On the Spectral and Energy Efficiency of Full-Duplex Small-Cell Wireless Systems With Massive MIMO

The achievable rate of full-duplex (FD) small-cell systems with massive multiple-input multiple-output (MIMO), in which a low-power base station (BS) equipped with large antenna arrays sends/receives data to and from multiple half-duplex (HD) users at the same time on the same frequency, is investigated. The BS uses imperfect channel state information (CSI) obtained from received pilots, nonideal hardware, and a linear transmitter and receiver, i.e., zero-forcing (ZF) or maximum-ratio transmission/maximum-ratio combining (MRT/MRC), to process the signals. The approximate closed-form expressions of the achievable rate for both the ZF and MRT/MRC processing are derived and used to analyze the effect of the number of antennas and the hardware imperfection on the self-interference (SI), which is a bottleneck of the FD systems. To maximize the spectral efficiency (SE) and the energy efficiency (EE) of this system, two nonconvex power-allocation optimization problems are formulated and solved by utilizing the sequential convex approximation technique and the fractional programming technique. Two iterative algorithms are proposed with proved local convergence. Numerical results illustrate that the analytical approximation of achievable rate matches well with the Monte Carlo simulation. It is also shown that the ZF processing has greater ability to suppress SI, compared with MRT/MRC processing. The proposed power-allocation algorithms are shown to increase the SE and EE significantly, compared with the uniform power-allocation scheme when the BS is equipped with moderately large antenna arrays.