Construction of Hopped-Sparse Code Multiple Access Codebooks Based on Chaotic Bernoulli Frequency-Hopping Sequence

Traditional sparse code multiple access (SCMA) systems, which transmit user codewords through fixed subcarrier allocations, exhibit vulnerability to external jamming and interference. To address this challenge, we propose a novel SCMA codebook design incorporating the frequency-hopping (FH) technique in this paper. The construction of FH-SCMA codebooks is developed by applying cyclic shifting operations to the factor graph matrix of the conventional SCMA codebooks, where the cyclic shifting patterns are governed by chaotic Bernoulli FH sequences. Through a comprehensive case study, the critical properties of the proposed FH-SCMA codebooks—the uniformity and the sparsity, along with its error-rate performance—are illustrated in detail. Through the proposed FH-SCMA codebooks, the subcarriers of FH-SCMA are randomly hopped over within the resource-block group, while retaining the sparsity requirement, thereby facilitating the multi-user detection at the receiver. The proposed FH-SCMA system (codebooks) achieves superior performance under jamming scenarios compared to both the traditional SCMA and the previous pseudo-random FH-SCMA.