In this letter, the performance improvement by the deployment of multiple antennas in cognitive radio systems is studied from a system-level view. The term opportunistic spectrum efficiency (OSE) is defined as the performance metric to evaluate the spectrum opportunities that can actually be exploited by the secondary user (SU). By applying a simple energy combining detector, we show that deploying multiple antennas at the SU transceiver can improve the maximum achievable OSE significantly. Numerical results also reveal that the improvement comes from the reduction of both the detection overhead and the false alarm probability.