Selective water-filling for decode-and-forward cooperative systems

Consider a decode-and-forward (DF) based cooperative system where a multi-antenna base-station (source) transmits information to a single-antenna destination (D) with the help of multiple single-antenna relays ({R_i}). The optimal transmit weighting vector at the source is not available in the literature due to the non-linear DF operation, which causes the problem non-convex. By investigating the single-relay system, we show that the optimal transmit vector for the single-relay system can be determined by comparing the S-D beamformer (maximum-ratio-transmit beamforming vector for the S-D link) with the one that utilizes “just sufficient” energy to activate the relay-link. This idea is then applied to the multi-relay system to propose a selective water-filling algorithm, where the optimal solution is obtained by comparing the S-D beamformer with schemes that selectively activate different combinations of relay-links.