  Sparse code multiple access (SCMA) is a promising technique for enabling
massive connectivity and high spectrum efficiency in future machine-type
communication networks. However, its performance crucially depends on
well-designed multi-dimensional codebooks. In this paper, we propose a novel
progressive codebook optimization scheme that can achieve near-optimal
performance over downlink fading channels. By examining the pair-wise error
probability (PEP), we first derive the symbol error rate (SER) performance of
the sparse codebook in downlink channels, which is considered as the design
criterion for codebook optimization. Then, the benchmark constellation group at
a single resource element is optimized with a sequential quadratic programming
approach. Next, we propose a constellation group reconstruction process to
assign the sub-constellations in each resource element (RE) progressively. For
the current RE, the assignment of the sub-constellations is designed by
minimizing the error performance of the product distance of the superimposed
codewords in previous REs. The design process involves both permutation and
labeling of the sub-constellations in the benchmark constellation group.
Simulation results show that the proposed codebooks exhibit significant
performance gains over state-of-the-art codebooks in the low signal-to-noise
ratio (SNR) region over various downlink fading channels.
