Optimum Discrete Beamforming via Minkowski Sum of Polygons

TL;DR

This paper presents a novel geometric approach to optimal discrete beamforming by computing the Minkowski sum of convex polygons, enabling efficient and exact solutions.

Contribution

It introduces a new formulation of the discrete beamforming problem as a Minkowski sum of polygons, improving computational efficiency and clarity.

Findings

Minkowski sum of convex polygons is itself convex.

The number of vertices in the Minkowski sum is at most the sum of original vertices.

The approach allows for efficient computation of optimal beamforming solutions.

Abstract

This letter casts the problem of optimum discrete beamforming as the computation of the Minkowski sum of convex polygons, which is itself a convex polygon. The number of vertices of the latter is at most the sum of the number of vertices of the original polygons, enabling its efficient computation. This original and intuitive formulation confirms that the optimum beamforming solution can be found efficiently.