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.

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 A Novel Dual Mode Decision Directed Multimodulus Algorithm (DM-DD-MMA) for Blind Adaptive Equalization

2021 ◽  
Author(s):  
Sagi Tadmor ◽  
Sapir Carmi ◽  
Monika Pinchas
Keyword(s):  
Power Input ◽  
Adaptive Equalization ◽  
Size Parameter ◽  
Constant Modulus Algorithm ◽  
Dual Mode ◽  
Step Size ◽  
Adaptive Equalizer ◽  
Blind Adaptive ◽  
Simulation Results ◽  
Blind Adaptive Equalization

In this paper, we propose for the 16 quadrature amplitude modulation (QAM) input case, a dual-mode (DM), decision directed (DD) multimodulus algorithm (MMA) algorithm for blind adaptive equalization which we name as DM-DD-MMA. In this new proposed algorithm, the MMA method is switched to the DD algorithm, based on a previously obtained expression for the step-size parameter valid at the convergence state of the blind adaptive equalizer, that depends on the channel power, input signal statistics and on the properties of the chosen algorithm. Simulation results show that improved equalization performance is obtained for the 16 QAM input case compared with the DM-CMA (where CMA is the constant modulus algorithm), DM-MCMA (where MCMA is the modified CMA) and MCMA-MDDMA (where MDDMA is the modified decision directed modulus algorithm).

scholarly journals The Tap-Length Associated with the Blind Adaptive Equalization/Deconvolution Problem

2020 ◽  
Vol 3 (1) ◽  
pp. 2
Author(s):  
Monika Pinchas
Keyword(s):  
Input Sequence ◽  
Point Of View ◽  
Adaptive Equalization ◽  
Size Parameter ◽  
Step Size ◽  
System Parameters ◽  
Large Step ◽  
Blind Adaptive ◽  
Deconvolution Problem ◽  
Blind Adaptive Equalization

The step-size parameter and the equalizer’s tap length are the system parameters in the blind adaptive equalization design. Choosing a large step-size parameter causes the equalizer to converge faster compared with applying a smaller value for the step size parameter. However, a higher step-size parameter leaves the system with a higher residual inter-symbol-interference (ISI) than does a lower step-size parameter. The equalizer’s tap length should be set large enough to compensate for the channel distortions. However, since the channel parameters are unknown, the required equalizer’s tap length is also unknown. The system parameters are usually designed via simulation trials, in such a way that the equalizer’s performance from the residual ISI point of view reaches a system desired residual ISI level. Recently, a closed-form approximated expression was derived for the residual ISI as a function of the system parameters, input sequence statistics and channel power. This expression was obtained under the assumption having a value for the equalizer’s tap length that is sufficient to compensate for the channel distortions. Based on this approximated expression, the outcome from the step-size parameter multiplied by the equalizer’s tap length can be derived when the residual ISI is given. By choosing a step-size parameter, we automatically have also the value for the equalizer’s tap length which might now not be large enough to compensate for the channel distortions and thus leaving the system with a higher residual ISI than the required one. In this work, we derive an expression that sets a condition on the equalizer’s tap length based on the input sequence statistics, on the chosen equalizer’s characteristics and required residual ISI. In addition, highlights are supplied on how to set the equalizer’s tap length for different channel cases based on this new derived expression. The findings are accompanied by simulation results.

scholarly journals An Active Equalization Method for Lithium-ion Batteries Based on Flyback Transformer and Variable Step Size Generalized Predictive Control

Energies ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 207
Author(s):  
Jianwen Cao ◽  
Bizhong Xia ◽  
Jie Zhou
Keyword(s):  
Energy Consumption ◽  
Lithium Ion Batteries ◽  
Predictive Control ◽  
Lithium Ion ◽  
Generalized Predictive Control ◽  
Variable Step Size ◽  
Size Factor ◽  
Step Size ◽  
Variable Step ◽  
Equalization Method

The inconsistency in large-scale battery pack significantly degrades the performance of electric vehicles. In order to diminish the inconsistency, the study designs an active equalization method comprising of equalizer and equalization strategy for lithium-ion batteries. A bidirectional flyback transformer equalizer (BFTE) is designed and analyzed. The BFTE is controlled by a pulse width modulation (PWM) controller to output designated balancing currents. Under the purpose of shortening equalization time and reducing energy consumption during the equalization process, this paper proposes an equalization strategy based on variable step size generalized predictive control (VSSGPC). The VSSGPC is improved on the generalized predictive control (GPC) by introducing the Step Size Factor. The VSSGPC surmounts the local limitation of GPC by expanding the control and output horizons to the global equalization process without increasing computation owing to the Step Size Factor. The experiment results in static operating condition indicate that the equalization time and energy consumption are reduced by 8.3% and 16.5%, respectively. Further validation in CC-CV and EUDC operating conditions verifies the performance of the equalizer and rationality of the VSSGPC strategy.

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