Trainable Projected Gradient Detector for Sparsely Spread Code Division Multiple Access

Abstract

Sparsely spread code division multiple access (SCDMA) is a promising non-orthogonal multiple access technique for future wireless communications. In this paper, we propose a novel trainable multiuser detector called sparse trainable projected gradient (STPG) detector, which is based on the notion of deep unfolding. In the STPG detector, trainable parameters are embedded to a projected gradient descent algorithm, which can be trained by standard deep learning techniques such as back propagation and stochastic gradient descent. Advantages of the detector are its low computational cost and small number of trainable parameters, which enables us to treat massive SCDMA systems. In particular, its computational cost is smaller than a conventional belief propagation (BP) detector while the STPG detector exhibits nearly same detection performance with a BP detector. We also propose a scalable joint learning of signature sequences and the STPG detector for signature design. Numerical results show that the joint learning improves multiuser detection performance particular in the low SNR regime.

Deep-Unfolded Sparse CDMA: Multiuser Detector and Sparse Signature Design

“…Inspired by the notion of deep unfolding, the authors [1] proposed a trainable multiuser detector for SCDMA systems with binary phase shift keying (BPSK) modulation. The proposed sparse trainable projected gradient (STPG) detector requires less computational complexity than a standard BP detector, whereas it achieves almost the same detection performance as the BP detector.…”

“…We first propose a deepunfolded multiuser detector suitable for SCDMA systems with higher-order modulations such as 8PSK. The proposed detector, called a complex sparse trainable projected gradient (C-STPG) detector, is a non-trivial extension of an STPG detector [1] to the complex field. The use of a complex MMSE function matched to the signal constellation plays a crucial role in this extension.…”

“…The second half of this paper is devoted to describing a sparse signature design through a deep unfolding. Another contribution of [1] is to clarify the potential of the deepunfolding approach for a sparse signature design. In a nutshell, the idea is as follows.…”

“…A signature sequence matrix is treated as trainable parameters, and an unfolded graph including the signature matrix is used for training these trainable parameters. It is experimentally shown that such a joint learning strategy for sparse signature sequences and the STPG detector is effective [1]. However, the training process shown in [1] exploits a projection onto a sparse binary matrix, that is, a support matrix to sparsify the signature matrix.…”

“…It is experimentally shown that such a joint learning strategy for sparse signature sequences and the STPG detector is effective [1]. However, the training process shown in [1] exploits a projection onto a sparse binary matrix, that is, a support matrix to sparsify the signature matrix. The detection performance depends heavily on the support matrix, and an appropriate support matrix cannot be easily obtained, which is an unsolved drawback of the joint learning strategy in [1].…”