Convex Optimization for Array Diagnosis Using Amplitude-Only Far Field Data in Impulsive Noise Environment

Abstract

In this paper, an array diagnosis method using amplitude-only far-field data in impulsive noise environment is proposed. For amplitude-only far-field data, the power of the observed field is quadratic with respect to array excitation, which leads to a nonlinear inverse problem to restore array excitation. Such a nonlinear inverse problem is transformed into a linear inverse problem, where array excitation vector is replaced by a lifted vector. Based on the structure of the lifted vector, an absolute array excitation vector that has an identical structure to that of array excitation vector is defined. Since these two vectors share the same structure, it is assumed that they also share the same kind of probability distribution. Specifically, the generalized Gaussian distribution with different parameters to address different element failing rates is used to model the probability distribution of the real array excitation vector and the absolute array excitation vector. To model the impulsive noise, the Laplacian probability distribution function is used. The maximum a posterior criterion is adopted to formulate the optimization problem that is eventually found to be convex. However, this convex optimization problem does not have an analytical solution. To solve it, a proximal gradient method is applied, which yields an iterative update algorithm. Finally, computer simulations and experiment are conducted to verify the validity and superiority of the proposed method.