A study of the rank-ambiguity issues in direction-of-arrival estimation

We first extend a theorem on linear independence of steering vectors proposed by Godara and Cantoni to include more array-sensor scenarios. We then show that an array can have pairwise linearly independent steering vectors even when all its intersensor spacings are more than λ/2 where λ is the wavelength of the signals. We next propose a theorem for characterizing rank-2 ambiguity, which is applicable to direction-of-arrival estimation applications where the array sensor locations are fixed and known. Subsequently, we identify a class of three-sensor arrays and a class of uniform circular arrays that have pairwise linearly independent steering vectors and are free of rank-2 ambiguity. We also show that collinearity of sensors, uniformity in intersensor spacings, the dimensions of intersensor spacings, or a combination of some or all of these may give rise to linearly dependent steering vectors. In particular, we demonstrate that for a m-sensor array, m linearly dependent steering vectors exist if the aperture is greater than [(m-1)/2]λ/2, or when at least ([(m+1)/2]+1) sensors are collinear