Optimal Relay-Subset Selection and Time-Allocation in Decode-and-Forward Cooperative Networks

We consider a half-duplex mesh network wherein a single source communicates to a destination with the help of N potential decode-and-forward relays. We develop the optimal selection of a relaying subset and allocation of transmission time. This resource allocation is found by maximizing over the rates achievable for each possible subset of active relays; in turn, the optimal time allocation for each subset is obtained by solving a linear system of equations. An assumed relay numbering imposes a causality constraint. We also present a recursive algorithm to solve the optimization problem which reduces the computational load of finding the required matrix inverses and the number of required iterations. We show that (i) optimizing transmission time significantly improves achievable rate; (ii) optimizing over the channel resources ensures that more relays are active over a larger range of signal-to-noise ratios; (iii) linear network constellations significantly outperform grid constellations; (iv) the achievable rate is robust to node ordering.