The application of antenna arrays has been suggested in recent years for mobile communications systems to overcome the problem of limited channel bandwidth, thereby satisfying an ever growing demand for a large number of high bit rate mobiles on communications channels. It has been shown by many studies that when an array is appropriately used in a mobile communications system, it helps in improving the system performance by increasing channel capacity and spectrum efficiency. It also extends the range of coverage, reduces multipath fading, and co-channel interference. These benefits are achieved by adjusting the antenna radiation pattern for a given wireless environment. The main objective of the adaptive antenna array is to reduce the received interference by forming nulls towards the co-channel interference sources, while tracking the desired signal by steering a beam towards it. The sensitivity pattern of the array is adjusted to suit these requirements by combining signals from different antenna elements with appropriate weighting. Here, the knowledge of a reference signal, a training signal, or the direction of the desired signal source is necessary to differentiate the desired signal from the interferers. The term adaptive antenna is used when the weights (gains and phases) applied to the signals induced on the array elements, are regularly updated before combining. The adaptation/updating is used to control the radiation pattern of the array dynamically, according to the requirements of the system. There are many adaptive methods and algorithms to modify the array weights, and to estimate the direction of arrival (DOA) of the desired and interference signals, each with its advantages and disadvantages. In an optimal adaptive antenna array system the gain and phase of each antenna element is adjusted to achieve the optimal performance of the array in some sense. For example, in steered beam adaptive arrays, the basis for adjusting gains and phases of each element is to obtain maximum output ...