Channel imperfections, obstacles, and the unpredictable movements of user equipment can create polarization-mismatch at the receiving antenna, which decreases the power of the received signal in practical wireless communications. In such environments, performance can be improved by opportunistic polarization-matching via dual-polarized (DP) transmitters for limited feedback systems. In this letter, we demonstrate the performance enhancement obtained from opportunistic polarization-matching between a DP transmitter and randomly rotated single-polarized (SP) receivers via a proposed DP multiple-input and SP single-output spatial channel model.