Maximum Element Dichotomous Coordinate Descent Based Minimum Variance Distortionless Response DoA Estimator

Zhi Quan,Yao Wang,Jie Liu,Yingying Zhang

doi:10.3390/electronics10232966

Zhi Quan, Yao Wang + Show 2 more

Open Access

https://doi.org/10.3390/electronics10232966

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Abstract

In this paper, we devise an efficient approach for estimating the direction of arrival (DoA). The proposed DoA estimation approach is based on minimum variance distortionless response (MVDR) criteria within a recursive least squares (RLS) framework. The dichotomous coordinate descent algorithm is used to modify the calculation of the output power spectrum, and a diagonal loading term is applied to improve the robustness of the DoA estimator. These modifications allow us to both reduce the computational complexity of the RLS DoA estimator and increase the estimation performance. A numerical comparison confirms that the proposed DoA estimator outperforms the conventional RLS DoA estimator in terms of the computational complexity and DoA estimation error. Finally, the proposed theoretical DoA estimator is implemented on a field-programmable gate array (FPGA) board to verify the feasibility of the method. The numerical results of a fixed-point implementation demonstrate that the performance of the proposed method is very close to that of its floating-point counterpart.

Highlights

Accurate source estimation is a key research topic in array signal processing [1].Direction-of-arrival (DoA) algorithms, which estimate the angle of arrival of an incoming signal, are commonly used in applications such as the localisation of sources, signal detection, and beamforming [2]
Instead of calculating the inversion of the correlation matrix directly, the maximum element DCD (MEDCD) algorithm estimates the multiplication of the inverse correlation matrix, and a diagonal loading term is applied to improve the robustness of the direction of arrival (DoA) estimator
MATLAB simulations are conducted to evaluate the performance of the proposed DoA estimator and provide a comparison with the performance of other algorithms in terms of the root mean square error (RMSE) and the signal to noise ratio (SNR)

Summary

Introduction

Accurate source estimation is a key research topic in array signal processing [1]. Direction-of-arrival (DoA) algorithms, which estimate the angle of arrival of an incoming signal, are commonly used in applications such as the localisation of sources, signal detection, and beamforming [2]. The direct inversion of an autocorrelation matrix based MVDR beamformer has a much higher convergence speed, but it requires O(M3) operations per update of the weight vector [7]. The proposed DCD based MVDR DoA estimation solution is easy to implement and numerically stable. Instead of calculating the inversion of the correlation matrix directly, the MEDCD algorithm estimates the multiplication of the inverse correlation matrix, and a diagonal loading term is applied to improve the robustness of the DoA estimator. These modifications allow us to both reduce the computational complexity of the RLS DoA estimator and increase the estimation performance.

System Model and Problem Formulation

Proposed ME-DCD-RLS-DL MVDR DoA Estimator

Computational Complexity

Numerical Results and Discussion

Implementation of the Proposed DoA Estimator

Conclusions