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In this paper, the power and rate control schemes for a single Cognitive Radio (CR) link are considered, which operate over multiple frequency bands in the presence of licensed Primary Radios (PRs). Specifically, with considerations of delay in spectrum sensing, an optimal algorithm based on Dynamic Programming (DP) is proposed to maximize the average rate of the CR link over a finite time horizon under the constraints on the total energy budget and the CR-to-PR interference. In the proposed algorithm, the PR occupancy of the channels is modeled as a Discrete-Time Markov Chain (DTMC). Based on such a model, the optimal power and rate control strategy is derived, which is a function of the delayed spectrum sensing output and the instantaneous battery level.
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