Smart Adaptive Array antenna can automatically track the unknown interference signal in real time applications, that it requires to provide nulls towards the interference and offer gain to the required signal to ensure the required signal reception, so it leads the output SINR (signal to Interference and Noise Ratio) is improved. There is a growing need for the development of efficient algorithms for real-time optimization. Several algorithms can be applied for Digital Signal Processors (DSP),

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... hich differ in their complexity, convergence and so on In this paper, an efficient method for the DOA estimation of the linear antenna arrays with the prescribed steering and nulling lobe is presented. The proposed method is based on Least Mean Square (LMS) algorithm; provide a comprehensive and detailed treatment of the signal model used for beam forming, as well as, describing adaptive algorithms to adjust the weights of an array. In order to improve the convergence rate of LMS algorithm in smart antenna system, this paper proposes the GNGD algorithm. By taking advantage of spatial filtering, the proposed scheme promises to reduce the bandwidth required for transmitting data by improving convergence rate. The performance of the GNGD algorithm in the presence of Multi-path effects and multiple users is analyzed using MATLAB simulations. The simulations when compared to that of the LMS algorithm greater improvement in the convergence rate are observed. The results suggest that GNGD algorithm can improve the convergence rate and lead to better system efficiency.