The Residual ISI for Which the Convolutional Noise Probability Density Function Associated with the Blind Adaptive...

Area of Science:

• Signal processing
• Communications engineering
• Information theory

Background:

• Blind adaptive deconvolution typically assumes Gaussian noise only when residual inter-symbol interference (ISI) is minimal.
• Existing literature lacks a closed-form expression for residual ISI to validate this Gaussian noise assumption.
• The Gaussian model is crucial for analyzing noise probability density functions (pdf) in deconvolution.

Purpose of the Study:

• To derive an approximated closed-form equation for residual ISI in blind adaptive deconvolution.
• To investigate the applicability of the Gaussian noise model beyond the deep convergence state.
• To challenge the conventional assumption that Gaussian noise modeling is only valid for small residual ISI.

Main Methods:

• Utilizing the Maximum Entropy density technique.
• Applying Lagrange's Integral method.
• Employing quasi-moment truncation techniques.

Main Results:

• An approximated closed-form equation for residual ISI has been successfully obtained.
• The Gaussian noise model is shown to be applicable even before the equalizer fully converges.
• This model's validity extends to situations with significant residual ISI, where the 'eye diagram' is closed.

Conclusions:

• The derived closed-form equation provides a new analytical tool for blind adaptive deconvolution.
• The Gaussian noise model can be approximately valid even when residual ISI is not small, broadening its application scope.
• This finding has implications for equalizer design and performance analysis in challenging signal conditions.