Channel Capacity Limits of Cognitive Radio with Imperfect Channel Knowledge

Cognitive radio 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 PU-SU CSI is imperfect as it is the practical case. 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 can not always satisfy the received peak 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. Our results are confirmed through comparison with simulations.