Abstract: Smart antenna systems plays an important role in wireless communications systems. This study begins with a heuristic approach about the optimization of Signal-to-Interference Ratio (SIR) to enhance the received signal and minimize the interfering signals in wireless communications. After that, the approach for improvisation of SIR of a desired signal is extended for a specified condition and for its formulation requires noise to be added in the system in this study. In this study, a rigorous derivation of the Signal-to-Interference Ratio (SIR) maximization is derived by considering a general non adaptive conventional or traditional narrowband array and finally the limitations of non-adaptive or fixed beamforming approach to enhance the desired signal.