Signal-to-noise-ratio maximisation for linear multi-antenna relay communications

The authors consider a linear relaying communication system using multiple antennas at a source, relay and destination. They maximise the end-to-end signal-to-noise-ratio (SNR) to find the relay transformation (RT) and the source transmit covariance (STC) matrices. For any given STC matrix, to maximise the SNR, they prove that the relay has to assign all its power in the direction of the dominant eigenmodes of the source-relay and the relay-destination channels. They also find the joint optimal rank-one matrices for the STC and RT. They prove that this solution also maximises the source-destination mutual information among all rank-one matrices. Furthermore, they find the optimal power budgets allocated to the source and relay that maximise the SNR under a constraint on the total transmit power of the system. This is a practical solution as only three positive quantities need to be communicated among the nodes to calculate these optimal power budgets. Interestingly, the authors computer simulations for multiple users reveal that the sum-rate significantly increases if users selfishly maximise their own SNRs using the proposed method, instead of maximising their own capacity. Thus, they conclude that the SNR-maximisation is spectrally more efficient as it consumes only the best subspaces and leaves the other subspaces free.