Cognitive radio (CR) design aims to increase spectrumutilization by allowing the secondary users (SUs) to coexistwith the primary users (PUs), as long as the interference caused bythe SUs to each PU is properly regulated. At the SU, channel-stateinformation (CSI) between its transmitter and the PU receiveris used to calculate the maximum allowable SU transmit powerto limit the interference. We assume that this CSI is imperfect,which is an important scenario for CR systems. In addition toa peak received interference power constraint, an upper limit tothe SU transmit power constraint is also considered. We derivea closed-form expression for the mean SU capacity under thisscenario. Due to imperfect CSI, the SU cannot always satisfy thepeak received interference power constraint at the PU and hasto back off its transmit power. The resulting capacity loss forthe SU is quantified using the cumulative-distribution functionof the interference at the PU. Additionally, we investigate theimpact of CSI quantization. To investigate the SU error performance,a closed-form average bit-error-rate (BER) expression wasalso derived. Our results are confirmed through comparison withsimulations.
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