Gain and Phase Calibration of Uniform Rectangular Arrays Based on Convex Optimization and Neural Networks

Xiran Jie,Boxuan Gu,Bolun Zheng

doi:10.3390/electronics11050718

Xiran Jie, Boxuan Gu + Show 1 more

Open Access

https://doi.org/10.3390/electronics11050718

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Journal: Electronics	Publication Date: Feb 25, 2022
Citations: 1	License type: CC BY 4.0

Affiliation: Zhejiang University, Hangzhou Dianzi University

Abstract

A calibration method based on convex optimization (CVX) and neural networks is proposed for the large planar arrays of phased array three-dimensional imaging sonar systems. The method only needs an acoustic calibration source at an unknown position in the far field, and the direction of arrival (DOA) and gain and phase error are jointly estimated. The method uses a CVX algorithm to solve an optimization problem and initially estimates the DOA of the calibration source robustly. Subsequently, according to the estimation results, a neural network is used for fitting to obtain off-grid DOA estimation of the calibration source. Thereafter, spatial matched filtering is performed to obtain the gain and phase residual estimations. The root mean square error (RMSE) of the beam pattern calibrated by the method for uniform planar arrays can reach a value of 4.9542 × 10−5. The experimental results demonstrate the efficiency of the proposed method for gain and phase calibration.

Highlights

In phased array three-dimensional (3D) sonar systems, the inconsistent sensor performances and sensor position deviation cause amplitude and phase errors in the array, leading to an increase in the sidelobe of the beam pattern and a shift in the focus direction
The beam strength was set as the input, and the neural network (NN) was used for fitting to estimate the off-grid direction
This method effectively avoided the ambiguity of phase 2π, and because the implementation of the convex optimization (CVX) algorithm to estimate direction of arrival (DOA) in the off-grid direction is complex, secondary estimation was employed to overcome this challenge

Summary

Introduction

In phased array three-dimensional (3D) sonar systems, the inconsistent sensor performances and sensor position deviation cause amplitude and phase errors in the array, leading to an increase in the sidelobe of the beam pattern and a shift in the focus direction. Owing to the 2π ambiguity of phase, the calibration method based on a neural network (NN) is prone to overfitting, which creates challenges in accurately estimating the correction source DOA.

Results

Conclusion