Geometric-Mean-Decomposition-Based Optimal Transceiver for a Class of Two-Hop MIMO-Aided Amplify-and-Forward Relay Channels

A geometric mean decomposition (GMD)-based joint transceiver is investigated in the context of a multiple-input-multiple-output (MIMO)-aided relay-assisted two-hop amplify-and-forward relaying system. The canonical form of the optimal weighting matrix is derived, which is capable of achieving the maximum received signal-to-noise ratio (SNR) at the destination. Furthermore, the optimal power allocation is formulated as a geometric programming problem. The proposed optimal design of the linear weighting matrix achieves an approximately 5-dB SNR gain over the naive weighting matrix at the bit error rate (BER) of 10^-3 as a benefit of efficiently exploiting the low-complexity linear signal processing capability of the relay.