Very Low-Complexity Algorithms for Beamforming in Two-Way Relay Systems

TL;DR

This paper introduces a low-complexity, numerically solvable approach for optimal beamforming in two-way relay systems, leveraging quadratic surface properties to reduce computational complexity.

Contribution

It presents a novel method that simplifies the beamforming optimization problem to a four-dimensional space, enabling efficient numerical solutions.

Findings

Reduced computational complexity for beamforming optimization

Effective numerical solution for optimal beamforming matrices

Enhanced understanding of quadratic surface properties in relay systems

Abstract

In this paper, we present a novel solution for optimal beamforming in a two-way relay (TWR) systems with perfect channel state information. The solution makes use of properties of quadratic surfaces to simplify the solution space of the problem to $\mathbb{R}^4$, and enables the formulation of a differential equation that can be solved numerically to obtain the optimal beamforming matrix.