Widely-Linear Precoding for Large-Scale MIMO with IQI: Algorithms and Performance Analysis

In this paper we study widely-linear precoding techniques to mitigate in-phase/quadrature-phase (IQ) imbalance (IQI) in the downlink of large-scale multiple-input multiple-output (MIMO) systems. We adopt a real-valued signal model which takes into account the IQI at the transmitter and then develop widely-linear zero-forcing (WL-ZF), widely-linear matched filter (WL-MF), widely-linear minimum mean-squared error (WL-MMSE) and widely-linear block-diagonalization (WL-BD) type precoding algorithms for both {\color{red} single- and multiple-antenna users.} We also present a performance analysis of WL-ZF and WL-BD. It is proved that without IQI, WL-ZF has exactly the same multiplexing gain and power offset as ZF, while when IQI exists, WL-ZF achieves the same multiplexing gain as ZF with ideal IQ branches, but with a minor power loss which is related to the system scale and the IQ parameters. We also compare the performance of WL-BD with BD. The analysis shows that with ideal IQ branches, WL-BD has the same data rate as BD, while when IQI exists, WL-BD achieves the same multiplexing gain as BD without IQ imbalance. Numerical results verify the analysis and show that the proposed widely-linear type precoding methods significantly outperform their conventional counterparts with IQI and approach those with ideal IQ branches.