Beam Selection Gain Versus Antenna Selection Gain

TL;DR

This paper analyzes beam selection using a fixed beamforming network at a base station, demonstrating its superiority over antenna selection in Rician channels through theoretical proofs and asymptotic bounds, with capacity growth of Θ(log(M)).

Contribution

It provides the first rigorous proof of beam selection gain properties and derives approximate closed-form expressions for capacity, highlighting its advantages over antenna selection.

Findings

Beam selection outperforms antenna selection in Rician channels.

Expected selection gain and ergodic capacity are approximated with tight bounds.

Ergodic capacity grows as Θ(log(M)) for beam selection, faster than Θ(log(log(M))) for antenna selection.

Abstract

We consider beam selection using a fixed beamforming network (FBN) at a base station with $M$ array antennas. In our setting, a Butler matrix is deployed at the RF stage to form $M$ beams, and then the best beam is selected for transmission. We provide the proofs of the key properties of the noncentral chi-square distribution and the following properties of the beam selection gain verifying that beam selection is superior to antenna selection in Rician channels with any $K$-factors. Furthermore, we find asymptotically tight stochastic bounds of the beam selection gain, which yield approximate closed form expressions of the expected selection gain and the ergodic capacity. Beam selection has the order of growth of the ergodic capacity $\mathnormal{\Theta}(\log(M))$ regardless of user location in contrast to $\mathnormal{\Theta}(\log(\log(M)))$ for antenna selection.