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We consider a two-hop MIMO-OFDM communication scheme with a source, an amplify-and-forward relay, and a destination. We examine the possibilities of power allocation (PA) over the subchannels in frequency and space domains to maximize the instantaneous rate of this link if channel state information at the transmitter (CSIT) is available. We consider two approaches: (i) separate optimization of the source or the relay PA with individual per node transmit power constraints and (ii) joint optimization of the source and the relay PA with joint transmit power constraint. We provide the optimal PA at the source (or the relay) with a node transmit power constraint that maximizes the instantaneous rate for a given relay (or source) PA. Furthermore, we show that repeating this separate optimization of the source and the relay PA alternately converges and improves the achievable rate of the considered link. Since the joint optimization of the source and the relay PA is analytically not tractable we use a high SNR approximation of the SNR at the destination. This approximation leads to rates which are quite tight to the optimum.
Hammerstrom et al. (2007) studied this question.