An optimized design of a sparse code multiple access (SCMA) codebook for uplink wireless communications is presented by dividing an optimized 16-point round quadrature amplitude modulation (QAM) into several subsets. The main goal of the scheme is to maximize the minimum Euclidean distance and thus reduces the collisions of the information bits on the resources. The final SCMA codebook is obtained with the mapping matrix, which indicates the sub-constellations generating by dividing the mother QAM constellation. Simulation results show that, in a Nakagami fading channel, the optimized SCMA scheme by the proposed design method achieves significantly performance gains approximately 1.0, 1.4, 2.5, 3.5, and 4.0 dB at bit error rate of $10^{-4}$ , respectively, when compared with those of an undivided 16-QAM constellation, a trellis code modulation (TCM) division, an original SCMA codebooks, a low-density signature (LDS), and an irregular LDS (IrLDS) schemes. In addition, at the signal-to-noise ratio ranging from 0 to 10 dB, the constellation constrained capacity of the scheme by the proposed method achieves more gains over those of the original SCMA, TCM, the undivided star-QAM, the LDS, and the IrLDS schemes. Thus, it can be combined with the grant-free random access mechanism to obtain rapid and low-cost access in next-generation wireless packet services and other applications.
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