A Novel Bitwise Factor Graph Belief Propagation Detection Algorithm for Massive MIMO System

As a low computational complexity detection algorithm for Massive Multi-Input-Multi-Output (MIMO) system, the well known factor graph belief propagation (BP) detection algorithm is effective for binary phase shift keying (BPSK) signal, but not appropriate for quadrature amplitude modulation (QAM) signal. In this paper, the complex transmitted signal vector modulated by QAM is transformed into the real valued bitwise vector which can be viewed as a transmitting signal vector modulated by BPSK. With the real valued bitwise vector and transformed channel gain matrix, an improved bitwise factor graph (BFG) graphic model is developed, and a BFG-BP algorithm is proposed to detect QAM signals in Massive MIMO system. Over a finite time of polynomial computational complexity of \(\text {O}(N_T)\) per symbol, where \(N_T\) denotes the number of transmitted antennas, the proposed BFG-BP detection algorithm obtains the approximate optimum BER performance of maximum likelihood detection algorithm with rapid convergence rate, and also achieves the theoretical spectral efficiency at medium high average received signal-to-noise ratio. Simulation results prove the effeteness of the proposed BFG-BP for detecting QAM signals in Massive MIMO system.