A closed-form approximated expression for the achievable residual ISI obtained by blind adaptive equalizers in a SIMO FIR channel

2012 ◽  
Author(s):  
Monika Pinchas
Keyword(s):  
Closed Form ◽  
Blind Adaptive ◽  
Adaptive Equalizers

scholarly journals Residual ISI Obtained by Blind Adaptive Equalizers and Fractional Noise

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Monika Pinchas
Keyword(s):  
Gaussian Process ◽  
Closed Form ◽  
Hurst Exponent ◽  
Signal To Noise Ratio ◽  
Size Parameter ◽  
Step Size ◽  
Input Noise ◽  
Fractional Noise ◽  
Blind Adaptive ◽  
Adaptive Equalizers

Recently, a closed-form approximated expression was derived by the same author for the achievable residual intersymbol interference (ISI) case that depends on the step-size parameter, equalizer’s tap length, input signal statistics, signal-to-noise ratio (SNR), and channel power. But this expression was obtained by assuming that the input noise is a white Gaussian process where the Hurst exponent (H) is equal to 0.5. In this paper, we derive a closed-form approximated expression (or an upper limit) for the residual ISI obtained by blind adaptive equalizers valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of0.5≤H<1. Up to now, the statistical behaviour of the residual ISI was not investigated. Furthermore, the convolutional noise for the latter stages of the deconvolutional process was assumed to be a white Gaussian process (H=0.5). In this paper, we show that the Hurst exponent of the residual ISI is close to one, almost independent of the SNR or equalizer’s tap length but depends on the step-size parameter. In addition, the convolutional noise obtained in the steady state is a noise process having a Hurst exponent depending on the step-size parameter.

scholarly journals Convolutional Noise PDF at the Convergence State of a Blind Adaptive Equalizer

2018 ◽  
Vol 210 ◽  
pp. 05003
Author(s):  
Monika Pinchas
Keyword(s):  
Closed Form ◽  
Gaussian Model ◽  
Size Parameter ◽  
Step Size ◽  
Adaptive Equalizer ◽  
Mathematical Basis ◽  
Channel Power ◽  
Blind Adaptive ◽  
Adaptive Equalizers ◽  
Equalization Method

In the literature, the convolutional noise obtained at the output of a blind adaptive equalizer, is often modeled as a Gaussian process during the latter stages of the deconvolution process where the process is close to optimality. However, up to now, no strong mathematical basis was given supporting this phenomenon. Furthermore, no closed-form or closed-form approximated expression is given that shows what are the constraints on the system’s parameters (equalizer’s tap-length, input signal statistics, channel power, chosen equalization method and step-size parameter) for which the assumption of a Gaussian model for the convolutional noise holds. In this paper, we consider the two independent quadrature carrier input case and type of blind adaptive equalizers where the error that is fed into the adaptive mechanism which updates the equalizer’s taps can be expressed as a polynomial function of the equalized output up to order three. We show based on strong mathematical basis that the convolutional noise pdf at the latter stages of the deconvolution process where the process is close to optimality, is approximately Gaussian if complying on some constraints depending on the step-size parameter, input constellation statistics, channel power, chosen equalization method and equalizer’s tap-length. Simulation results confirm our findings.

On the admissibility of blind adaptive equalizers

2002 ◽  
Author(s):  
Z. Ding ◽  
C.R. Johnson ◽  
R.A. Kennedy
Keyword(s):  
Blind Adaptive ◽  
Adaptive Equalizers

scholarly journals Symbol Error Rate for Nonblind Adaptive Equalizers Applicable for the SIMO and FGn Case

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Monika Pinchas
Keyword(s):  
Closed Form ◽  
Error Rate ◽  
Hurst Exponent ◽  
Symbol Error Rate ◽  
Closed Form Expression ◽  
Form Expression ◽  
Single Input Single Output ◽  
Single Output ◽  
Adaptive Equalizers ◽  
Single Input

A nonzero residual intersymbol interference (ISI) causes the symbol error rate (SER) to increase where the achievable SER may not answer any more on the system’s requirements. Recently, a closed-form approximated expression was derived by the same author for the residual ISI obtained by nonblind adaptive equalizers for the single-input single-output (SISO) case. Up to now, there does not exist a closed-form expression for the residual ISI obtained by nonblind adaptive equalizers for the single-input multiple-output (SIMO) case. Furthermore, there does not exist a closed-form expression for the SER valid for the SISO or SIMO case that takes into account the residual ISI obtained by nonblind adaptive equalizers and is valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of0.5≤H<1. In this paper, we derive a closed-form approximated expression for the residual ISI obtained by nonblind adaptive equalizers for the SIMO case (where SISO is a special case of SIMO), valid for fGn input where the Hurst exponent is in the region of0.5≤H<1. Based on this new expression for the residual ISI, a closed-form approximated expression is obtained for the SER valid for the SIMO and fGn case.

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