Power allocation strategies across N orthogonal channels for singe-relay networks at both source and relay

We consider a wireless relay network with one source, one relay and one destination, where communications between nodes are preformed over N orthogonal channels. This, for example, is the case when orthogonal frequency division multiplexing is employed for data communications. Since the power available at the source and relay is limited, we study optimal power allocation strategies at the source and relay in order to maximize the overall source-destination capacity. Depending on the availability of the channel state information at both the source and relay or only at the relay, power allocation is performed at both the source and relay or only at the relay. Considering different setups for the problem, various optimization problems are formulated and solved. Some properties of the optimal solution are also proved.