Sum-rate maximization for active channels
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In conventional wireless channel models, there is no control on the gains of different subchannels. In such channels, the transmitted signal undergoes attenuation and phase shift and is subject to multi-path propagation effects. We herein refer to such channels as passive channels. In this dissertation, we study the problem of joint power allocation and channel design for a parallel channel which conveys information from a source to a destination through multiple orthogonal subchannels. In such a link, the power over each subchannel can be adjusted not only at the source but also at each subchannel. We refer to this link as an active parallel channel. For such a channel, we study the problem of sum-rate maximization under the assumption that the source power as well as the energy of the active channel are constrained. This problem is investigated for equal and unequal noise power at different subchannels. For equal noise power over different subchannels, although the sum-rate maximization problem is not convex, we propose a closed-form solution to this maximization problem. 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 switched off. This is in contrast with passive parallel channels with equal subchannel signal-tonoise- ratios (SNRs), where water-filling solution to the sum-rate maximization under a total source power constraint leads to an equal power allocation among all subchannels. Furthermore, we prove that the number of active channels 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 viii ix of the total available power should be allocated to the source and the remaining half should be allocated to the active channel. We extend our analysis to the case where the noise powers are unequal over different subchannels. we show that the sum-rate maximization problem is not convex. Nevertheless, with the aid of Karush-Kuhn-Tucker (KKT) conditions, we propose a computationally efficient algorithm for optimal source and channel power allocation. To this end, first, we obtain the feasible number of active subchannels. Then, we show that the optimal solution can be obtained by comparing a finite number of points in the feasible set and by choosing the best point which yields the best sum-rate performance. The worst-case computational complexity of this solution is linear in terms of number of subchannels.