Smart antennas are a promising technology for providing large capacity, coverage and high gain for cellular mobile radio systems. An adaptive phased array antenna is considered as one of the required features of the next generation of personal wireless indoor system and it is highly suitable for mobile application. Such technology will make the communication system much less affected by interference and other impairments that the signal faces in its path. This project discusses adaptive phased array based on nonlinear numerical methods. Zero knowledge Beamforming algorithm which aims to maximize the array output power to adjust a phase angle, is applied to antenna system in order to control automatically its directivity pattern. This project shows a design for transmitter/receiver phased array antenna, the simulation was done using MATLAB program to show the radiation pattern for two types of arrays; linear-array and circular array with different number of array elements, amplitudes and phase shifts. The results were discussed for all cases, in certain cases the linear was better and in some the circular was better. Phased array antenna is not the best choice for all situations it has to be modified with DOA processing to enhance its work.