Direction of Arrival Estimation Using Augmentation of Coprime Arrays

Recently, direction of arrival (DOA) estimation premised on the sparse arrays interpolation approaches, such as co-prime arrays (CPA) and nested array, have attained extensive attention because of the effectiveness and capability of providing higher degrees of freedom (DOFs). The co-prime array interpolation approach can detect O(MN) paths with O(M + N) sensors in the array. However, the presence of missing elements (holes) in the difference coarray has limited the number of DOFs. To implement co-prime coarray on subspace based DOA estimation algorithm namely multiple signal classification (MUSIC), a reshaping operation followed by the spatial smoothing technique have been presented in the literature. In this paper, an active coarray interpolation (ACI) is proposed to efficiently recovering the covariance matrix of the augmented coarray from the original covariance matrix of source signals with no vectorizing and spatial smoothing operation; thus, the computational complexity reduces significantly. Moreover, the numerical simulations of the proposed ACI approach offers better performance compared to its counterparts.

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Novel Diagonal Reloading Based Direction of Arrival Estimation in Unknown Non-Uniform Noise

Mathematical Problems in Engineering ◽

10.1155/2018/3084516 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9

Author(s):

Hao Zhou ◽

Guoping Hu ◽

Junpeng Shi ◽

Ziang Feng

Keyword(s):

Covariance Matrix ◽

Degrees Of Freedom ◽

Direction Of Arrival ◽

Estimation Algorithm ◽

Doa Estimation ◽

Main Diagonal ◽

Sample Covariance ◽

Uniform Noise ◽

Negative Effect ◽

Signal Covariance Matrix

Nested array can expand the degrees of freedom (DOF) from difference coarray perspective, but suffering from the performance degradation of direction of arrival (DOA) estimation in unknown non-uniform noise. In this paper, a novel diagonal reloading (DR) based DOA estimation algorithm is proposed using a recently developed nested MIMO array. The elements in the main diagonal of the sample covariance matrix are eliminated; next the smallest MN-K eigenvalues of the revised matrix are obtained and averaged to estimate the sum value of the signal power. Further the estimated sum value is filled into the main diagonal of the revised matrix for estimating the signal covariance matrix. In this case, the negative effect of noise is eliminated without losing the useful information of the signal matrix. Besides, the degrees of freedom are expanded obviously, resulting in the performance improvement. Several simulations are conducted to demonstrate the effectiveness of the proposed algorithm.

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Coherent Target Direction-of-Arrival Estimation for Coprime Arrays: From Spatial Smoothing Perspective

Wireless Communications and Mobile Computing ◽

10.1155/2021/9983615 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Dongming Wu ◽

Fangzheng Liu ◽

Zhihui Li ◽

Zhenzhong Han

Keyword(s):

Direction Of Arrival ◽

Doa Estimation ◽

Spatial Spectrum ◽

Spatial Smoothing ◽

Phase Ambiguity ◽

Coherent Signals ◽

Music Algorithm ◽

Multiple Signal Classification ◽

Common Peak ◽

Coprime Arrays

In this paper, we investigate the issue of direction-of-arrival (DOA) estimation of multiple signals in coprime arrays. An algorithm based on multiple signal classification (MUSIC) and forward and backward spatial smoothing (FBSS) is used for DOA estimation of this signal caused by multipath and interference. The large distance between adjacent elements of each subarray in the coprime arrays will bring phase ambiguity issues. According to the feature of the coprime number, the ambiguity problem can be eliminated. The correct DOA estimation can be obtained by searching for the common peak of the spatial spectrum and finding the overlapping peaks in the MUSIC spectrum of the two subarrays. For the rank deficit problem caused by the coherent signal, the FBSS algorithm is used for signal preprocessing before the MUSIC algorithm. Theoretical analysis and simulation results show that the algorithm can effectively solve the rank deficiency and phase ambiguity problems caused by coherent signals and sparse arrays in the coprime arrays.

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An Enhanced Smoothed L0-Norm Direction of Arrival Estimation Method Using Covariance Matrix

Sensors ◽

10.3390/s21134403 ◽

2021 ◽

Vol 21 (13) ◽

pp. 4403

Author(s):

Ji Woong Paik ◽

Joon-Ho Lee ◽

Wooyoung Hong

Keyword(s):

Covariance Matrix ◽

Phased Array ◽

Null Space ◽

Estimation Method ◽

Direction Of Arrival ◽

Estimation Algorithm ◽

Doa Estimation ◽

Direction Of Arrival Estimation ◽

Improve Performance ◽

Space Projection

An enhanced smoothed l0-norm algorithm for the passive phased array system, which uses the covariance matrix of the received signal, is proposed in this paper. The SL0 (smoothed l0-norm) algorithm is a fast compressive-sensing-based DOA (direction-of-arrival) estimation algorithm that uses a single snapshot from the received signal. In the conventional SL0 algorithm, there are limitations in the resolution and the DOA estimation performance, since a single sample is used. If multiple snapshots are used, the conventional SL0 algorithm can improve performance in terms of the DOA estimation. In this paper, a covariance-fitting-based SL0 algorithm is proposed to further reduce the number of optimization variables when using multiple snapshots of the received signal. A cost function and a new null-space projection term of the sparse recovery for the proposed scheme are presented. In order to verify the performance of the proposed algorithm, we present the simulation results and the experimental results based on the measured data.

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2D DOA Estimation Using Sparse Representation of Higher-Order Power of Covariance Matrix

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.998-999.779 ◽

2014 ◽

Vol 998-999 ◽

pp. 779-783

Author(s):

Zheng Luo ◽

Fei Yu ◽

Lin Wu ◽

Yuan Liu

Keyword(s):

Covariance Matrix ◽

Estimation Algorithm ◽

Doa Estimation ◽

Higher Order ◽

Eigenvalue Decomposition ◽

Coherent Signals ◽

Sparse Decomposition ◽

Sparse Signal Representation ◽

2D Doa Estimation ◽

Source Signals

A novel two-dimensional (2D) direction-of-arrival (DOA) estimation algorithm utilizing a sparse signal representation of higher-order power of covariance matrix is proposed. Through applying the higher-order power of covariance matrix to construct a new sparse decomposition vector, this algorithm avoids the estimation of incident signal number and eigenvalue decomposition. And the hierarchical granularity-dictionary is studied, which forms the over-complete dictionary adaptively in the light of source signals’ distribution. Compared with MUSIC and L1-SVD, this algorithm not only provides a better 2D DOA performance but also possesses the capability of coherent signals estimation. Theoretical analysis and simulation results demonstrate the validity and robust of the proposed algorithm.

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An Improved Two-Dimensional Direction-Of-Arrival Estimation Algorithm for L-Shaped Nested Arrays with Small Sample Sizes

Sensors ◽

10.3390/s19092176 ◽

2019 ◽

Vol 19 (9) ◽

pp. 2176 ◽

Cited By ~ 2

Author(s):

Xiaofeng Gao ◽

Xinhong Hao ◽

Ping Li ◽

Guolin Li

Keyword(s):

Correlation Matrix ◽

Degrees Of Freedom ◽

Full Rank ◽

Direction Of Arrival ◽

Estimation Algorithm ◽

Doa Estimation ◽

Covariance Matrices ◽

Small Sample ◽

Two Dimensional ◽

Nested Arrays

In this paper, an improved two-dimensional (2-D) direction of arrival (DOA) estimation algorithm for L-shaped nested arrays is proposed. Unlike the approach for a classical nested array, which use the auto-correlation matrix (ACM) to increase the degrees of freedom (DOF), we utilize the cross-correlation matrix (CCM) of different sub-arrays to generate two long consecutive virtual arrays. These acquire a large number of DOF without redundant elements and eliminate noise effects. Furthermore, we reconstruct the CCM based on the singular value decomposition (SVD) operation in order to reduce the perturbation of noise for small numbers of samples. To cope with the matrix rank deficiency of the virtual arrays, we construct the full rank equivalent covariance matrices by using the output and its conjugate vector of virtual arrays. The unitary estimation of signal parameters via rotational invariance technique (ESPRIT) is then performed on the covariance matrices to obtain the DOA of incident signals with low computational complexity. Finally, angle pairing is achieved by deriving the equivalent signal vector of the virtual arrays using the estimated angles. Numerical simulation results show that the proposed algorithm not only provides more accurate 2-D DOA estimation performance with low complexity, but also achieves angle estimation for small numbers of samples compared to existing similar methods.

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Computationally Efficient Direction-of-Arrival Estimation Algorithms for a Cubic Coprime Array

Sensors ◽

10.3390/s22010136 ◽

2021 ◽

Vol 22 (1) ◽

pp. 136

Author(s):

Pan Gong ◽

Xixin Chen

Keyword(s):

Covariance Matrix ◽

Lower Boundary ◽

Direction Of Arrival ◽

Doa Estimation ◽

Mimo Radar ◽

Signal Classification ◽

Computationally Efficient ◽

Music Algorithm ◽

Multiple Signal Classification ◽

Multiple Signal

In this paper, we investigate the problem of direction-of-arrival (DOA) estimation for massive multi-input multi-output (MIMO) radar, and propose a total array-based multiple signals classification (TA-MUSIC) algorithm for two-dimensional direction-of-arrival (DOA) estimation with a coprime cubic array (CCA). Unlike the conventional multiple signal classification (MUSIC) algorithm, the TA-MUSIC algorithm employs not only the auto-covariance matrix but also the mutual covariance matrix by stacking the received signals of two sub cubic arrays so that full degrees of freedom (DOFs) can be utilized. We verified that the phase ambiguity problem can be eliminated by employing the coprime property. Moreover, to achieve lower complexity, we explored the estimation of signal parameters via the rotational invariance technique (ESPRIT)-based multiple signal classification (E-MUSIC) algorithm, which uses a successive scheme to be computationally efficient. The Cramer–Rao bound (CRB) was taken as a theoretical benchmark for the lower boundary of the unbiased estimate. Finally, numerical simulations were conducted in order to demonstrate the effectiveness and superiority of the proposed algorithms.

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High-Resolution Direction-of-Arrival Estimation via Concentric Circular Arrays

ISRN Signal Processing ◽

10.1155/2013/859590 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 5

Author(s):

Serdar Ozgur Ata ◽

Cevdet Isik

Keyword(s):

Antenna Arrays ◽

Linear Array ◽

Signal To Noise Ratio ◽

Sensor Arrays ◽

Direction Of Arrival ◽

Doa Estimation ◽

Circular Array ◽

Multiple Signal Classification ◽

Circular Arrays ◽

Source Signals

Estimating the direction of arrival (DOA) of source signals is an important research interest in application areas including radar, sonar, and wireless communications. In this paper, the problem of DOA estimation is addressed on concentric circular antenna arrays (CCA) in detail as an alternative to the well-known geometries of the uniform linear array (ULA) and uniform circular array (UCA). We define the steering matrix of the CCA geometry and investigate the performance analysis of the array in the DOA-estimation problem by simulations that are realized through varying the parameters of signal-to-noise ratio, number of sensors, and resolution angle of sensor arrays by using the MUSIC (Multiple Signal Classification) algorithm. The results present that CCA geometries provide higher angle resolutions compared to UCA geometries and require less physical area for the same number of sensor elements. However, as a cost-increasing effect, higher computational power is needed to estimate the DOA of source signals in CCAs compared to ULAs.

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Direction-of-Arrival Estimation for Coprime Array Using Compressive Sensing Based Array Interpolation

International Journal of Antennas and Propagation ◽

10.1155/2017/6425067 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 6

Author(s):

Aihua Liu ◽

Qiang Yang ◽

Xin Zhang ◽

Weibo Deng

Keyword(s):

Covariance Matrix ◽

Degrees Of Freedom ◽

Linear Array ◽

Estimation Method ◽

Direction Of Arrival ◽

Doa Estimation ◽

Interpolation Algorithm ◽

Estimation Performance ◽

Sample Covariance ◽

Coprime Array

A method of direction-of-arrival (DOA) estimation using array interpolation is proposed in this paper to increase the number of resolvable sources and improve the DOA estimation performance for coprime array configuration with holes in its virtual array. The virtual symmetric nonuniform linear array (VSNLA) of coprime array signal model is introduced, with the conventional MUSIC with spatial smoothing algorithm (SS-MUSIC) applied on the continuous lags in the VSNLA; the degrees of freedom (DoFs) for DOA estimation are obviously not fully exploited. To effectively utilize the extent of DoFs offered by the coarray configuration, a compressing sensing based array interpolation algorithm is proposed. The compressing sensing technique is used to obtain the coarse initial DOA estimation, and a modified iterative initial DOA estimation based interpolation algorithm (IMCA-AI) is then utilized to obtain the final DOA estimation, which maps the sample covariance matrix of the VSNLA to the covariance matrix of a filled virtual symmetric uniform linear array (VSULA) with the same aperture size. The proposed DOA estimation method can efficiently improve the DOA estimation performance. The numerical simulations are provided to demonstrate the effectiveness of the proposed method.

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Generalized Sparse Polarization Array for DOA Estimation Using Compressive Measurements

Wireless Communications and Mobile Computing ◽

10.1155/2021/5539709 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Tao Chen ◽

Jian Yang ◽

Weitong Wang ◽

Muran Guo

Keyword(s):

Degrees Of Freedom ◽

Elevation Angle ◽

Least Square Method ◽

Estimation Algorithm ◽

Doa Estimation ◽

Least Square ◽

Polarization Angle ◽

Estimation Performance ◽

The Difference ◽

Cramer Rao Bound

The compressive array method, where a compression matrix is designed to reduce the dimension of the received signal vector, is an effective solution to obtain high estimation performance with low system complexity. While sparse arrays are often used to obtain higher degrees of freedom (DOFs), in this paper, an orthogonal dipole sparse array structure exploiting compressive measurements is proposed to estimate the direction of arrival (DOA) and polarization signal parameters jointly. Based on the proposed structure, we also propose an estimation algorithm using the compressed sensing (CS) method, where the DOAs are accurately estimated by the CS algorithm and the polarization parameters are obtained via the least-square method exploiting the previously estimated DOAs. Furthermore, the performance of the estimation of DOA and polarization parameters is explicitly discussed through the Cramér-Rao bound (CRB). The CRB expression for elevation angle and auxiliary polarization angle is derived to reveal the limit of estimation performance mathematically. The difference between the results given in this paper and the CRB results of other polarized reception structures is mainly due to the use of the compression matrix. Simulation results verify that, compared with the uncompressed structure, the proposed structure can achieve higher estimated performance with a given number of channels.

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A Direction-of-Arrival Estimation Algorithm Based on Compressed Sensing and Density-Based Spatial Clustering and Its Application in Signal Processing of MEMS Vector Hydrophone

Sensors ◽

10.3390/s21062191 ◽

2021 ◽

Vol 21 (6) ◽

pp. 2191

Author(s):

Huichao Yan ◽

Ting Chen ◽

Peng Wang ◽

Linmei Zhang ◽

Rong Cheng ◽

...

Keyword(s):

Compressed Sensing ◽

Spatial Clustering ◽

Direction Of Arrival ◽

Estimation Algorithm ◽

Doa Estimation ◽

Cluster Center ◽

Direction Of Arrival Estimation ◽

Vector Hydrophone ◽

Regularization Parameters ◽

Selection Of

Direction of arrival (DOA) estimation has always been a hot topic for researchers. The complex and changeable environment makes it very challenging to estimate the DOA in a small snapshot and strong noise environment. The direction-of-arrival estimation method based on compressed sensing (CS) is a new method proposed in recent years. It has received widespread attention because it can realize the direction-of-arrival estimation under small snapshots. However, this method will cause serious distortion in a strong noise environment. To solve this problem, this paper proposes a DOA estimation algorithm based on the principle of CS and density-based spatial clustering (DBSCAN). First of all, in order to make the estimation accuracy higher, this paper selects a signal reconstruction strategy based on the basis pursuit de-noising (BPDN). In response to the challenge of the selection of regularization parameters in this strategy, the power spectrum entropy is proposed to characterize the noise intensity of the signal, so as to provide reasonable suggestions for the selection of regularization parameters; Then, this paper finds out that the DOA estimation based on the principle of CS will get a denser estimation near the real angle under the condition of small snapshots through analysis, so it is proposed to use a DBSCAN method to process the above data to obtain the final DOA estimate; Finally, calculate the cluster center value of each cluster, the number of clusters is the number of signal sources, and the cluster center value is the final DOA estimate. The proposed method is applied to the simulation experiment and the micro electro mechanical system (MEMS) vector hydrophone lake test experiment, and they are proved that the proposed method can obtain good results of DOA estimation under the conditions of small snapshots and low signal-to-noise ratio (SNR).

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