Bilinear Gaussian Belief Propagation for Large MIMO Channel and Data Estimation

This paper proposes bilinear Gaussian belief propagation (BiGaBP) for joint channel and data estimation (JCDE) in large multi-user multi-input multi-output (MU-MIMO) systems. JCDE is a well-known strategy for realizing a high-precision MU detection (MUD) with short pilots by utilizing the orthogonality of data sequences. For massive MIMO scenarios, the JCDE via bilinear generalized approximate message-passing (BiGAMP), which is systematically derived by extending AMP to the bilinear inference problem (BIP), achieves extremely low computational cost. However, the use of short non-orthogonal pilots to reduce the channel acquisition overhead significantly degrades the convergence property of BiGAMP. To resolve the lack of an appropriate JCDE scheme based on insufficient pilots, we design a novel MP rule based on GaBP, which is given by relaxing the large-system approximation from AMP. Furthermore, the belief scaling complying with the detection state in each iteration step is introduced to suppress the negative impact of non-orthogonal pilots even in the insufficient large-system conditions. Numerical results show the validity of our proposed method in terms of bit error rate (BER) and mean square error (MSE) performances.