The CBFM-Enhanced Jacobi Method for Efficient Finite Antenna Array Analysis

Ludick, D. J.; Botha, Matthys M.; Maaskant, Rob; Davidson, David

doi:10.1109/lawp.2017.2742059

Cited by 19 publications

(15 citation statements)

References 11 publications

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“…× Diag(exp( j δ phase e phase )) × a(θ, δ pos e pos ) (41) where δ (•) is used to indicate whether a certain kind of imperfection exists, I M is the M × M unitary matrix, Diag(•) forms diagonal matrices with the given vector on the diagonal, E mc is a toeplitz matrix with parameter vector e mc [22], and a(θ, δ pos e pos ) is the actual array responding vector corresponding to the signal from direction θ when position error e pos is embedded in the array geometry. The array responding function given in (41) has been largely simplified when compared with its counterpart in practical applications, which can be measured more precisely with computational electromagnetic methods, such as [54]- [56]. The array imperfection formulations in (37)- (40) can also be modeled more precisely following previous studies, such as [57]- [60] for mutual coupling.…”

Section: A Simulation Settingsmentioning

confidence: 99%

Direction-of-Arrival Estimation Based on Deep Neural Networks With Robustness to Array Imperfections

Liu

Zhang

2018

IEEE Trans. Antennas Propagat.

395

273

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Lacking of adaptation to various array imperfections is an open problem for most high-precision directionof-arrival (DOA) estimation methods. Machine learning-based methods are data-driven, they do not rely on prior assumptions about array geometries, and are expected to adapt better to array imperfections when compared with model-based counterparts. This paper introduces a framework of the deep neural network to address the DOA estimation problem, so as to obtain good adaptation to array imperfections and enhanced generalization to unseen scenarios. The framework consists of a multitask autoencoder and a series of parallel multilayer classifiers. The autoencoder acts like a group of spatial filters, it decomposes the input into multiple components in different spatial subregions. These components thus have more concentrated distributions than the original input, which helps to reduce the burden of generalization for subsequent DOA estimation classifiers. The classifiers follow a one-versus-all classification guideline to determine if there are signal components near preseted directional grids, and the classification results are concatenated to reconstruct a spatial spectrum and estimate signal directions. Simulations are carried out to show that the proposed method performs satisfyingly in both generalization and imperfection adaptation.

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Section: A Simulation Settingsmentioning

confidence: 99%

Direction-of-Arrival Estimation Based on Deep Neural Networks With Robustness to Array Imperfections

Liu

Zhang

2018

IEEE Trans. Antennas Propagat.

395

273

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“…The array response function given by ( 37) has been simplified compared with the actual application, which can be measured more accurately by the computational electromagnetic method [51][52][53]. The array imperfection formulations in ( 33)- (36) can also be modelled more accurately based on techniques from previous studies, such as mutual coupling [22,23].…”

Section: Musicmentioning

confidence: 99%

Robust direction‐of‐arrival estimation approach using beamspace‐based deep neural networks with array imperfections and element failure

Wen

Huang

et al. 2022

IET Radar Sonar & Navi

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Direction-of-arrival (DOA) estimation is a fundamental functionality of sensor array systems. Previous methods only consider element failure or array imperfections. In fact, the co-existence of element failure and array imperfections is more in line with the realistic operation conditions of an array system. However, the performance of previous methods degrades significantly in the presence of both array imperfections and element failure. To deal with this problem, a robust DOA estimation method is proposed based on a deep neural network (DNN). The proposed DNN consists of a denoising autoencoder (DAE) and a parallel network. The DAE can restore damaged array signals to "non-corrupted" signals, and the parallel network is able to process signals with different levels of loss to improve DOA estimation accuracy. At the training stage, array imperfections are modelled as a spherical distribution, and the training samples are extracted under this distribution to improve the generalisation capability of the proposed network to various array imperfections. In addition, the authors propose to estimate the spatial spectrum in a virtual array beamspace, which can reduce the computational complexity as well as signal-to-noise ratio resolution threshold, and further enhance the robustness to array imperfections. Numerical results show that the proposed DOA estimation approach works well in the presence of both array imperfections and element failure.

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“…Moreover, the convergence of a preconditioned iterative method may still be suboptimal when dealing with large and ill-conditioned problems. This limitation may be largely overcome by introducing the CBFM into a classical iterative scheme, as has been demonstrated in [43], [44] for the case of the CBFM-enhanced Jacobi method. Similarly, the relation between the Krylov methods and the CBFs (or MBFs in general) has been discussed in [45]- [48].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we compare the performances of different iterative solvers enhanced by the CBFM, which are used for the analysis of MoM-based systems related to different array configurations of disjoint antenna elements. While the analyses performed in [43]- [48] provide insight into the performances of particular iterative methods, a comprehensive comparative analysis of different iterative techniques in terms of their respective convergence rates and computational requirements, which is based on a wider palette of MoM-based problems, has not been reported in the literature yet. Similar comparison of the MBF-enhanced iterative techniques has been performed in [49], however, it is based on the finite element approach and limited to the analysis of the plane wave scattering by a collection of cylindrical obstacles, while our comparison is based on the MoM analysis of realistic antenna elements.…”

Section: Introductionmentioning

confidence: 99%

“…Similar comparison of the MBF-enhanced iterative techniques has been performed in [49], however, it is based on the finite element approach and limited to the analysis of the plane wave scattering by a collection of cylindrical obstacles, while our comparison is based on the MoM analysis of realistic antenna elements. Specifically, we analyze the CBFM-enhanced schemes based on stationary-type methods (Jacobi [43], Gauss-Seidel) as well as on the nonstationary GMRES method [47]. In addition, we propose an acceleration scheme for the CBFM-enhanced Jacobi method, based on the macro-block (MB) concept described in [50], and formulate the CBFM-enhanced alternating GMRES-Jacobi (AGJ) method.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of CBFM-Enhanced Iterative Methods for MoM-Based Finite Antenna Array Analysis

Marinovic

Maaskant

Mittra

et al. 2022

IEEE Trans. Antennas Propagat.

Self Cite

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In this paper we compare different iterative techniques enhanced by the CBFM, that are used to analyze finite arrays of disjoint antenna elements. These are based on the stationary-type methods (Jacobi, Gauss-Seidel, macro-block Jacobi), the nonstationary GMRES and the hybrid alternating GMRES-Jacobi (AGJ) method which combines these two types. In each iteration, the reduced CBFM system is constructed based on the previous iterates, the solution of which is used to update the solution vector in the next iteration with improved accuracy. In this way, the convergence of the classical iterative techniques can be greatly improved. The convergence rates and computational costs of the CBFM-enhanced iterative methods are analyzed by considering several MoM-based problems. The GMRES-based method, which employs the block-Jacobi preconditioner, outperforms the other methods when the MoM matrix is ill-conditioned. For well-conditioned MoM matrices with reduced diagonal dominance due to increased presence of the inter-element coupling effects, the AGJ method or the methods based on the stationary-type iterations may require smaller computational effort to converge to the desired solution accuracy in comparison to the GMRES-based approach.

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The CBFM-Enhanced Jacobi Method for Efficient Finite Antenna Array Analysis

Cited by 19 publications

References 11 publications

Direction-of-Arrival Estimation Based on Deep Neural Networks With Robustness to Array Imperfections

Direction-of-Arrival Estimation Based on Deep Neural Networks With Robustness to Array Imperfections

Robust direction‐of‐arrival estimation approach using beamspace‐based deep neural networks with array imperfections and element failure

Comparison of CBFM-Enhanced Iterative Methods for MoM-Based Finite Antenna Array Analysis

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