Performance Analysis of Uplink Massive Multiuser SM-MIMO System With Imperfect Channel State Information

In this paper, the error performance and spectrum efficiency (SE) of uplink massive multiuser spatial modulation (SM) MIMO systems with zero-forcing detection for perfect and imperfect channel state information (CSI) are investigated over composite Rayleigh fading channels. We firstly derive the error probabilities of transmit antenna index detection and transmitted symbol detection of each user. Using these results, the bit error rate (BER) performance of the system under perfect CSI is analyzed. Furthermore, a closed-form average BER of the system is derived. We generalize the analytical results of perfect CSI to those of imperfect CSI for practicality, and derive a closed-form BER for the system with imperfect CSI. Based on this, two asymptotic BER expressions are developed to characterize the error performance of the system for large-scale receive antennas and high SNR. By means of the asymptotic expressions, the diversity order of the system is attained. Besides, we derive a lower bound on the achievable SE of the system with imperfect CSI. With this lower bound, an approximate expression of the achievable SE is obtained in closed form. Simulation results indicate that our theoretical analysis is valid, and agrees with simulation results well.