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Joint Source and Relay Optimization for a Non-Regenerative MIMO Relay

We consider a non-regenerative MIMO relay system where the source, relay and destination are all equipped with multiple antennas. The relay does not decode the packets but performs a multi-dimensional amplify-and-forward function (a relay matrix) on the baseband signals. Under the condition that the source is white, the relay matrix that maximizes the capacity between the source and the destination has been previously found. In this paper, we show a new result on how the source covariance matrix and the relay matrix can be jointly optimized to maximize the source-destination capacity. It is shown that the optimal coordinate system governed by the previously discovered relay matrix is still valid under the joint optimization, and the joint optimization yields a further capacity gain when the SNR at the relay is low