Generalized Approximate Message Passing Detection with Row-Orthogonal Linear Preprocessing for Uplink Massive MIMO Systems

In this paper, we investigate the uplink multi-user generalized approximate message passing (GAMP) detection for massive MIMO system. As practical channels are spatially correlated, the conventional GAMP performs poorly and its fixed points fall into locally-optimal solutions. In order to analyse the fixed points of GAMP, we regard the detection problem of massive MIMO systems as the Gibbs free energy minimization and derive GAMP by Bethe method to upper-bound Gibbs free energy. To improve the convergence performance of GAMP detection, we propose linear preprocessing with row-orthogonalization for GAMP (RO-GAMP) at the receiver before GAMP detection is executed. Firstly, we derive the structure of linear preprocessing consisted of four design principles: orthogonality of rows of sensing matrices, irrelevance of noise, low-dimension of observation vector and equivalence of Bethe free energy minimization. Secondly, some conditions are presented on preprocessing matrix to satisfy these design principles. Then, we propose two optimal preprocessing matrices for RO-GAMP. When these two matrices are used for massive MIMO OFDM with slow-varying channels, a low-complexity preprocessing method is presented finally. Our numerical results demonstrate the advantage of RO-GAMP over GAMP, in terms of symbol error rate (SER) and convergence rate, for practical massive MIMO channels which exhibits spatial correlation.