Sparse code multiple access (SCMA) is a multi-dimensional codebook based on a class of non-orthogonal multiple access (NOMA) technologies enabling the delivery of non-orthogonal resource elements to numerous users in 5G wireless communications without increasing complexity. This paper proposes a computer-generated sparse code multiple access (CG-SCMA) technique, where the minimum Euclidian distance (MED) of a star 16-point quadrature amplitude modulation is maximized by CG-SCMA, thus creating a complex SCMA codebook based on optimizing the difference between the first and other radiuses over rotated constellations. To specify the most suitable values for this constellation, it is divided into four sub-constellations using trellis coded modulation (TCM) in an effort to optimize MED. The new codebook has four sub-constellations with MED values of 3.85, 2.26, 2.26, and 3.85, respectively. Application of the message passing algorithm (MPA) ensures low complexity of the decoding process.

In 5G wireless communications, sparse code multiple access (SCMA) – a multi-dimensional codebook based on a specific category of the non-orthogonal multiple access (NOMA) technique - enables many users to share non-orthogonal resource components with a low level of detection complexity. The multi-dimensional SCMA (MD-SCMA) codebook design presented in this study is based on the constellation rotation and interleaving method. Initially, a subset of the lattice Z 2 is used to form the mother constellation’s initial dimension. The first dimension is then rotated to produce other dimensions. Additionally, interleaving is employed for even dimensions to enhance fading channel performance. Arnold’s chaotic cat map is proposed as the interleaving method to reduce computational complexity. Performance of the SCMA codebook based on interleaving is evaluated by comparing it with selected codebooks for SCMA multiplexing. The metrics used for performance evaluation purposes include bit error rate (BER), peak to average power ratio (PAPR), and minimum Euclidean distance (MED), as well as complexity. The results demonstrate that the suggested codebook with chaotic interleaving offers performance that is equivalent to that of the conventional codebook based on interleaving. It is characterized by lower MED and higher BER compared to computer-generated and 16-star QAM codebook design approaches, but its complexity is lower than that of the conventional codebook based on interleaving.