RF imperfections in antenna arrays: Response analysis and widely-linear digital beamforming

In this paper, we analyze the impact of radio frequency (RF) circuit imperfections on the digital beamforming capabilities of linear antenna arrays. Special emphasis is on the I/Q imbalances and common channel responses of all individual parallel radio chains, and their impact on the radiation pattern is analyzed in closed form. We also propose an extension on the digital signal processing side, called widely-linear (WL) digital beamforming, in order to mitigate the influence of RF I/Q imbalances in digital beamforming processing instead of individually calibrating all the parallel radio chains. This is shown to efficiently recover the desired beamforming capabilities and directional properties which are initially corrupted by RF imperfections. As a practical example, a widely linear normalized least-mean square (WL-NLMS) algorithm with a known training signal is formulated to get optimal weights for signals from different antennas. The proposed method enables more accurate direction of arrival (DOA) estimations and beam steering properties even when operating under substantial RF imperfections in the RF circuits of a receiver.