Wireless Communications

Digital filters underpin the performance of coherent optical receivers which exploit digital signal processing (DSP) to mitigate transmission impairments. We outline the principles of such receivers and review our experimental investigations into compensation of polarization mode dispersion. We then consider the details of the digital filtering employed and present an analytical solution to the design of a chromatic dispersion compensating filter. Using the analytical solution an upper bound on the number of taps required to compensate chromatic dispersion is obtained, with simulation revealing an improved bound of 2.2 taps per 1000ps/nm for 10.7GBaud data. Finally the principles of digital polarization tracking are outlined and through simulation, it is demonstrated that 100krad/s polarization rotations could be tracked using DSP with a clock frequency of less than 500MHz.

Digital filters for coherent optical receivers.

This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical decisions utilized in this tutorial can be used to help catalog the emerging literature on the CM criterion and on the behavior of (stochastic) gradient descent algorithms used to minimize it.

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Blind equalization using the constant modulus criterion: a review

A review of blind channel estimation algorithms is presented. From the (second-order) moment-based methods to the maximum likelihood approaches, under both statistical and deterministic signal models. We outline basic ideas behind several new developments, the assumptions and identifiability conditions required by these approaches, and the algorithm characteristics and their performance. This review serves as an introductory reference for this currently active research area.

Multichannel blind identification: from subspace to maximum likelihood methods

Blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown. Recent algorithms have afforded dramatic progress, yet many aspects of the problem remain challenging and hard to understand. The goal of this paper is to analyze and evaluate recent blind deconvolution algorithms both theoretically and experimentally. We explain the previously reported failure of the naive MAP approach by demonstrating that it mostly favors no-blur explanations. We show that, using reasonable image priors, a naive simulations MAP estimation of both latent image and blur kernel is guaranteed to fail even with infinitely large images sampled from the prior. On the other hand, we show that since the kernel size is often smaller than the image size, a MAP estimation of the kernel alone is well constrained and is guaranteed to succeed to recover the true blur. The plethora of recent deconvolution techniques makes an experimental evaluation on ground-truth data important. As a first step toward this experimental evaluation, we have collected blur data with ground truth and compared recent algorithms under equal settings. Additionally, our data demonstrate that the shift-invariant blur assumption made by most algorithms is often violated.

Understanding Blind Deconvolution Algorithms

Advances in blind identification of fractionally-spaced models for digital communication channels and blind fractionally-spaced equalizer adaptation rely on the assumption that the time span chosen for the fractionally-spaced equalizer exceeds that of the channel. This paper considers time-domain design formulas minimizing the mean-squared symbol recovery error achieved by a finite-length FIR fractionally-spaced equalizer with a time span shorter than the channel impulse response time span for white zero-mean QAM sources in the presence of white zero-mean channel noise. For minimum mean-squared error designs the symbol error rates achievable are plotted versus the ratio of the source variance to the channel noise variance (with the channel model power normalized to achieve a received signal of unit variance) for different fractionally-spaced equalizer lengths on 64-QAM for several T/2-spaced channel models derived from experimental data. Our intent is to fuel the ongoing debate about fractionally-spaced equalizer length selection.

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On fractionally-spaced equalizer design for digital microwave radio channels

The open literature is replete with claims about convergence benefits associated with second-order-statistics (SOS) blind channel estimation/equalization algorithms. At the same time, the literature is sparse in addressing robustness concerns of these algorithms. This paper is intended to motivate interest in the study of such robustness concerns by providing a simulation-based comparison between some popular SOS algorithms and CMA for various classes of channels of interest to both the practitioner and researcher. © 1998 John Wiley & Sons, Ltd.

Simulated comparisons of blind equalization algorithms for cold start‐up applications

This article studies robustness properties of the constant modulus (CM) criterion and the constant modulus algorithm (CMA) to the suboptimal but practical situation where the number of fractionally-spaced equalizer coefficients is less than what is needed to remove all intersymbol interference (ISI). Hence, there necessarily exists an error in the equalized signal. Relationships between CM and mean squared error cost functions are established.

Robustness to fractionally-spaced equalizer length using the constant modulus criterion

This paper studies the robustness properties of the constant modulus (CM) criterion specifically when the fractionally-spaced equalizer time span is less than that of the channel. Hence, there necessarily exists an error in the equalized signal. Noiseless, binary signalling is considered. The change in CM cost from a perfect equalization setting is derived for two cases: (i) perturbations to the channel outside the time span of the equalizer, and (ii) equalizer truncation. This CM cost is related to the mean squared error (MSE) cost and a design guideline for length selection is proposed. This guideline is shown by example to be robust when noisy, multi-level complex signalling is considered.

https://ieeexplore.ieee.org/iel3/4966/13657/00630054.pdf

T.J. Endres

Papers

Blind equalization using the constant modulus criterion: a review

On fractionally-spaced equalizer design for digital microwave radio channels

Simulated comparisons of blind equalization algorithms for cold start‐up applications

Robustness to fractionally-spaced equalizer length using the constant modulus criterion

On the robustness of the fractionally-spaced constant modulus criterion to channel order undermodeling. I