Joint Gaussian Approximation Message Passing Assisted Detection for Uplink AFDM-SCMA Systems

The integration of affine frequency division multiplexing (AFDM) and sparse code multiple access (SCMA), termed AFDM-SCMA, has emerged as a promising solution to support massive connectivity in high-mobility scenarios. However, in uplink channels, the intertwined delay-Doppler interference and multi-user interference make the multi-user detection more challenging. The computational complexity of the generalized message passing (MP) algorithm increases significantly due to the coupled delay-Doppler interference and multi-user interference. To address these issues, we propose a low-complexity joint Gaussian approximation message passing (GA-MP) assisted detection scheme. Leveraging the sparsity of the joint effective channel matrix, we establish a joint factor graph that represents SCMA codewords as variable nodes and the received signals on AFDM subcarriers as observation nodes. The vector-wise products of these codewords with the channel-coefficient vectors are treated as aggregate interference and approximated by a Gaussian distribution. Simulation results demonstrate that, compared to the generalized MP detection scheme, the proposed joint GA-MP assisted detection scheme achieves substantial computational complexity reduction with only a slight bit error rate (BER) performance degradation.