Estimating bearing when the source is endfire to an array

Consider the problem of estimating the direction of arrival of a plane wave using a linear array of length L with M sensors. Let 0 denote the direction with respect to the array axis. Assume that we know that 0 >0. The sign of 0 is ambiguous, given data from a linear array. The approximations to the rms errors of the maximum likelihood 1-a and the least-squares 4 estimators of 0 are proportional to I sin0 1 'l. The Cramer-Rao bound also has this property. 5 This seems to imply that these estimators have infinite variances as 0-0. This is not the case, as I will now show.