Optimal Beamforming for Two-Way Multi-Antenna Relay Channel with Analogue Network Coding

TL;DR

This paper investigates optimal beamforming strategies for a two-way multi-antenna relay channel using analogue network coding, deriving capacity regions and proposing algorithms for optimal and suboptimal relay processing.

Contribution

It introduces the optimal relay beamforming structure for ANC-based TWRC with multi-antenna relays and develops efficient algorithms for capacity-achieving and suboptimal schemes.

Findings

Optimal beamforming structure derived for ANC-based TWRC.

Convex optimization algorithms for computing the optimal beamforming matrix.

Suboptimal schemes with performance close to the optimal capacity.

Abstract

This paper studies the wireless two-way relay channel (TWRC), where two source nodes, S1 and S2, exchange information through an assisting relay node, R. It is assumed that R receives the sum signal from S1 and S2 in one time-slot, and then amplifies and forwards the received signal to both S1 and S2 in the next time-slot. By applying the principle of analogue network (ANC), each of S1 and S2 cancels the so-called "self-interference" in the received signal from R and then decodes the desired message. Assuming that S1 and S2 are each equipped with a single antenna and R with multi-antennas, this paper analyzes the capacity region of an ANC-based TWRC with linear processing (beamforming) at R. The capacity region contains all the achievable bidirectional rate-pairs of S1 and S2 under the given transmit power constraints at S1, S2, and R. We present the optimal relay beamforming structure as well as an efficient algorithm to compute the optimal beamforming matrix based on convex optimization techniques. Low-complexity suboptimal relay beamforming schemes are also presented, and their achievable rates are compared against the capacity with the optimal scheme.