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

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.