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Scalable Hardware Architecture for High-Throughput Implementation of ESPRIT algorithm

IEEE Sensors Journal 2025年

作者： Huang, Yanjie Wang, Weijiang Xue, Chengbo Jiang, Rongkun Dang, Hua Ren, Shiwei Beijing Institute of Technology (BIT) School of Integrated Circuits and Electronics Beijing 100081 China BIT Chongqing Institute of Microelectronics and Microsystems Chongqing 401332 China

Estimating signal parameter via rotational invariance technique (ESPRIT) algorithm is a high-performance method for direction of arrival (DOA) estimation. Its most cumbersome aspect is performing eigenvalue decomposition twice, particularly with general square matrices. Current implementations lack flexibility in configuring the number of array elements, signal sources, and snapshots at the same time. To tackle these challenges, we propose a scalable hardware acceleration scheme for the qr decomposition algorithm on a Field Programmable Gate Array (FPGA). Our qr decomposition (qrD) module leverages orientation displacement, parallel computing, and logic reuse to enhance speed and generality. Building upon this foundation, a reconfigurable design scheme with a parallel covariance matrix computation module for ESPRIT is proposed to increase calculation speed and throughput. Our ESPRIT implementation supports up to 26 array elements, 25 signal sources, and 2,048 snapshots. As evidenced by experiments, the root mean squared error (RMSE) of the qrD module and ESPRIT implementation achieve 0.02 and 0.04° respectively. On average, when the number of array elements, signal sources, and snapshots are set to 4, 1, 64 and 8, 1, 128 individually, our ESPRIT implementation completes DOA estimation in 22.04 µs and 60.50 µs, with throughput of 45,372 and 16,529 separately. In comparison with CPU implementations, our FPGA implementations offer up to 88.66% and 89.84% time savings for qrD and ESPRIT respectively. © 2001-2012 IEEE.

关键词： Direction of arrival (DOA) estimation estimating signal parameter via rotational invariance technique (ESPRIT) algorithm field programmable gate array (FPGA) hardware implementation qr decomposition algorithm uniform linear array (ULA)

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Application of qr decomposition algorithm for Multivariate Calibration in High Overlapping Systems

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SPECTROSCOPY LETTERS 2012年第4期45卷 269-272页

作者： Khanmohammadi, Mohammadreza Azghandi, Mohammad Hossein Ahmadi IKIU Dept Chem Fac Sci Qazvin Iran

An accurate and stable algorithm, qr decomposition algorithm (qrDA) is initially presented into the chemistry field. The basic principle of qr Multivariate Calibration algorithm (qrMCA) is investigated, and the complexes system of sodium tripolyphosphate (STPP), sodium sulfate (SS), and sodium Carbonate (SC) with serious overlapping absorption peaks is analyzed by qrMCA. According to our survey, qrDA can avoid matrix inverting, reduce the orders of matrixes, and speed up the operation of matrices. So, it has bright prospects in chemometrics. The process of the qr decomposition algorithm (qrDA) was implemented by an orthogonal and upper triangular matrix decomposition that is robust and convenient. Then it was applied to overcome the problem of overlapping spectra of different components in detergent-washing powder.

关键词： complexes system high overlapping Multivariate Calibration algorithm qr decomposition algorithm spectroscopy

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Downlink MIMO signal detection algorithm in TD-LTE system

Downlink MIMO signal detection algorithm in TD-LTE system

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International Conference on Business Computing and Global Informatization

作者： Xiaolin Li Wenwen Liu Chongqing Key Lab of Mobile Communications ChongQing University of Posts and Telecommunications

ISBN: (纸本)9781467344692

MIMO (Multiple input multiple output) technology is a key technology in the LTE system. The quality of signal detection directly affects the performance of the system. This paper introduced several traditional detection algorithms-ML (Maximum Likelihood) algorithm, MMSE (Minimum mean square error) algorithm, the optimal ordering SIC (serial interference cancellation) algorithm, the qr decomposition algorithm and the iterative cycle qr decomposition algorithm. The simulation shows that, ML algorithm has the best performance, but it is a great amount of computation. Secondly, the iterative cycle qr decomposition algorithm has a better performance.

关键词： TD-LTE system MIMO qr decomposition algorithm Iterative cycle qr decomposition algorithm

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BEAMFORMING algorithm OF DIAGONAL LOADING BASED ON MATRIX decomposition

BEAMFORMING ALGORITHM OF DIAGONAL LOADING BASED ON MATRIX DE...

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4th IEEE International Conference on Broadband Network and Multimedia Technology (IEEE IC-BNMT 2011)

作者： Zeng, Zhaohua Liang, Wenjuan Zhang, Jianhong Xian Univ Scinece & Technol Commun & Informat Engn Coll Xian 710054 Peoples R China

ISBN: (纸本)9781612841564

In the beamforming algorithm of the matrix decomposition, through qr decomposition of data matrix, the qr decomposition algorithm transforms the problem of solving the weighted vector into the problem of solving a triangular linear equations, which avoids to estimating and inversing of array signal covariance matrix, improves the robustness of the data;But when the Smaller sample number, the noise eigenvalue dispersion of the sample covariance matrix leads to the degradation of the beamforming algorithm performance and qr algorithm performance will be decreased. According to this shortcoming, the SVD algorithm of the diagonal loading is proposed in this paper, the simulation results showed that DL-SVD algorithm not only improve the performance of the algorithm but also reduce complexity.

关键词： Beamforming qr decomposition algorithm SVD decomposition algorithm of the Diagonal Loading(DL-SVD)

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BEAMFORMING algorithm OF DIAGONAL LOADING BASED ON MATRIX decomposition

BEAMFORMING ALGORITHM OF DIAGONAL LOADING BASED ON MATRIX DE...

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2011 4th IEEE International Conference on Broadband Network & Multimedia Technology(第四届IEEE宽带网络与多媒体国际会议 4th IEEE IC-BNMT2011)

作者： Zhaohua Zeng Wenjuan Liang Jianhong Zhang Communication and Information Engineering College Xi’an University of Scinece and Technology Xi’an 710054 China

In the beamforming algorithm of the matrix decomposition, through qr decomposition of data matrix, the qr decomposition algorithm transforms the problem of solving the weighted vector into the problem of solving a triangular linear equations, which avoids to estimating and inversing of array signal covariance matrix, improves the robustness of the data;But when the smaller sample number, the noise eigenvalue dispersion of the sample covariance matrix leads to the degradation of the beamforming algorithm performance and qr algorithm performance will be decreased. According to this shortcoming, the SVD algorithm of the diagonal loading is proposed in this paper, the simulation results showed that DL-SVD algorithm not only improve the performance of the algorithm but also reduce complexity.

关键词： Beamforming qr decomposition algorithm SVD decomposition algorithm of the Diagonal Loading(DL-SVD)

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BEAMFORMING algorithm OF DIAGONAL LOADING BASED ON MATRIX decomposition

BEAMFORMING ALGORITHM OF DIAGONAL LOADING BASED ON MATRIX DE...

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2011 4th IEEE International Conference on Broadband Network and Multimedia Technology

作者： Zhaohua Zeng,Wenjuan Liang,Jianhong Zhang Communication and Information Engineering College Xi’an University of Scinece and Technology,Xi’an 710054,China

In the beamforming algorithm of the matrix decomposition,through qr decomposition of data matrix,the qr decomposition algorithm transforms the problem of solving the weighted vector into the problem of solving a triangular linear equations,which avoids to estimating and inversing of array signal covariance matrix, improves the robustness of the data;But when the smaller sample number,the noise eigenvalue dispersion of the sample covariance matrix leads to the degradation of the beamforming algorithm performance and qr algorithm performance will be *** to this shortcoming,the SVD algorithm of the diagonal loading is proposed in this paper,the simulation results showed that DL-SVD algorithm not only improve the performance of the algorithm but also reduce complexity.

关键词： Beamforming qr decomposition algorithm SVD decomposition algorithm of the Diagonal Loading(DL-SVD)

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Reduced complexity detection technique for layered space time block coded multiple-input multiple-output orthogonal frequency division multiplexing

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IET COMMUNICATIONS 2009年第1期3卷 115-122页

作者： Yousafzai, A. K. Nakhai, M. R. Center for Telecommunications Research King's College London Strand Westminster WC2R 2LS UK

The combination of vertical Bell Labs layered space time (V-BLAST) and space time block coding (STBC), known as a Layered STBC (LSTBC) system, offers high spectral efficiency with a higher order of diversity. The system structure, computational complexity and error performance of the V-BLAST and LSTBC multiple-input multiple-output orthogonal frequency division multiplexing systems are analysed and compared. It is shown that, compared with V-BLAST, the overall diversity order of LSTBC increases two fold. This diversity gain is achieved at the expense of a four-fold increase in the computational complexity of the qr decomposition (qrD) algorithm, required at the receiver of both LSTBC and V-BLAST. The authors propose a modified qrD algorithm which reduces this four-fold complexity to two fold.

关键词： diversity reception qr decomposition algorithm diversity gain diversity order block codes space-time codes error performance OFDM modulation layered space time block coded MIMO OFDM system vertical Bell Labs layered space time complexity detection technique multiple-input multiple-output orthogonal frequency division multiplexing V-BLAST computational complexity modulation coding MIMO communication

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Elimination of the computational broadcast in systolic arrays: An application to the qr decomposition algorithm

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2000年第4期74卷 449-469页

作者： Gusev, M Evans, DJ Loughborough Univ Technol Parallel Algorithms Res Ctr Loughborough LE11 3TU Leics England

Two types of broadcast in algorithms are determined: (1) a data broadcast, where one data value is used for more than one computation and (2) a computational broadcast where one variable is computed in more then one computation. Both types of broadcast are preferred to be eliminated when a processor array implementation is desired by using VLSI technology. When the algorithm computes only one variable value for each index vector then the computational broadcast can be eliminated in a straight forward manner by introducing counter values resulting in a single assignment code. However in cases when the algorithm computes two or more variable values that are specified by a different computational broadcast, has not been considered. As far as is known it has been solved by deriving localized algorithms in single assignment code heuristically. In this paper we define this problem in terms of a system of affine recurrence equations and analyze the data dependencies introduced. Then we show a synthesis procedure that eliminates the computational broadcast and a few examples of implementation are shown. The qr decomposition algorithm is also presented in a localized single assignment code by using the proposed method and several different parallel implementations are discussed.

关键词： computational broadcast elimination data broadcast elimination data dependence algorithm transformation qr decomposition algorithm

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Localized algorithms for VLSI processor arrays

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2000年第2期75卷 149-166页

作者： Evans, DJ Gusev, M Univ Technol Loughborough Parallel Algorithms Res Ctr Loughborough Leics England Univ Kiril & Metodij Skopje PMF Inst Informat Skopje 91000 North Macedonia

In this paper we analyze the algorithms expressed as a system of recurrence equations. The algorithms are called 2*1 output algorithms if two output values of one function (variable identification) are specified by the system of recurrence equations for each index point in the algorithm. The algorithm is in free form if the indexes of these two values are not dependent. Two standard classes are determined by this criteria: the nearest neighbour and the all pair form. For example the sorting algorithm can be expressed in the all pair form i.e., the linear insertion algorithm or in the nearest neighbour form i.e., the bubble sort algorithm. However these algorithms are different in their nature. A procedure to eliminate the computational broadcast for the all pair 2*1 output algorithm has been proposed by the authors in [1]. The result obtained by implementing this procedure was a localized form of the algorithm and a system of uniform recurrence equations by eliminating the computational and data broadcast. So the data dependence method can be efficiently used for parallel implementations. The proposed procedure cannot be implemented directly on the nearest neighbour form algorithms. Here we show how the algorithm can be restructured into a form where the computational and data broadcast can be eliminated. These transformations result in localized algorithms. A few examples show how these algorithms can be implemented on processor arrays. For example, the Gentleman Kung triangular array [2] can be used for solving the qr decomposition algorithm for both forms of the algorithm. The implementations differ in the order of the data flow and the processor operation. We show that the implementation of the nearest neighbour algorithm is even better than the standard one.

关键词： computational broadcast elimination data broadcast elimination data dependence algorithm transformation linear insertion and bubble sort qr decomposition algorithm

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