand for rate and energy for the wireless powered communication arXiv:2004.09976v2 [eess.SP] 1 Sep 2020 massive connection, low latency, high spectral efficiency and networks. Similarly, [30] analyzes the energy efficiency for energy efficiency has become a vital necessity. Indeed, this non-orthognal multple access network by providing an ana- scenario may make a turning point from orthogonality to non- lytic framework, which is also used to derive and simulate orthogonality[5], [6]. Sparse code multiple access (SCMA) as the SCMA energy efficiency in the uplink scheme. Through a potential non-orthogonal multiple access technique is the simulation and prototype measurement, [31] investigated a key technology of the 5th generation mobile communication method to solve the EE maximization problem with sum systems (5G). It allows multiple users share the same RB and rate requirements. Since EE maximization problem is a non- offers 300% overloading number of user access links [7]–[13]. convex fractional programming problem [32], we use symbol SCMA first introduced in [7], is developed from the low transformation and utilize Dinkelbach method to transfer the density signature (LDS). In SCMA the user codeword is non-convex problem to a convex problem and derive the global mapped directly into the layer vector, while in LDS, the maximum by using an iterative method [33]–[37]. user codeword is repeated in layer vector element. Therefore In this paper, we will investigate the spectral efficiency SCMA has more diversity gain compared with LDS. SCMA and energy efficiency of SCMA with an individual rate requirement, which have not been studies before. Since it is the power resources reasonably and effectively according to diffcult to derive the analytic solution of the SE and EE the specific optimization objectives. optimization problem, we developed iterative methods to solve Set up M codebook labels. Set an SCMA codebook and the SE and EE optimization problem. Since EE maximization its associated subcarriers can be regarded as a layer of SCMA is a non-convex problem, the Dinkelbach method is used to resources. So there are N SCMA layer resources on each time- transfer the non-convex problem to a convex problem and then frequency resource. Therefore, different users obtain multiple solved by iterative method. Simulations show that the SCMA access by sharing time-frequency resources on SCMA layer. outperforms CDMA and OFDMA both in the terms of SE and The codebook size is defined by the length of the codeword EE with QoS. and the number of non-zero elements. Assume that the number of SCMA layers in a time-frequency resource block is m, II.SYSTEMMODEL and the number of subcarriers is n. Indicator variable cnm Consider a scenario of single-cell uplink in SCMA networks represents the mapping between the SCMA layer m and the K N M with users, subcarriers and codebooks, where the base subcarrier n. So if layer m occupies subcarrier n, then cnm = station (BS) and users are equipped with a single antenna. 1 otherwise 0. The sets of users and subcarriers are respectively denoted Define S = {sk,m} as SCMA layer distribution matrix, by K={1, 2, ..., K} and N={1, 2, ..., N}. SCMA codebook and where sk,m = 1 when layer m is assigned to user k, otherwise subcarriers are the basic resource units [7], [20], similar as sk,m = 0. Define P = {pk,m} as power allocation matrix. OFDMA [38],[39]. Consider overloading access, the user K is Then, the total power can be written as greater than the subcarrier N, and K/N is called overloading rate. Each user has a codebook and each codeword of size N K M tot X X in the codebook has sparsity. Let d be the non-zero element P = sk,mpk,m. (1) in a codeword. Then d N. k=1 m=1 The power ratio factor assigned to user k using subcarrier n on SCMA layer m is defined as αn,m, where 0 < αn,m < 1 PN and n=1 αn,m = 1. Then, the SNR [40], [41] of user k over layer m is

PN n=1 αn,mpk,mhk,n SNRk,m = 2 , (2) σk

where hk,n is the channel state information from user k to 2 base station on subcarrier n, σk represents the noise power to user k with white additive Gaussian noise. Therefore, the achievable rate of user k is

M X Rk = sk,m log2(1 + SNRk,m). (3) m=1

III.SCMASPECTRAL EFFICIENCY WITH QOS Fig. 1: SCMA system network block diagram. In order to maximize the network rate, we take into con- sideration the constraints of QoS (Quality of Service). Let The SCMA system network diagram with 6 users and req wk denote the weight factor, Rk be the minimum data 4 subcarriers is shown in Fig. 1. Because of the sparsity rate requirement of user k, and P max be the maximum of SCMA codeword, the receiver can use message passing transmission power of system. The optimization model can algorithm (MPA) to detect multi-user. For MPA receiver, be established as follows. codewords allocated to different layers can be regarded as K orthogonal resources, so the interference only occurs among X max wkRk, users using the same layer. P,S The SCMA uplink system, with minimum rate requirement k=1 s.t. C : R ≥ Rreq, ∀k, of all users, aims to maximize the total system rate, and 1 k k tot max establishes an optimal mathematical model for the power C2 : P ≤ P , (4) allocation and SCMA layer allocation problem. Based on the K X advocacy of green communication, it is desirable to minimize C3 : sk,m ≤ 1, ∀m, the transmission power of the system under certain communi- k=1 cation guarantees. Therefore, the power allocation scheme is C4 : sk,m ∈ {0, 1} , ∀k, m, needed. The important content of the research needs to manage C5 : pk,m ≥ 0, ∀k, m. The physical meaning of the optimization problem (4) is to where β is the iteration step size. Through iterations of (8), jointly consider SCMA layer allocation and power allocation, (11) and (12), the optimal solution of (5) can be obtained, by maximizing the network capacity. The constraint C1 guar- where one of the metric for the convergence of the iteration antees that the data rate of each user is lower-bounded for is such that maxkHk,m close to 0. This is summarized in fairness. The constraint C2 requires that the total transmis- Algorithm 1. sion power is below the maximum transmission power. The Algorithm 1 SCMA Spectrum Efficiency constraint C3 and C4 jointly ensure that each SCMA layer is allocated to one user at most. Constraint C5 is made to Initialization the multipliers λk(0) and µ(0), tolerance ; ensure that the layer allocated by the user is powered. Note Step 1: Update pˆk,m by (8), that problem (4) is a mixed integer optimization problem. Step 2: Update sˆk,m by (10) and (11), We use the Lagrange dual decomposition method to solve If max Hk,m > the optimization problem (4). Its partial Lagrange function is Then l = l + 1, goto Step 1, End If L (X, S, λ, µ) Output pˆk,m, sˆk,m. K X req max tot = [wkRk + λk(Rk − Rk )] + µ(P − P ), (5) IV. SCMA ENERGY EFFICIENCY WITH QOS k=1 In this section, to maximize the energy efficiency of the sys- where λ = {λ1, λ2, . . . , λk} and µ are Lagrange multipliers. tem, the objective function is established. Based on the quasi- Then its dual problem is convex optimization theory, the objective function is analyzed, and a joint power and SCMA layer assignment algorithm is min max L(X, S, λ, µ), ∀λ, µ ≥ 0. (6) λ,µ X,S proposed, which improves the network energy efficiency while satisfying all individual users’ QoS requirements. The total The optimal {p } can be obtained by finding the partial k,m power consumption of the SCMA system is derivative of (6) and making it equal to zero, i.e., tot ∂L P = ε0P + P0, (13) = 0. (7) ∂pk,m where the coefficient ε0 is the power amplifier factor, and P0 is the circuit power. According to (1), (2) and (3), the system Then the optimal power can be calculated as follows. energy efficiency (EE) is defined by " #+ 2 PK wk + λk σk R Rk pˆk,m = − , (8) k=1 PN ηEE = = K M . (14) µ ln 2 αn,mhk,n P P P n=1 ε0 k=1 m=1 sk,mpk,m + P0 where [x]+ = max(0, x), means that its takes x if x > 0 the Based on the system model, the energy efficiency of power- value is x and 0 otherwise. Using the derived optimal power constrained single cell multi-user networks is planned by joint pˆk,m, consider the partial derivative of L with respect to sk,m. power allocation and codebook allocation, and formulated as follows. ∂L PK = Hk,m, (9) k=1 Rk ∂sk,m max , P,S PK PM ε0 k=1 m=1 sk,mpk,m + P0 where req s.t. C1 : Rk ≥ Rk , ∀k, PN ! tot max n=1 αn,mpˆk,mhk,n C2 : P ≤ P , Hk,m = (wk + λk) log2 1 + 2 σ K (15) k X PN C3 : sk,m ≤ 1, ∀m, wk + λk n=1 αn,mpˆk,m 2 − × σk k=1 ln 2 hk,n C4 : sk,m ∈ {0, 1} , ∀k, m, N X C5 : pk,m ≥ 0, ∀k, m. + αn,mpˆk,mhk,n − µpˆk,m. (10) n=1 In the optimization problem (15), the constraint C1 guarantees Then m will be assigned to the user k• with the maximum that individual user’s rate meets its minimum rate requirement satisfying the QoS, C requires that the total transmission Hk,m, i,e., 2 power is not greater than its maximum transmission power, sˆ • = 1| • , ∀m. k ,m k =arg maxkHk,m (11) C3 and C4 ensures that each user can allocate up to one layer of SCMA resources, and lastly C ensures the power allocated Subsequently, the Lagrangian multiplier λ and µ can be 5 by users to SCMA layer is non-negative. updated by the following formulas. The optimization problem (15) is a fractional programming req + λk(l + 1) = [λk(l + 1) − β(Rk(l) − R )] , problem with combinatorial properties and belongs to non- k (12) µ(l + 1) = [µ(l + 1) − β(P max − P tot(l))]+, convex optimization problem, it is hard to directly solve this problem. In order to facilitate operation, define X = The optimal xk,m can be obtained by finding the partial {xk,m|xk,m = sk,mpk,m}. Therefore, the problem (15) can derivative of (19) and making it equal to 0, i.e., be rewritten as follows. ∂L(X, S, λ, µ) = 0. (21) ∂xk,m PK PM s log (1 + SNR ) max k=1 m=1 k,m 2 k,m , X,S PK PM ε0 k=1 m=1 xk,m + P0 This lead to M PN ! X αn,mxk,mhk,n req 2 s.t. C : s log 1 + n=1 ≥ R , (1 + λk)sk,m σksk,m 1 k,m 2 2 k x = − . σ sk,m k,m N (22) m=1 k (µ + qε ) ln P 0 2 n=1 αn,mhk,n K M X X max C2 : xk,m ≤ P , Hence the optimal power can be written as k=1 m=1 K + " 2 # X xk,m (1 + λk) σk C3 : sk,m ≤ 1, ∀m, pˆk,m = = − N . (23) sk,m (µ + qε0) ln 2 P k=1 n=1 αn,mhk,n C4 : 0 ≤ xk,m ≤ 1, ∀k, m, The partial derivative L with respect to sk,m is as follows. C5 : xk,m ≥ 0, ∀k, m. (16) ∂L(X, S, λ, µ) = Hk,m, (24) At this stage, the optimization problem (16) is still a non- ∂sk,m convex optimization problem, which needs further transformation. Assuming that the objective function of the optimization where problem (16) is q, and write PN ! n=1 αn,mpˆk,mhk,n K M Hk,m = (1 + λk) log2 1 + 2 4 X X σk F (q, sk,m, xk,m) = sk,m log2 (1 + SNRk,m) PN k=1 m=1 1 + λk n=1 αn,mpˆk,mhk,n − × − µpˆk,m. K M ! (µ + qε ) ln 2 2 PN X X 0 σk + n=1 αn,mpˆk,mhk,n − q ε0 xk,m + P0 . (17) (25) k=1 m=1 The codebook layer m should be allocated to have the maxi- If F (q, sk,m, xk,m) = 0, the optimal solution (ˆsk,m) and mum Hk,m: (ˆxk,m) of the optimization problem (16) in term of q is obtained, and q is the optimal EE. Therefore, the original sˆ • = 1| • , ∀m (26) optimization problem can be further transformed into k ,m k =arg maxk Hk,m

max F (q, sk,m, xk,m), According to the sub-gradient algorithm, the Lagrangian X,S (18) multipliers λk and µ can be updated as follows. s.t. C1,C2,C3,C4,C5 in problem (16). req + At this stage, the optimization problem (18) is a convex λk(l + 1) = [λk(l + 1) − β(Rk(l) − R )] , k (27) optimization problem, and Lagrange function is µ(l + 1) = [µ(l + 1) − β(P max − P tot(l))]+,

where β is the iteration step. Through iterations of (23), (26) K K M ! X X X and (27), the optimal solution of (19) can be obtained, where L(X, S, λ, µ) = Rk − q ε0 xk,m + P0 the metrics for the convergence of the iteration are such that k=1 k=1 m=1 maxX,S F (q, sk,m, xk,m) and maxkHk,m close to 0. This is K X req max tot summarized in Algorithm 2. + λk(Rk − Rk ) + µ(P − P ), k=1 K K Algorithm 2 SCMA Energy Efficiency X X req Initialization: The multipliers λ (0) and µ(0), the energy = Rk(1 + λk) − λkRk k k=1 k=1 efficiency q, tolerance > 0; K M Step 1: Update the power allocation pˆk,m by (23); X X tot max − qε0 xk,m − µP − qP0 + µP , (19) Step 2: Update the assignment index sˆk,m by (25) and (26); k=1 m=1 Step 3: Update q, update λk and µ by (27); If max F (q, p , x ) > , where λ = {λ , λ , ..., λ } and µ are Lagrange multipliers. k,m k,m 1 2 k Then l = l + 1; goto Step 1, Its dual problems is End If min max L(X, S, λ, µ), λ, µ ≥ 0. (20) Output the maximum EE q, sk,m and pk,m. λ,µ X,S V. SIMULATION RESULTS In this simulation section, the Algorithm 1 and the Algo- rithm 2 are simulated and compared. The simulation parameters are given in the Table 1. The following Fig. 2 and Fig. 3 respectively show a comparison of the spectral performance and energy efficiency for SCMA, CDMA, and OFDMA. It is found that SCMA perfoms better than CDMA and OFDMA both in SE and EE. TABLE I: Simulation parameters. Parameter Value Number of subcarriers 4 Number of codebooks 6 Circuit power consumption 1w R 500m h 30m Subcarrier bandwidth 156kHz SCMA layer 12 Noise power -112dBm Iteration times 100 Weight factor 1 P0 1w req Fig. 3: The EE performance for SCMA, OFDMA and CDMA. Rk 120Kbps P max 100w Power amplifier factor 1/0.37 VI.CONCLUSION This paper maximizes the spectral efficiency and the en- Fig. 2 shows that SCMA spectral efficiency outperforms ergy efficiency for SCMA network with the individual user’s both OFDMA and CDMA. Meanwhile, OFDMA had a bet- rate requirements. The formulated optimization problem is ter spactral efficiency performance comparing to CDMA at fractional programming non-convex problem. Using symbol roughly 50 BSs, where CDMA spectral efficiency remains transformation and Dinkelbach method, the original problem stable; hence, OFDMA supports higher modulation and coding is transformed into convex problems, and solved by Lagrange leading to a better spectral efficiency, enhancement of reacha- dual decomposition method. The proposed algorithms are bility and provides a significant improvement in spectral usage simulated to compare with CDMA and OFDMA. It is found comparing to CDMA tehcnology performance. that the SCMA performs better than CDMA and OFDMA Fig. 3 illustrates a significant decrease of OFDMA energy both in SE and EE, since the proposed method has shown a efficiency when the number of users increases due to the high better network mapping matrix based on power allocation and level consumption of the power; while SCMA proves a better codebook assignment. In perspective, the continuity of this energy efficiency achievement. paper will discuss the impact of the number of subcarriers and SCMA layers in the system as well as its feasibility and expertise.

ACKNOWLEDGMENT This paper is supported in part by National Key Project 2018YFB1801102, and in part by NSFC 61671294.

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