Matching in the Air: Optimal Analog Beamforming under Angular Spread

Gbps wireless transmission over long distance at high frequency bands has great potential for 5G and beyond, as long as high beamforming gain could be delivered at affordable cost to combat the severe path loss. With limited number of RF chains, the effective beamwidth of a high gain antenna will be "widened" by channel angular spread, resulting in gain reduction. In this paper, we formulate the analog beamforming as a constrained optimization problem and present closed form solution that maximizes the effective beamforming gain. The optimal beam pattern of antenna array turns out to "match" the channel angular spread, and the effectiveness of the theoretical results has been verified by numerical evaluation via exhaustive search and system level simulation using 3D channel models. Furthermore, we propose an efficient angular spread estimation method using as few as three power measurements and validate its accuracy by lab measurements using a \(16{\times}16\) phased array at 28 GHz. The capability of estimating angular spread and matching the beam pattern on the fly enables high effective gain using low cost analog/hybrid beamforming implementation, and we demonstrate a few examples where substantial gain can be achieved through array geometry optimization.