• Title/Summary/Keyword: Gaussian Q-function

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Approximation for the Two-Dimensional Gaussian Q-Function and Its Applications

  • Park, Jin-Ah;Park, Seung-Keun
    • ETRI Journal
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    • v.32 no.1
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    • pp.145-147
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    • 2010
  • In this letter, we present a new approximation for the twodimensional (2-D) Gaussian Q-function. The result is represented by only the one-dimensional (1-D) Gaussian Q-function. Unlike the previous 1-D Gaussian-type approximation, the presented approximation can be applied to compute the 2-D Gaussian Q-function with large correlations.

A Generic Craig Form for the Two-Dimensional Gaussian Q-Function

  • Park, Seung-Keun;Choi, U-Jin
    • ETRI Journal
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    • v.29 no.4
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    • pp.516-517
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    • 2007
  • In this letter we present a generic Craig form for the two-dimensional (2-D) Gaussian Q-function. The presented Craig form provides an alternative solution to the problems of computing probabilities involving a form of the 2-D Gaussian Q-function.

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A Geometric Derivation of the Craig Representation for the Two-Dimensional Gaussian Q-Function (이변량 가우시안 Q-함수의 Craig 표현에 대한 기하학적인 유도)

  • Park, Seung-Keun;Lee, Il-Kyoo
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.36 no.4A
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    • pp.325-328
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    • 2011
  • In this paper, we present a new and simple derivation of the Craig representation for the two-dimensional (2-D) Gaussian Q-function in the viewpoint of geometry. The geometric derivation also leads to an alternative Craig form for the 2-D Gaussian Q-function. The derived Craig form is newly obtained from the geometry of two wedge-shaped regions generated by the rotation of Cartesian coordinates over two correlated Gaussian noises. The presented Craig form can play a important role in computing the probability represented by the 2-D Gaussian Q-function.

IDENTITIES INVOLVING q-ANALOGUE OF MODIFIED TANGENT POLYNOMIALS

  • JUNG, N.S.;RYOO, C.S.
    • Journal of applied mathematics & informatics
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    • v.39 no.5_6
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    • pp.643-654
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    • 2021
  • In this paper, we define a modified q-poly-Bernoulli polynomials of the first type and modified q-poly-tangent polynomials of the first type by using q-polylogarithm function. We derive some identities of the modified polynomials with Gaussian binomial coefficients. We also explore several relations that are connected with the q-analogue of Stirling numbers of the second kind.

MATHIEU-TYPE SERIES BUILT BY (p, q)-EXTENDED GAUSSIAN HYPERGEOMETRIC FUNCTION

  • Choi, Junesang;Parmar, Rakesh Kumar;Pogany, Tibor K.
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.789-797
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    • 2017
  • The main purpose of this paper is to present closed integral form expressions for the Mathieu-type a-series and its associated alternating version whose terms contain a (p, q)-extended Gauss' hypergeometric function. Certain upper bounds for the two series are also given.

ON FULLY MODIFIED q-POLY-EULER NUMBERS AND POLYNOMIALS

  • C.S. RYOO
    • Journal of Applied and Pure Mathematics
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    • v.6 no.1_2
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    • pp.1-11
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    • 2024
  • In this paper, we define a new fully modified q-poly-Euler numbers and polynomials of the first type by using q-polylogarithm function. We derive some identities of the modified polynomials with Gaussian binomial coefficients. We also explore several relations that are connected with the q-analogue of Stirling numbers of the second kind.

On the Radial Basis Function Networks with the Basis Function of q-Normal Distribution

  • Eccyuya, Kotaro;Tanaka, Masaru
    • Proceedings of the IEEK Conference
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    • 2002.07a
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    • pp.26-29
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    • 2002
  • Radial Basis Function (RBF) networks is known as efficient method in classification problems and function approximation. The basis function of RBF networks is usual adopted normal distribution like the Gaussian function. The output of the Gaussian function has the maximum at the center and decrease as increase the distance from the center. For learning of neural network, the method treating the limited area of input space is sometimes more useful than the method treating the whole of input space. The q-normal distribution is the set of probability density function include the Gaussian function. In this paper, we introduce the RBF networks with the basis function of q-normal distribution and actually approximate a function using the RBF networks.

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지자기 전달함수의 로버스트 추정

  • Yang, Jun-Mo;O, Seok-Hun;Lee, Deok-Gi;Yun, Yong-Hun
    • Journal of the Korean Geophysical Society
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    • v.5 no.2
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    • pp.131-142
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    • 2002
  • Geomagnetic transfer function is generally estimated by choosing transfer to minimize the square sum of differences between observed values. If the error structure sccords to the Gaussian distribution, standard least square(LS) can be the estimation. However, for non-Gaussian error distribution, the LS estimation can be severely biased and distorted. In this paper, the Gaussian error assumption was tested by Q-Q(Quantile-Quantile) plot which provided information of real error structure. Therefore, robust estimation such as regression M-estimate that does not allow a few bad points to dominate the estimate was applied for error structure with non-Gaussian distribution. The results indicate that the performance of robust estimation is similar to the one of LS estimation for Gaussian error distribution, whereas the robust estimation yields more reliable and smooth transfer function estimates than standard LS for non-Gaussian error distribution.

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Tight Bounds and Invertible Average Error Probability Expressions over Composite Fading Channels

  • Wang, Qian;Lin, Hai;Kam, Pooi-Yuen
    • Journal of Communications and Networks
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    • v.18 no.2
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    • pp.182-189
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    • 2016
  • The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

SER Analysis of Arbitrary Two-Dimensional Signaling over Nonlinear AWGN Channels (비선형 채널에서 임의의 2차원 변조 신호의 SER 분석)

  • Lee, Jae-Yoon;Yoon, Dong-Weon;Cho, Kyong-Kuk
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.32 no.7A
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    • pp.738-745
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    • 2007
  • The non-linearity of HPA(high power amplifier) which is an important component in modern communications systems introduces AM/AM and AM/PM distortion so that the transmitted signal is deteriorated. And, the I/Q unbalances and phase error which are generated by non-ideal components are inevitable physical phenomena and lead to performance degradation when we implement a practical two-dimensional (2-D) modulation system. In this paper, we provide an exact and general expression involving the 2-D Gaussian Q-function for the error probabilities of arbitrary 2-D signaling with I/Q amplitude and phase unbalances in nonlinear additive white Gaussian noise (AWGN) channels by using the coordinate rotation and shifting technique.