Achievable Rate Analysis of the Generalized Spatial Modulation Uplink in Multi-Cell Multi-User Systems in the Face of Pilot Contamination

In this paper, the achievable rate of the multi-cell multi-user generalized spatial modulation uplink is analyzed in the presence of realistic pilot contamination. A practical channel model associated with arbitrary transmit and receive correlation matrices is assumed for each user and base station (BS). Imperfect channel estimation is assumed with pilot contamination. The performance of a single-cell based minimum mean squared error (SMMSE) combiner is analyzed and compared to the ubiquitous zero forcing (ZF) combiner as well as matched filtering (MF). The transmit antenna (TA) index detection and the classic amplitude/phase modulation signal detection process are carried out separately for the sake of low complexity. Moreover, an algorithm based on order statistics is proposed for calculating the antenna detection probability conditioned on the actual TA. Finally, an approximation of the achievable rate is derived by exploiting the characteristics of massive multiple-input multiple-outputs (MIMO). Simulation results show that SMMSE has the best performance, followed by ZF, and then MF. Furthermore, the relationships between the system's achievable rate and three systems' parameters, namely the number of BS antennas, the signal-to-noise-ratio (SNR), and the interference factor of pilot contamination, are presented. The performance of different number of activated antennas is also compared.