A new spectrum sharing strategy based on coupled detection and estimation is proposed for cognitive radio networks. The strategy consists of the following steps: First the secondary user (SU) listens to the spectrum allocated to the primary user (PU) to detect the state of the PU and transmits if the PU is inactive. However, if the PU is active, the SU estimates the PU location and then makes a decision about the reliability of the estimate. The SU transmits via beamforming, with a null in the estimated direction of the PU, only when the estimate is classified as reliable. Therefore, the proposed method is able to trade-off throughput for reduced interference at the PU. We formulate this problem mathematically and derive the optimum strategy that maximizes the throughput of the cognitive radio system under average interference power constraint at the PU. Finally, we provide simulation results to demonstrate the performance of the proposed spectrum sharing strategy.