The Forward Order Law for Least Squareg-Inverse of Multiple Matrix Products

Xiong, Zhiping

doi:10.3390/math7030277

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…On this basis, the design relies on the GMD hybrid precoding optimization matrix, to achieve the optimized value of spectral efficiency under the lower complexity of coding, decoding and modulation, and demodulation. From (2), the spectral efficiency of the system is defined by (5) [30].…”

Section: Problem Descriptionmentioning

confidence: 99%

A Highly Efficient Algorithm for Phased-Array mmWave Massive MIMO Beamforming

Althuwayb¹,

Hashim²,

Liew³

et al. 2021

Computers, Materials &Amp; Continua

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With the rapid development of the mobile internet and the internet of things (IoT), the fifth generation (5G) mobile communication system is seeing explosive growth in data traffic. In addition, low-frequency spectrum resources are becoming increasingly scarce and there is now an urgent need to switch to higher frequency bands. Millimeter wave (mmWave) technology has several outstanding features-it is one of the most well-known 5G technologies and has the capacity to fulfil many of the requirements of future wireless networks. Importantly, it has an abundant resource spectrum, which can significantly increase the communication rate of a mobile communication system. As such, it is now considered a key technology for future mobile communications. MmWave communication technology also has a more open network architecture; it can deliver varied services and be applied in many scenarios. By contrast, traditional, all-digital precoding systems have the drawbacks of high computational complexity and higher power consumption. This paper examines the implementation of a new hybrid precoding system that significantly reduces both calculational complexity and energy consumption. The primary idea is to generate several sub-channels with equal gain by dividing the channel by the geometric mean decomposition (GMD). In this process, the objective function of the spectral efficiency is derived, then the basic tracking principle and least square (LS) techniques are deployed to design the proposed hybrid precoding. Simulation results show that the proposed algorithm significantly improves system performance and reduces computational complexity by more than 45% compared to traditional algorithms.

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Section: Problem Descriptionmentioning

confidence: 99%

A Highly Efficient Algorithm for Phased-Array mmWave Massive MIMO Beamforming

Althuwayb¹,

Hashim²,

Liew³

et al. 2021

Computers, Materials &Amp; Continua

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“…The reverse order laws for the generalized inverse of multiple matrix products (1) yield a class of interesting problems that are fundamental in the theory of the generalized inverse of matrices; see [1,[4][5][6]. As a hot topic in current matrix research, the necessary and sufficient conditions for the reverse order laws for the generalized inverse of matrix products are useful in both theoretical study and practical scientific computing; hence, this has attracted considerable attention and several interesting results have been obtained; see [10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Forward Order Law for the Reflexive Inner Inverse of Multiple Matrix Products

Zhou

Xiong

Qin

2022

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The generalized inverse has numerous important applications in aspects of the theoretic research of matrices and statistics. One of the core problems of generalized inverse is finding the necessary and sufficient conditions for the reverse (or the forward) order laws for the generalized inverse of matrix products. In this paper, by using the extremal ranks of the generalized Schur complement, some necessary and sufficient conditions are given for the forward order law for A1{1,2}A2{1,2}…An{1,2}⊆(A1A2…An){1,2}.

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“…This will reveal a higher efficiency index for the discussed scheme in computing the Drazin inverse. For more studies and investigations in this field and related issues of generalized matrix inverses, interested readers are guided to [19][20][21][22].…”

mentioning

confidence: 99%

A Seventh-Order Scheme for Computing the Generalized Drazin Inverse

et al. 2019

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One of the most important generalized inverses is the Drazin inverse, which is defined for square matrices having an index. The objective of this work is to investigate and present a computational tool in the form of an iterative method for computing this task. This scheme reaches the seventh rate of convergence as long as a suitable initial matrix is chosen and by employing only five matrix products per cycle. After some analytical discussions, several tests are provided to show the efficiency of the presented formulation.

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The Forward Order Law for Least Squareg-Inverse of Multiple Matrix Products

Cited by 4 publications

References 18 publications

A Highly Efficient Algorithm for Phased-Array mmWave Massive MIMO Beamforming

A Highly Efficient Algorithm for Phased-Array mmWave Massive MIMO Beamforming

Forward Order Law for the Reflexive Inner Inverse of Multiple Matrix Products

A Seventh-Order Scheme for Computing the Generalized Drazin Inverse

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