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.

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

With an abundance of tools based on kernel methods and information theoretic learning, a void still exists in incorporating both the time structure and the statistical distribution of the time series in the same functional measure. In this paper, a new generalized correlation measure is developed that includes the information of both the distribution and that of the time structure of a stochastic process. It is shown how this measure can be interpreted from a kernel method as well as from an information theoretic learning points of view, demonstrating some relevant properties. To underscore the effectiveness of the new measure, a simple blind equalization problem is considered using a coded signal.

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Generalized correlation function: definition, properties, and application to blind equalization

We consider the problem of recovering two unknown vectors, w and x, of length L from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with dimension N and the other with dimension K. Although the observed convolution is nonlinear in both w and x, it is linear in the rank-1 matrix formed by their outer product wx*. This observation allows us to recast the deconvolution problem as low-rank matrix recovery problem from linear measurements, whose natural convex relaxation is a nuclear norm minimization program. We prove the effectiveness of this relaxation by showing that, for “generic” signals, the program can deconvolve w and x exactly when the maximum of N and K is almost on the order of L. That is, we show that if x is drawn from a random subspace of dimension N, and w is a vector in a subspace of dimension K whose basis vectors are spread out in the frequency domain, then nuclear norm minimization recovers wx* without error. We discuss this result in the context of blind channel estimation in communications. If we have a message of length N, which we code using a random L x N coding matrix, and the encoded message travels through an unknown linear time-invariant channel of maximum length K, then the receiver can recover both the channel response and the message when L ≳ N + K, to within constant and log factors.

Blind Deconvolution Using Convex Programming

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.

/pdf/blind-equalization-using-the-constant-modulus-criterion-a-2gf351pnrk.pdf

Blind equalization using the constant modulus criterion: a review

A method for selecting an antenna direction setting for optimum signal reception prior to channel equalization provides a set of metrics, referred to as channel quality metrics (CQM), that characterize the quality of the received signal for a given antenna setting and a generic algorithm that uses these metrics to select the antenna setting for an optimum reception. This invention utilizes five main CQMs: a Signal Strength Metric (SSM), a minimum mean squared error of a decision feedback equalizer (MMSE (DFE)) channel quality metric, a MMSE for a linear equalizer (MMSE(LE)) channel quality metric, a Spectral Flatness Metric (SFM) and an interference degradation metric (IDM).

Method and apparatus for controlling a smart antenna using metrics derived from a single carrier digital signal

In a digital communications receiver configured to receive, via a communications channel, a received first signal representing a sequence of symbols, each symbol being encoded to be representative of data bits, a method of processing the received signal includes adjusting a magnitude, filtering, and applying cyclic prefix restoration, to the received signal to produce a second signal, converting the second signal from time domain to frequency domain to produce a frequency domain signal, and determining a first quantity of values representing a first portion of the symbols by evaluating a relationship of channel values representing characteristics of the communications channel and a second quantity of values representing a portion of the frequency domain signal, the first quantity being smaller than the second quantity.

Symmetrical data signal processing

This work proposes a frequency domain turbo equalization (FDTE) scheme for the reception of transmissions that employ vestigial sideband modulation and punctured trellis coding, as specified by the ATSC North American terrestrial digital television (DTV) standard. The proposed FDTE scheme enables low-cost and high performance reception of highly impaired DTV signals. Through numerical simulation, we demonstrate that our FDTE scheme outperforms the traditional joint DFE/decoding approach at a fraction of the implementation cost.

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Frequency Domain Turbo Equalization for Vestigial Sideband Modulation with Punctured Trellis Coding

An apparatus, for use in a receiver configured to receive electronic signals, for identifying digital signals that are available for reception, includes a timing recovery device configured to receive an incoming signal, related to a transmitted signal, the incoming signal having a first symbol rate, and to re-sample the incoming signal to provide a second symbol rate, and an analyzer that is in communication with the timing recovery device and that is configured to make a determination as to whether a difference between the second symbol rate and a third symbol rate of a transmitter providing the transmitted signal is within an acceptable tolerance and to use the determination in an analysis of whether the transmitted signal is available for reception.

Raul A. Casas

Papers

Blind equalization using the constant modulus criterion: a review

Method and apparatus for controlling a smart antenna using metrics derived from a single carrier digital signal

Symmetrical data signal processing

Frequency Domain Turbo Equalization for Vestigial Sideband Modulation with Punctured Trellis Coding

Rapid channel signal identification