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Spectrum sharing has been considered an effective method of mitigating the spectrum scarcity in wireless communications by allowing the coexistence of both unlicensed and licensed devices in the same frequency bands, something which can be done by limiting the received interference power at the licensed user at an acceptable low level. In this paper, we study the outage and truncated channel inversion with fixed rate (TIFR) capacity of a sensing-enhanced spectrum sharing (SESS) cognitive radio system (CRS) under missed-detection interference power constraints for the protection of the primary users. In our analysis, we consider (i) average transmit power constraints, (ii) peak interference power constraints and (iii) average interference power constraints, and derive the power allocation strategy, as well as the TIFR and outage capacity for Nakagami-m fading channels. We provide numerical results which show that a SESS CRS can achieve improved outage and TIFR capacity compared to a conventional non-sensing spectrum sharing CRS.