Sum Rate Analysis and Power Allocation for Massive MIMO Systems With Mismatch Channel

Massive multiple-input multiple-output (MIMO) has been regarded as one of the key technologies of fifth-generation cellular systems due to its excellent performance in spectral and energy efficiency, whose performance has also been widely studied. However, most related works focus only on the impact of the wireless channels. In fact, its performance is affected not only by the wireless channel but also by the transceiver radio frequency (RF) circuits. Random variation of RF gain would lead to a mismatch channel, where the downlink is not the transpose of the uplink in time-division duplex (TDD) mode. Therefore, the impact of the transceiver RF circuits should be considered when we evaluate the performance of the massive MIMO systems. In this paper, we develop a detailed analysis on the downlink sum rate of the massive MIMO systems and derive its closed-form expressions using maximum ratio transmission and zero-forcing (ZF) precoding. The derived results provide some good insight into how the system performance is affected by the RF mismatch parameters. Based on the analytical results, we further investigate the optimal power allocation scheme to maximize the sum rate subject to the total power constraint and lowest rate requirement. For the simplest case of user equipment side mismatch with the ZF precoding, we apply the water-filling solution, while for the other mismatch cases, we conduct a convex relaxation on the non-convex problem through lower bound inequality, variable substitution, and Taylor expansion techniques, before applying some convex optimization solving tools. In the end, we propose an iterative algorithm to successively improve the iterative results for approaching the optimal solution. Simulations demonstrate that, for the massive MIMO systems with RF mismatch, our power allocation schemes achieve significant capacity improvement relative to an equal power scheme, and it performs well for the ZF precoding in the case of the RF mismatch only at the base station.