In a cost-effective implementation, we address the problem of cross-interference in cognitive multiple-input multiple-output (MIMO) spectrum sharing where mutual co-channel interference (CCI) between the primary and secondary systems is of major concern. First, we propose an optimal transmit-antenna selection (TAS) strategy that instead maximizes the received signal-to-interference-plus-noise ratio (SINR) after maximum-ratio combining (MRC). We statistically analyze the combined SINR structure and derive new expressions of its cumulative and probability distribution functions. Interestingly, we accurately show the substantial gains offered by the proposed TAS strategy in terms of the secondary system outage performance compared to the existent state-of-the-art TAS strategies. Finally, our analytical results are validated by simulations and some important insights are also underlined.