Optimal beamforming for MIMO shared relaying in downlink cellular networks with ARQ

In this paper, we study the performance of the downlink of a cellular network with automatic repeat-request (ARQ) and a half duplex decode-and-forward shared relay. In this system, two multiple-input-multiple-output (MIMO) base stations serve two single antenna users. A MIMO shared relay retransmits the lost packets to the target users. First, we study the system with direct retransmission from the base station and derive a closed form expression for the outage probability of the system. We show that the direct retransmission can overcome the fading, however, it cannot overcome the interference. After that, we invoke the shared relay and design the relay beamforming matrices such that the signal-to-interference-and-noise ratio (SINR) is improved at the users subject to power constraints on the relay. In the case when the transmission of only one user fails, we derive a closed form solution for the relay beamformers. On the other hand when both transmissions fail, we pose the beamforming problem as a sequence of non-convex feasibility problems. We use semidefinite relaxation (SDR) to convert each feasibility problem into a convex optimization problem. We ensure a rank one solution, and hence, there is no loss of optimality in SDR. Simulation results are presented showing the superior performance of the proposed relay beamforming strategy compared to direct ARQ system in terms of the outage probability.