Sidelobe level distribution computation for antenna arrays with arbitrary element distributions

This paper discusses the conditions in which the sidelobe level distribution can be calculated in closed form for arrays with randomly located antenna elements with arbitrary element probability distributions. By using the number of times a beampattern crosses a certain level in an upward direction, sidelobe level distributions are found for beampatterns with angle-dependent and angle-independent statistics. The evaluation of the probability of exceeding a given peak sidelobe is investigated as a function of the antenna array spatial position variance in the asymptotic limit of a large number of antennas. Examples are presented including a multi-input multi-output (MIMO) radar illustration.