scholarly journals Super-Resolution DoA Estimation on a Co-Prime Array via Positive Atomic Norm Minimization

Energies ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3609
Author(s):  
Hyeonjin Chung ◽  
Young Mi Park ◽  
Sunwoo Kim
Keyword(s):  
Optimization Problem ◽  
Super Resolution ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Real Numbers ◽  
Positive Real ◽  
Norm Minimization ◽  
Atomic Norm ◽  
Lower Complexity ◽  
Simulation Results

A super-resolution direction-of-arrival (DoA) estimation algorithm that employs a co-prime array and positive atomic norm minimization (ANM) is proposed. To exploit larger array cardinality, the co-prime array vector is constructed by arranging elements of a correlation matrix. The positive ANM is a technique that can enhance resolution when the coefficients of the atoms are the positive real numbers. A novel optimization problem is proposed to ensure the coefficients of the atoms are the positive real numbers, and the positive ANM is employed after solving the optimization problem. The simulation results show that the proposed algorithm achieves high resolution and has lower complexity than the other ANM-based super-resolution DoA estimation algorithm.

scholarly journals Superresolution 2D DOA Estimation for a Rectangular Array via Reweighted Decoupled Atomic Norm Minimization

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Ming-Ming Liu ◽  
Chun-Xi Dong ◽  
Yang-Yang Dong ◽  
Guo-Qing Zhao
Keyword(s):  
Computational Complexity ◽  
Optimization Problem ◽  
Toeplitz Matrices ◽  
Doa Estimation ◽  
Rank Minimization ◽  
Rectangular Array ◽  
Angle Estimation ◽  
Norm Minimization ◽  
Atomic Norm ◽  
Surrogate Function

This paper proposes a superresolution two-dimensional (2D) direction of arrival (DOA) estimation algorithm for a rectangular array based on the optimization of the atomic l0 norm and a series of relaxation formulations. The atomic l0 norm of the array response describes the minimum number of sources, which is derived from the atomic norm minimization (ANM) problem. However, the resolution is restricted and high computational complexity is incurred by using ANM for 2D angle estimation. Although an improved algorithm named decoupled atomic norm minimization (DAM) has a reduced computational burden, the resolution is still relatively low in terms of angle estimation. To overcome these limitations, we propose the direct minimization of the atomic l0 norm, which is demonstrated to be equivalent to a decoupled rank optimization problem in the positive semidefinite (PSD) form. Our goal is to solve this rank minimization problem and recover two decoupled Toeplitz matrices in which the azimuth-elevation angles of interest are encoded. Since rank minimization is an NP-hard problem, a novel sparse surrogate function is further proposed to effectively approximate the two decoupled rank functions. Then, the new optimization problem obtained through the above relaxation can be implemented via the majorization-minimization (MM) method. The proposed algorithm offers greatly improved resolution while maintaining the same computational complexity as the DAM algorithm. Moreover, it is possible to use a single snapshot for angle estimation without prior information on the number of sources, and the algorithm is robust to noise due to its iterative nature. In addition, the proposed surrogate function can achieve local convergence faster than existing functions.

scholarly journals DOA estimation based on sum–difference coarray with virtual array interpolation concept

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yarong Ding ◽  
Shiwei Ren ◽  
Weijiang Wang ◽  
Chengbo Xue
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Doa Estimation ◽  
Superior Performance ◽  
Norm Minimization ◽  
Atomic Norm ◽  
Virtual Array ◽  
Simulation Results ◽  
The Difference ◽  
Coprime Array

AbstractThe sum–difference coarray is the union of difference coarray and the sum coarray, which is capable to obtain a higher number of degrees of freedom (DOF) than the difference coarray. However, this method fails to use all information provided by the coprime array because of the existence of holes. In this paper, we introduce the virtual array interpolation into the sum–difference coarray domain. After interpolating the virtual array, we estimate the DOA by reconstructing the covariance matrix to resolve an atomic norm minimization problem in a gridless way. The proposed method is gridless and can effectively utilize the DOF of a larger virtual array. Numerical simulation results verify the effectiveness and the superior performance of the proposed algorithm.

scholarly journals Low Complexity Beamspace Super Resolution for DOA Estimation of Linear Array

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2222
Author(s):  
Jie Pan ◽  
Fu Jiang
Keyword(s):  
Array Signal Processing ◽  
Linear Array ◽  
Mimo Systems ◽  
Super Resolution ◽  
Doa Estimation ◽  
Superior Performance ◽  
Estimation Methods ◽  
Iteration Algorithm ◽  
Norm Minimization ◽  
Atomic Norm

Beamspace processing has become much attractive in recent radar and wireless communication applications, since the advantages of complexity reduction and of performance improvements in array signal processing. In this paper, we concentrate on the beamspace DOA estimation of linear array via atomic norm minimization (ANM). The existed generalized linear spectrum estimation based ANM approaches suffer from the high computational complexity for large scale array, since their complexity depends upon the number of sensors. To deal with this problem, we develop a low dimensional semidefinite programming (SDP) implementation of beamspace atomic norm minimization (BS-ANM) approach for DFT beamspace based on the super resolution theory on the semi-algebraic set. Then, a computational efficient iteration algorithm is proposed based on alternating direction method of multipliers (ADMM) approach. We develop the covariance based DOA estimation methods via BS-ANM and apply the BS-ANM based DOA estimation method to the channel estimation problem for massive MIMO systems. Simulation results demonstrate that the proposed methods exhibit the superior performance compared to the state-of-the-art counterparts.

scholarly journals Off-Grid DoA Estimation on Non-Uniform Linear Array Using Constrained Hermitian Matrix

Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5775
Author(s):  
Hyeonjin Chung ◽  
Jeungmin Joo ◽  
Sunwoo Kim
Keyword(s):  
Toeplitz Matrix ◽  
Linear Array ◽  
Hermitian Matrix ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Estimation Accuracy ◽  
Uniform Linear Array ◽  
Atomic Norm ◽  
Array Structures ◽  
Simulation Results

In this paper, an off-grid direction-of-arrival (DoA) estimation algorithm which can work on a non-uniform linear array (NULA) is proposed. The original semidefinite programming (SDP) representation of the atomic norm exploits a summation of one-rank matrices constructed by atoms, where the summation of one-rank matrices equals a Hermitian Toeplitz matrix when using the uniform linear array (ULA). On the other hand, when the antennas in the array are placed arbitrarily, the summation of one-rank matrices is a Hermitian matrix whose diagonal elements are equivalent. Motivated by this property, the proposed algorithm replaces the Hermitian Toeplitz matrix in the original SDP with the constrained Hermitian matrix. Additionally, when the antennas are placed symmetrically, the performance can be enforced by adding extra constraints to the Hermitian matrix. The simulation results show that the proposed algorithm achieves higher estimation accuracy and resolution than other algorithms on both array structures; i.e., the arbitrary array and the symmetric array.

scholarly journals DOA Estimation Based on Sum-Difference Coarray with Virtual Array Interpolation Concept

2021 ◽  
Author(s):  
Yarong Ding ◽  
Shiwei Ren ◽  
Weijiang Wang ◽  
Chengbo Xue
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Doa Estimation ◽  
Superior Performance ◽  
Norm Minimization ◽  
Atomic Norm ◽  
Virtual Array ◽  
Simulation Results ◽  
The Difference ◽  
Coprime Array

Abstract The sum-difference coarray is the union of difference coarray and the sum coarray, which is capable to obtain a higher number of degrees of freedom (DOF) than the difference coarray. However, this method fails to use all information provided by the coprime array because of the existence of holes. In this paper, we introduce the virtual array interpolation into the sum-difference coarray domain. After interpolating the virtual array, we estimate the DOA by reconstructing the covariance matrix to resolve an atomic norm minimization problem in a gridless way. The proposed method is gridless and can effectively utilize the DOF of a larger virtual array. Numerical simulation results verify the effectiveness and the superior performance of the proposed algorithm.

scholarly journals Super-Resolution-Based DOA Estimation with Wide Array Distance and Extrapolation for Vital FMCW Radar

2021 ◽  
Vol 21 (1) ◽  
pp. 23-34
Author(s):  
Sangdong Kim ◽  
Bongseok Kim ◽  
Youngseok Jin ◽  
Jonghun Lee
Keyword(s):  
Continuous Wave ◽  
Super Resolution ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Low Complexity ◽  
Field Of View ◽  
Mean Square ◽  
Fmcw Radar ◽  
Simulation Results ◽  
Resolution Algorithm

This paper proposes a super-resolution-based direction-of-arrivals (DOA) estimation with wide array distance and extrapolation for vital frequency-modulated continuous-wave (FMCW) radar. Most super-resolution algorithms employ the distance between adjacent arrays of half a wavelength, i.e., λ/2. Meanwhile, in the case of narrow field of view of FMCW radar, the resolution of the angle is maintained by increasing the spacing between the arrays even if the number of arrays decreases. In order to employ these characteristics of array spacing and resolution, the proposed algorithm confirms whether or not to use the case where the distance between the adjacent arrays is greater than λ/2. In the case of an array distance >λ/2, a super-resolution algorithm is performed to obtain the enhanced DOA resolution. Moreover, the proposed algorithm virtually generates data between antennae by using extrapolation in order to further improve the performance of the resolution. The simulation results show that the proposed algorithm achieves the results of root-mean-square error similar to conventional super-resolution algorithms while maintaining low complexity. In order to further verify the performance of the proposed estimation algorithm, we demonstrate its employment in practice: experiments in a chamber room and an indoor room were conducted.

scholarly journals Wideband DOA Estimation on Co-prime Array via Atomic Norm Minimization

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3235 ◽  
Author(s):  
Hyeonjin Chung ◽  
Young Mi Park ◽  
Sunwoo Kim
Keyword(s):  
Compressive Sensing ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Low Complexity ◽  
Time Saving ◽  
Estimation Algorithms ◽  
Norm Minimization ◽  
Atomic Norm ◽  
Multiple Measurement Vector ◽  
Low Dimensional

This paper introduces a low complexity wideband direction-of-arrival (DOA) estimation algorithm on the co-prime array. To increase the number of the detectable signal sources and to prevent an unnecessary increase in complexity, the low dimensional co-prime array vector is constructed by arranging elements of the correlation matrix at every frequency bin. The atomic norm minimization (ANM)-based approach resolves the grid-mismatch, which causes an inevitable error in the compressive sensing (CS)-based DOA estimation. However, the complexity surges when the ANM is exploited to the wideband DOA estimation on the co-prime array. The surging complexity of the ANM-based wideband DOA estimation on the co-prime array is handled by solving the time-saving semidefinite programming (SDP) motivated by the ANM for multiple measurement vector (MMV) case. Simulation results show that the proposed algorithm has high accuracy and low complexity compared to compressive sensing (CS)-based wideband DOA estimation algorithms that exploit the co-prime array.

scholarly journals DOA Estimation for Coprime Linear Array Based on MI-ESPRIT and Lookup Table

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 3043 ◽  
Author(s):  
Weike Zhang ◽  
Xi Chen ◽  
Kaibo Cui ◽  
Tao Xie ◽  
Naichang Yuan
Keyword(s):  
Linear Array ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Spatial Spectrum ◽  
Angle Measurement ◽  
Lookup Table ◽  
Signal Parameters ◽  
Estimation Precision ◽  
Simulation Results ◽  
The Relationship

In order to improve the angle measurement performance of a coprime linear array, this paper proposes a novel direction-of-arrival (DOA) estimation algorithm for a coprime linear array based on the multiple invariance estimation of signal parameters via rotational invariance techniques (MI-ESPRIT) and a lookup table method. The proposed algorithm does not require a spatial spectrum search and uses a lookup table to solve ambiguity, which reduces the computational complexity. To fully use the subarray elements, the DOA estimation precision is higher compared with existing algorithms. Moreover, the algorithm avoids the matching error when multiple signals exist by using the relationship between the signal subspace of two subarrays. Simulation results verify the effectiveness of the proposed algorithm.

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