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Linear transformations of vertex operators presentations of coupled Hall-Littlewood functions

ANALYSIS AND MATHEMATICAL PHYSICS 2023年第2期13卷 1-34页

作者： Zhang, Xin Yan, Zhaowen Inner Mongolia Univ Sch Math Sci Hohhot 010021 Inner Mongolia Peoples R China

We apply linear transformations to vertex operator presentations of coupled Hall-Littlewood functions. Various properties of linearly transformed coupled Hall-Littlewood functions are investigated, including generating functions, combinatorial formulas and stability property. Furthermore, the specializations of linear transformations of coupled Hall-Littlewood functions show that linear transformations of universal character and generalized q-function present all polynomial tau-functions (PTFs) of the universal character hierarchy and the universal character hierarchy of B-type. In addition, it is proved that linear transformations of symplectic and orthogonal universal characters are PTFs of the symplectic and orthogonal universal character hierarchies, respectively.

关键词： Coupled Hall-Littlewood functions Linear transformations Universal character generalized q-function Polynomial tau-functions

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Unified Performance Analysis of Maximal Ratio Combining in η - μ, λ - μ and κ - μgeneralized Fading Channels 80

Unified Performance Analysis of Maximal Ratio Combining in ...

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80th IEEE Vehicular Technology Conference (VTC Fall)

作者： Salahat, Ehab Khalifa Univ Sci Technol & Res Abu Dhabi U Arab Emirates

ISBN: (纸本)9781479944491

This paper introduces novel performance analysis for the recently introduced generalized fading models, namely the try, eta - mu, lambda - mu distributions. These generalized fading enclose the Rice, the Hoyt, the Rayleigh the Nakagami-m, and the One-Sided Gaussian as special cases. Novel unified, generic and simple expressions for the Average Channel Capacity and the Average Error Rates in Additive White generalized Gaussian Noise (AWGGN), that includes the AWGN, the Laplacian, the Gamma, and the impulsive noise as special cases, are developed deploying multichannel Maximal Ratio Combining (MRC) receiver. The unified expressions are based on new generalized q function and log2(1+gamma) approximations. Published results from the technical literature as well as Monte Carlo simulations corroborate the generality and accuracy of the derived unified expressions under the different test scenarios.

关键词： generalized Fading Channels Additive White generalized Gaussian Noise generalized q-function Maximal Ratio Combining Unified Expressions

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Novel Unified Expressions for Error Rates and Ergodic Channel Capacity Analysis over generalized Fading Subject to AWGGN

Novel Unified Expressions for Error Rates and Ergodic Channe...

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IEEE Global Communications Conference (GLOBECOM)

作者： Salahat, Ehab Hakam, Ali Khalifa Univ Sci Technol & Res Abu Dhabi U Arab Emirates United Arab Emirates Univ Al Ain U Arab Emirates

ISBN: (纸本)9781479935123

Many generalized fading distributions are given in terms of special functions, complicating the analysis of wireless performance metrics. This paper presents novel approximations to the extended incomplete gamma function, the modified Bessel function of the second type, and the generalized q-function. New simpler and unified form for the probability density function of the extended generalized-K (EGK) and M-N distributions is developed, avoiding complicated and computationally-expensive functions, e. g. Fox and Meijer-G. Based on the new unified PDF and the proposed approximations, we derive novel generic and unified expressions for the average bit error rate and average channel capacity for the recently introduced six most generalized fading channels, namely the EGK, the M-N, the alpha-eta-mu, alpha-lambda-mu, alpha-kappa-mu, and alpha-lambda-eta-mu, including the generalized-K, generalized Nakagami-m, the alpha-mu, the eta-mu, the lambda-mu, the kappa-mu, the Nakagami-Lognormal, the Weibull, the Rice, the Hoyt, the Maxwell and other fading scenarios as special cases. The Additive White generalized Gaussian Noise (AWGGN) is considered as the noise model, that includes the AWGN, the Laplacian, the Gamma and the impulsive noise as special cases, being an application to the generalized q-function approximation. Moreover, novel analysis for Space-Time Block Codes in generalized-K fading is also developed as an application to the developed approximation of the modified Bessel function. The derived expressions are very simple and analytically traceable. Monte Carlo simulation and published work corroborate our obtained results.

关键词： Extended Incomplete Gamma function Additive White generalized Gaussian Noise generalized q-function Modified Bessel function M-N-Distribution alpha-lambda-eta-mu a-kappa-mu Extended generalized-K Space-Time Block Coding

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Polynomial tau-functions of the orthogonal KP, multicomponent orthogonal KP and BUC hierarchies

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JOURNAL OF GEOMETRY AND PHYSICS 2023年第1期189卷

作者： Li, Denghui Li, Chuanzhong Yan, Zhaowen Inner Mongolia Univ Sch Math Sci Hohhot 010021 Inner Mongolia Peoples R China Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Shandong Peoples R China

This paper is concerned with the construction of the polynomial tau-functions (PTFs) of the orthogonal KP (OKP) hierarchy, multicomponent OKP hierarchy and universal character hi-erarchy of B-type (BUC hierarchy), which are proved as zero modes of certain combinations of the generating functions. By carrying out the action of the (multicomponent) quantum fields on vacuum vector 1, the generating functions for the orthogonal Schur function, mul-ticomponent orthogonal Schur function and generalized q-function have been presented. The remarkable feature is that PTFs are the coefficients of certain family of generating func-tions. Furthermore, in terms of the Vandermonde-like identity and properties of Pfaffian, it is showed that the PTFs of the OKP and BUC hierarchies can be written as determinant and Pfaffian forms, respectively. Meanwhile, the PTFs of the multicomponent OKP hierarchy can be expressed as the product of determinants. In addition, the soliton solutions of the OKP hierarchy have also been discussed.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Polynomial tau-functions Orthogonal Schur function generalized q-function Generating functions Soliton solutions

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Novel Unified Expressions for Error Rates and Ergodic Channel Capacity Analysis over generalized Fading Subject to AWGGN

Novel Unified Expressions for Error Rates and Ergodic Channe...

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IEEE Global Communications Conference

作者： Ehab Salahat Ali Hakam Khalifa University of Science Technology and Research United Arab Emirates University

ISBN: (纸本)9781479935130

Many generalized fading distributions are given in terms of special functions, complicating the analysis of wireless performance metrics. This paper presents novel approximations to the extended incomplete gamma function, the modified Bessel function of the second type, and the generalized q-function. New simpler and unified form for the probability density function of the extended generalized-K (EGK) and M-N distributions is developed, avoiding complicated and computationally-expensive functions, e.g. Fox and Meijer-G. Based on the new unified PDF and the proposed approximations, we derive novel generic and unified expressions for the average bit error rate and average channel capacity for the recently introduced six most generalized fading channels, namely the EGK, the M-N, the a-η-μ, a-λ-μ, a-κ-μ, and a-λ-η-μ, including the generalized-K, generalized Nakagami-m, the a-μ, the η-μ, the λ-μ, the κ-μ, the Nakagami-Lognormal, the Weibull, the Rice, the Hoyt, the Maxwell and other fading scenarios as special cases. The Additive White generalized Gaussian Noise (AWGGN) is considered as the noise model, that includes the AWGN, the Laplacian, the Gamma and the impulsive noise as special cases, being an application to the generalized q-function approximation. Moreover, novel analysis for Space-Time Block Codes in generalized-K fading is also developed as an application to the developed approximation of the modified Bessel function. The derived expressions are very simple and analytically traceable. Monte Carlo simulation and published work corroborate our obtained results.

关键词： Extended Incomplete Gamma function Additive White generalized Gaussian Noise generalized q-function Modified Bessel function M-N-Distribution A-λ-η-μ A-κ-μ Extended generalized-K Space-Time Block Coding

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Unified Performance Analysis of Maximal Ratio Combining in η - μ, λ - μ and κ - μ generalized Fading Channels

Unified Performance Analysis of Maximal Ratio Combining in ...

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IEEE Vehicular Technology Conference

作者： Ehab Salahat Khalifa University of Science Technology and Research

ISBN: (纸本)9781479944484

This paper introduces novel performance analysis for the recently introduced generalized fading models, namely the η-μ, λ-μ and κ-μ distributions. These generalized fading enclose the Rice, the Hoyt, the Rayleigh the Nakagami-m, and the One-Sided Gaussian as special cases. Novel unified, generic and simple expressions for the Average Channel Capacity and the Average Error Rates in Additive White generalized Gaussian Noise (AWGGN), that includes the AWGN, the Laplacian, the Gamma, and the impulsive noise as special cases, are developed deploying multichannel Maximal Ratio Combining (MRC) receiver. The unified expressions are based on new generalized q-function and log_2(1+γ) approximations. Published results from the technical literature as well as Monte Carlo simulations corroborate the generality and accuracy of the derived unified expressions under the different test scenarios.

关键词： generalized Fading Channels Additive White generalized Gaussian Noise generalized q-function Maximal Ratio Combining Unified Expressions

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