Using Limited Feedback in Power Allocation Design for a Two-Hop Relay OFDM System

In this paper, we study power allocation (PA) in a single-relay OFDM system with limited feedback. We propose a PA scheme that uses a codebook of quantized PA vectors designed offline and known to the source, relay, and destination. The destination, which has full knowledge of channel side information (CSI), chooses one of the codebook vectors and conveys back to the source and relay. With the limited amount of available feedback, the design of an appropriate codebook is central to PA, which varies depending on the destination's strategy to choose the optimal PA vector. Assuming high received SNR on either link in the relay path, we first derive the optimal PA solutions as the function of channel realizations with two design criteria, maximizing capacity and minimizing error rate. It is found that when there is high received SNR in either the relay path or the direct path, the optimal solutions for both criteria reduce to simple forms. For maximizing capacity, the available power should be equally allocated to each OFDM subcarrier shared by the source and relay; while for minimum error rate, the available power should be allocated such that the received SNRs for all subcarriers at the destination are the same. The findings lead us to the sub-optimal solutions with great complexity reduction. We then present an adaptation of Lloyd's algorithm to construct a codebook to quantize the optimal PA vectors subject to the amount of feedback. Simulations show that a mild to negligible performance loss can be achieved with only a few bits of feedback at different SNR values.