Robust Nonlinear Array Interpolation for Direction of Arrival Estimation of Highly Correlated Signals

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Important signal processing techniques need that the response of the different elements of a sensor array have specific characteristics. For physical systems this often is not achievable as the array elements’ responses are affected by mutual coupling or other effects. In such cases, it is necessary to apply array interpolation to allow the application of ESPRIT, Forward Backward Averaging (FBA), and Spatial Smoothing (SPS). Array interpolation provides a model or transformation between the true and a desired array response. If the true response of the array becomes more distorted with respect to the desired one or the considered region of the field of view of the array increases, nonlinear approaches become necessary. This work presents two novel methods for sector discretization. An Unscented Transform (UT) based method and a principal component analysis (PCA) based method are discussed. Additionally, two novel nonlinear interpolation methods are developed based on the nonlinear regression schemes Multivariate Adaptive Regression Splines (MARS) and Generalized Regression Neural Networks (GRNNs). These schemes are extended and applied to the array interpolation problem. The performance of the proposed methods is examined using simulated and measured array responses of a physical system used for research on mutual coupling in antenna arrays.