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.

翻译：稀疏码多址接入（SCMA）是未来机器类通信网络中实现大规模连接和高频谱效率的一项有前景的技术。然而，其性能关键依赖于精心设计的多维码本。本文提出了一种新颖的渐进式码本优化方案，可在下行衰落信道上实现接近最优的性能。通过分析成对错误概率（PEP），我们首先推导了下行信道中稀疏码本的符号错误率（SER）性能，并将其作为码本优化的设计准则。然后，采用序列二次规划方法优化单个资源元素（RE）上的基准星座组。接下来，我们提出一种星座组重构过程，以逐步为每个资源元素分配子星座。对于当前资源元素，子星座的分配通过最小化先前资源元素中叠加码字的乘积距离的误差性能来设计。该设计过程同时涉及基准星座组中子星座的排列和标记。仿真结果表明，在各种下行衰落信道的低信噪比（SNR）区域，所提出的码本相较于现有最优码本展现出显著的性能增益。