Soft Sensing and Optimal Power Control for Cognitive Radio

We consider a cognitive radio system where the secondary transmitter varies its transmit power based on the information available from the spectrum sensor. The operation of the secondary user is governed by its peak transmit power constraint and an average interference constraint at the primary receiver. Without restricting the sensing scheme (total received energy, or correlation etc), we characterize the power adaptation strategies that maximize the secondary user's SNR and capacity. We show that, in general, the capacity optimal power adaptation requires decreasing the secondary transmit power from the peak power to zero in a continuous fashion as the probability of the primary user being present increases. In contrast, we find that that power control that maximizes the SNR is binary, i.e., if there is any transmission, it takes place only at the peak power level. Numerical results for common spectrum sensing schemes show that the SNR and capacity maximizing schemes can be very different. With an average transmit power constraint at the secondary radio, both the SNR and capacity optimal power control schemes are observed to be non-binary. Further, we find that with secondary channel knowledge at the cognitive transmitter, the optimal SNR with an average transmit power constraint is unbounded.