An Uplink SCMA Codebook Design Combining Probabilistic Shaping and Geometric Shaping

Sparse Code Multiple Access (SCMA) is a promising non-orthogonal multiple access scheme owning to the shaping gain of its multi-dimensional codebook. Most of the existing designs of the codebook are based on geometric shaping (GS), while probabilistic shaping (PS) has important advantages in increasing channel capacity and reducing bit error rate. In this paper, an uplink SCMA codebook optimization algorithm which combines PS and GS is proposed. The algorithm adopts the bare bones particle swarm optimization algorithm based on maximizing the AMI. Based on the non-equiprobable codebook, a message passing algorithm with non-equalprobable distribution is introduced as the multiuser detection algorithm for SCMA scheme. We theoretically analyze the superiority of the codebooks combining PS and GS over others in terms of the average mutual information (AMI). Simulation results show that our proposed codebooks outperform the reference GS based codebooks under different overloading, different channels and different codebook sizes, and with the increase of overloading or codebook sizes, the gains are greater, which is up to 2.1dB gain in terms of block error rate performance. This observation also validates the theoretical analysis based on the AMI.