DIRECTION FINDING FOR WIDE-BAND SIGNALS USING AN INTERPOLATED ARRAY

We derive a new direction finding algorithm for multiple wide-band signals received by an arbitrary array, and analyze its performance. Using an interpolation technique we generate a set of virtual arrays, each for a different frequency band, having the same array manifold. The covariance matrices of these arrays are added up to produce a composite covariance matrix. Direction-of-arrival (DOA) estimates are obtained by eigendecomposition of this composite covariance matrix using the narrow-band MUSIC algorithm or its variants. By choosing the virtual arrays to be linear and equally spaced we are able to apply the root-MUSIC algorithm to this problem. Closed form expressions for the asymptotic covariance matrix of the DOA estimation errors are derived using a perturbation analysis. Evaluating these expressions for specific cases and comparing them with the Cramer-Rao lower bound for the DOA estimates provides insight into the statistical efficiency of this algorithm. We pay special attention to correlated and coherent signals. The formulas for the error covariance are quite general, and can be modified to provide results for other wide-band DOA estimation algorithms as well.