An alternative approach is based on statistically computed signal analysis technique for the design of antenna array exhibiting lower side lobes in their radiation pattern. New and generalized expressions for the array factor of all physically realizable linear antenna arrays are introduced. An algorithm based on the statistically computed signal analysis is designed. By considering the random elements, distance between the sensors, their mean, variance, average amplitude pattern and correlation of the amplitude between the two angles, some mathematical formulations have been done and shown with the help of MATLAB. Based on these generalized expressions, a new way of synthesizing arrays with reduced side lobes is available. It applies to end fire antenna array, which may have either even or odd numbers of sensors with restricted elements spacing. Final expressions shown are a clear relationship between elements excitation and null location in the radiation patterns.