We consider an underlay cognitive radio system consisting of a secondary transmitter (ST), K secondary receivers (SRs) and a primary receiver (PR). Data transmission is granted to the ST under the constraint that the generated peak interference to the PR is below a predetermined interference temperature level. Assuming that the ST can adaptively adjust its transmit power according to the fading state of the channel, our objective is to analyze the link reliability in terms of the symbol error rate (SER). In particular, we derive the exact SER expressions under the assumption that opportunistic scheduling is applied at the ST, where the SR with the highest channel gain is exclusively selected for data transmission. Numerical simulations are performed to verify the obtained SER expressions. Our results show that there exists an error floor region due to the interference constraint, i.e., the SER approaches to a certain constant as the allowed peak transmit power threshold increases. Moreover, we show that opportunistic scheduling can improve the SER performance under a fixed interference constraint.