Joint signal-to-noise ratio-based transceiver design for amplify-and-forward multiple-input multiple-output relay systems

In this study, the authors address the problem of transceiver design in an amplify-and-forward multiple-input multiple-output relay system with full or partial channel state information (CSI), where linear processing is applied to maximise the average received signal-to-noise ratio (SNR) at source, relay and destination, respectively. This joint design problem is a non-convex optimisation problem, so the authors convert it into a scalar problem and derive the optimal unitary decoder under average power constraint. The precoder at source and relay can be obtained by employing generalised Rayleigh quotient method. Specifically, two CSI assumptions are considered: (i) the authors first derive the precoder and decoder with full CSI; (ii) assumimg the statistical independence between the channel estimated value and channel estimation errors, the problem with partial CSI can be solved as the same way as full CSI case. Numerical results show a great improvement on the average received SNR by applying the proposed scheme. On the other hand, the authors also illustrate the impact on received SNR arose by the channel estimation errors.