Sparse code multiple access (SCMA) is one of the competitive non-orthogonal multiple access (NOMA) techniques for the next generation communication systems. In this paper, we put forward a simple and efficient design method named divided extended mother codebook (DEMC) to construct SCMA codebooks based on golden angle modulation (GAM) constellation points. First, we generate a vector defined by the GAM. Second, we design the extended mother codebook (EMC) by introducing the power and phase dependent constraints of symbols in multi-dimension codewords. The power constraints can ensure the power of each codeword is the same which leads to the optimal peak to average power ratio (PAPR) especially for the uplink channel. Third, we divide the EMC into several mother codebooks (MCs) to generate the constant bit rate (CBR) or variable bit rate (VBR) SCMA codebooks. The structure of the VBR SCMA codebooks is compatible with that of CBR. The VBR codebooks and CBR codebooks use the same factor graph, therefore, the users employed the VBR codebooks can also utilize the efficient message passing algorithm (MPA) for multi-user detection. Simulations reveal that the bit error rate (BER) performance of the proposed CBR DEMC-SCMA codebooks is outstanding with low complexity. The VBR DEMC-SCMA codebooks can flexibly satisfy the different service requirements, and the BER performance of the VBR DEMC-SCMA codebooks is close to each other though their modulation orders are various. This feature shows that the users can apply for a high order codebook to get a faster information transfer rate without increasing transmission power and bandwidth.INDEX TERMS sparse code multiple access (SCMA), constant bit rate (CBR) codebook, variable bit rate (VBR) codebook, design of dependent multi-dimension codeword

In this study, we propose a method named decomposition of the superposed constellation (DCSC) to design sparse code multiple access (SCMA) codebooks for the additive white Gaussian noise (AWGN) channel. We prove that the power of the user symbols (USs) is accurately determined by the power of the superposed constellation (SC). Thus, we select quadrature amplitude modulation (QAM) constellations as the SC and decompose the SC into several groups of USs with power diversity. The minimum Euclidean distance (MED) between superposed symbols (SS-MED) in the receiver is determined by the selected QAM and MED between the multi-dimensional codewords (CW-MED) is optimized by matching the symbols on different dimensions. We propose a simplified DCSC (S-DCSC) by modifying the factor graph and avoiding the transmission of USs with low power, which greatly reduces the complexity of the message passing algorithm (MPA). The simulations show that the SS-MEDs of DCSC and S-DCSC are larger than those in previous papers and the BER performance of the proposed codebooks is better than others.

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