Accurate Parametric Analytic Manifold Using a Nonlinear Mutual Coupling Model

The precise mutual coupling model is the key to obtain an accurate parametric analytic manifold, which is the prerequisite to achieve superresolution direction of arrival estimation and high-precision beamforming. The widely used mutual coupling model is linear and cannot describe the direction-dependent characteristics of mutual coupling, which leads to serious performance deterioration of array signal processing algorithms. In this letter, a new nonlinear mutual coupling model named high-order broad mutual coupling matrix (MCM) is established based on the Taylor expansion to describe the directional-dependent coupling relationship between two adjacent antenna elements. Then, an accurate parametric analytic manifold using a finite-order approximation of the high-order broad MCM is yielded by the antenna pattern reconstruction method. Numerical examples verify that the array manifold reconstruction errors can be reduced exponentially by the proposed parametric analytic manifold. Especially when the piecewise fitting strategy is adopted, the reconstruction errors of the fourth-order approximated analytic manifold can be reduced to less than 1% of those of the conventional array manifold.