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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.

SCMA Codebook Design Based on Divided Extended Mother Codebook