Average rate maximization in relay networks over slow fading channels

In this paper, the average rate maximization problem given transmission power constraints in a decode-and-forward (DF) relay network over slow fading channels is studied. For the problem, either a long- or short-term power constraint is imposed on the source and relays. In each combination of the power constraints at the source and relays, the original optimization problem is decomposed into subproblems, each corresponding to a specific channel gain realization. For each subproblem, a fast algorithm with closed-form solutions is provided. The case with additional peak power spectrum density constraints is also investigated. Numerical results are presented to demonstrate the effectiveness of the algorithms.