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In this paper, we study transmission policies for opportunistic spectrum access over multiple Rayleigh fading channels. We formulate the opportunistic spectrum access problem as a joint channel access and power control problem with the objective that maximizes expectation sum of throughput under the constraint of limited battery capacity over finite time slots. In this problem, we consider the transmission power limitation for each channel to guarantee fairness of spectrum access. Furthermore, we propose a discrete-time Markov chain model, which can account for primary users' (PUs) activities and the fading characteristics. Based on this Markov model, we efficiently solve the problem via dynamic programming and propose the optimal transmission policy. Extensive simulations verify the performance of the proposed scheme.