An Efficient SCMA Codebook Design Based on 1-D Searching Algorithm

This letter proposes an efficient sparse code multiple access (SCMA) codebook design, in which 1-D searching algorithm is introduced to minimize the upper bound of pair-wise error probability (PEP). Firstly, an SCMA signal model is given according to superposition modulation. Our analysis shows that under the proposed amplitude and phase rotation settings, each user has the same mutual information lower bound. In addition, the superimposed constellation points on each sub-channel belong to the same set, which depends on only one amplitude variable. Therefore, 1-D searching on this variable is introduced and the performance metric is upper bound of PEP. It is demonstrated that the calculated upper bound can well predict the receiver performance with maximum likelihood detection. In addition, the performance of the proposed codebook is verified with message passing algorithm at the receiver. The simulation results show that the PEP and bit error rate of the proposed codebook is better than that of the existing codebooks.