A Deep-Learning-Aided Message Passing Detector for MIMO SC-FDMA

In this paper, a multiple-input multiple-output (MIMO) single carrier frequency division multiple access (SC-FDMA) detector is proposed, named simplified generalized approximate message passing (Sim-GAMP), which is derived from the existing low-complexity GAMP (LC-GAMP). To improve its BER performance, Sim-GAMP is further developed by means of deep learning (DL) techniques, which is called DL-GAMP in this work. Specifically, the layers of DL-GAMP are constructed by unfolding iterations of Sim-GAMP and introducing learnable parameters, thus contributing to better BER performance. Numerical results demonstrate that DL-GAMP can mitigate the performance loss of Sim-GAMP and present good robustness in mismatched cases. Compared with state-of-the-art (SOA) MIMO SC-FDMA detectors, the proposed DL-GAMP enjoys advances in both BER performance (up to $\mathbf {0.83}$ dB gain at BER $=\mathbf {10^{-3}}$ ) and computational complexity ( $\mathbf {66.44}$ % reduction at most).