Combining Self-Organizing Map and Lipschitz Condition for Estimation in Direction of Arrival

There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA) estimation system based on self-organizing map (SOM) and designed for arbitrarily distributed sensor array is proposed. The essential principle of this method is that the map from distance difference of arrival (DDOA) to DOA is Lipschitz continuity, it indicates the similar topology between them, and thus Kohonen SOM is a suitable network to classify DOA through DDOA. The simulation results show that the DOA estimation errors are less than 1° for most signals between 0° to 180°. Compared to MUSIC, Root-MUSIC, ESPRIT, and RBF, the errors of signals under signal-to-noise ratios (SNR) declines from 20 dB to 2 dB are robust, SOM is better than RBF and almost close to MUSIC. Further, the network can be trained in advance, which makes it possible to be implemented in real-time.

Direction-of-arrival estimation for co-located multiple-input multiple-output radar using structural sparsity Bayesian learning

This paper addresses the direction of arrival （DOA） estimation problem for the co-located multiple-input multiple- output （MIMO） radar with random arrays. The spatially distributed sparsity of the targets in the background makes com- pressive sensing （CS） desirable for DOA estimation. A spatial CS framework is presented, which links the DOA estimation problem to support recovery from a known over-complete dictionary. A modified statistical model is developed to ac- curately represent the intra-block correlation of the received signal. A structural sparsity Bayesian learning algorithm is proposed for the sparse recovery problem. The proposed algorithm, which exploits intra-signal correlation, is capable being applied to limited data support and low signal-to-noise ratio （SNR） scene. Furthermore, the proposed algorithm has less computation load compared to the classical Bayesian algorithm. Simulation results show that the proposed algorithm has a more accurate DOA estimation than the traditional multiple signal classification （MUSIC） algorithm and other CS recovery algorithms.

Direction-of-arrival estimation of quasi-stationary signals using two-level Khatri-Rao subspace and four-level nested array

The Khatri-Rao(KR) subspace method is a high resolution method for direction-of-arrival(DOA) estimation.Combined with 2q level nested array,the KR subspace method can detect O(N2q) sources with N sensors.However,the method cannot be applicable to Gaussian sources when q is equal to or greater than 2 since it needs to use 2q-th order cumulants.In this work,a novel approach is presented to conduct DOA estimation by constructing a fourth order difference co-array.Unlike the existing DOA estimation method based on the KR product and 2q level nested array,the proposed method only uses second order statistics,so it can be employed to Gaussian sources as well as non-Gaussian sources.By exploiting a four-level nested array with N elements,our method can also identify O(N4) sources.In order to estimate the wideband signals,the proposed method is extended to the wideband scenarios.Simulation results demonstrate that,compared to the state of the art KR subspace based methods,the new method achieves higher resolution.

Direction-of-arrival estimation based on direct data domain (D3) method

A direction-of-arrival （DOA） estimation algorithm based on direct data domain （D3） approach is presented. This method can accuracy estimate DOA using one snapshot modified data, called the temporal and spatial two-dimensional vector reconstruction （TSR） method. The key idea is to apply the D3 approach which can extract the signal of given frequency but null out other frequency signals in temporal domain. Then the spatial vector reconstruction processing is used to estimate the angle of the spatial coherent signal source based on extract signal data. Compared with the common temporal and spatial processing approach, the TSR method has a lower computational load, higher real-time performance, robustness and angular accuracy of DOA. The proposed algorithm can be directly applied to the phased array radar of coherent pulses. Simulation results demonstrate the performance of the proposed technique.

Wideband direction-of-arrival estimation based on cubic spline function

A new direction-of-arrival （DOA） estimation algorithm for wideband sources is introduced, The new method obtains the output of the virtual arrays in the signal bandwidth using cubic spline function interpolation techniques. The narrowband high- resolution algorithm is then used to get the DOA estimation. This technique does not require any preliminary knowledge of DOA angles. Simulation results demonstrate the effectiveness of the method.

Refractivity estimations from an angle-of-arrival spectrum

This paper addresses the probability of atmospheric refractivity estimation by using field measurements at an array of radio receivers in terms of angle-of-arrival spectrum. Angle-of-arrival spectrum information is simulated by the ray optics model and refractivity is expressed in the presence of an ideal tri-linear profile. The estimation of the refractivity is organized as an optimization problem and a genetic Mgorithm is used to search for the optimal solution from various trial refractivity profiles. Theoretical analysis demonstrates the feasibility of this method to retrieve the refractivity parameters. Simulation results indicate that this approach has a fair anti-noise ability and its accuracy performance is mainly dependent on the antenna aperture size and its positions.

Direction of arrival estimation method based on quantum electromagnetic field optimization in the impulse noise

In order to resolve direction finding problems in the impulse noise,a direction of arrival(DOA)estimation method is proposed.The proposed DOA estimation method can restrain the impulse noise by using infinite norm exponential kernel covariance matrix and obtain excellent performance via the maximumlikelihood(ML)algorithm.In order to obtain the global optimal solutions of this method,a quantum electromagnetic field optimization(QEFO)algorithm is designed.In view of the QEFO algorithm,the proposed method can resolve the difficulties of DOA estimation in the impulse noise.Comparing with some traditional DOA estimation methods,the proposed DOA estimation method shows high superiority and robustness for determining the DOA of independent and coherent sources,which has been verified via the Monte-Carlo experiments of different schemes,especially in the case of snapshot deficiency,low generalized signal to noise ratio(GSNR)and strong impulse noise.Beyond that,the Cramer-Rao bound(CRB)of angle estimation in the impulse noise and the proof of the convergence of the QEFO algorithm are provided in this paper.

Ambiguity Resolution in Direction of Arrival Estimation with Linear Antenna Arrays Using Differential Geometry

Linear antenna arrays(LAs)can be used to accurately predict the direction of arrival(DOAs)of various targets of interest in a given area.However,under certain conditions,LA suffers from the problem of ambiguities among the angles of targets,which may result inmisinterpretation of such targets.In order to cope up with such ambiguities,various techniques have been proposed.Unfortunately,none of them fully resolved such a problem because of rank deficiency and high computational cost.We aimed to resolve such a problem by proposing an algorithm using differential geometry.The proposed algorithm uses a specially designed doublet antenna array,which is made up of two individual linear arrays.Two angle observation models,ambiguous observation model(AOM)and estimated observation model(EOM),are derived for each individual array.The ambiguous set of angles is contained in the AOM,which is obtained from the corresponding array elements using differential geometry.The EOM for each array,on the other hand,contains estimated angles of all sources impinging signals on each array,as calculated by a direction-finding algorithm such as the genetic algorithm.The algorithm then contrasts the EOM of each array with its AOM,selecting the output of that array whose EOM has the minimum correlation with its corresponding AOM.In comparison to existing techniques,the proposed algorithm improves estimation accuracy and has greater precision in antenna aperture selection,resulting in improved resolution capabilities and the potential to be used more widely in practical scenarios.The simulation results using MATLAB authenticates the effectiveness of the proposed algorithm.

Beamforming and Angle-of-Arrival Estimation of Square Planar Antenna Array

This paper presents a dual-band planar antenna array for ISM band applications (2.4 GHz and 2.45 GHz). This antenna is proposed for indoor applications and enables adaptive beamforming and angle of arrival (AOA) estimation. An adaptive beamforming algorithm is applied for a planar antenna array, which is able to steer its main beam and nulls in azimuth and elevation planes over a wide frequency band. Planar antenna array operates as a spatial filter in 3D space, processing the received signals with weighting schemes. A planar antenna array is designed for AOA estimation in azimuth and elevation planes by using MUltiple SIgnal Classification (MUSIC) based on subspace algorithm. The Base Station (BS) equipped with this planar antenna is preferred to be at the center position on the room ceiling to cover all sectors of the room. It is designed to use four directional triangular elements arranged to form a square planar antenna array. Planar antenna with four elliptical slotted triangular elements (PAFESTE) is used to obtain optimal directivity in four directions in azimuth plane with specific orientation of 30? in elevation plane. It is characterized by half power beamwidth in elevation plane of about 60? and half power beamwidth in azimuth plane of about 90?.

High-Precision Time Delay Estimation Based on Closed-Form Offset Compensation

To improve the estimation accuracy,a novel time delay estimation(TDE)method based on the closed-form offset compensation is proposed.Firstly,we use the generalized cross-correlation with phase transform(GCC-PHAT)method to obtain the initial TDE.Secondly,a signal model using normalized cross spectrum is established,and the noise subspace is extracted by eigenvalue decomposition(EVD)of covariance matrix.Using the orthogonal relation between the steering vector and the noise subspace,the first-order Taylor expansion is carried out on the steering vector reconstructed by the initial TDE.Finally,the offsets are compensated via simple least squares(LS).Compared to other state-of-the-art methods,the proposed method significantly reduces the computational complexity and achieves better estimation performance.Experiments on both simulation and real-world data verify the efficiency of the proposed approach.

Computationally efficient MUSIC based DOA estimation algorithm for FMCW radar

This paper proposes low-cost yet high-accuracy direction of arrival(DOA)estimation for the automotive frequency-modulated continuous-wave(FMcW)radar.The existing subspace-based DOA estimation algorithms suffer fromeither high computational costs or low accuracy.We aim to solve such contradictory relation between complexity and accuracy by using randomizedmatrix approximation.Specifically,we apply an easily-interpretablerandomized low-rank approximation to the covariance matrix(CM)and R∈C^(M×M)throughthresketch maties in the fom of R≈OBQ^(H).Here the approximately compute its subspaces.That is,we first approximate matrix Q∈C^(M×z)contains the orthonormal basis for the range of the sketchmatrik C∈C^(M×z)cwe whichis etrated fom R using randomized unifom counsampling and B∈C^(z×z)is a weight-matrix reducing the approximation error.Relying on such approximation,we are able to accelerate the subspacecomputation by the orders of the magnitude without compromising estimation accuracy.Furthermore,we drive a theoretical error bound for the suggested scheme to ensure the accuracy of the approximation.As validated by the simulation results,the DOA estimation accuracy of the proposed algorithm,eficient multiple signal classification(E-MUSIC)s high,closely tracks standardMUSIC,and outperforms the well-known algorithms with tremendouslyreduced time complexity.Thus,the devised method can realize high-resolutionreal-time target detection in the emerging multiple input and multiple output(MIMO)automotive radar systems.

Temporal-spatial subspaces modern combination method for 2D-DOA estimation in MIMO radar

A 2D-direction of arrival estimation (DOAE) for multi input and multi-output (MIMO) radar using improved multiple temporal-spatial subspaces in estimating signal parameters via rotational invariance techniques method (TS-ESPRIT) is introduced. In order to realize the improved TS-ESPRIT, the proposed algorithm divides the planar array into multiple uniform sub-planar arrays with common reference point to get a unified phase shifts measurement point for all sub-arrays. The TS-ESPRIT is applied to each sub-array separately, and in the same time with the others to realize the parallelly temporal and spatial processing, so that it reduces the non-linearity effect of model and decreases the computational time. Then, the time difference of arrival (TDOA) technique is applied to combine the multiple sub-arrays in order to form the improved TS-ESPRIT. It is found that the proposed method achieves high accuracy at a low signal to noise ratio (SNR) with low computational complexity, leading to enhancement of the estimators performance.

Blind identification and DOA estimation for array sources in presence of scattering

A novel identification method for point source,coherently distributed（CD） source and incoherently distributed（ICD） source is proposed.The differences among the point source,CD source and ICD source are studied.According to the different characters of covariance matrix and general steering vector of the array received source,a second order blind identification method is used to separate the sources,the mixing matrix could be obtained.From the mixing matrix,the type of the source is identified by using an amplitude criterion.And the direction of arrival for the array received source is estimated by using the matching pursuit algorithm from the vectors of the mixing matrix.Computer simulations validate the efficiency of the method.

Low-complexity method for DOA estimation based on ESPRIT

A low-complexity method for direction of arrival（DOA） estimation based on estimation signal parameters via rotational invariance technique（ESPRIT） is proposed.Instead of using the cross-correlation vectors in multistage Wiener filter（MSWF）,the orthogonal residual vectors obtained in conjugate gradient（CG） method span the signal subspace used by ESPRIT.The computational complexity of the proposed method is significantly reduced,since the signal subspace estimation mainly needs two matrixvector complex multiplications at the iteration of data level.Furthermore,the prior training data are not needed in the proposed method.To overcome performance degradation at low signal to noise ratio（SNR）,the expanded signal subspace spanned by more basis vectors is used and simultaneously renders ESPRIT yield redundant DOAs,which can be excluded by performing ESPRIT once more using the unexpanded signal subspace.Compared with the traditional ESPRIT methods by MSWF and eigenvalue decomposition（EVD）,numerical results demonstrate the satisfactory performance of the proposed method.

Generalized Parallel Coprime Array for Two-Dimensional DOA Estimation:A Perspective from Maximizing Degree of Freedom

Parallel arrays with coprime subarrays have shown its potential advantages for two dimensional direction of arrival(DOA)estimation.In this paper,by introducing two flexible coprime factors to enlarge the inter-element spacing of parallel uniform subarrays,we propose a generalized parallel coprime array(GPCA)geometry.The proposed geometry enjoys flexible array layouts by the coprime factors and enables to extend the array aperture to achieve great improvement of estimation performance.Meanwhile,we verify that GPCA always can obtain M2 degrees of freedom(DOFs)in co-array domain via 2M sensors after optimization,which outperforms sparse parallel array geometries,such as parallel coprime array(PCA)and parallel augmented coprime array(PACA),and is the same as parallel nested array(PNA)with extended aperture.The superiority of GPCA geometry has been proved by numerical simulations with sparse representation methods.

Joint Estimation of 2-D DOA and Polarization by Using the Linear Array with Diverse Polarizations

A linear array of diversely polarized antennas with one pair of identical sensors is used to obtain closed-form unambiguous estimation of 2-D direction of arrival （DOA） and polarization. Spatial phase information together with weighted 3-D polarization-angular coherence structure （PACS） are first recovered with fourth-order cumulants manipulation via a new 2-D ESPRIT variant. Spatial filtering is performed to obtain the scaled PACS, from which the closed-form 2-D DOA and polarization estimates can be derived with only quadrant ambiguity involved. The undesired quadrant ambiguity can be further resolved by using the acquired estimate of spatial phase factor.

A Real-Valued 2D DOA Estimation Algorithm of Noncircular Signal via Euler Transformation and Rotational Invariance Property

The problem of two-dimensional(2 D)direction of arrival(DOA)estimation for double parallel uniform linear arrays is investigated in this paper.A real-valued DOA estimation algorithm of noncircular(NC)signal is proposed,which combines the Euler transformation and rotational invariance(RI)property between subarrays.In this work,the effective array aperture is doubled by exploiting the noncircularity of signals.The complex arithmetic is converted to real arithmetic via Euler transformation.The main contribution of this work is not only extending the NC-Euler-ESPRIT algorithm from uniform linear array to double parallel uniform linear arrays,but also constructing a new 2 Drotational invariance property between subarrays,which is more complex than that in NCEuler-ESPRIT algorithm.The proposed 2 DNC-Euler-RI algorithm has much lower computational complexity than2 DNC-ESPRIT algorithm.The proposed algorithm has better angle estimation performance than 2 DESPRIT algorithm and 2 D NC-PM algorithm for double parallel uniform linear arrays,and is very close to that of 2 D NC-ESPRIT algorithm.The elevation angles and azimuth angles can be obtained with automatically pairing.The proposed algorithm can estimate up to 2(M-1)sources,which is two times that of 2 D ESPRIT algorithm.Cramer-Rao bound(CRB)of noncircular signal is derived for the proposed algorithm.Computational complexity comparison is also analyzed.Finally,simulation results are presented to illustrate the effectiveness and usefulness of the proposed algorithm.

Low complexity DOA estimation for massive UCA with single snapshot

In this paper, a low complexity direction of arrival(DOA) estimation method for massive uniform circular array(UCA) with single snapshot is proposed.Firstly, the coarse DOAs are estimated by finding the peaks from the circular convolution between a fixed coefficient vector and the received data vector.Thereafter, in order to refine coarse DOA estimates, we reconstruct the direction matrix based on the coarse DOA estimations and take the first order Taylor expansion with DOA estimation offsets into account.Finally, the refined estimations are obtained by compensating the offsets, which are obtained via least squares(LS) without any complex searches.In addition, the refinement can be iteratively implemented to enhance the estimation results.Compared to the offset search method, the proposed method achieves a better estimation performance while requiring lower complexity.Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

Low-Complexity DOA Estimation of Noncircular Signals for Coprime Sensor Arrays

This paper presents a low?complexity method for the direction?of?arrival(DOA)estimation of noncircular signals for coprime sensor arrays.The noncircular property is exploited to improve the performance of DOA estimation.To reduce the computational complexity,the rotational invariance propagator method(RIPM)is included in the algorithm.First,the extended array output is reconstructed by combining the array output and its conjugated counterpart.Then,the RIPM is utilized to obtain two sets of DOA estimates for two subarrays.Finally,the true DOAs are estimated by combining the consistent results of the two subarrays.This illustrates the potential gain that both noncircularity and coprime arrays provide when considered together.The proposed algorithm has a lower computational complexity and a better DOA estimation performance than the standard estimation of signal parameters by the rotational invariance technique and Capon algorithm.Numerical simulation results illustrate the effectiveness and superiority of the proposed algorithm.

Super-resolution DOA estimation for correlated off-grid signals via deep estimator

This paper develops a deep estimator framework of deep convolution networks(DCNs)for super-resolution direction of arrival(DOA)estimation.In addition to the scenario of correlated signals,the quantization errors of the DCN are the major challenge.In our deep estimator framework,one DCN is used for spectrum estimation with quantization errors,and the remaining two DCNs are used to estimate quantization errors.We propose training our estimator using the spatial sampled covariance matrix directly as our deep estimator’s input without any feature extraction operation.Then,we reconstruct the original spatial spectrum from the spectrum estimate and quantization errors estimate.Also,the feasibility of the proposed deep estimator is analyzed in detail in this paper.Once the deep estimator is appropriately trained,it can recover the correlated signals’spatial spectrum fast and accurately.Simulation results show that our estimator performs well in both resolution and estimation error compared with the state-of-the-art algorithms.