Weighted sum power minimisation for multichannel decode-and-forward relaying

Weighted sum power (WSP) minimisation problems are addressed for a source-relay-destination communication link subject to a minimum rate requirement. The destination cannot receive the source´s signals, while there exist K source-to-relay and M relay-to-destination orthogonal subchannels (in general, K≠M). Two decode-and-forward (DF) transmission protocols are considered. The first one uses subchannel-pair-based DF relaying, which has been the focus of existing work in the literature. The second protocol uses joint coding over all subchannels. For each protocol, the closed-form expression for the minimum WSP is derived. Numerical results show that the second protocol leads to a much smaller minimum WSP, especially when the required minimum rate is high and K≠M.