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.