DOA estimation for noninteger linear antenna arrays with more uncorrelated sources than sensors

We investigate direction-of-arrival (DOA) estimation involving nonuniform linear arrays, where the sensor positions may be noninteger values expressed in half-wavelength units, with some number of uncorrelated Gaussian sources that is greater than or equal to the number of sensors. We introduce an approach whereby the (noninteger) co-array is treated as the most appropriate virtual array when considering an augmented covariance matrix. Since such virtual arrays have an incomplete set of covariance lags, we discuss various completion philosophies to fill in the missing elements of the associated partially specified Hermitian covariance matrix. This process is followed by the application of an algorithm that searches for a specific number of plane wavefronts, yielding the minimum fitting error for the specified covariance lags in the neighborhood of the completion-initialized DOA estimates. In this way, we are able to resolve possible ambiguity and to achieve asymptotically optimal estimation accuracy. Numerical simulations of DOA estimation demonstrate a close proximity to the Cramér–Rao bound.