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This paper considers a hybrid beamforming massive multiple-input multiple-output (MIMO) system operating in time-division duplex (TDD) mode. We investigate the combined impacts of quantized phase shifters (QPSs), channel non-reciprocity and channel estimation errors on the achievable spectral efficiency (SE) of the considered system. We first introduce an equivalent hybrid beamforming structure, based on which, a generic and practical channel non-reciprocity model is built for massive MIMO systems with hybrid structure. This model jointly considers the mismatch between transceiver and receiver circuits, as well as the mutual coupling between antennas. Then we derive the generic expression of achievable SE for both the ideal phase shifters (IPSs) and QPSs cases. Furthermore, the closed-form expressions of SE are derived for IPSs and QPSs cases, respectively. The asymptotic performance in large antenna regime is also analyzed based on these expressions. Simulation results demonstrate the validity and accuracy of the derived analytical expressions. In addition, results show that the phase quantization and channel non-reciprocity both contributes to the SE degradation and the detrimental effects cannot be canceled completely even in the large-antenna regime.

Achievable Spectral Efficiency of Hybrid Beamforming Massive MIMO Systems With Quantized Phase Shifters, Channel Non-Reciprocity and Estimation Errors