A New Beamforming Design for MIMO AF Relaying Systems With Direct Link

In this paper, we propose a new beamforming technique that maximizes the end-to-end signal-to-noise ratio (SNR) for amplify-and-forward multiple-input-multiple-output cooperative relaying systems with direct link between the source and the destination. Instead of conventional schemes resorting to an iterative method, such as a gradient ascent algorithm, our scheme provides a simple closed-form solution for source-relay joint beamformer designs. To this end, we first derive a new expression of the end-to-end SNR for the cooperative relaying systems and its lower bound, which is given as the harmonic mean of two individual SNRs. Then, a new beamforming scheme, which adaptively optimizes one of the two SNRs depending on the channel condition, is proposed. In addition, we perform a diversity order analysis of the proposed scheme and show that our scheme achieves a full diversity order of relaying systems with direct link. It is confirmed by simulation results that the proposed technique obtains almost identical performance to the gradient ascent algorithm with much reduced complexity, and our analytical work accurately predicts the numerical results.