Spectrum sharing systems have been introduced to alleviate the problem of spectrum scarcity by allowing secondary unlicensed networks to share the spectrum with primary licensed networks under acceptable interference levels to the primary users. In this paper, we develop interference-aware random beam selection schemes that provide enhanced throughput for the secondary link under the condition that the interference observed at the primary link is within a predetermined acceptable value. For a secondary transmitter equipped with multiple antennas, our schemes select a random beam, among a set of power- optimized orthogonal random beams, that maximizes the capacity of the secondary link while satisfying the interference constraint at the primary receiver for different levels of feedback information describing the interference level at the primary receiver. For the proposed schemes, we develop a statistical analysis for the signal-to-noise and interference ratio (SINR) statistics as well as the capacity of the secondary link. Finally, we present numerical results that study the effect of system parameters including number of beams and the maximum transmission power on the capacity of the secondary link attained using the proposed schemes.