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