Sparse Planar Array Synthesis Using Matrix Enhancement and Matrix Pencil

Zheng, Mei-yan; Ke-song, Chen; Wu, Honggang; Xianpan, Liu

doi:10.1155/2013/147097

Cited by 10 publications

(6 citation statements)

References 17 publications

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“…Once the low-rank matrix

is acquired, the parameters

corresponding to the positions of the new sparse array with

elements can be calculated by solving the following generalized eigenvalue problem [ 28 ],

where

and

are obtained by deleting the first L rows and the last L rows of

. Besides this, we can obtain eigenvalues more computationally efficient by solving the following equation

where

and

are obtained by removing the first L rows and the last L rows of

which contain only principal right singular vectors of

.…”

Section: Proposed Synthesis Methods For Sparse Fdamentioning

confidence: 99%

See 1 more Smart Citation

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

Shao

Zhang

et al. 2022

Sensors

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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.

show abstract

“…Once the low-rank matrix

is acquired, the parameters

corresponding to the positions of the new sparse array with

elements can be calculated by solving the following generalized eigenvalue problem [ 28 ],

where

and

are obtained by deleting the first L rows and the last L rows of

. Besides this, we can obtain eigenvalues more computationally efficient by solving the following equation

where

and

are obtained by removing the first L rows and the last L rows of

which contain only principal right singular vectors of

.…”

Section: Proposed Synthesis Methods For Sparse Fdamentioning

confidence: 99%

“…Similarly, another set of eigenvalues

corresponding to the frequency offsets also can be obtained. Next, utilize the pairing algorithm in [ 28 ] to get the correct pairing of

and

. Finally the locations and frequency offsets of the resulting sparse SFDA can be given by

where

…”

Section: Proposed Synthesis Methods For Sparse Fdamentioning

confidence: 99%

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

Shao

Zhang

et al. 2022

Sensors

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show abstract

“…The main CS-based algorithms are Bayesian compressive sampling (BCS) algorithms [ 20 , 21 , 22 ], focal under-determined system solver (FOCUSS) algorithms [ 23 , 24 ], and convex optimization algorithms [ 25 , 26 , 27 ]. Moreover, some shaped beam patterns (such as flat-top BP and asymmetric sidelobe BP) are employed in sparse array synthesis via CS-based methods [ 28 , 29 , 30 ].…”

Section: Introductionmentioning

confidence: 99%

Optimization of Sparse Cross Array Synthesis via Perturbed Convex Optimization

Chen

Jiang

et al. 2020

Sensors

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Three-dimensional (3-D) imaging sonar systems require large planar arrays, which incur hardware costs. In contrast, a cross array consisting of two perpendicular linear arrays can also support 3-D imaging while dramatically reducing the number of sensors. Moreover, the use of an aperiodic sparse array can further reduce the number of sensors efficiently. In this paper, an optimized method for sparse cross array synthesis is proposed. First, the beamforming of a cross array based on a multi-frequency algorithm is simplified for both near-field and far-field. Next, a perturbed convex optimization algorithm is proposed for sparse cross array synthesis. The method based on convex optimization utilizes a first-order Taylor expansion to create position perturbations that can optimize the beam pattern and minimize the number of active sensors. Finally, a cross array with 100 + 100 sensors is employed from which a sparse cross array with 45 + 45 sensors is obtained via the proposed method. The experimental results show that the proposed method is more effective than existing methods for obtaining optimum results for sparse cross array synthesis in both the near-field and far-field.

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“…The challenge of determining optimum parameter values simultaneously stems from the nonlinear and nonconvex dependency of the array factor to the weights and the sensor positions [4]. In [13], the authors revealed that the synthesis of nonuniform array elements' positions, excitations, and phases is a complicated nonlinear problem which contains a number of decision variables. The performance of the employed optimization scheme is an important factor in the success of a pattern synthesis method, in terms of solution quality, computational load, and stability.…”

Section: Introductionmentioning

confidence: 99%

Array Pattern Synthesis Using Particle Swarm Optimization with Dynamic Inertia Weight

Han

2016

International Journal of Antennas and Propagation

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A Feedback Particle Swarm Optimization (FPSO) with a family of fitness functions is proposed to minimize sidelobe level (SLL) and control null. In order to search in a large initial space and converge fast in local space to a refined solution, a FPSO with nonlinear inertia weight algorithm is developed, which is determined by a subtriplicate function with feedback taken from the fitness of the best previous position. The optimized objectives in the fitness function can obtain an accurate null level independently. The directly constrained SLL range reveals the capability to reduce SLL. Considering both element positions and complex weight coefficients, a low-level SLL, accurate null at specific directions, and constrained main beam are achieved. Numerical examples using a uniform linear array of isotropic elements are simulated, which demonstrate the effectiveness of the proposed array pattern synthesis approach.

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Sparse Planar Array Synthesis Using Matrix Enhancement and Matrix Pencil

Cited by 10 publications

References 17 publications

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

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

Optimization of Sparse Cross Array Synthesis via Perturbed Convex Optimization

Array Pattern Synthesis Using Particle Swarm Optimization with Dynamic Inertia Weight

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