A STUDY OF THE RANK-AMBIGUITY ISSUES IN DIRECTION-OF-ARRIVAL ESTIMATION

We first extend a theorem on linear independence of steering vectors p roposed by Godara and Cantoni to include more array-sensor scenarios, We then show that an array can have pairwise linearly independent stee ring vectors even when all its intersensor spacings are more than lamb da/2 where lambda is the wavelength of the signals, We next propose a theorem for characterizing rank-2 ambiguity, which is applicable to di rection-of-arrival estimation applications where the array sensor loca tions are fixed and known. Subsequently, we identify a class of three- sensor arrays and a class of uniform circular arrays that have pairwis e linearly independent steering vectors and are free of rank-2 ambigui ty, We also show that collinearity of sensors, uniformity in intersens or spacings, the dimensions of intersensor spacings, or a combination of some or all of these may give rise to linearly dependent steering v ectors, In particular, we demonstrate that for a m-sensor array, m lin early dependent steering vectors exist if the aperture is greater than [(m - 1)/2]lambda/2, or when at least ([(m + 1)/2] + 1) sensors are c ollinear.