Stochastic amplify-and-forward schemes for multigroup multicast transmission in a distributed relay network

In this paper, we study amplify-and-forward (AF) schemes to for multigroup multicast information delivery between long-distance users. The target scenario is a two-hop distributed one-way relay network where the transmitters, relays and receivers are all equipped with a single antenna. Assuming that channel state information (CSI) is perfectly known, our goal here is to design the AF weights at the relays so that the system rate performance can be optimized. A classic AF scheme in this context is to employ a rank-one beamformed AF (BF-AF) strategy with a max-min-fair (MMF) achievable rate objective. In this way, the semidefinite relaxation (SDR) technique is widely used to provide an (approximate) solution for the MMF problem. It is known that the achievable rate performance of the SDR-based BF-AF scheme tends to degrade seriously with the number of users served in the relay network. This motivates us to propose stochastic beamformed AF (SBF-AF) schemes to improve the achievable rate performance. The salient feature of the SBF-AF schemes is that it employs time-varying AF weights and bypass some inherent issues in the SDR-based BF-AF scheme. Our theoretical analysis and numerical results both show that the SBF-AF schemes can outperform the BF-AF scheme.