The peak sidelobe of the phased array having randomly located elements

A formula is derived for the peak sidelobe level of a phased array in which the elements are randomly located. The parameters of the formula are the number and size of the array elements, size of the array, wavelength, beamsteering angle, and signal bandwidth. The theory is tested by measurement of the peak sidelobe of several hundred computer-simulated random arrays. Unlike the case for the conventional array the effect of spatial taper (nonuniform density of element location) upon the peak sidelobe level is minor. The peak sidelobe of the two-dimensional planar array is approximately 3 dB higher than that of the linear array of the same length and same number of elements.