Soft-Output Deep LAS Detection for Coded MIMO Systems: A Learning-Aided LLR Approximation

The multiple-input-multiple-output-orthogonal frequency division multiplexing (MIMO-OFDM) receiver aims to softly decode the transmitted information from the observed received signal. However, soft-output detection requires additional computation and leads to higher overall detection complexity in high-dimensional MIMO and higher-order modulation. Therefore, accurate and low-complexity soft-output detection is a challenging task in such systems. The conventional likelihood ascent search (LAS) detectors perform well in large antenna setups, however, multiple symbol updates and the soft-output estimation using brute force search further boost its complexity. In this paper, we propose a model-based soft-output LAS detector to jointly detect and precisely estimate the soft output in MIMO-OFDM systems. Furthermore, we propose a data-driven deep-LAS (Deep LAS) architecture for MIMO detection which is a multi-layer perception (MLP), and a gated recurrent unit (GRU)-based hybrid trainable learning framework to unfold the proposed two-stage LAS algorithm by directly learning the soft output from the received equalized signals. Numerical results demonstrate that the proposed two-stage soft-output LAS detector precisely computes the log-likelihood ratio (LLR) and provides better performance than the conventional LAS detector. Alternatively, the proposed Deep LAS efficiently estimates the LLR values by achieving a performance gain of 2.55 dB and 3 dB compared to the conventional LAS algorithm. Furthermore, the proposed Deep LAS outperforms the counterpart model-based and standalone data-driven learning schemes and provides a comparable signal-to-noise ratio (SNR) gap of 0.4 dB and 1.2 dB with the optimal soft output sphere decoding (SD) to achieve a BER of 10^-5 for 4-QAM and 16-QAM, respectively.