A Stochastic Beamformed Amplify-and-Forward Scheme in a Multigroup Multicast MIMO Relay Network with Per-Antenna Power Constraints

TL;DR

This paper introduces a stochastic beamformed amplify-and-forward scheme for multigroup multicast MIMO relay networks, improving fairness and performance in large-scale systems with per-antenna power constraints.

Contribution

It proposes the SBF-AF scheme that uses time-varying weights, providing a performance guarantee close to the optimal SDR rate regardless of system size.

Findings

SBF-AF achieves rates within 0.8317 bits/s/Hz of SDR rate.

BF-AF performance degrades with more users and constraints.

Numerical results confirm the effectiveness of SBF-AF in large systems.

Abstract

In this paper, we consider a two-hop one-way relay network for multigroup multicast transmission between long-distance users, in which the relay is equipped with multiple antennas, while the transmitters and receivers are all with a single antenna. Assuming that perfect channel state information is available, we study amplify-and-forward (AF) schemes that aim at optimizing the max-min-fair (MMF) rate. We begin by considering the classic beamformed AF (BF-AF) scheme, whose corresponding MMF design problem can be formulated as a rank-constrained fractional semidefinite program (SDP). We show that the gap between the BF-AF rate and the SDR rate associated with an optimal SDP solution is sensitive to the number of users as well as the number of power constraints in the relay system. This reveals that the BF-AF scheme may not be well suited for large-scale systems. We therefore propose the stochastic beamformed AF (SBF-AF) schemes, which differ from the BF-AF scheme in that time-varying AF weights are used. We prove that the MMF rates of the proposed SBF-AF schemes are at most $0.8317$ bits/s/Hz less than the SDR rate, irrespective of the number of users or power constraints. Thus, SBF-AF can outperform BF-AF especially in large-scale systems. Finally, we present numerical results to demonstrate the viability of our proposed schemes.