Cognitive radio (CR) design aims to increase spectrum utilization by allowing the secondary users (SUs) to coexist with the primary users (PUs), as long as the interference caused by the SUs to each PU is properly regulated. At the SU, channel-state information (CSI) between its transmitter and the PU receiver is used to calculate the maximum allowable SU transmit power to limit the interference. We assume that this CSI is imperfect, which is an important scenario for CR systems. In addition to a peak received interference power constraint, an upper limit to the SU transmit power constraint is also considered. We derive a closed-form expression for the mean SU capacity under this scenario. Due to imperfect CSI, the SU cannot always satisfy the peak received interference power constraint at the PU and has to back off its transmit power. The resulting capacity loss for the SU is quantified using the cumulative-distribution function of the interference at the PU. Additionally, we investigate the impact of CSI quantization. To investigate the SU error performance, a closed-form average bit-error-rate (BER) expression was also derived. Our results are confirmed through comparison with simulations.

Capacity Limits and Performance Analysis of Cognitive Radio With Imperfect Channel Knowledge