Expectation Propagation Aided Signal Detection for Uplink Massive Generalized Spatial Modulation MIMO Systems

In this paper, we propose a joint signal detection algorithm under the framework of the expectation propagation (EP) algorithm for uplink massive multiuser multiple-input multiple-output (MIMO) systems with generalized spatial modulation (GSM). By projecting the discrete probability distribution into a multivariate complex Gaussian function, the symbol beliefs of the tridimensional GSM constellation are calculated via the iterative propagation of the mean vectors and covariance matrices. To reduce the computational complexity, an efficient separate signal detection called two-stage EP (TS-EP) algorithm is designed. In the first stage, the active transmit antenna indices are determined via the EP. Each vector-valued variable node (VN) in the factor graph is decomposed into multiple sub-VNs, and the invalid sub-VNs of the determined silent transmit antennas are pruned from the factor graph. In the second stage, since the modulation symbols are independent conditioned on the active transmit antennas, the symbols are independently detected by adopting the EP with univariate complex Gaussian approximations, and the number of probability calculations for each symbol belief is significantly reduced in the subsequent EP update. Simulation results illustrate that the proposed EP and TS-EP signal detection schemes outperform the recently proposed counterparts. Moreover, the proposed TS-EP algorithm strikes a desirable and flexible performance-complexity tradeoff.