Variational Bayes’ Joint Channel Estimation and Soft Symbol Decoding for Uplink Massive MIMO Systems With Low Resolution ADCs

We consider the problem of joint channel estimation and data decoding in uplink massive multiple input multiple output systems with low resolution analog-to-digital converters (ADCs) at the base station. The nonlinearities introduced by the ADCs make the problem challenging: in particular, the existing linear detectors perform poorly. Also, the channel coding used in commercial wireless systems necessitates soft symbol detection to obtain satisfactory performance. In this paper, we present a low-complexity variational Bayesian (VB) inference procedure to jointly solve the (possibly correlated) channel estimation and soft symbol decoding problem. We present the approach in progressively more complex scenarios, including the case where even the channel statistics are not available at the receiver. Finally, we combine our proposed VB procedure with a belief propagation (BP) based channel decoder, which further enhances the performance without any additional complexity. We numerically evaluate the bit error rate (BER) and the normalized mean squared error (NMSE) in the channel estimates obtained by our algorithm as a function of various system parameters, and benchmark the performance against genie-aided and state-of-the-art receivers. The results show that VB procedure is a promising technique for the design of low-complexity advanced receivers in low resolution ADC based systems.