Unified analysis of co-array interpolation for direction-of-arrival estimation

This paper considers the problem of co-array interpolation for direction-of-arrival (DOA) estimation with sparse nonuniform arrays. By utilizing the much longer difference co-array associated with these arrays, it is possible to perform DOA estimation of more sources than sensors. Since the co-array may contain holes (or missing lags), interpolation algorithms have been proposed to fully utilize the remaining elements of the co-array beyond that captured in the contiguous ULA segment. However, the quality and stability of interpolation performed by such algorithms (especially in presence of modeling errors) have not been analyzed. This paper provides a unified analysis of co-array interpolation algorithms to bound the interpolation error in terms of modeling errors. The results are universal in the sense that they can be applied to analyze any algorithm that utilizes the positive semidefinite (PSD) structure of the interpolated covariance matrix. The general framework is then applied to analyze specific algorithms and simulations are conducted to study their interpolation errors.