A cyclic prefixed single-carrier (CP-SC) relaying system is considered for cognitive radio networks under spectrum sharing condition. The outage probability of secondary users employing a two-hop amplify-and-forward (AF) relay protocol is investigated under an interference constraint inflicted by the secondary user-source and the secondary user-relay on a primary user (PU). Assuming channel-state-information (CSI) is available, the end-to-end signal-to-noise-ratio (e2e-SNR) is first derived, and then an analytical expression for the cumulative distribution function (CDF) of this e2e-SNR is derived. Based on this derived CDF, analytical expressions for the exact outage probability, the approximate symbol error rate (SER), and approximate achievable rate can be obtained. In addition, to reveal further insights into the impact of channel lengths on the diversity and coding gains, the asymptotic outage probability and SER are provided. It is important to note that the performance of cognitive radio networks is degraded due to the limited power constraint inflicted on the primary network. As such, the optimal power allocation (OPA) is also derived to achieve a better asymptotic outage probability.