Optimal adaptive transmission for a cognitive radio with sensing

We propose a randomized transmission scheme for minimizing a time-averaged cost metric in a cognitive radio. We assume that a single cognitive radio (i.e., a transmitter and receiver) hops over N orthogonal channels, each occupied by a primary user whose ON- OFF activity is modeled by a two-state Markov chain. We assume that the cognitive radio senses the activity in each channel at the beginning of every symbol period, and that a usage cost is assigned to each channel that depends on the channel's physical-layer characteristics and the sensing outcome. We fully characterize the transmission scheme that minimizes the time-averaged cost, subject to interference constraints imposed by the primaries. Finally, we evaluate the performance for two special cases of the cost: the bit error rate and (lower and upper bounds on) the channel capacity.