Sum-rate maximization for active channels: Unequal noise power over different subchannels

In this paper, we study the problem of sum-rate maximization for an active channel subject to two constraints, one on the source total transmit power and one on the channel energy (or total power). Here, active channel refers to a parallel channel where not only can the source transmit power over different subchannels can be optimally calculated but also the gains of the subchannels can also be adjusted. Despite the non-convexity of this sum-rate maximization problem for active channels, using Karush-Kuhn-Tucker (KKT) conditions, we determine the number of subchannels that can be active for the source power constraint to be feasible. Then, for any feasible number of active subchannels, we obtain the optimal source power allocation. The optimal solution can then be obtained by comparing a finite number of points in the feasible set and by choosing the point which yields the best sum-rate performance. Our analysis and simulation results show that active channels can offer signifcantly higher sum-rate compared to their passive counterparts.