Sum-Rate Maximization for Active Channels With Unequal Subchannel Noise Powers

In this paper, an active channel, between a source and a destination, refers to a parallel channel where the source transmits power over different subchannels as well as the powers of the subchannels can be adjusted. We herein study the sum-rate maximization for an active channel subject to two constraints, one on the source total transmit power and one on the total channel power. Although this maximization is not convex, we use Karush-Kuhn-Tucker (KKT) conditions to develop a computationally efficient algorithm for optimal source and channel power allocation. To do so, we first show how KKT conditions can be used to determine the number of subchannels that can be active in order for the source power constraint to be feasible. Indeed, we show that not all subchannels but only a subset of them may receive transmit power from the source. Then, for any feasible number of active subchannels, we obtain the optimal source power allocation. In fact, we prove that for any feasible number of active subchannels, there is only one or two solutions for the optimal source power allocation. As such, the optimal solution can be obtained by comparing a finite number of points in the feasible set and by introducing the point, which yields the best sum-rate performance, as the optimal solution. Our analysis and simulation results show that active channels can offer a significantly higher sum-rate compared to their passive counterparts, which rely on water-filling scheme for source power allocation across subchannels.