Sum-Rate Maximization for Active Channels

In this letter, we study the problem of joint power allocation and channel design for an active link which conveys information from a source to a destination through multiple orthogonal subchannels. In such a link, the power can be injected into the channel not only at the source but also at each subchannel. For such a parallel channel, we study the problem of sum-rate maximization under the assumption that the source power as well as the total power of the active channel are limited. Although this problem is not convex, we present an efficient solution to this sum-rate maximization. An interesting aspect of this solution is that it requires only a subset of the subchannels to be active and the remaining subchannels should be turned off. This is in contrast with passive parallel channels with equal subchannel signal-to-noise-ratios (SNRs), where water-filling solution to the sum-rate maximization under a source total power constraint leads to an equal power allocation among all subchannels. Furthermore, we prove that the number of active subchannels depends on the product of the source and channel powers. We also prove that if the total power available to the source and to the channel is limited, then in order to maximize the sum-rate via optimal power allocation to the source and to the active channel, half of the total available power should be allocated to the source and the remaining half should be allocated to the active channel.