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Three low-complexity relay-selection strategies, namely, selective amplify and forward (S-AF), selective decode and forward (S-DF), and amplify and forward with partial relay selection (PRS-AF) in a spectrum-sharing scenario are studied. First, we consider a scenario where perfect channel state information (CSI) is available. For these scenarios, the respective asymptotic outage behaviors of the secondary systems are analyzed, from which the diversity and coding gains are derived and compared. Unlike the coding gain, which is shown to be very sensitive with the position of the primary receiver, the diversity gain of the secondary system is the same as the nonspectrum-sharing system. In addition, depending on the cooperative strategy employed, an increase in the number of relays may lead to severe loss of the coding gain. Afterwards, the impacts of imperfect CSI regarding the interference and transmit channels on the outage behavior of the secondary systems are analyzed. On one hand, the imperfect CSI concerning the interference channels only affects the outage performance of the primary system, whereas it has no effect on the diversity gain of the secondary system. On the other hand, the imperfect CSI concerning the transmit channels of the secondary systems may reduce the diversity gain of the three relay-selection strategies to unity, which is validated by both theoretical and numerical results.