Negentropy-Aware Loss Function for Trainable Belief Propagation in Coded MIMO Detection

We consider large multi-user detection (MUD) via deep unfolding-aided belief propagation (BP) in coded multi-user MIMO (MU-MIMO) systems. A BP detector optimized (trained) by data-driven-tuning of embedded internal parameters achieves low-complexity and high-accuracy MUD while compensating practical imperfections. However, in actual implementation, these parameters should be optimized according to system parameters, e.g., modulation and coding scheme (MCS). In particular, when channel coding is used, it is vital not only to minimize the mean square error (MSE) but also to enhance the Gaussianity of the output log-likelihood ratio (LLR), in order to maximize the error correction capability of the subsequent soft-decision decoder. To that end, a novel loss function based on a weighted average of negentropy, which is a key measure to evaluate the Gaussianity, and MSE of the detector output is proposed. Simulation results show that the trainable Gaussian BP (T-GaBP) detector optimized with the proposed negentropy-aware loss function significantly improves the bit error rate (BER) performance of the decoder output and substantially outperforms the T-GaBP optimized with the typical MSE loss function.