Identification of non-minimum phase finite impulse response systems using the fourth-order cumulants

Abderrahim, Kamel; Abdennour, Ridha Ben; M’Śahli, Faouzi; Ksouri, Mekki; Favier, Gérard

doi:10.1007/bfb0110532

Cited by 3 publications

(4 citation statements)

References 11 publications

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“…However, the linear algorithms based on third and fourth order cumulants proposed in the literature [5,12] for linear case is extended to the non linear case for identification of quadratic systems.…”

Section: Extension Of Linear Algorithms To Non Linear Algorithmsmentioning

confidence: 99%

“…Abderrahim, et al [12] use also the relationship (16), based on fourth order cumulants, for developing an algorithm based an fourth order cumulants in linear case. This algorithm is extended to the general case of the non linear quadratic systems, with β 1 = β 2 = 0, τ 1 = q and τ 2 = 0:…”

Section: Third Algorithm: Algcum3mentioning

confidence: 99%

“…Indeed, we develop the relationship linking third order cumulants and the coefficients of non linear channels, then the method developed [11] for linear channels, is extended to the general case of the non linear quadratic systems identification. Secondly, these theoretical analyses are used to develop an extension of linear algorithms based on third and fourth order cumulants proposed by safi, et al [5] and Abderrahim, et al [12] …”

Section: Introductionmentioning

confidence: 99%

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Extension of Linear Channels Identification Algorithms to Non Linear Using Selected Order Cumulants

Zidane¹,

Safi²,

Sabri³

2016

IJEECS

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In this paper, we present an extension of linear communication channels identification algorithms to non linear channels using higher order cumulants (HOC). In the one hand, we develop a theoretical analysis of non linear quadratic systems using second and third order cumulants. In the other hand, the relationship linking cumulants and the coefficients of non linear channels presented in the linear case is extended to the general case of the non linear quadratic systems identification. This theoretical development is used to develop three non linear algorithms based on third and fourth order cumulants respectively. Numerical simulation results example show that the proposed methods able to estimate the impulse response parameters with different precision.Keywords: Higher order cumulants, Blind identification, Non linear quadratic systems. Copyright c 2016 Institute of Advanced Engineering and Science IntroductionApplications of higher order cumulants theory in the blind identification domain are widely used in various works [1]-[3], [6,7]. Several models are identified in the literature such as the linear and non linear systems. In the part of the linear case, we have important results established that the blind identification is possible only from the second order cumulants (autocorrelation function) of the output stationary signal, but these methods is not able to identify correctly the channel models excited by non Gaussian signal and affected by Gaussian noise, because the additive Gaussian noise will be vanish in the higher order cumulants domain. The sensitivity of the second order cumulants to the additive Gaussian noise appealed to other blind identification methods exploiting the cumulants of order superieur than two [4,5]. There are several motivations behind this interest, first the methods based on HOC are blind to any kind of a Gaussian process, whereas autocorrelation function (second order cumulants) is not. Consequently, cumulants based methods boost signal to noise ratio (SNR) when signals are corrupted by Gaussian measurement noise. Second, the HOC methods are useful in identifying non minimum phase systems and in reconstructing non minimum phase signals when the signals are non Gaussian.The linear models are not efficient for representing and modeling all systems, because the majority of systems are represented by non linear models [7,8]. However, when linear modeling of the channel is not adequate, the non linear modeling appeared like an alternative efficient solution in most real cases. Moreover, quadratic non linear systems are widely used in various engineering fields such as signal processing, system filtering, predicting, identification and equalization [9,10].In this contribution, firstly we present a theoretical development of non linear quadratic systems using higher order cumulants. Indeed, we develop the relationship linking third order cumulants and the coefficients of non linear channels, then the method developed [11] for linear channels, is extended to the general case ...

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Section: Extension Of Linear Algorithms To Non Linear Algorithmsmentioning

confidence: 99%

Section: Third Algorithm: Algcum3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extension of Linear Channels Identification Algorithms to Non Linear Using Selected Order Cumulants

Zidane¹,

Safi²,

Sabri³

2016

IJEECS

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“…Abderrahim, et al [10] use the relationship (7), based on fourth order cumulants, with β 1 = β 2 = 0, t 1 = q and t 2 = 0. This algorithm is given by the following relation:…”

Section: B Basic Relationshipsmentioning

confidence: 99%

Non Minimum Phase Channel Estimation by Blind and Adaptive algorithms

Zidane

Safi²,

Sabri³

et al. 2015

International Journal of Advances in Telecommunications, Electrotechnics, Signals and Systems

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Abstract-In this paper the problem of the Non Minimum Phase (NMP) channel identification using blind and adaptive algorithms is theoretically and numerically evaluated in noise environment case for different signal to noise ratio (SNR). For this problem, three blind algorithms based on Higher Order Cumulants (HOC) versus adaptive algorithms, i.e. Recursive Least Squares (RLS) and Least Mean Squares (LMS) are presented. In order to assess the performance of these approaches to identify the parameters of non minimum phase channels, we have selected the Macchi channel model. The simulation results in noisy environment and for different data input channel, provided to illustrate the performance of the blind approaches and compare them with adaptive algorithms.

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New approaches to finite impulse response systems identification using higher-order statistics

Abderrahim

Mathlouthi

M’Śahli

2010

IET Signal Process.

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Identification of non-minimum phase finite impulse response systems using the fourth-order cumulants

Cited by 3 publications

References 11 publications

Extension of Linear Channels Identification Algorithms to Non Linear Using Selected Order Cumulants

Extension of Linear Channels Identification Algorithms to Non Linear Using Selected Order Cumulants

Non Minimum Phase Channel Estimation by Blind and Adaptive algorithms

New approaches to finite impulse response systems identification using higher-order statistics

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