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.

Matrix inference and estimation in multi-layer models*

We consider the problem of estimating the input and hidden variables of a stochastic multi-layer neural network (NN) from an observation of the output. The hidden variables in each layer are represented as matrices with statistical interactions along both rows as well as columns. This problem applies to matrix imputation, signal recovery via deep generative prior models, multi-task and mixed regression, and learning certain classes of two-layer NNs. We extend a recently-developed algorithm—multi-layer vector approximate message passing, for this matrix-valued inference problem. It is shown that the performance of the proposed multi-layer matrix vector approximate message passing algorithm can be exactly predicted in a certain random large-system limit, where the dimensions N × d of the unknown quantities grow as N → ∞ with d fixed. In the two-layer neural-network learning problem, this scaling corresponds to the case where the number of input features as well as training samples grow to infinity but the number of hidden nodes stays fixed. The analysis enables a precise prediction of the parameter and test error of the learning.

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.

Optimal Combination of Linear and Spectral Estimators for Generalized Linear Models

We study the problem of recovering an unknown signal $${\varvec{x}}$$ x given measurements obtained from a generalized linear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and a spectral estimator $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s . The former is a data-dependent linear combination of the columns of the measurement matrix, and its analysis is quite simple. The latter is the principal eigenvector of a data-dependent matrix, and a recent line of work has studied its performance. In this paper, we show how to optimally combine $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s . At the heart of our analysis is the exact characterization of the empirical joint distribution of $$({\varvec{x}}, \hat{\varvec{x}}^\mathrm{L}, \hat{\varvec{x}}^\mathrm{s})$$ ( x , x ^ L , x ^ s ) in the high-dimensional limit. This allows us to compute the Bayes-optimal combination of $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s , given the limiting distribution of the signal $${\varvec{x}}$$ x . When the distribution of the signal is Gaussian, then the Bayes-optimal combination has the form $$\theta \hat{\varvec{x}}^\mathrm{L}+\hat{\varvec{x}}^\mathrm{s}$$ θ x ^ L + x ^ s and we derive the optimal combination coefficient. In order to establish the limiting distribution of $$({\varvec{x}}, \hat{\varvec{x}}^\mathrm{L}, \hat{\varvec{x}}^\mathrm{s})$$ ( x , x ^ L , x ^ s ) , we design and analyze an approximate message passing algorithm whose iterates give $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and approach $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s . Numerical simulations demonstrate the improvement of the proposed combination with respect to the two methods considered separately.

A Low-Complexity and High-Decoding Performance Scheme for the MIMO-SCMA System

Sparse code multiple access (SCMA) has been proposed to obtain high capacity and support massive connections. When combined with the multiple-input multiple-output (MIMO) techniques, the spectrum efficiency of the SCMA system can be further improved. However, the detectors of the MIMO-SCMA system have high computational complexity. For the maximum likelihood (ML) detection, though it is optimal decoding algorithm for the MIMO-SCMA system, the detection complexity would grow exponentially with the number of both the antennas and users increase. In this paper, we consider a space-time block code (STBC) based MIMO-SCMA system where SCMA is used for multiuser access. Besides, we propose a low-complexity utilizing joint message passing algorithm (JMPA) detection, which narrowing the range of superimposed constellation points, called joint message passing algorithm based on sphere decoding (S-JMPA). But for the S-JMPA detector, the augment of the amount of access users and antennas leads to the degradation of decoding performance, the STBC is constructed to compensate the performance loss of the S-JMPA detector and ensure good bit error rate (BER) performance. The simulation results show that the proposed method achieves a close error rate performance to ML, JMPA, and a fast convergence rate. Moreover, compared to the ML detector, it also significantly reduces the detection complexity of the algorithms.