In this paper, a transmit antenna selection scheme, which is based on shadowing side information, is investigated. In this scheme, the selected single transmit antenna provides the highest shadowing coefficient between transmitter and receiver. By the proposed technique, the frequency of the usage of the feedback channel from the receiver to the transmitter and also channel estimation complexity at the receiver can be reduced. We study the performance of our proposed technique and in the analysis, we consider an independent but not identically distributed Generalized-K composite fading model. More specifically exact and closed-form expressions for the outage probability, the moment generating function, the moments of signal-to-noise ratio, and the average symbol error probability are derived. In addition, asymptotic outage probability and symbol error probability expressions are also presented in order to investigate the diversity order and the array gain. Finally, our theoretical performance results are validated by Monte Carlo simulations.