scholarly journals Crosscorrelation and DOA Estimation for L-Shaped Array via Decoupled Atomic Norm Minimization

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yu Zhang ◽  
Yinan Sun ◽  
Gong Zhang ◽  
Xinhai Wang ◽  
Yu Tao
Keyword(s):  
Prior Information ◽  
Doa Estimation ◽  
Phase Method ◽  
Second Phase ◽  
Two Dimensional ◽  
Two Phase ◽  
Norm Minimization ◽  
Atomic Norm ◽  
Matrix Reconstruction ◽  
Source Number

A novel two-phase method for two-dimensional (2D) direction-of-arrival (DOA) estimation with L-shaped array based on decoupled atomic norm minimization (DANM) is proposed in this paper. In the first phase, given the sample crosscorrelation matrix, the gridless DANM technique considering the noise and finite snapshots effects is employed to exploit the structure and sparse properties of the crosscorrelation matrix. The resulting DANM-based algorithm not only enables the crosscorrelation matrix reconstruction (CCMR) but also reconstructs the covariance matrix of the L-shaped array. Hence, sequentially, in the second phase, the conventional 2D DOA estimators for the L-shaped array can be adopted for the angle estimation. With appropriate 2D DOA estimators, the resulting proposed algorithms can not only achieve better performance but also detect more source number, compared with conventional crosscorrelation-based DOA estimators. Moreover, the proposed method, termed CCMR-DANM, not only has blind characteristic that it does not require the prior information of source numbers but also is more efficient than the existing CCMR-based counterparts. Numerical simulations demonstrate the effectiveness and outperformance of the proposed method.

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 Two-Dimensional Spatial Frequency Content and Confusions among Dot Matrix Characters

1979 ◽  
Vol 23 (1) ◽  
pp. 384-388
Author(s):  
Michael E. Maddox
Keyword(s):  
Spatial Frequency ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Final Analysis ◽  
Second Phase ◽  
Two Dimensional ◽  
Two Phase ◽  
Frequency Spectra ◽  
Character Size ◽  
Point Fast Fourier Transform

A two-phase study was conducted which related the confusions among dot matrix characters to the two-dimensional spatial frequency similarity of these characters. During the first phase of the study, subjects were shown single alphanumeric characters from four different dot matrix fonts and five matrix size/character sub-tense combinations. Data from this phase of the research were analyzed in terms of both correctness and character confusion frequencies. The second phase of the study consisted of digitizing and analyzing all characters from two of the fonts used in the first phase. The fonts chosen represent the most and least confusable of the four, based on the performance data obtained. These characters were scanned photometrically using a computer-controlled X-Y stage and subjected to a 512 × 512 point fast Fourier transform (FFT). The Fourier coefficients were correlated for all possible character pairs within each font-matrix/character size cell. These correlations provided an objective similarity measure among characters based upon their 2-D spatial frequency spectra. In addition to the spatial frequency similarity measure, a simple digital Phi coefficient was calculated for each character pair. The final analysis performed in this study was the correlation of observed performance (confusions) with objective similarity measures (2-D spectra and Phi coefficients).

scholarly journals Grid-Free DOD and DOA Estimation for MIMO Radar via Duality-Based 2D Atomic Norm Minimization

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 60827-60836 ◽  
Author(s):  
Wen-Gen Tang ◽  
Hong Jiang ◽  
Shuai-Xuan Pang
Keyword(s):  
Doa Estimation ◽  
Mimo Radar ◽  
Norm Minimization ◽  
Atomic Norm

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 Virtual interpolation of discrete multi-objective programming solutions with probabilistic operation

2011 ◽  
Vol 22 (4) ◽  
pp. 379-389
Author(s):  
Ricardo C. Silva ◽  
Edilson F. Arruda ◽  
Fabrício O. Ourique
Keyword(s):  
Probability Distributions ◽  
Phase Method ◽  
Second Phase ◽  
Pareto Optimal ◽  
Two Phase ◽  
Term Operation ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Objective Programming

This work presents a novel framework to address the long term operation of a class of multi-objective programming problems. The proposed approach considers a stochastic operation and evaluates the long term average operating costs/profits. To illustrate the approach, a two-phase method is proposed which solves a prescribed number of K mono-objective problems to identify a set of K points in the Pareto-optimal region. In the second phase, one searches for a set of non-dominated probability distributions that define the probability that the system operates at each point selected in the first phase, at any given operation period. Each probability distribution generates a vector of average long-term objectives and one solves for the Pareto-optimal set with respect to the average objectives. The proposed approach can generate virtual operating points with average objectives that need not have a feasible solution with an equal vector of objectives. A few numerical examples are presented to illustrate the proposed method.

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.

Sign in / Sign up

Export Citation Format

Share Document