  Successful deployment of cognitive radios requires efficient sensing of the
spectrum and dynamic adaptation of the available resources according to the
sensed (imperfect) information. While most works design these two tasks
separately, in this paper we address them jointly. In particular, we
investigate an overlay cognitive radio with multiple secondary users that
access orthogonally a set of frequency bands originally devoted to primary
users. The schemes are designed to minimize the cost of sensing, maximize the
performance of the secondary users (weighted sum rate), and limit the
probability of interfering the primary users. The joint design is addressed
using dynamic programming and nonlinear optimization techniques. A two-step
strategy that first finds the optimal resource allocation for any sensing
scheme and then uses that solution as input to solve for the optimal sensing
policy is implemented. The two-step strategy is optimal, gives rise to
intuitive optimal policies, and entails a computational complexity much lower
than that required to solve the original formulation.
