Two-Dimensional Separable Gridless Direction-of-Arrival Estimation Based on Finite Rate of Innovation

Kunda Wang,Tao Chen,Lin Shi

doi:10.1109/access.2021.3054660

Abstract

In order to solve the problem that the gridless DOA estimation algorithms based on generalized finite rate of innovation (FRI) signal reconstruction model are not suitable for two-dimensional DOA estimation using planar array, a separable gridless DOA estimation algorithm exploiting bi-orthogonal sparse linear array (BSLA) structure is proposed in this article, which is called 2D-SGFRI. The 2D-SGFRI algorithm firstly recovers the covariance data of the virtual array formed by BSLA through the matrix completion method, so as to obtain the complete covariance data vectors about two independent parameters respectively. Next, since the covariance data vector satisfies the constraints of annihilation filter equations, the generalized FRI signal reconstruction model can be utilized to retrieve DOA from the covariance data vector. Compared with the existing DOA estimation algorithms based on generalized FRI signal reconstruction model, the 2D-SGFRI algorithm can be can be effectively applied to two-dimensional DOA estimation, and can obtain stable estimation results. At the same time, due to the reduction of the dimension of positive semidefinite matrix, the 2D-SGFRI algorithm can significantly reduce the computational complexity compared with the two-dimensional DOA estimation algorithms based on atomic norm minimization (ANM). A series of simulation experiments are shown to verify the effectiveness and superiority of 2D-SGFRI algorithm.

Highlights

As the key and difficult issue in DOA estimation, twodimensional DOA estimation has been widely concerned and studied [1], [2]
Compared with other two-dimensional gridless DOA estimation algorithms, 2D-SGFRI algorithm has the following two advantages: (a) Extension in application scenarios: Due to the introduction of bi-orthogonal sparse linear array (BSLA), 2D-SGFRI algorithm transforms a two-dimensional DOA estimation problem into two independent one-dimensional DOA estimation problems, which effectively solves the problem that the gridless DOA estimation algorithm based on generalized finite rate of innovation (FRI) signal reconstruction model cannot be applied in the field of two-dimensional DOA estimation using planar antenna array; (b) Reduction in algorithm complexity: Compared with the two-dimensional gridless DOA estimation algorithm based on atomic norm minimization (ANM), the dimension of semidefinite programming (SDP) problem in 2D-SGFRI is lower, which saves the computational cost
The detailed derivation of formula (16) is given in the appendix of this article. It can be seen from formula (16) that compared with the existing generalized FRI signal reconstruction model, the computational burden of solving the bi-variate optimization problem in the proposed algorithm becomes lighter

Summary

INTRODUCTION

As the key and difficult issue in DOA estimation, twodimensional DOA estimation has been widely concerned and studied [1], [2]. (a) Extension in application scenarios: Due to the introduction of BSLA, 2D-SGFRI algorithm transforms a two-dimensional DOA estimation problem into two independent one-dimensional DOA estimation problems, which effectively solves the problem that the gridless DOA estimation algorithm based on generalized FRI signal reconstruction model cannot be applied in the field of two-dimensional DOA estimation using planar antenna array;. 2D-SGFRI ALGORITHM we first introduce the two-dimensional signal model of DOA estimation based on BSLA, and the matrix completion theory is exploited to recover the complete covariance data of received signal satisfying the annihilation filtering equation. It is not difficult to see that the two-dimensional DOA estimation model can be transformed into two independent one-dimensional DOA estimation models by using the special geometric structure of BSLA, which provides support for the promotion of one-dimensional DOA estimation algorithm in two-dimensional estimation problems

COVARIANCE DATA RECOVERY BASED ON MATRIX COMPLETION THEORY

SIMPLIFIED SEPARATER TWO-DIMENSIONAL

CONCLUSION