Joint source-and-relay beamforming for multiple-input multiple-output systems with single-antenna distributed relays

A joint source-and-relay beamforming scheme is proposed for multiple-input multiple-output (MIMO) systems with distributed single-antenna relays. First, a lower-bound of the signal-to-noise ratio at the destination is derived as an objective function to formulate a constrained beamforming optimisation problem. The joint beamforming problem is then divided into two sub-optimisation problems corresponding to the source and the relay beamforming, respectively. The first sub-problem is shown to be a quadratic concave minimisation, and is tackled by developing an iterative algorithm with each iteration solving a linear problem. The second one corresponds to a Rayleigh-Ritz ratio problem which is then solved by the generalised singular-value decomposition in a closed form. Based on the solutions to the subproblems, a global iterative algorithm is designed to implement the joint source-and-relay beamforming. Simulation results show that the proposed method outperforms some existing relaying schemes in terms of the capacity and outage probability of the whole MIMO relay system.