In this paper, belief propagation (BP) detection in real domain for large-scale multiple-in multiple-out (MIMO) systems is proposed. The mathematical analysis of message updating rules for independent identically distributed (i.i.d.) and correlated fading MIMO channels are given in detail. The damped BP with damping on the a priori probability vector is employed to improve the performance for the uplink large-scale MIMO systems with correlation among transmitting antennas or loading factor rho = 1. Based on the convergence analysis, the method of selecting message damping factor delta is presented also. In addition, the adaptive message updating for BP detection is first proposed to provide a good trade-off between performance and complexity. Simulation results have shown that, for 16 x 16 MIMO with quadrature phase shift keying (QPSK) modulation, this approach can show 1 dB performance improvement at BER of 10(-2), compared to complex domain single-edge based BP (SE-BP). For 8 x 32 MIMO with correlation among transmitting and receiving antennas, where 16-Quadrature Amplitude Modulation (16-QAM) is employed, simulation results have shown that the proposed adaptive BP detection achieves a complexity reduction of 50% compared to the general BP detection with negligible performance loss. For i.i.d. and correlated fading channels with various antennas configurations, advantages of the proposed approach over existing BP detections as well as MMSE approach have been demonstrated by thorough simulations. Hence, the proposed BP detection is suitable for large-scale MIMO systems, especially for those with high-order modulations. Furthermore, the adaptive BP detection together with message damping is expected to be a good choice for low complexity detection.
