Sparse Code Multiple Access Codebook Research Articles

Interleaving based SCMA Codebook Design Using Arnold’s Cat Chaotic Map

Non-orthogonal multiple access (NOMA) technology is a significant topic of the present 5G investigation. A possible NOMA approach is Sparse Code Multiple Access (SCMA), increasing next-generation communication's ability to handle multiple users. In SCMA, codebook designing and optimization are crucial components that define the performance of multiple access systems. In this work, the complete design procedure of the SCMA codebook based on interleaving is explained and simulated. Furthermore, a chaotic interleaving based onArnold’sCat map is proposed to reduce the computational complexity. The performance of the SCMA codebook based on interleaving is evaluated through comparison with selected codebooks for SCMA multiplexing. The measures used for performance evaluation include Bit Error rate (BER), Peak to Average Power Ratio(PAPR), and minimum EuclidianDistance(MED). The results show that the proposed codebook with chaotic interleaving achieves comparable performance to the traditional codebook based on interleaving and less MED and higher BER compared to computer-generated and 16-star QAM codebook design methods but with reduced complexity.

A Design of Low-Projection SCMA Codebooks for Ultra-Low Decoding Complexity in Downlink IoT Networks

This paper conceives a novel sparse code multiple access (SCMA) codebook design which is motivated by the strong need for providing ultra-low decoding complexity and good error performance in downlink Internet-of-things (IoT) networks, in which a massive number of low-end and low-cost IoT communication devices are served. By focusing on the typical Rician fading channels, we analyze the pair-wise error probability of superimposed SCMA codewords and then deduce the design metrics for multi-dimensional constellation construction and sparse codebook optimization. For significant reduction of the decoding complexity, we advocate the key idea of projecting the multi-dimensional constellation elements to a few overlapped complex numbers in each dimension, called low projection (LP). An emerging modulation scheme, called golden angle modulation (GAM), is considered for multi-stage LP optimization, where the resultant multi-dimensional constellation is called LP-GAM. Our analysis and simulation results show the superiority of the proposed LP codebooks (LPCBs) including one-shot decoding convergence and excellent error rate performance. In particular, the proposed LPCBs lead to decoding complexity reduction by at least 97% compared to that of the conventional codebooks, whilst owning large minimum Euclidean distance. Some examples of the proposed LPCBs are available at https://github.com/ethanlq/SCMA-codebook.

Sum-Rate Maximization of IRS-Aided SCMA System

We study an intelligent reflecting surface (IRS)-aided downlink sparse code multiple access (SCMA) system for massive connectivity in future machine -type communication networks. Our objective is to maximize the system sum-rate subject to the constraint of minimum user data rate, the total power of base station, SCMA codebook structure, and IRS channel coefficients. To this end, a joint optimization problem involving IRS phase vector, factor graph matrix assignment, and power allocation problem is formulated, which is non-convex in nature. This problem is solved by developing an alternating optimization (AO) algorithm. A key idea is to first divide the formulated non-convex problem into three subproblems (i.e., factor graph matrix assignment, power allocation, and phase vector of IRS) and then tackle them iteratively. The validity of the proposed schemes is shown using the simulation results. Moreover, compared to the SCMA system without IRS, a significant performance improvement in the IRS-aided SCMA system is shown in terms of achievable sum-rate.

Intelligent Reflecting Surface-Aided Downlink SCMA

Recently, intelligent reflecting surfaces (IRSs) and nonorthogonal multiple-access (NOMA) have emerged as energy and spectrally efficient techniques for next-generation wireless networks. Thus, in this article, IRS-aided downlink sparse code multiple access (SCMA) system is analyzed for the next-generation wireless networks. In the proposed IRS-aided SCMA (IRS-SCMA), the base station (BS) communicates with single-antenna users with the help of an IRS. The impact of different phase shift methods at the IRS panel is studied in the IRS-SCMA, and observed that the average phase shift method has a very close performance to the perfect phase shift (optimal) with low complexity. We analyze symbol error rate and sum-rate performance of the IRS-SCMA. Simulation results show that the proposed IRS-SCMA outperforms the corresponding IRS-aided power domain nonorthogonal multiple access (PD-NOMA), and SCMA without IRS schemes. Further, the impacts of various system's parameters, such as the number of IRS reflecting elements, channel fading, SCMA codebooks, IRS location, and the number of users on the system performance are studied.

SCMA-Enabled Multi-Cell Edge Computing Networks: Design and Optimization

Multi-access edge computing (MEC) is regarded as a promising approach for providing resource-constrained mobile devices with computing resources through task offloading. Sparse code multiple access (SCMA) is a code-domain non-orthogonal multiple access (NOMA) scheme that can meet the demands of multi-cell MEC networks for high data transmission rates and massive connections. In this paper, we propose an optimization framework for SCMA-enabled multi-cell MEC networks. The joint resource allocation and computation offloading problem is formulated to minimize the system cost, which is defined as the weighted energy cost and latency. Due to the nonconvexity of the proposed optimization problem induced by the coupled optimization variables, we first propose an algorithm based on the block coordinate descent (BCD) method to iteratively optimize the transmit power and edge computing resources allocation by deriving closed-form solutions, and further develop an improved low-complexity simulated annealing (SA) algorithm to solve the computation offloading and multi-cell SCMA codebook allocation problem. To solve the problem of partial state observation and timely decision-making in long-term optimization environment, we put forward a multiagent deep deterministic policy gradient (MADDPG) algorithm with centralized training and distributed execution. Furthermore, we extend the framework to the partial offloading case and propose an algorithm based on alternating convex search for solving the task offloading ratio. Numerical results show that the proposed multi-cell SCMA-MEC scheme achieves lower energy consumption and system latency in comparison to the orthogonal frequency division multiple access (OFDMA) and power-domain (PD) NOMA techniques.

CG-SCMA Codebook Design Based on Maximized Euclidian Distance

Sparse code multiple access (SCMA) is a multi-dimensional codebook based on a class of non-orthogonal multiple access (NOMA) technologies enabling the delivery of non-orthogonal resource elements to numerous users in 5G wireless communications without increasing complexity. This paper proposes a computer-generated sparse code multiple access (CG-SCMA) technique, where the minimum Euclidian distance (MED) of a star 16-point quadrature amplitude modulation is maximized by CG-SCMA, thus creating a complex SCMA codebook based on optimizing the difference between the first and other radiuses over rotated constellations. To specify the most suitable values for this constellation, it is divided into four sub-constellations using trellis coded modulation (TCM) in an effort to optimize MED. The new codebook has four sub-constellations with MED values of 3.85, 2.26, 2.26, and 3.85, respectively. Application of the message passing algorithm (MPA) ensures low complexity of the decoding process.

Evaluation of Codebook Design Using SCMA Scheme Based on An and Dn Lattices

The sparse code multiple access (SCMA) scheme is a Non-Orthogonal Multiple Access (NOMA) type of scheme that is used to handle the uplink component of mobile communication in the current generation. A need of the 5G mobile network is the ability to handle more users. To accommodate this, the SCMA allows each user to deploy a variety of sub-carrier broadcasts, and several consumers may contribute to the same frequency using superposition coding. The SCMA approach, together with codebook design for each user, is used to improve channel efficiency through better management of the available spectrum. However, developing a codebook with a greater number of value sets is still another challenge. With enhanced techniques of encoding and decoding for 5G networks, mapping the multidimensional constellations in the SCMA system plays a significant role in improving the system performance and enhancing the overall system performance. The creation of a codebook utilizing the SCMA approach in conjunction with the lattice theory is suggested in this study. The prototype is shaped using a popular lattice, such as A n and D n, as the basis. Afterward, from the primary lattice constellation, the multidimensional complex mother constellation with the most noticeable variance in power is discovered. The lattice-based coding is generated by combining the codebooks with the mother constellation, and the codes in the matrices are mapped by rotating the constellations in this context. The suggested technique, in conjunction with the investigation of novel SCMA codebook sets, provides improved performance in terms of Bit Error Rate (BER) and complexity with regard to Signal to Noise Ratio (SNR). Finally, the bit error rate is reduced for various SNRs during transmission in the channel.

Design Low Complexity SCMA Codebook Using Arnold’s Cat Map

In 5G wireless communications, sparse code multiple access (SCMA) – a multi-dimensional codebook based on a specific category of the non-orthogonal multiple access (NOMA) technique - enables many users to share non-orthogonal resource components with a low level of detection complexity. The multi-dimensional SCMA (MD-SCMA) codebook design presented in this study is based on the constellation rotation and interleaving method. Initially, a subset of the lattice Z 2 is used to form the mother constellation’s initial dimension. The first dimension is then rotated to produce other dimensions. Additionally, interleaving is employed for even dimensions to enhance fading channel performance. Arnold’s chaotic cat map is proposed as the interleaving method to reduce computational complexity. Performance of the SCMA codebook based on interleaving is evaluated by comparing it with selected codebooks for SCMA multiplexing. The metrics used for performance evaluation purposes include bit error rate (BER), peak to average power ratio (PAPR), and minimum Euclidean distance (MED), as well as complexity. The results demonstrate that the suggested codebook with chaotic interleaving offers performance that is equivalent to that of the conventional codebook based on interleaving. It is characterized by lower MED and higher BER compared to computer-generated and 16-star QAM codebook design approaches, but its complexity is lower than that of the conventional codebook based on interleaving.

Sparse Code Multiple Access Scheme Based on Variational Learning

Sparse code multiple access (SCMA) technology has been widely studied thanks to its outstanding overload performance, which provides greater device access on limited time-frequency resources. We propose a variational learning based end-to-end SCMA network model termed as V-SCMA. In our model, SCMA codebooks are generated by a deep neural network (DNN) encoder. Motivated by the idea of variational learning, we derive the posterior probability of SCMA codeword send by each user from the point view of binary coding using the variational method. Then, we design an SCMA decoding network to learn this process of approaching the real posterior probability. The SCMA decoding network designed by us is a truncated recurrent neural network, which is simpler than other networks. In addition, a novel loss function is proposed to optimize V-SCMA. Compared with previous works, the new loss function is a tighter variational lower bound which improves the BER performance. Simulation results show that the proposed V-SCMA offers a better bit error rate (BER) performance and a lower computational complexity than conventional schemes.

A Joint Design of SCMA Codebook and PTS-Based PAPR Reduction for Downlink OFDM Scheme

In this paper, a joint design of sparse code multiple access (SCMA) codebook and peak-to-average power ratio (PAPR) reduction based on the partial transmit sequence (PTS) technique is proposed for the downlink orthogonal frequency division multiplexing (OFDM) scheme. A benchmark scheme is firstly devised based on a direct extension of the conventional PTS-based OFDM scheme. Based on the characteristics of the near-optimal SCMA codebook designs reported in our previous work, a PTS-based SCMA-OFDM design is proposed by carefully determining the rotation angles of the SCMA codebooks, according to the adopted signal sub-constellations. A receiver which does not need the side information is further devised. Considering the phase ambiguity issue of the receiver, the PTS angles have been carefully refined. When compared to both the original scheme that does not consider PAPR reduction techniques and the benchmark scheme, the proposed scheme achieves a significantly enhanced PAPR performance with approximately the same error performance. In addition, a comparable PAPR performance, an improved error performance, and a lower computational complexity can be achieved when compared to the clipping-based SCMA-OFDM scheme reported in the previous literature.

A Comprehensive Technique to Design SCMA Codebooks

Sparse code multiple access (SCMA) is a potential candidate for improving spectral efficiency through overloading over resources. This letter proposes a comprehensive approach to achieve near-optimal SCMA codebooks designs for 150% and 200% overloading factors under various channel environments. This approach is based on a novel diversity analysis framework presented in this letter. Following this diversity analysis for the Rayleigh fading channel, we formulate a new key performance indicator (KPI) of the average symbol error rate (SER). The SER performance of an SCMA codebook is sensitive to KPIs. Thus, a suitable selection of the KPIs can improve performance. The proposed codebook design technique involves constellation rotation and dimensional permutation to optimize the KPIs. The proposed method can yield an SCMA codebook, which works equally well for uplink (UL) and downlink (DL) Rayleigh fading channels. This aspect of the proposed method eliminates the requirement of different designs for UL and DL. The SER is calculated through extensive Monte-Carlo simulations for all the proposed codebooks (with varying factors of overloading and alphabet sizes). The proposed codebooks outperform the state-of-the-art SCMA codebooks.

A Low-Complexity Codebook Design Scheme for SCMA Systems Over an AWGN Channel

As a promising wireless access technique, sparse code multiple access (SCMA) directly maps the input bits to the transmitted multidimensional codewords according to the SCMA codebook. In general, SCMA codebook optimization and detector simplification are independent of each other. In this article, we propose a simplified SCMA codebook with a separable structure for implementing a low-complexity detector. For codebook design, a separable codebook structure is proposed to simplify the maximization of the minimum Euclidean distance (MED). With this structure, multiple one-dimensional complex codebooks corresponding to one resource element (RE) are determined by maximizing the MED of the superimposed codewords. Then, the entire codebook set is obtained based on a structure indicator matrix and the separable codebook structure. The proposed codebook has a larger MED than obtained by existing codebooks. Benefiting from the separable codebook structure, the signals transmitted over each RE can be independently used to recover the corresponding input bit information. Therefore, we propose a parallel maximum a posteriori (P-MAP) detector consisting of several low-complexity MAP detectors to reduce the complexity of the conventional multiuser message passing (MP) detector in SCMA. At the receiver, each RE is assigned a low-complexity MAP detector. Simulation results show that the proposed codebook outperforms the known optimal codebook over an AWGN channel. Moreover, the run time of the P-MAP detection algorithm is reduced by 99.8% compared to the Log-MPA algorithm. With the proposed codebook design scheme and the P-MAP detector, an SCMA unit can be separated into two independent non-SCMA units, which significantly increases system flexibility.

Adaptive Modulation SCMA Codebook Design Based on Constellation Rotation

Sparse Code Multiple Access (SCMA) is one of the competitive nonorthogonal multiple access (NOMA) techniques for the fifth-generation (5G) communication system. The SCMA codebook design is particularly important for SCMA systems. However, according to the results of our investigation of as many literature as possible, there is no research on adaptive modulation SCMA at present. Also, there is no systematic study concerning adaptive modulation SCMA codebook optimization. In this paper, an adaptive modulation SCMA transmission mechanism in different fading channels is proposed. Then, we optimize the adaptive modulation SCMA codebook design based on constellation rotation (AMSCR) for each adaptive mode including different modulation methods. The codebook optimization criterion is to maximize the minimum Euclidean distance between joint codewords. Since the space of the set of joint codewords is too large, the calculation of the minimum Euclidean distance has become an NP-hard problem. We use a genetic algorithm to solve this problem. As compared with the traditional SCMA codebook, the proposed AMSCR has better bit error rate performance in Gaussian channel and Rayleigh channel. The adaptive modulation strategy can maximize the throughput and has the best throughput performance compared with the traditional SCMA system and adaptive modulation SCMA system using traditional codebook.

Downlink SCMA Codebook Design With Low Error Rate by Maximizing Minimum Euclidean Distance of Superimposed Codewords

Sparse code multiple access (SCMA), as a codebook-based non-orthogonal multiple access (NOMA) technique, has received research attention in recent years. The codebook design problem for SCMA has also been studied to some extent since codebook choices are highly related to the system's error rate performance. In this paper, we approach the SCMA codebook design problem by formulating an optimization problem to maximize the minimum Euclidean distance (MED) of superimposed codewords under power constraints. While SCMA codebooks with a larger MED are expected to obtain a better BER performance, no optimal SCMA codebook in terms of MED maximization, to the authors' best knowledge, has been reported in the SCMA literature yet. In this paper, a new iterative algorithm based on alternating maximization with exact penalty is proposed for the MED maximization problem. The proposed algorithm, when supplied with appropriate initial points and parameters, achieves a set of codebooks of all users whose MED is larger than any previously reported results. A Lagrange dual problem is derived which provides an upper bound of MED of any set of codebooks. Even though there is still a nonzero gap between the achieved MED and the upper bound given by the dual problem, simulation results demonstrate clear advantages in error rate performances of the proposed set of codebooks over all existing ones not only in AWGN channels but also in some downlink scenarios that fit in 5G/NR applications, making it a good codebook candidate thereof. The proposed set of SCMA codebooks, however, are not shown to outperform existing ones in uplink channels or in the case where non-consecutive OFDMA subcarriers are used. The correctness and accuracy of error curves in the simulation results are further confirmed by the coincidences with the theoretical upper bounds of error rates derived for any given set of codebooks.

A Low-Complexity Codebook Optimization Scheme for Sparse Code Multiple Access

Sparse code multiple access (SCMA) is a promising non-orthogonal multiple access technique to support massive connectivity for future wireless Internet of Things (IoT) networks. As the main feature of SCMA, modulation and spread spectrum is embedded into codebook mapping, offering significant codebook shaping gains to mitigate inter-cell interference. Maximizing the constellation-constrained average mutual information (AMI) is an effective way for SCMA codebook optimization. However, deriving a closed-form expression of the AMI is analytically intractable, while it is computationally costly to estimate the AMI by numerical methods. To address this challenge, this paper first derives a lower bound of the AMI with a closed-form expression. On this basis, we propose a novel codebook optimization method referred to as joint bare bones particle swarm optimization (JBBPSO) through maximizing the AMI lower bound. The proposed low-complexity method jointly optimizes the mother codebook including basic constellation and other non-zero-dimensional constellations, and the rotation angles of multiple users. Numerical results show that our proposed optimized codebooks outperform the state-of-the-art SCMA codebooks in terms of both the lower bound and the error performance.

SCMA-Based Multiaccess Edge Computing in IoT Systems: An Energy-Efficiency and Latency Tradeoff

Sparse code multiple access (SCMA) is a kind of code-domain non-orthogonal multiple access (NOMA) scheme, which can support the increasing requirements for high spectral efficiency and massive connections. Meanwhile, multi-access edge computing (MEC) is a promising technology for providing resource-constrained users with computing resources. In this paper, we propose a novel optimization scheme in SCMA-based MEC network from the perspective of energy and latency for the Internet of Things (IoT) devices. Specifically, a system utility is first used to calculate the weighted energy consumption and task execution latency. The initial utility minimization problem is non-convex and then can be subdivided into two tractable subproblems by fixing task offloading decisions, namely, optimal local computing via CPU frequency scheduling and optimal edge computing via SCMA codebook assignment, subcarrier power allocation, and MEC server computing resources distribution. Primarily, a joint SCMA codebook assignment based on the bidirectional matching principle and optimal power allocation algorithm is proposed. Moreover, we come up with CPU frequency scheduling strategies utilizing convex optimization to optimize the computing resources allocation of local devices and the MEC server. Finally, a low-complexity task offloading policy based on simulated annealing is presented. Numerical results show that our proposed joint optimization algorithm for resource allocation and task offloading can achieve a good compromise between time delay and energy consumption for IoT devices. It is demonstrated that the proposed strategy has a remarkable advantage compared to previous SCMA-MEC schemes.

Design of Power-Imbalanced SCMA Codebook

Sparse code multiple access (SCMA) is a promising multiuser communication technique for the enabling of future massive machine-type networks. Unlike existing codebook design schemes assuming uniform power allocation, we present a novel class of SCMA codebooks which display power imbalance among different users for downlink transmission. Based on the Star-QAM mother constellation structure and with the aid of genetic algorithm, we optimize the minimum Euclidean distance (MED) and the minimum product distance (MPD) of the proposed codebooks. Numerical simulation results show that our proposed codebooks lead to significantly improved error rate performances over Gaussian channels and Rayleigh fading channels.

A Novel Scheme for the Construction of the SCMA Codebook

As a code-domain non-orthogonal multiple access technique, sparse code multiple access (SCMA) is considered as a promising technique for future wireless Internet of Things (IoT) networks. The minimum Euclidean distance (MED) and minimum product distance (MPD) have been highlighted as the key performance indicators of the codebook in additive gaussian white noise (AWGN) and downlink Rayleigh channels respectively. In this paper, based on the mother codebook, a novel codebook design scheme is proposed to achieve better error performance in both AWGN and downlink Rayleigh channels. The problem of constructing the mother codebook is considered as the quadratic assignment problem (QAP), where the Tabu searching algorithm is employed to reduce the complexity of searching for the best permutation result. Then, the rotation matrix is adopted to find the best degrees for the generation of the constellation group, and two algorithms are proposed to assign the obtained constellation in factor graph matrix. Taking the degree optimization and the constellation assignments into joint consideration, an improved unified optimization is further explored to maximize the MED of each user. Besides, a novel polarized modulation scheme is proposed, which places the symbols in the three dimensional (3D) stokes parameters to improve the performance of the system. Finally, simulation results are provided to show the performance of the proposed codebooks, and the comparisons of symbol error performance (SER) in different codebooks are also discussed in detail.

A Simplified Sphere Decoding-Based Detector for Generalized SCMA Codebooks

Sparse code multiple access (SCMA) is one of the promising schemes to meet high connectivity and spectral efficiency in the future wireless networks. The iterative detectors, for example message passing algorithm (MPA), can provide near optimal multiuser detection (MUD) performance but becomes infeasible when the codebook size is large or the overloading factor is high. Recently, sphere decoding (SD) has been considered in the MUD of SCMA by rewriting the generalized transmission into a linear system. In this work, we first review the state-of-the-art SD-based detectors for SCMA: sphere decoding for SCMA (SD-SCMA) and generalized SD-SCMA (GSD-SCMA). We not only explain the state-of-the-art in a comprehensive way, but also exploit the sorted QR decomposition and Schnorr-Euchner enumeration to accelerate the tree search. Although GSD-SCMA overcomes the codebook constraint of SD-SCMA, its computational complexity is extremely sensitive to the overloading factor. To satisfy the trade-off between complexity and MUD performance, we propose two pruning algorithms, PRUN1 and PRUN2, and introduce the simplified GSD-SCMA (SGSD-SCMA). In the paper, error probabilities of the proposed pruning algorithms are derived. Simulation results show that the proposed detector outperforms the iterative detectors and SD-based state-of-the-art when the overloading factor is moderate and the codebook size is large.

SCMA Codebook Design Based on Decomposition of the Superposed Constellation for AWGN Channel

In this study, we propose a method named decomposition of the superposed constellation (DCSC) to design sparse code multiple access (SCMA) codebooks for the additive white Gaussian noise (AWGN) channel. We prove that the power of the user symbols (USs) is accurately determined by the power of the superposed constellation (SC). Thus, we select quadrature amplitude modulation (QAM) constellations as the SC and decompose the SC into several groups of USs with power diversity. The minimum Euclidean distance (MED) between superposed symbols (SS-MED) in the receiver is determined by the selected QAM and MED between the multi-dimensional codewords (CW-MED) is optimized by matching the symbols on different dimensions. We propose a simplified DCSC (S-DCSC) by modifying the factor graph and avoiding the transmission of USs with low power, which greatly reduces the complexity of the message passing algorithm (MPA). The simulations show that the SS-MEDs of DCSC and S-DCSC are larger than those in previous papers and the BER performance of the proposed codebooks is better than others.