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We present the optimal relay-subset selection and transmission-time for adecode-and-forward, half-duplex cooperative network of arbitrary size. Theresource allocation is obtained by maximizing over the rates obtained for eachpossible subset of active relays, and the unique time allocation for each setcan be obtained by solving a linear system of equations. We also present asimple recursive algorithm for the optimization problem which reduces thecomputational load of finding the required matrix inverses, and reduces thenumber of required iterations. Our results, in terms of outage rate, confirmthe benefit of adding potential relays to a small network and the diminishingmarginal returns for a larger network. We also show that optimizing over thechannel resources ensures that more relays are active over a larger SNR range,and that linear network constellations significantly outperform gridconstellations. Through simulations, the optimization is shown to be robust tonode numbering.

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