Direct versus iterative methods for fixed-point implementation of matrix inversion

Ylinen, Maija; Burian, A.; Takala, Jarmo

doi:10.1109/iscas.2004.1328724

Cited by 17 publications

(13 citation statements)

References 9 publications

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“…The Newton iterative method for matrix inversion [9][10] is an extension of the Newton method used for locating the root of a function ݂ሺܺሻ. According to this procedure, the generic step ݅ of the iterative process is:…”

Section: B Newton Methods For Matrix Inversionmentioning

confidence: 99%

“…The dynamics of the signal in the critical points of the algorithm has been analysed to achieve an optimal trade-off between math precision and calculation effort. A careful use of fixed and block floating point math, the exploitation of the Newton method for matrix inversion [9][10], several simplifications and approximations, allowed reducing the calculations load without compromising the accuracy. An in vivo test on the carotid artery of a volunteer is presented.…”

Section: Introductionmentioning

confidence: 99%

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Real-time BAPES implementation for fast spectral Doppler estimation

Ricci

Matera

Tortoli

2013

2013 IEEE International Ultrasonics Symposium (IUS)

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The echoes backscattered from blood red cells moving in a vessel are typically elaborated though a spectral analysis and then displayed in the sonogram. The preferred frequency estimator is the Welch method, which is robust and fast, but requires at least 64-128 samples, gathered one per pulse repetition interval (PRIs), to guarantee adequate spectral resolution. The Blood Amplitude and Phase EStimator (BAPES) is an alternative technique that was recently proven suitable for producing good spectrograms using down to 16 PRIs per frame. This achievement allows a better time resolution and/or higher Bmode frame rates when working in Duplex mode, but unfortunately BAPES requires much more calculations than Welch, making its real-time employment quite challenging. In this work we present a BAPES implementation on a state-of-theart fixed point DSP. This implementation, exploiting the Newton method for inverse matrix approximation, produces a 128 frequency-point frame in less than 5 ms. The error measured in a test on the common carotid artery of a volunteer was lower than 0.2% with respect to a floating-point reference implementation.

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Section: B Newton Methods For Matrix Inversionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Real-time BAPES implementation for fast spectral Doppler estimation

Ricci

Matera

Tortoli

2013

2013 IEEE International Ultrasonics Symposium (IUS)

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“…2) Newton Iteration method: The Newton iteration (NI) is also known as the Newton-Raphson method and it is an iterative method for finding the approximation of the matrix inverse [66]. For G, estimation of the matrix inversion at nth iteration is given by…”

Section: A Linear Detectors Based On the Approximate Matrix Inversionmentioning

confidence: 99%

Massive MIMO Detection Techniques: A Survey

Albreem

Juntti

Shahabuddin

2019

IEEE Commun. Surv. Tutorials

339

229

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“…This Because Gauss-Seidel method [6] emphasizes the precision more, and we emphasizes the low complexity more, so we mainly compare with PE method. In this paper, we adopt matrix inversion based on Newton iteration (NI) [7], [8] in massive MIMO data detection, and introduce the relationship between NI-based and PE-based matrix inversion method. Compared with [3], NI method can obtain the same precision and complexity, or higher precision at the cost of complexity by controlling the number of iterations.…”

Section: Introductionmentioning

confidence: 99%

High Precision Low Complexity Matrix Inversion Based on Newton Iteration for Data Detection in the Massive MIMO

et al. 2016

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Currently, massive multiple input multiple output (MIMO) is one of the most promising wireless transmission technologies for 5G. Massive MIMO requires handling with largescale matrix computation, especially for matrix inversion. In this paper, we find that matrix inversion based on Newton iteration (NI) is suitable for data detection in massive MIMO system. In contrast with recently proposed polynomial expansion (PE) method for matrix inversion, we analyse both the algorithm complexity and precision in detail, and propose a diagonal band Newton iteration (DBNI) method which is an approximate method for NI. Compared with PE method, DBNI can obtain higher precision and approximately equal complexity, and we give an explanation of how to select the band width of DBNI.

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Direct versus iterative methods for fixed-point implementation of matrix inversion

Cited by 17 publications

References 9 publications

Real-time BAPES implementation for fast spectral Doppler estimation

Real-time BAPES implementation for fast spectral Doppler estimation

Massive MIMO Detection Techniques: A Survey

High Precision Low Complexity Matrix Inversion Based on Newton Iteration for Data Detection in the Massive MIMO

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