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.

A fast failure diagnosis method based on structure features of planar arrays

“…In this case, compressed sensing and its variants are utilized for array diagnosis when the number of faults is far smaller than that of the total array elements [6][7][8][9]. Moreover, when the transformation from the excitation of array elements to the field pattern is not linear, optimization theory is used to find the optimal solution of excitation [10,11]. The third type of failure diagnosis is Artificial Intelligence, which uses the strategies of learning, including support vector machines and artificial neural networks [12,13].…”

“…There is no difference of diagnosis between using near-field and far-field measurements, except that their radiation matrices are not the same. Considering the limitations of real measurements, the second scenario focuses on the amplitude-only data to avoid phase measuring because of its complex process and high cost [10,11,14]. The third category is about some particular situations that diagnosis methods are applied in, such as array mismatch and impluse noise, which are more challenging for researchers and engineers [10,11].…”

A Diagnosing Method for Phased Antenna Array Element Excitation Amplitude and Phase Failures Using Random Binary Matrices

“…In order to detect AUT via magnitude data only, approximations and modifications are provided in [21], [24]. Convex optimizations for different configurations are assessed in [28], [29]. The measurement number is further reduced by sparsity promotion methods [30].…”

Optimal Control of Ascent Trajectory for Launch Vehicles: A Convex Approach

“…The convex optimization techniques have been successfully applied in powered landing vehicles [20], rockets [21]- [22],UAVs [23], spacecrafts [24], high-speed atmospheric vehicles [25], etc. [26], [27].…”