An important question in array design is that of where to place the elements of a sparse array for optimal performance in terms of its ability to detect and resolve a greater number of sources than conventionally possible. In particular, it has been shown that when sensor elements are arranged in the minimum redundancy fashion, by performing an augmentation technique on the covariances obtained from the array outputs, an M element array can be made to estimate the directions of arrival of as many as M(M-1)/2 uncorrelated sources unambiguously. Constructive procedures are developed to evaluate integer locations for an array of given sensors that span a prescribed distance, such that any missing integer is expressible as the difference of two sensor locations. New upper bounds for the ratio of the square of the minimum number of elements to the spanning distance are also established.
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