Beamforming Gain with Nonideal Phase Shifters

This research sets forth a universal framework to characterize the beamforming gain achievable with arbitrarily nonideal phase shifters. Precisely, the maximum possible shortfall relative to the gain attainable with ideal phase shifters is established. Such shortfall is shown to be fundamentally determined by the perimeter of the convex hull of the set of feasible beamforming coefficients on the complex plane. This result holds regardless of whether the beamforming is at the transmitter, at the receiver, or at a reconfigurable intelligent surface. In i.i.d. fading channels, the shortfall hardens to the maximum possible shortfall as the number of antennas grows.