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In this paper, we analyze the performance of cooperative spectrum sharing single-carrier (SC) relay systems. Taking into account the peak interference power at the primary user (PU) and the maximum transmit power at the secondary user (SU) network, two separate power allocation constraints are formed. For a two-hop decode-and-forward (DF) relaying protocol and two power allocation constraints, two relay selection schemes, namely, a full-channel state information (CSI)-based best relay selection (BRS) and a partial CSI-based best relay selection (PBRS), are proposed. The distributions of the end-to-end signal-to-noise ratios (e2e-SNRs) for the four cases are derived first, and then their outage probabilities and asymptotic outage probabilities are derived in closed-form. The derived asymptotic outage probabilities are utilized to see different diversity gains. Monte Carlo simulations have verified the derived diversity gains for the four different cases. We also present upper bounds on the ergodic capacities for two particular cases.