A STUDY OF THE UNIQUENESS OF STEERING VECTORS IN ARRAY-PROCESSING

We first analyze the relationship between the severity of rank-one amb iguity of steering vectors and the inter-sensor spacing for uniform li near arrays (ULAs). We next identify a class of non-uniform linear arr ay suffering from rank-one ambiguity. Subsequently. we show that by an appropriate choice of some inter-sensor spacings of a non-uniform lin ear array, one may remove completely rank-one ambiguity, and we propos e a general approach to constructing such an array. It is interesting to note that the average inter-sensor spacing of such an array can be infinitely large. We also analyze higher-rank ambiguity associated wit h linear arrays and identify a class of non-uniform arrays with such a mbiguity. We show analytically that if the aperture of a p-sensor line ar array with arbitrary inter-sensor spacings is greater than or equal to (p - 1) A/2, where A is the wavelength of the signal of interest, then rank-(p - 1) ambiguity exists. Although this result is well known for ULAs, its validity to general linear arrays has not been mentione d before. Finally, we propose a procedure for analyzing the closeness of steering vectors to rank-(p - 1) ambiguity by computation.