Abstract
We consider joint optimization for sensing-channel selection and ensuing power control problem with cognitive radios over time-varying fading channels. It is shown that this joint design can be judiciously formulated as a convex optimization problem. Optimal joint sensing-channel selection and power control scheme is then derived in closed-form under the constraints of average power budget and maximum allowable probability of collisions with the primary communications. In addition, we develop a stochastic optimization algorithm that can operate without a-priori knowledge of the fading channel statistics. It is rigourously established that the proposed stochastic scheme is capable of dynamically learning the intended wireless channels on-the-fly to approach the optimal strategy almost surely. Numerous results are also provided to evaluate the proposed schemes for cognitive transmissions over block fading channels.
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