A study of the uniqueness of steering vectors in array processing

Abstract We first analyze the relationship between the severity of rank-one ambiguity of steering vectors and the inter-sensor spacing for uniform linear arrays (ULAs). We next identify a class of non-uniform linear arrays suffering from rank-one ambiguity. Subsequently, we show that by an appropriate choice of some inter-sensor spacings of a non-uniform linear array, one may remove completely rank-one ambiguity, and we propose 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 with linear arrays and identify a class of non-uniform arrays with such ambiguity. We show analytically that if the aperture of a p -sensor linear array with arbitrary inter-sensor spacings is greater than or equal to ( p −1)λ/2, where λ 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 mentioned before. Finally, we propose a procedure for analyzing the closeness of steering vectors to rank-( p −1) ambiguity by computation.