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In this letter, we address the problem of element placement in a linear aperiodic array for use in spatial spectrum estimation. By making use of a theorem by Caratheodory, it is shown that, for a given number of elements, there exists a distribution of element positions which, for uncorrelated sources, results in superior spatial spectrum estimators than are otherwise achievable. The improvement is obtained by constructing an augmented covariance matrix, made possible by the choice of element positions, with dimension greater than the number of array elements. The augmented matrix is then used in any of the known spectrum estimation methods in conjunction with a correspondingly augmented search pointing vector. Examples are given to show the superior detection capability, the larger dynamic range for spectral peak to background level, the lower sidelobes, and the relatively low bias values, when one of the known spectrum estimation techniques based on eigenstructure is used.