Power allocation strategies for channel switching and wireless localization
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Optimal power allocation is an important approach for enhancing performance of both communication and localization systems. In this dissertation, optimal channel switching problems are investigated for average capacity maximization via optimization of power resources in general. In addition, power control games are designed for a wireless localization network including anchor and jammer nodes which compete for the localization performance of target nodes. First, an optimal channel switching strategy is proposed for average capacity maximization in the presence of average and peak power constraints. Necessary and sufficient conditions are derived in order to determine when the proposed optimal channel switching strategy can or cannot outperform the optimal single channel strategy, which performs no channel switching. Also, it is obtained that the optimal channel switching strategy can be realized by channel switching between at most two different channels. In addition, a low-complexity optimization problem is derived in order to obtain the optimal channel switching strategy. Furthermore, based on some necessary conditions that need to be satisfied by the optimal channel switching solution, an alternative approach is proposed for calculating the optimal channel switching strategy. Second, the optimal channel switching problem is studied for average capacity maximization in the presence of additive white Gaussian noise channels and channel switching delays. Initially, an optimization problem is formulated for the maximization of the average channel capacity considering channel switching delays and constraints on average and peak powers. Then, an equivalent optimization problem is obtained to facilitate theoretical investigations. The optimal strategy is derived and the corresponding average capacity is specified when channel switching is performed among a given number of channels. Based on this result, it is shown that channel switching among more than two different channels is not optimal. In addition, the maximum average capacity achieved by the optimal channel switching strategy is formulated as a function of the channel switching delay parameter and the average and peak power limits. Then, scenarios under which the optimal strategy corresponds to the exclusive use of a single channel or to channel switching between two channels are described. Furthermore, sufficient conditions are obtained to determine when the optimal single channel strategy outperforms the optimal channel switching strategy. Third, the optimal channel switching problem is studied for average capacity maximization in the presence of multiple receivers in the communication system. At the beginning, the optimal channel switching problem is proposed for average capacity maximization of the communication between the transmitter and the secondary receiver while fulfilling the minimum average capacity requirement of the primary receiver and considering the average and peak power constraints. Then, an alternative equivalent optimization problem is provided and it is shown that the solution of this optimization problem satisfies the constraints with equality. Based on the alternative optimization problem, it is obtained that the optimal channel switching strategy employs at most three communication links in the presence of multiple available channels in the system. In addition, the optimal strategies are specified in terms of the number of channels employed by the transmitter to communicate with the primary and secondary receivers. Last, a game theoretic framework is proposed for wireless localization networks that operate in the presence of jammer nodes. In particular, power control games between anchor and jammer nodes are designed for a wireless localization network in which each target node estimates its position based on received signals from anchor nodes while jammer nodes aim to reduce localization performance of target nodes. Two different games are formulated for the considered wireless localization network: In the first game, the average Cram´er-Rao lower bound (CRLB) of the target nodes is considered as the performance metric, and it is shown that at least one pure strategy Nash equilibrium exists in the power control game. Also, a method is presented to identify the pure strategy Nash equilibrium, and a sufficient condition is obtained to resolve the uniqueness of the pure Nash equilibrium. In the second game, the worst-case CRLBs for the anchor and jammer nodes are considered, and it is shown that the game admits at least one pure Nash equilibrium.