Signaling Design of Two-Way MIMO Full-Duplex Channel: Optimality Under Imperfect Transmit Front-End Chain

TL;DR

This paper investigates optimal signaling strategies for MIMO full-duplex two-way channels with imperfect transmit front-end chains, using game theory to characterize rate regions and Nash equilibria, and proposes beamforming solutions with practical benefits.

Contribution

It derives the optimal beamforming for MISO channels and establishes NE existence and uniqueness conditions for MIMO channels, including an iterative algorithm for reaching NE.

Findings

Beamforming achieves any point on the Pareto boundary for MISO channels.

The proposed beamforming outperforms zero-forcing in achievable rates.

Full-duplex NE outperforms half-duplex below a certain self-interference threshold.

Abstract

We derive the optimal signaling for a multiple input multiple output (MIMO) full-duplex two-way channel under the imperfect transmit front-end chain. We characterize the two-way rates of the channel by using a game-theoretical approach, where we focus on the Pareto boundary of the achievable rate region and Nash equilibia (NE). For a MISO full-duplex two-way channel, we prove that beamforming is an optimal transmission strategy which can achieve any point on the Pareto boundary. Furthermore, we present a closed-form expression for the optimal beamforming weights. In our numerical examples we quantify gains in the achievable rates of the proposed beamforming over the zero-forcing beamforming. For a general MIMO full-duplex channel, we establish the existence of NE and present a condition for the uniqueness of NE. We then propose an iterative water-filling algorithm which is capable of reaching NE. Through simulations the threshold of the self-interference level is found, below which the full-duplex NE outperforms the half-duplex TDMA.