Resource allocation for the parallel relay channel with multiple relays

A cooperative network where the transmission between two nodes is assisted by many half-duplex relays over parallel Gaussian channels is considered. The parallel channel model is suitable for a broadband system, such as orthogonal frequency division multiplexing or a block fading channel. For the decode-and-forward protocol, an optimization problem for joint power, time and subchannel allocation under per-node power constraints is formulated to maximize the total transmission rate between the source and the destination. To solve this optimization problem, first the optimal power allocation for a given subchannel allocation is found. Then a greedy algorithm that jointly allocates subchannels and power is described. Finally, the time allocation is optimized by a numerical search procedure. The limiting case where the number of subchannels goes to infinity is also studied. Numerical results reveal that the achieved rate for the infinite number of subchannels is an upper bound for the finite subchannel case and the proposed greedy algorithm results in rates close to those for infinite number of subchannels when the number of subchannels is sufficiently large. Furthermore, most of the cooperative gains can be achieved by the use of a small number of relays.