Array antenna systems are often used to enhance the received signal to interference and noise ratio wh en the signal operates in heavily jammed environment. Proper modeling of the received data at different antenna elements is impo rtant when evaluating the performance of this system, especially when both th e signal and interference have wide frequency bands .. The antenna output is the linear combination of data from all the antenna ele ments. In conventional narrowband beam forming, tim e sequences at different antenna elements are related by some fixed phase sh ift. The phase shift is determined by the wave form s direction of arrival (DOA). In this paper, an efficient method for the pattern synthesis of the linear antenna arrays with the pre scribed nulling and steering lobe is presented. The proposed method is based on Least Me an Square (LMS) algorithm provide a comprehensive atreatment of the signal model used for beam forming, as well as, describing adaptive algorithms to adjust the weigh ts of an array. In order to improve the convergence rate of LMS algorithm in sm art antenna system, in this paper we proposes a ne w normalized LMS (NLMS) algorithm, This new algorithm can be treated as a b lock based simplification of NLMS algorithm which gsatisfactory performance in certain applications in comparison w ith conventional NLMS recursion, i.e., BBNLMS algor ithm. By taking advantage of spatial filtering, the proposed scheme promises to reduce the bandwidth required for transmitting d ata by improving convergence rate. The performance of the BBNLMS algorithm in th e presence of Multi-path effects and multiple users is analyzed using MATLAB simulations. The simulations when compared to that of the LMS algorithm, the results suggest that BB NLMS algorithm can improve the convergence rate and lead to better system effi ciency.