A Condition for Unbiased Direction-of-Arrival Estimation with Toeplitz Decorrelation Techniques

Toeplitz decorrelation techniques, as applied towards direction-of-arrival estimation of coherent narrowband signals using a sensor array, significantly improve the accuracy of subspace methods without reducing the effective array aperture. The novel contribution of this paper is a necessary and sufficient condition that any jointly Toeplitz and Hermitian matrix produced by these techniques must satisfy in order to facilitate unbiased estimation via a subspace method. The condition is derived for a uniform linear array and additive white Gaussian noise model. The row-selection and diagonal-averaging strategies for generating Toeplitz matrices are evaluated against the condition, for the case where all sources are coherent. It is proved that row selection accommodates unbiased estimation if and only if the first row of the deficient covariance matrix is selected, whereas diagonal averaging invariably leads to bias.