Secondary access to the licensed spectrum is viable only if the interference is avoided at the primary system. In this regard, different paradigms have been conceptualized in the existing literature. Among these, interweave systems (ISs) that employ spectrum sensing have been widely investigated. Baseline models investigated in the literature characterize the performance of the IS in terms of a sensing-throughput tradeoff, however, this characterization assumes perfect knowledge of the involved channels at the secondary transmitter, which is unavailable in practice. Motivated by this fact, we establish a novel approach that incorporates channel estimation in the system model, and consequently investigate the impact of imperfect channel knowledge on the performance of the IS. More particularly, the variation induced in the detection probability affects the detector's performance at the secondary transmitter, which may result in severe interference at the primary receivers. In this view, we propose employing average and outage constraints on the detection probability, in order to capture the performance of the IS. Our analysis reveals that with an appropriate choice of the estimation time determined by the proposed approach, the performance degradation of the IS can be effectively controlled, and subsequently the achievable secondary throughput can be significantly enhanced.