Sparse Code Multiple Access Detection Research Articles

A Knowledge-Based Deep Learning Detection Scheme for Downlink SCMA Systems

Sparse code multiple access (SCMA) is a promising code-domain non-orthogonal multiple access technology for future wireless communication systems. In the SCMA detector, deep learning (DL) technology has been adopted to improve the detection efficiency. However, most previous schemes are completely data-driven designed without using prior knowledge. In this letter, we propose a knowledge-based deep learning detection scheme (K-DLD) that incorporates prior knowledge into SCMA detection to lighten the neural network. Moreover, we propose to use a thinner but deeper network to further reduce the model complexity. Simulation results show that the proposed schemes significantly reduce the computation time without any performance loss.

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.

An Ultra-Reliable Low-Latency Non-Binary Polar Coded SCMA Scheme

The joint transmission scheme of polar codes and sparse code multiple access (SCMA) has been regarded as a promising technology for future wireless communication systems. However, most of the existing polar-coded SCMA (PC-SCMA) systems suffer from high latency caused by the feedback iteration and list decoding. In addition, the error performance of PC-SCMA systems is unsatisfactory for ultra-reliable transmission. Inspired by the compelling benefits of non-binary polar codes, in this paper, we design a non-binary polar-coded SCMA (NB-PC-SCMA) system with a free order matching strategy to address the issues of delay and reliability. Specifically, we first formulate a joint factor graph for NB-PC-SCMA and propose a non-binary successive cancellation list (NB-SCL) and damping based joint iterative detection and decoding (NSD-JIDD) multiuser receiver to improve the BER and latency performance. Then, a lazy-search based NB-SCL (L-NB-SCL) decoding is proposed to reduce the computational complexity by simplifying the path search pattern of the list decoder. After that, we modify the update of user nodes for SCMA detection to improve the convergence error and finally propose the improved NSD-JIDD (ISD-JIDD) algorithm, which can avoid redundant operations by exploiting L-NB-SCL decoding. Simulation results show that the proposed NB-PC-SCMA system achieves better bit error rate (BER) performance and considerable latency gain when compared to its counterparts. In particular, the proposed ISD-JIDD can achieve similar BER performance of NSD-JIDD with less complexity.

Comparative Analytical Study of SCMA Detection Methods for PA Nonlinearity Mitigation.

Non-orthogonal multiple access (NOMA) has emerged as a promising technology that allows for multiplexing several users over limited time-frequency resources. Among existing NOMA methods, sparse code multiple access (SCMA) is especially attractive; not only for its coding gain using suitable codebook design methodologies, but also for the guarantee of optimal detection using message passing algorithm (MPA). Despite SCMA’s benefits, the bit error rate (BER) performance of SCMA systems is known to degrade due to nonlinear power amplifiers at the transmitter. To mitigate this degradation, two types of detectors have recently emerged, namely, the Bussgang-based approaches and the reproducing kernel Hilbert space (RKHS)-based approaches. This paper presents analytical results on the error-floor of the Bussgang-based MPA, and compares it with a universally optimal RKHS-based MPA using random Fourier features (RFF). Although the Bussgang-based MPA is computationally simpler, it attains a higher BER floor compared to its RKHS-based counterpart. This error floor and the BER’s performance gap are quantified analytically and validated via computer simulations.

Deep Neural Network Aided Low-Complexity MPA Receivers for Uplink SCMA Systems

Sparse code multiple access (SCMA) has exhibited superiority in spectrum efficiency, which is particularly essential in the Internet of Things (IoT) system where a steadily increasing number of device connections are accommodated. However, the computational complexity of the conventional message passing algorithm (MPA) for the multiuser SCMA detection increases exponentially with the degree of resource nodes (RNs). To address this issue, two low complexity MPA schemes are proposed by utilizing the sparse feature of codewords. First, a sorted MPA (SMPA) detector is introduced to reduce the message exchanging from RNs to variable nodes (VNs) by dropping the redundant superposed constellation points outside a belief interval. Next, in order to further speed up the sorting process of the Euclidean distances between the received signal and codeword combinations, a deep neural network aided MPA (DNNMPA) is proposed, in which, the DNN behaves as a function approximator to generate the belief interval and operates in parallel with the initialization procedure before iterative message passing. Simulation results illustrate that the proposed SMPA and DNNMPA detectors significantly reduce the computational complexity of the conventional MPA one, but with comparable decoding capabilities, for the uplink SCMA system.

OTFS-SCMA: A Code-Domain NOMA Approach for Orthogonal Time Frequency Space Modulation

Orthogonal time frequency space (OTFS) modulation is a two-dimensional (2-D) modulation technique that has the potential to overcome the challenges faced by orthogonal frequency division multiplexing (OFDM) in high Doppler environments. The performance of OTFS in a multi-user scenario with orthogonal multiple access (OMA) techniques has been impressive. Due to the requirement of massive connectivity in 5G and beyond, it is essential to devise and examine the OTFS system with the existing non-orthogonal multiple access (NOMA) techniques. This paper proposes a multi-user OTFS system based on a code-domain NOMA technique called sparse code multiple access (SCMA). This system is referred to as the OTFS-SCMA model. The framework for OTFS-SCMA is designed for both downlink and uplink. First, the sparse SCMA codewords are strategically placed on the delay-Doppler plane. The overall overloading factor of the OTFS-SCMA system is equal to that of the underlying basic SCMA system. The receiver in downlink performs the detection in two sequential phases: first, the conventional OTFS detection using the method of linear minimum mean square error (LMMSE) estimation, and then the SCMA detection. We propose a single-phase detector based on a message-passing algorithm (MPA) to detect multiple users’ symbols for the uplink. The expressions for the asymptotic diversity orders of the proposed OTFS-SCMA system are derived for downlink and uplink. OTFS-SCMA provides a significant diversity gain over other multiple access systems for OTFS. Based on the diversity analysis, an algorithm is proposed to devise an optimal codeword allocation scheme. The performance of the proposed OTFS-SCMA system is validated through extensive simulations both in downlink and uplink. We consider delay-Doppler planes of different parameters and various SCMA systems of overloading factor up to 200%. The performance of OTFS-SCMA is compared with those of the existing OTFS-OMA, OFDM-SCMA and OTFS-power-domain (PD)-NOMA techniques. The analysis of OTFS-SCMA with channel estimation is also presented along with the BER performance.

Low-Complexity SCMA Detection for Unsupervised User Access

Non-orthogonal multiple access schemes (NOMA), such as sparse code multiple access (SCMA), are among the most promising technologies to support massive numbers of connected devices. Still, to minimize the transmission delay and to maximize the utilization of the transmission channel, “grant-free” NOMA techniques are required that eliminate any prior information exchange between the users and the base-stations. However, if a large number of users transmit simultaneously in an “unsupervised” manner, (i.e., without any prior signaling for controlling the number of users and the corresponding transmission patterns), it is likely that a large number of users may share the same frequency-resource element, rendering the corresponding user detection impractical. In this context, we present a new multi-user detection approach, which aims to maximize the detection performance, with respect to given processing and latency limitations. We show that our approach enables practical detection for grant-free SCMA schemes that support hundreds of interfering users, with a complexity that is up to two orders of magnitude less than that of conventional detection approaches.

Joint Channel Estimation and Decoding for Polar Coded SCMA System Over Fading Channels

Sparse code multiple access (SCMA) and polar codes are key techniques for 5G systems. Towards to the realization of massive machine type communications (mMTC) in Internet of Things (IoT), we propose a joint channel estimation and decoding (JCD) scheme to enhance the performance of polar coded SCMA system. There are three parts in our JCD scheme. First, a sparse Bayesian learning (SBL) algorithm is proposed to measure the initial channel state information (CSI) for the JCD scheme. Then, the JCD receiver performs an iterative channel estimation and detection and decoding (ICED) scheme between the SCMA detector and the polar decoder, where the log-likelihood ratio (LLR) from SCMA detector and polar decoder can iteratively update, and the channel gain is also adjusted by the frozen bit error rate (FBER) from the polar decoder in each ICED iteration. In addition, we propose a soft successive cancellation list (soft-SCL) decoding algorithm by calculating the path metric from an LLR based logarithm method, then the soft-SCL decoder outputs the LLR information and the SCMA detector can update the symbol probability in this ICED scheme. Simulation results demonstrate the superior performance of our JCD scheme over fading channels.

A Novel SD-Based Detection for Generalized SCMA Constellations

Sphere decoding (SD) based detection schemes for sparse code multiple access (SCMA) systems have recently received attention due to their promising features. However, the existing SD-based schemes can only be applied to SCMA systems with constellations that possess a certain structure. In this paper, we propose a novel SD-based detection scheme, namely improved SD (ISD), for SCMA that achieves the optimal maximum likelihood detector for any arbitrary regular or irregular constellations. To overcome the rank deficiency problem of the SCMA channel matrix, we fix a portion of the transmitted symbols and obtain an optimal detection problem that is equivalent to the original SCMA detection problem for all types of constellations. Moreover, due to the sparse nature of SCMA, the partial metric at each layer is evaluated in such a way that is independent of users assigned to each resource element. This, in turn, reduces the average complexity of ISD.

An LDPC-Coded SCMA Receiver With Multi-User Iterative Detection and Decoding

This paper presents the first low-complexity realization of an LDPC-code sparse code multiple access (SCMA) receiver with a high-throughput LDPC decoder and a multi-mode SCMA detector. The minimum mean-square error with parallel interference cancellation (MMSE-PIC) algorithm is adopted in the SCMA detection. The modified user-node operations in the MMSE-PIC-based message-passing detector improve the convergence rate in error performance. The proposed receiver also supports multi-user iterative detection and decoding (MU-IDD) to improve the error rate performance. The proposed receiver supports both $4\times 6$ and $8\times 12$ SCMA systems. The proposed MU LDPC decoder has a 57.1% lower hardware complexity than the direct-mapped design that is achieved through hardware sharing and memory access scheduling. Designed in a 40-nm CMOS technology, the SCMA receiver integrates 10.9M logic gates in an area of $3.382\times 3.382$ mm2. The proposed design achieves a gross throughput of 1.198 Gb/s and 599 Mb/s for $8\times 12$ and $4\times 6$ SCMA systems, respectively, under a practical situation. It dissipates 813 mW at a clock frequency of 300 MHz from a 0.9-V supply.

A Low-Complexity Energy-Minimization-Based SCMA Detector and Its Convergence Analysis

Sparse code multiple access (SCMA) has emerged as a promising non-orthogonal multiple access technique for the next-generation wireless communication systems. Since the signal of multiple users is mapped to the same resources in SCMA, its detection imposes a higher complexity than that of the orthogonal schemes, where each resource slot is dedicated to a single user. In this paper, we propose a low-complexity receiver for SCMA systems based on the radical variational free energy framework. By exploiting the pairwise structure of the likelihood function, the Bethe approximation is utilized for estimating the data symbols. The complexity of the proposed algorithm only increases linearly with the number of users, which is much lower than that of the maximum a posteriori detector associated with exponentially increased complexity. Furthermore, the convergence of the proposed algorithm is analyzed, and its convergence conditions are derived. Simulation results demonstrate that the proposed receiver is capable of approaching the error probability performance of the conventional message-passing-based receiver.

Modified Sphere Decoding for Sparse Code Multiple Access

Sparse code multiple access (SCMA), a novel non-orthogonal multiple access scheme for fifth generation wireless, has drawn much attention. Since optimal SCMA detection incurs high computational complexity, we develop a modified single tree search (MSTS) to obtain soft outputs for coded SCMA. The MSTS algorithm incorporates the sorting of the channel matrix and computing a non-zero low bound before searching in order to reduce complexity during the search stage. The simulation results show that MSTS not only has lower computational complexity than detectors based on the message passing algorithm (MPA) and repeat tree search but also keeps its performance level close to that of MPA.

A Low-Complexity SCMA Detector Based on Discretization

As a new multiple access technique, sparse code multiple access (SCMA) combines quadrature amplitude modulation mapper and spreading together and thus significantly improves spectral efficiency. However, the computation complexity of most existing detection algorithms increases exponentially with $d_{f}$ (the degree of the resource nodes). The parameter $d_{f}$ must be designed to be very small, which largely limits the choice of codebooks. Even if the codebooks are designed to have low density, the detection still takes considerable time. In this paper, a new detection algorithm is proposed by discretizing the probability density functions (PDFs) in the layer nodes. Actually, the PDFs are updated according to the constraints in the factor graph after discretization. Compared with the conventional message passing algorithm (MPA) detector, the proposed detector only takes polynomial time to update one message in resource nodes instead of exponential time with negligible performance loss. In particular, it only needs near-linear time, if the real part is independent with the imaginary part in SCMA system. Furthermore, this paper presents a new design for codebooks by greedy strategy and exhaustive search in each step. The search is feasible with the help of discretization, and the resulting codebooks have good performance in the proposed detection algorithm, as well as in the conventional MPA.

A Low Complexity Sparse Code Multiple Access Detector Based on Stochastic Computing

Sparse code multiple access (SCMA) is a promising multiple access technology candidate for the next-generation communication system, which can dramatically improve spectral efficiency. However, the major challenge of SCMA is the very high detection complexity. Stochastic computing is a new number representation, which can carry out complex computations with very simple logics. In this paper, we extend the application of stochastic computing to SCMA detection and propose a low complexity stochastic SCMA detector. We also design three novel stochastic logic architectures: a new low hardware cost bit stream generation architecture, a low hardware cost stochastic function node update architecture and a fast converging stochastic variable node update architecture. Analysis and simulation results show that the proposed stochastic SCMA detector saves 69% complexity compared with the traditional SCMA detectors with a comparable bit error rate performance. The synthesis results with SIMC 65-nm CMOS technology show that the proposed stochastic SCMA detector achieves 640 Mbps total system throughput with only 1.45-mm $^{{{2}}}$ cell area.

Sub-Graph Based Joint Sparse Graph for Sparse Code Multiple Access Systems

Sparse code multiple access (SCMA) is a promising air interface candidate technique for next-generation mobile networks, especially for massive machine-type communications. In this paper, we design a low-density parity-check (LDPC) coded SCMA detector by combining the sparse graphs of LDPC and SCMA into one joint sparse graph (JSG). In our proposed scheme, the SCMA sparse graph defined by small size indicator matrix is utilized to construct the JSG, which is termed as sub-graph-based JSG of SCMA (SG-JSG-SCMA). In this paper, we first study the binary-LDPC coded SG-JSG-SCMA system. To combine the SCMA variable node and LDPC variable node into one joint variable node, a non-binary LDPC (NB-LDPC) coded SG-JSG-SCMA is also proposed. Furthermore, to reduce the complexity of NB-LDPC coded SG-JSG-SCMA, a joint trellis representation (JTR) is introduced to represent the search space of NB-LDPC coded SG-JSG-SCMA. Based on JTR, a low complexity joint trellis-based detection and decoding algorithm is proposed to reduce the computational complexity of the NB-LDPC coded SG-JSG-SCMA system. According to the simulation results, SG-JSG-SCMA brings significant performance improvement compare with the conventional receiver using the disjoint approach, and it can also outperform a turbo-structured receiver with comparable complexity. Moreover, the joint approach also has advantages in terms of processing latency compare with the turbo approaches.

Improved Message Passing Algorithms for Sparse Code Multiple Access

Sparse code multiple access (SCMA) is one of the nonorthogonal multiple access techniques for the 5G system. SCMA can provide different levels of overloading to meet the diverse traffic connectivity requirements. However, its relatively high computational complexity of multiuser detection is still a significant concern for practical implementation, even when the sparse structure has already been employed. In this paper, a design framework for an improved SCMA multiuser detector is proposed based on the message passing algorithm (MPA). As the primary SCMA detector, two aspects of MPA are simplified and optimized. First, we introduce a lookup table (LUT) scheme to reduce the computational complexity of the ${\max }^*$ operation in the MPA. In contrast to the extensive Jacobian approximation, the proposed LUT method can guarantee the stable convergence of the MPA for SCMA. Second, a series of novel scheduling schemes are proposed to speed up the convergence. A single scheduling MPA (SS-MPA) method is given to enhance the convergence performance of MPA, where the soft messages in the function nodes and variable nodes are serially calculated and synchronously updated. To further improve the throughput of the MPA, a multiple scheduling MPA (MS-MPA) is proposed. In this method, multiple detectors are used to calculate in parallel and update the node messages by different orders. Since the scheduling strategies of message update are optimized, both the SS-MPA and MS-MPA can converge more quickly than the conventional MPA. Theoretical analyses and simulation results regarding the error performance and convergence properties of the above schemes are included.