Sum-rate maximization for two-way active channel with unequal subchannel noise powers
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Wireless parallel channels refer to certain wireless links, where the information is conveyed from a source to a destination through a set of parallel orthogonal subchannels. In such channels, the transmitted signals undergo path loss, phase shift, and can also be affected by multi-path propagation effects. In conventional wireless channel models, there is no control over the gain of each individual subchannel. We herein refer to these conventional channels as passive channels. In this thesis, we study the problem of joint power allocation and design of a parallel channel with orthogonal subchannels where not only the source transmit power(s) over subchannels can be adjusted, but also the powers of each subchannel can be carefully chosen for optimal performance. We herein refer to such wireless links as active channels. We study the problem of sum-rate maximization of a two-way active channel with unequal noise powers over the subchannels, conveying information between two sources (two transceivers that can transmit and receive signals), subject to three constraints. The first two constraints are on the sources’ total transmit powers and the last constraint is on the total active channel’s power. Although this maximization problem is not convex, we develop an analytical method with efficient computations for optimal sources and channel power allocation, by utilizing Karush-Kuhn-Tucker (KKT) conditions. To do so, we first show that not all subchannels, but only a subset may receive transmit power from the sources and the active channel. We then use KKT conditions to determine the necessary conditions for optimality. By searching through the solutions obtained by KKT conditions, we find the number of subchannels which should be active in order for the power constraints to be feasible. We subsequently obtain the optimal channel power allocation for any feasible number of active subchannels. Hence, the optimal solution can be obtained by comparing a finite number of points in the feasible set and introducing the point which yields the best sum-rate performance, as the optimal point that represents the maximum sum-rate.