Design of phased arrays in terms of random subarrays

Analysis and systematic design of uniform phased arrays with subarrays of unequal sizes are absent from the literature, in spite of the appeal of such architectures to wide-bandwidth beam steering. Unequally sized subarrays are expected to outperform identical, contiguous subarrays in terms of array grating lobes, A uniform linear array that is divided into contiguous subarrays of random sizes is studied. Each array element is connected to a phase shifter, and each subarray is implemented with a common time delayer. Closed-form expressions for the average array factor and the variance of the array factor are developed. These expressions enable the formulation of a design procedure that includes the estimation of the peak-grating-lobe level in terms of the probability that the grating lobes will exceed a desired level