Spectrum sharing systems have been introduced to alleviate the problem of spectrum scarcity by allowing an unlicensed secondary user (SU) to share the spectrum with a licensed primary user (PU) under acceptable interference levels to the primary receiver (PU-Rx). In this paper, we consider a secondary link composed of a secondary transmitter (SU-Tx) equipped with multiple antennas and a single-antenna secondary receiver (SU-Rx). The secondary link is allowed to share the spectrum with a primary network composed of multiple PUs communicating over distinct frequency spectra with a primary base station. We develop a transmission scheme where the SU-Tx initially broadcasts a set of random beams over all the available primary spectra for which the PU-Rx sends back the index of the spectrum with the minimum interference level, as well as information that describes the interference value, for each beam. Based on the feedback information on the PU-Rx, the SU-Tx adapts the transmitted beams and then resends the new beams over the best primary spectrum for each beam to the SU-Rx. The SU-Rx selects the beam that maximizes the received signal-to-interference-plus-noise ratio (SINR) to be used in transmission over the next frame. We consider three cases for the level of feedback information describing the interference level. In the first case, the interference level is described by both its magnitude and phase; in the second case, only the magnitude is considered; and in the third case, we focus on a q-bit description of its magnitude. In the latter case, we propose a technique to find the optimal quantizer thresholds in a mean-square-error sense. We also develop a statistical analysis for the SINR statistics and the capacity and bit error rate of the secondary link and present numerical results that study the impact of the different system parameters.