Fast Implementation for the Singular Value and Eigenvalue Decomposition Based on FPGA

Zhang, Shuiping; Tian, Xin; Xiong, Caiming; Tian, Jinwen; Ming, Delie

doi:10.1049/cje.2016.06.033

Cited by 24 publications

(8 citation statements)

References 16 publications

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“…Many methods exist for finding the eigenvalues of the incident signal covariance matrix like the Exact Jacobi method, the Jacobi method [14], [15], and the algebraic method [16]. Some other techniques for fast computation of SVD (Singular Value Decomposition) and EVD have also been proposed in [17]. Among all these techniques [16] is found to be the most efficient and has less computational requirements.…”

Section: Eigen Value Decompositionmentioning

confidence: 99%

Towards Low Latency and Resource-Efficient FPGA Implementations of the MUSIC Algorithm for Direction of Arrival Estimation

Butt

Khan

Ullah

et al. 2021

IEEE Trans. Circuits Syst. I

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The estimation of the Direction of Arrival (DoA) is one of the most critical parameters for target recognition, identification and classification. MUltiple SIgnal Classification (MUSIC) is a powerful technique for DoA estimation. The algorithm requires complex mathematical operations like the computation of the covariance matrix for the input signals, eigenvalue decomposition and signal peak search. All these signal processing operations make real-time and resource-efficient implementation of the MUSIC algorithm on Field Programmable Gate Arrays (FPGAs) a challenge.In this paper, a novel design approach is proposed for the FPGAimplementation of the MUSIC algorithm. This approach enables a significant reduction in both FPGA resources and latency. In more detail, the proposed design enables the estimation of DoA in real-time scenarios in 2µsec with 30% to 50% fewer resources as compared to existing techniques.

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Section: Eigen Value Decompositionmentioning

confidence: 99%

Towards Low Latency and Resource-Efficient FPGA Implementations of the MUSIC Algorithm for Direction of Arrival Estimation

Butt

Khan

Ullah

et al. 2021

IEEE Trans. Circuits Syst. I

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“…The implementation managed to compute the SVD of an 32 × 127 matrix in 13 ms while occupying 20% and 67% slice registers and LUTs respectively on a Virtex-6 FPGA. Fast and efficient FPGA implementation for computing the singular and eigen value decomposition based on a simplified CORDIC-like algorithm is presented in [21]. The implementation uses fixed-point arithmetic for sequential and parallel operations leading about 3× faster computation in an image denoising application compared to computations via an Intel CPU based PC.…”

Section: A Literature Reviewmentioning

confidence: 99%

A Shallow Neural Network for Real-Time Embedded Machine Learning for Tensorial Tactile Data Processing

Younes

Ibrahim

Rizk

et al. 2021

IEEE Trans. Circuits Syst. I

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This paper presents a novel hardware architecture of the Tensorial Support Vector Machine (TSVM) based on Shallow Neural Networks (NN) for the Single Value Decomposition (SVD) computation. The proposed NN achieves a comparable Mean Squared Error and Cosine Similarity to the widely used one-sided Jacobi algorithm. When implemented on an FPGA, the NN offers 324× faster computations than the one-sided Jacobi with reductions up to 58% and 67% in terms of hardware resources and power consumption respectively. When validated on a touch modality classification problem, the NN-based TSVM implementation has achieved a real-time operation while consuming about 88% less energy per classification than the Jacobi-based TSVM with an accuracy loss of at most 3%. Such results offer the ability to deploy intelligence on resource-limited platform for energy-constrained applications.

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“…We develop a unitary transformation 33 to further transform the pertinent persymmetric Hermitian matrix into a real symmetric matrix. In this way, the classic Jacobi rotation method 34 can thus be exploited to perform orthogonal similarity transformation on this real symmetric matrix. When all the non‐diagonal elements in the square matrix are close to zero, we can obtain an approximate diagonal matrix, and its diagonal elements are the desired eigenvalues.…”

Section: Noise Variance Estimationmentioning

confidence: 99%

An improved time support estimation method for overlapping automatic dependent surveillance‐broadcast signals in low signal‐to‐noise ratio region

Ren

Wang

Zhang

et al. 2020

Satell Commun Network

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Summary In the satellite‐based application, due to the low signal‐to‐noise ratio (SNR) of received signals, it is highly difficult to estimate the time support of overlapping automatic dependent surveillance‐broadcast (ADS‐B) signals, resulting in the failure of many separation algorithms. Besides, it is troublesome to determine the detection threshold for unknown noise variance. In this paper, we first present three estimation methods of noise variance based on eigenvalue decomposition, which are suitable for constant and slowly varying noise variance, respectively. The proposed time support estimation is therefore of constant false alarm rate property. Moreover, according to the characteristic of ADS‐B signals, we design a matched filter and propose two estimation schemes of direct form and indirect form, which significantly improves the estimation accuracy and detection probability. Finally, in combination of the well‐known projection algorithm (PA), it is concluded that with the proposed estimation method, PA exhibits a satisfactory separation performance at low SNRs.

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Fast Implementation for the Singular Value and Eigenvalue Decomposition Based on FPGA

Cited by 24 publications

References 16 publications

Towards Low Latency and Resource-Efficient FPGA Implementations of the MUSIC Algorithm for Direction of Arrival Estimation

Towards Low Latency and Resource-Efficient FPGA Implementations of the MUSIC Algorithm for Direction of Arrival Estimation

A Shallow Neural Network for Real-Time Embedded Machine Learning for Tensorial Tactile Data Processing

An improved time support estimation method for overlapping automatic dependent surveillance‐broadcast signals in low signal‐to‐noise ratio region

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