The spectrum sharing has recently passed into a mainstream Cognitive Radio (CR) strategy. We investigate the core issue in this strategy: interference mitigation at Primary Receiver (PR). We propose a linear precoder design which aims at alleviating the interference caused by Secondary User (SU) from the source for Orthogonal Space-Time Block Coding (OSTBC) based CR. We resort to Minimum Variance (MV) approach to contrive the precoding matrix at Secondary Transmitter (ST) in order to maximize the Signal to Noise Ratio (SNR) at Secondary Receiver (SR) on the premise that the orthogonality of OSTBC is kept, the interference introduced to Primary Link (PL) by Secondary Link (SL) is maintained under a tolerable level and the total transmitted power constraint at ST is satisfied. Moreover, the selection of polarization mode for SL is incorporated in the precoder design. In order to provide an analytic solution with low computational cost, we put forward an original precoder design algorithm which exploits an auxiliary variable to treat the optimization problem with a mixture of linear and quadratic constraints. Numerical results demonstrate that our proposed precoder design enable SR to have an agreeable SNR on the prerequisite that the interference at PR is maintained below the threshold.