Fractional cooperation and the max-min rate in a multi-source cooperative network

We maximize the minimum rate among sources in a multi-source, multi-relay, single destination cooperative network. The relays use the decode-and-forward protocol while all transmissions use orthogonal frequency division multiplexing. The key to our approach is fractional cooperation: there may be fewer relays than sources and not all source subcarriers are relayed. Optimal matching of the sources subcarriers with those of the relays is a combinatorial problem with exponential complexity. We develop an upper bound on the max-min rate and present an algorithm with a close to optimum performance. Furthermore, our simulation results show that for certain number of sources in a network, accounting for the overhead due to relaying, there is an optimal number of relays maximizing the max-min rate. This number is in general less than the number of sources.