DOA estimation of coexisted noncoherent and coherent signals via sparse representation of cleaned array covariance matrix

A new direction finding method is presented to deal with coexisted noncoherent and co- herent signals without smoothing operation. First the direction-of-arrival （DOA） estimation task is herein reformulated as a sparse reconstruction problem of the cleaned array covariance matrix, which is processed to eliminate the affection of the noise. Then by using the block of matrices, the information of DOAs which we pursuit are implied in the sparse coefficient matrix. Finally, the sparse reconstruction problem is solved by the improved M-FOCUSS method, which is applied to the situation of block of matrices. This method outperforms its data domain counterpart in terms of noise suppression, and has a better performance in DOA estimation than the customary spatial smoothing technique. Simulation results verify the efficacy of the proposed method.

Power Estimation of Acoustic Sources by Sensor Array Processing

A constant problem is to localize a number of acoustic sources, to separate their individual signals and to estimate their strengths in a propagation medium. An acoustic receiving array with signal processing algorithms is then used. The most widely used algorithm is the conventional beamforming algorithm but it has a very low resolution and high sidelobes that may cause a signal leakage problem. Several new signal processors for arrays of sensors are derived to evaluate the strengths of acoustic signals arriving at an array of sensors. In particular, we present the covariance vector estimator and the pseudoinverse of the array manifold matrix estimator. The covariance vector estimator uses only the correlations between sensors and the pseudoinverse of the array manifold matrix estimator operates with the minimum eigenvalues of the covariance matrix. Numerical and experimental results are presented.

Polynomial-rooting based fourth-order MUSIC for direction-of-arrival estimation of noncircular signals

A polynomial-rooting based fourth-order cumulant algorithm is presented for direction-of-arrival（DOA） estimation of second-order fully noncircular source signals, using a uniform linear array（ULA）. This algorithm inherits all merits of its spectralsearching counterpart except for the applicability to arbitrary array geometry, while reducing considerably the computation cost.Simulation results show that the proposed algorithm outperforms the previously developed closed-form second-order noncircular ESPRIT method, in terms of processing capacity and DOA estimation accuracy, especially in the presence of spatially colored noise.

Estimating DOA and polarization with spatially spread loop and dipole pair array

The nonuniform L-shaped spatially spread loop and dipole（SSLD） array whose inter-element spacing is greater than half a wavelength is studied. A joint parameter estimation algorithm of direction of arrival（DOA）, frequency and polarization is presented for plane-wave signals. The direct sampling and the corresponding delayed sampling data are used to construct the data correlation matrix. On the basis of the subspace theory and the least square method, the frequency and the steering vector of the whole array are obtained. According to the relationship of the array manifold vector between electric dipoles and magnetic loops,the polarization parameters are given. The unambiguous phase estimates are acquired by applying virtual baseline array transformation to the spatial steering vectors, and they are used as coarse references to disambiguate the cyclic phase ambiguities in phase differences between two adjacent array elements on the array,then the high accuracy DOA estimates are obtained. Closed-form solutions for each parameter are obtained. This method has advantages of lower calculation complexity and no parameter matching. The experiment results verify the effectiveness and feasibility of the presented algorithm.

New direction of arrival estimation method for wideband coherent signals

To estimate the direction-of-arrival （DOA） of wideband coherent signals, a new method by modifying the orthogonality of the projected suhspaces method is proposed. And it can deal with randomly position perturbed arrays by using the Toeplitz method. This method needn＇t the primary information of DOA for focusing matrix and the sector dividing of interpolated method, which improving the precision of estimation and reducing the computational complexity. Simulations illustrate the effectiveness of this method.

Wideband angle of arrival estimation of chirp signals using virtual Wignerville distribution

To estimate the angle of arrivals （AOA） of wideband chirp sources, a new timo-frequency algorithm is proposed. In this method, virtual sensors are constructed based on the fact that the steering vectors of wideband chirp signals are linear and vary with time. And the randon Wignersville distribution （RWVD） of real sensors and virtual sensors are calculated to yield the new time-invariable steering vectors, furthermore, the noise and cross terms are suppressed. In addition, the multiple chirp signals are selected by their time-frequency points. The cost of computation is lower than the common AOA estimation methods of wideband sources due to nonrequirement of frequency focusing, interpolating and matrix decomposition, including subspace decomposition. Under the lower signal noise ratio （SNR） condition, the proposed method exhibits better precision than the method of frequency focusing （FF）. The proposed method can be further applied to nonuniform linear array （NLA） since it is not confined to the array geometry. Simulation results illustrate the efficacy of the proposed method.

A Modified Root-MUSIC Algorithm for Signal DOA Estimation

This paper presents a modified Root-MUSIC algorithm by which the signal DOA estimation performance can be improved when the snapshot number is limited. The operation principlesof this algorithm are described in detail. It is also pointed out theoretically that this is equivalentto have increased the snapshot number and can make the DOA estimation better. Finally, somesimulating results to verify the theoretical analyses are presented.

An Array Extension Method in a Noisy Environment

An array extension method in a noisy environment was proposed to improve angular resolution and array gain. The proposed method combines the FOC （fourth-order cumulants） technique with the ETAM （extended towed array measurements） method to extend array aperture and suppress Gaussian noise, First, successive measurements of a virtual uniform linear array were constructed by applying lburth-order cumulants to measurements of uniform linear array; Gaussian noise in these measurements was also eliminated. Then, the array was extended by compensating phase differences using the ETAM method, Finally, the synthetic aperture was extended further by the fourth-order cumulants technique. The proposed FOC-ETAM-FOC method not only improves angular resolution and array gain, but also effectively suppresses Gaussian noise. Furthermore, it inherits the advantages of the ETAM method. Simulation results showed that the FOC-ETAM-FOC method achieved better angular resolution and array gain than the ETAM method. Furthermore this method outperforms the ETAM method in Gaussian noise environment.

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.

Array-error estimation method for multi-channel SAR systems in azimuth

For multi-channel synthetic aperture radar（SAR） systems, since the minimum antenna area constraint is eliminated,wide swath and high resolution SAR image can be achieved.However, the unavoidable array errors, consisting of channel gainphase mismatch and position uncertainty, significantly degrade the performance of such systems. An iteration-free method is proposed to simultaneously estimate position and gain-phase errors.In our research, the steering vectors corresponding to a pair of Doppler bins within the same range bin are studied in terms of their rotational relationships. The method is based on the fact that the rotational matrix only depends on the position errors and the frequency spacing between the paired Doppler bins but is independent of gain-phase error. Upon combining the projection matrices corresponding to the paired Doppler bins, the position errors are directly obtained in terms of extracting the rotational matrix in a least squares framework. The proposed method, when used in conjunction with the self-calibration algorithm, performs stably as well as has less computational load, compared with the conventional methods. Simulations reveal that the proposed method behaves better than the conventional methods even when the signal-to-noise ratio（SNR） is low.

Detection of Number of Wideband Signals Based on Support Vector Machine

In array signal processing,number of signals is often a premise of estimating other parameters.For the sake of determining signal number in the condition of strong additive noise or a little sample data,an algorithm for detecting number of wideband signals is provided.First,technique of focusing is used for transforming signals into a same focusing subspace.Then the support vector machine(SVM)can be deduced by the information of eigenvalues and corresponding eigenvectors.At last,the signal number can be determined with the obtained decision function.Several simulations have been carried on verifying the proposed algorithm.

Robust adaptive beamforming for constant modulus signal of interest

It is required in the diagonally loaded robust adaptive beamforming the automatic determination of the loading level which is practically a challenging problem.A constant modulus restoral method is herein presented to choose the diagonal loading level adaptively for the extraction of a desired signal with constant modulus(a common feature of the phase modulation signals).By introducing the temporal smoothing technique,the proposed constant modulus restoral diagonally loaded robust adaptive beamformer provides increased capability compared with some existing robust adaptive beamformers in rejecting interferences and noise while protecting the signal-of-interest.Simulation results are included to illustrate the performance of the proposed beamformer.

Space discriminative function for microphone array robust speech recognition

Based on W-disjoint orthogonality of speech mixtures, a space d,scnmlnative tunetlon was proposer1 to enumerate and localize competing speakers in the surrounding environments. Then, a Wiener-like postfiherer was developed to adaptively suppress interferences. Experimental results with a hands-free speech recognizer under various SNR and competing speakers settings show that nearly 69 % error reduction can be obtained with a two-channel small aperture microphone array against the conventional single microphone baseline system. Comparisons were made against traditional delay-and-sum and Griffiths-Jim adaptive beamforming techniques to further assess the effectiveness of this method.

Pattern Synthesis via Accurate Array Response Control:An Overview

Array pattern synthesis is an important research direction in array processing.It is a signal processing technology that uses sensor arrays to send and receive signals directionally.Pattern design and synthesis play an important role in the high performance of the array system.In this paper,we give an overview about the recently developed pattern synthesis algorithms with the concept of accurate array response control theory.

Array processing for the GD signal model with angular spread

Array processing is to process the signals carried by the propagating waves received at an array of sensors. When the signals propagate through the practical random time-variant medium, their wavefronts can show the progressive losses of coherence with increasing spatial separation. These decorrelations of wavefronts result in an angular spread in the wavenumber spectrum centered about the true signal dircction-of-arrival. This paper puts the emphasis upon the array processing of the angular-spread signal which is called the Generalized Directional (GD) signal and aims to match array processing to this signal model in the energy sense. In this paper, we also present a method of the computer simulation of the generalized directional signal model. Some results of computer simulation experiments and lake-tests in Xinanjiang River are given.

DOA and polarization estimation via signal reconstruction with linear polarization-sensitive arrays

This paper addresses the problem of direction-of-arrival （DOA） and polarization estima- tion with polarization sensitive arrays （PSA）, which has been a hot topic in the area of array signal processing during the past two or three decades. The sparse Bayesian learning （SBL） technique is introduced to exploit the sparsity of the incident signals in space to solve this problem and a new method is proposed by reconstructing the signals from the array outputs first and then exploit- ing the reconstructed signals to realize parameter estimation. Only 1-D searching and numerical calculations are contained in the proposed method, which makes the proposed method computa- tionally much efficient. Based on a linear array consisting of identically structured sensors, the proposed method can be used with slight modifications in PSA with different polarization structures. It also performs well in the presence of coherent signals or signals with different degrees of polarization. Simulation results are given to demonstrate the parameter estimation precision of the proposed method.

DOA Estimation Algorithm Based on Adaptive Filtering in Spatial Domain

In this paper, a novel DOA estimation methodology based upon the technology of adaptive nulling antenna is proposed. Initially, the nulling antenna obtains the weight vector by LMS algorithm and power inversion criterion.Afterwards, reciprocal of the antenna pattern is defined as the spatial spectrum and the extracted peak values are corresponded to the estimated DOA. Through observation of the spectrum and data analysis of variable steps and SNRs, the simulation results demonstrate that the proposed method can estimate DOA above board. Furthermore, the estimation error of the proposed technique is directly proportional to step size and is inversely proportional to SNR. Unlike the existing MUSIC algorithm, the proposed algorithm has less computational complexity as it eliminates the need of estimating the number of signals and the eigenvalue decomposition of covariance matrix. Also it outperforms MUSIC algorithm, the recently proposed MUSIC-Like algorithm and classical methods by achieving better resolution with narrow width of peaks.

Minimum geometric power distortionless response beamforming against heavy-tailed noise of unknown statistics

A minimum geometric power distortionless response beamforming approach against impulsive noise （including all α- stable noise） of unknown statistics is proposed. Due to that definite logarithmic moments require no priori knowledge of impulsive noise, this new beamformer substitutes the logarithmic moments for the second-order moments and iteratively minimizes the ＂ge- ometric power＂ of the beamformer.s output snapshots, subjected to a linear constraint. Therefore, the proposed beamformer can provide significantly higher output geometric signal-to-noise-andinterference ratio. Moreover, the optimum weight vector is obtained by using a new iteration process. The simulation results prove that the new method is effective.

COMPUTATIONALLY EFFICIENT ESPRIT METHOD FOR DIRECTION FINDING

In this paper,a low complexity ESPRIT algorithm based on power method and Orthogo- nal-triangular (QR) decomposition is presented for direction finding,which does not require a priori knowledge of source number and the predetermined threshold (separates the signal and noise ei- gen-values).Firstly,according to the estimation of noise subspace obtained by the power method,a novel source number detection method without eigen-decomposition is proposed based on QR de- composition.Furthermore,the eigenvectors of signal subspace can be determined according to Q matrix and then the directions of signals could be computed by the ESPRIT algorithm.To determine the source number and subspace,the computation complexity of the proposed algorithm is approximated as (2log_2 n+2.67)M^3,where n is the power of covariance matrix and M is the number of array ele- ments.Compared with the Single Vector Decomposition (SVD) based algorithm,it has a substantial computational saving with the approximation performance.The simulation results demonstrate its effectiveness and robustness.

Focused Widely Linear Beamforming

The problem addressed in this paper concerns the extension of widely linear beamforming to the wideband case,developing a wide-focused linear beamformer for the extraction of a wideband second-order(SO)noncircular signal-of-interest(SOI)contaminated by uncorrelated interferences and noise.In the proposed beamformer,the beamforming array observation is first focused to adopt a standard linear minimum variance distortionless response(MVDR)framework.The augmented SOI steering vector then is obtained by estimating the SOI noncircularity parameter with the newly proposed oblique projection with an augmented sparse representation scheme.The covariance matrix of the virtual interference,true interference and noise is further reconstructed using the newly presented complementary spatial spectrum technique.The wideband widely linear spatial filtering is finally realized via MVDR like beamforming.The performance of the proposed beamformer is verified by simulation.