Matrix Enhancement And Matrix Pencil Research Articles

An Effective Method for the Synthesis of Wideband and Wide-Scanning Sparse Planar Array

The matrix enhancement and matrix pencil (MEMP) has been used to reduce the number of array elements in the planar array with a shaped-beam pattern. This work extends the MEMP-based synthesis method to the synthesis of pattern reconfigurable sparse planar arrays in wide angle scanning and wide-band, which exploits a necessary restriction on finding the common element positions and individual element excitations for multiple patterns. Moreover, a unitary transformation is exploited into the multiple-composite equivalent Hankel matrix, which converts the complex computations of singular value decomposition (SVD) and eigenvalue decomposition (EVD) courses into real ones and effectively reduces the computation complexity. A new tactic is also restricted on avoiding too small element spacing with the consideration of the size of array antenna element. A set of numerical experiments is provided to validate the effectiveness and advantages of the proposed method.

Efficient Beampattern Synthesis for Sparse Frequency Diverse Array via Matrix Pencil Method.

Due to the introduction of frequency offsets, the pattern synthesis problem of sparse Frequency diverse array (FDA) becomes more complicated than that of the phased array. A typical way to solve this problem is to use a global optimization algorithm, but this is usually time-consuming. In this paper, we propose an efficient non-iterative beampattern synthesis approach for sparse FDA. For a given reference pattern, which can be generated by other synthesis methods, we first sample it uniformly and construct the Hankel matrix with the sampled data. By low-rank processing, a low-rank approximation version of the Hankel matrix can then be obtained. Finally, the matrix enhancement and matrix pencil (MEMP) and matrix pencil (MP) methods are applied to estimate the antenna positions, frequency offsets, and excitations of the obtained array from the approximated matrix. Besides this, two typical FDA frameworks including multi-carrier FDA (MCFDA) and standard FDA (SFDA) are considered. Numerical simulation results prove that the proposed method outperforms the existing methods in terms of synthesis error, average runtime, and percentage of saving elements.

Three‐dimensional decoupling imaging method for wideband two‐dimensional multiple‐input‐multiple‐output radar

Wideband two-dimensional multiple input multiple output (MIMO) radar can be used for target three-dimensional (3-D) imaging. As the echo of wideband MIMO radar is derived from both time and spatial sampling, the time-frequency coupling is contained, resulting in imaging defocussing. To solve this problem, a time-frequency decoupling algorithm based on matrix enhancement and matrix pencil (MEMP) is proposed to achieve high-resolution 3-D imaging. By combining the enhanced matrix constructed via MEMP with the modern spectral estimation theory, the time-frequency coupling term is regarded as a space rotation factor and is eliminated in the process of target position estimation. Simulation results show that the proposed algorithm can reduce the negative influence of time-frequency coupling and improve the imaging accuracy of wideband two-dimensional MIMO radar.

Design of Wide Scanning Sparse Planar Array Using Both Matrix-Pencil and Space-Mapping Methods

A hybrid efficient optimizing method of wide scanning sparse planar array involving mutual coupling is investigated in this letter. The former work of matrix enhancement and matrix pencil (MEMP)-based synthesis method is extended to the design of pattern reconfigurable sparse arrays in wide-angle scanning. The genetic algorithm was utilized to further optimize the reconstructed sparse array including the actual antenna element, which differs from the only array factor synthesis of MEMP. To improve the optimization efficiency and design accuracy, the space mapping technique was exploited to accomplish the optimizing design, which also involves the interactions among elements during the optimizing process. A wide-scanning sparse array can be realized by the new relationship of parameter mapping courses between low-cost coarse model optimizations and high-accuracy fine model validations based on the characteristic mode and multilevel fast multipole algorithm. Numerical examples show the efficiency of the proposed method.

An Efficient Approach for the Synthesis of Large Sparse Planar Array

An innovative noniterative approach based on the matrix enhancement and matrix pencil (MEMP) is proposed for the synthesis of arbitrary sparse planar arrays. In this study, the estimation of array parameters is recast as a 2-D pole extraction problem, and the number of array elements is minimized by the reduced rank processing. Subsequently, the Hankel matrix decomposition algorithm is exploited to accelerate the singular value decomposition (SVD) of the Hankel matrix constructed by the desired pattern samples, which conquers the restriction on the matrix dimension of the sampled Hankel matrix with the increasing of the number of array elements. The MEMP approach is further extended to the synthesis of shaped-beam patterns by using the forward–backward matrix enhancement and matrix pencil method (FBMEMP). A set of representative numerical experiments is provided to validate the effectiveness and advantages of the proposed method.

ISAR Imaging Based on MEMP Method and Low Rank Matrix Denoising Technique

Matrix enhancement and matrix pencil (MEMP) method is an efficient approach for 2-D frequencies estimation in ISAR imaging. However, the MEMP method belongs to the category of spectral estimation algorithm and is sensitive to noise. In the MEMP method, an enhanced matrix formed using the echo matrix is leveraged to extract the 2-D frequencies. Based on the low rank property of this enhanced matrix, we propose a low rank matrix denoising technique for MEMP method. Simulation and quasi real data results demonstrate the effectiveness and robustness of the proposed denoising approach. With the proposed denoising technique, the tolerance to noise of MEMP method has been improved by 10dB.

Sparse Planar Array Synthesis Using Matrix Enhancement and Matrix Pencil

The matrix enhancement and matrix pencil (MEMP) plays important roles in modern signal processing applications. In this paper, MEMP is applied to attack the problem of two-dimensional sparse array synthesis. Firstly, the desired array radiation pattern, as the original pattern for approximating, is sampled to form an enhanced matrix. After performing the singular value decomposition (SVD) and discarding the insignificant singular values according to the prior approximate error, the minimum number of elements can be obtained. Secondly, in order to obtain the eigenvalues, the generalized eigen-decomposition is employed on the approximate matrix, which is the optimal low-rank approximation of the enhanced matrix corresponding to sparse planar array, and then the ESPRIT algorithm is utilized to pair the eigenvalues related to each dimension of the planar array. Finally, element positions and excitations of the sparse planar array are calculated according to the correct pairing of eigenvalues. Simulation results are presented to illustrate the effectiveness of the proposed approach.

레이다 표적 인식에서 3D MEMP 기법을 이용한 표적의 3차원 산란점 예측

본 논문은 레이다 표적 인식에서 레이다 산란신호에 대한 3차원 산란점 추출을 위한 고해상도 기법에 대해 기술하고 있다. 또한, 3차원 산란점 추출에서 신호의 극점을 획득하기 위해 3차원 짝 맞춤 절차를 소개하고 있다. 짝 맞춤 절차는 기존의 일반적인 방법보다 더 정확하고 견고한 특징을 가지고 있다. 3차원 산란점을 추출하기 위해서는 우선 주어진 3차원 레이다 산란 데이터로부터 상호 분산 행렬을 생성해야 한다. 그리고 matrix pencil 기법을 이용하여 3차원 산란점을 추출한다. 본 논문에서 MSSP를 이용하여 상호 분산 행렬을 생성하였으며, 관측 행렬은 sparse scanning order conception 방법을 이용하여 만들었다. 제시한 기법의 성능을 보여주기 위해서 본 논문에서는 이상적인 점 산란체를 생성하여 이에 대한 결과를 보여주고 있다. This paper presents high resolution techniques of three-dimensional(3D) scattering center extraction for a radar backscattered signal in radar target recognition. We propose a 3D pairing procedure, a new approach to estimate 3D scattering centers. This pairing procedure is more accurate and robust than the general criterion. 3D MEMP(Matrix Enhancement and Matrix Pencil) with the 3D pairing procedure first creates an autocorrelation matrix from radar backscattered field data samples. A matrix pencil method is then used to extract 3D scattering centers from the principal eigenvectors of the autocorrelation matrix. An autocorrelation matrix is constructed by the MSSP(modified spatial smoothing preprocessing) method. The observation matrix required for estimation of 3D scattering center locations is built using the sparse scanning order conception. In order to demonstrate the performance of the proposed technique, we use backscattered field data generated by ideal point scatterers.

레이다 표적 인식에서 표적에 대한 2차원 산란점 추출 및 ISAR 영상 형성에 대한 성능 개선

본 논문에서는 표적에 의해서 산란된 산란파에 대한 2차원 산란점 추출 및 2차원 ISAR(Inverse SAR) 영상 형성에 대해서 기술하였다. 표적 에 대 한 2차원 산란점과 ISAR 영상을 획득하는 방법에는 일반적으로 2-D IFFT(Inverse Fast Fourier Transform)가 널리 사용되고 있다. 그러나 이는 영상의 해상도 면에서 질이 떨이진다는 단점이 있다. 이러한 퓨리에 변환을 바탕으로 한 방법의 단점을 보완하기 위해서 여러 가지 고해상도 신호처리의 방법이 개발되어 왔다. 본 논문에서는 2차원 산란점 추출 및 ISAR 영상을 형성하기 위해서 2-D MEMP 알고리즘과 2-D ESPRIT 알고리즘에 대해서 기술하고 있다. 이러한 각 알고리즘에 대한 성능을 나타내기 위해서 이상적인 점 산란체와 F-18 전투기에 대한 산란파를 이용하여 2차원 산란점을 예측하고 2차원 ISAR 영상을 획득하였다. This paper presents techniques of 2-D scattering center extraction and 2-B ISAR(Inverse SAR) image formation for scattering wave which is scattered by a target. In general, 2-D IFFT is widely used to obtain 2-D scattering center and ISAR image of targets. But, this method has drawbacks, that is poor in a resolution aspect. To overcome these shortcomings with the FT(Fourier Transform)-based method, various techniques of high resolution signal processing were developed. In this paper, algorithms of 2-D scattering center extraction and ISAR image formation such as 2-D MEMP(Matrix Enhancement and Matrix Pencil), 2-D ESPRIT(Estimation of Signal Parameter via Rotational Invariance Techniques) are described. In order to show the performances of each algorithm, we use scattering wave of the ideal point scatterers and F-18 aircraft to estimate 2-D scattering center and abtain 2-D ISAR image.

Estimation of frequencies and damping factors by two-dimensional ESPRIT type methods

In this paper, we consider two-dimensional (2-D) signals modeled by the sum of damped cisoids. We propose two high-resolution approaches to estimate their frequencies and damping factors. Both high-resolution methods are based on the shift-invariance structure of the signal subspace related to each dimension. The first one estimates the frequency components in both dimensions as in the matrix enhancement and matrix pencil (MEMP) method before pairing them with a new algorithm. The second one consists of the direct estimation of the signal frequency pairs without an additional step to pair the frequencies related to each dimension. We show how these methods can estimate the scattering points of radar images.

High SNR perturbation in single 2-D frequency estimate using matrix pencil

An exact and most revealing expression of the high signal-to-noise (SNR) first-order perturbation variance of the single 2D frequency estimate using the matrix enhancement and matrix pencil (MEMP) method is provided. This expression is a general form consistent with several previously reported expressions for the 1D frequency case. Based on this expression, the statistical efficiency of the MEMP method is discussed. The optimum efficiency of the MEMP method is shown to be achieved by its 1D specialized version. >

Estimating two-dimensional frequencies by matrix enhancement and matrix pencil

A new method, called the matrix enhancement and matrix pencil (MEMP) method, is presented for estimating two-dimensional (2-D) frequencies. In the MEMP method, an enhanced matrix is constructed from the data samples, and then the matrix pencil approach is used to extract out the 2-D sinusoids from the principal eigenvectors of the enhanced matrix. The MEMP method yields the estimates of the 2-D frequencies efficiently, without solving the roots of a 2-D polynomial or searching in a 2-D space. It is shown that the MEMP method can be faster than a 2-D FFT method if the number of the 2-D sinusoids is much smaller than the data set. Simulation results are provided to show that the accuracy of the MEMP method can be very close to the Cramer-Rao lower bound. >