Givens rotation‐based QR decomposition for MIMO systems

Fan, Wen; Alimohammad, Amirhossein

doi:10.1049/iet-com.2016.0789

Cited by 4 publications

(4 citation statements)

References 22 publications

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“…Q is the orthogonal matrix, while R is the upper triangular matrix. The literature proposes three main approaches for QR factorization, namely, Gram-Schmidt approach [17], Householder transformation [18] and approach based on Givens rotation [19,20]. This work adopts the third approach, i.e.…”

Section: Qr Factorizationmentioning

confidence: 99%

Real-time implementation of fast discriminative scale space tracking algorithm

Walid

Awais

Ahmed

et al. 2021

J Real-Time Image Proc

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Real-time object tracking is an important step of many modern image processing applications. The efficient hardware design of real-time object tracker must achieve the desired accuracy while satisfying the frame rate requirements for a variety of image sizes. The existing methods of visual tracking employ sophisticated algorithms and challenge the capabilities of most embedded architectures. Discriminative scale space tracking is one algorithm that is capable of demonstrating good performance with affordable complexity. It has a high degree of parallelism which can be exploited for efficient implementation of reconfigurable hardware architectures. This paper proposes a real-time implementation of the discriminative scale-space tracker on FPGA for the major blocks. A careful design exploration of core mathematical operations of the tracking algorithm is performed to improve their hardware utilization and timing performance. Among the core functional units optimized in this work, the discrete Fourier transform achieves a computational time improvement of 92% relative to existing works, QR factorization achieves a 2.3$$\times$$ × reduction in resource utilization, and singular value decomposition yields a 3.8$$\times$$ × improvement in processing time. The proposed data path architecture is designed using Vivado HLS tool set and implemented for Zync Zed Board (xc7z020clg484-1). For an input image size of 320 $$\times$$ × 240, the proposed architecture achieves a mean 25.38 fps.

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Section: Qr Factorizationmentioning

confidence: 99%

Real-time implementation of fast discriminative scale space tracking algorithm

Walid

Awais

Ahmed

et al. 2021

J Real-Time Image Proc

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show abstract

“…where H f p is the H matrix floating-point representation, H f x is the H matrix fixed-point representation, L is the square matrix size, and x, y is the H matrix term indices (Figs. 3,4,5).…”

Section: The Mean Square Error Evaluation Of the Different Qr Decomposition Fixed-point Hardware Architecturesmentioning

confidence: 99%

“…A pipelined architectures as well as a parallel architectures leads to increase a hardware costs, but gives an ability to improve computation speed up to 100 MHz. In other hand to decrease requirements to the memory usage may be used coding techniques for an input data or an pre-computed data such as an approximation function coefficients [3]. Moreover the QR decomposition computation architecture based on a fixed-point arithmetic is may be evaluated in a computation accuracy field of view [4].…”

mentioning

confidence: 99%

Hardware Architectures of the QR-Decomposition Based on a Givens Rotation Technique

Sokolovskiy

Вейсов

Tyapkin

et al. 2019

Journal of Siberian Federal University. Mathematics &Amp; Physics

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The fixed-point hardware architecture of the QR decomposition is constrained by a several issues that leads to decrease of a compute accuracy depending on a matrix size. In this article described the hardware architectures based on CORDIC algorithm and approximation functions. As a basis technique is used a Givens rotation technique, because it is a most suitable technique for hardware implementation

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“…Existing QRD/SQRD algorithms are mainly based on four methods-Householder transformation (HT) method [11,12], Gram-Schmidt (GS) method [13][14][15], Givens rotation (GR) method [6,16,17], and Cholesky method [7], of which the complexity is analysed in [7,18]. As HT method is undesirable for hardware implementation, the practical SQRD/SQRD architectures in wireless communication are mainly based on the remaining three methods.…”

Section: Introductionmentioning

confidence: 99%

Low latency group‐sorted QR decomposition algorithm for larger‐scale MIMO systems

et al. 2021

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Sorted QR decomposition (SQRD) has been extensively adopted for various multipleinput-multiple-output (MIMO) detectors, in which the sorting process incurs severe latency when it comes to larger-scale MIMO situations. This paper proposes a group-SQRD (GSQRD) algorithm to alleviate the latency problem of general SQRD architectures for larger-scale MIMO systems. Via predictively sorting a group of 4 columns at one stage, the GSQRD could eliminate the processing latency by 41% for decomposing 16×16 complex-valued matrices. Additionally, this percentage even rises up to 68% for decomposing 128×128 matrices. To analyse the side effects, the GSQRD is applied in various MIMO detectors in a simulation link, which exhibits a negligible performance degradation for MIMO detection. Moreover, GSQRD is a hardware-friendly algorithm because the division and square root operations in GSQRD are converted to multiplications for simplifying the hardware implementation. Based on this algorithm, two corresponding hardware architectures, which contains 2 and 4 columns respectively in a sorting group, are also implemented with 65-nm CMOS technology. These architectures can work at 513 MHz to decompose 16×16 complex-valued matrices. The processing latencies are respectively 0.32 and 0.26 s, superior to the state-of-art designs.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Givens rotation‐based QR decomposition for MIMO systems

Cited by 4 publications

References 22 publications

Real-time implementation of fast discriminative scale space tracking algorithm

Real-time implementation of fast discriminative scale space tracking algorithm

Hardware Architectures of the QR-Decomposition Based on a Givens Rotation Technique

Low latency group‐sorted QR decomposition algorithm for larger‐scale MIMO systems

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