John R. Treichler

Fractionally spaced equalizers

Modern digital transmission systems commonly use an adaptive equalizer as a key part of the receiver. The design of this equalizer is important since it determines the maximum quality attainable from the system, and represents a high fraction of the computation used to implement the demodulator. Analytical results offer a new way of looking at fractionally spaced equalizers and have some surprising practical implications. This article describes the data communications problem, the rationale for introducing fractionally spaced equalizers, new results, and their implications. We then apply those results to actual transmission channels.

SHARF: An algorithm for adapting IIR digital filters

The concept of adaptation in digital filtering has proven to be a powerful and versatile means of signal processing in applications where precise a priori filter design is impractical. Adaptive filters have traditionally been implemented with FIR structures, making their analysis fairly straightforward but leading to high computation cost in many cases of practical interest (e.g, sinusoid enhancement). This paper introduces a class of adaptive algorithms designed for use with IIR digital filters which offer a much reduced computational load for basically the same performance. These algorithms have their basis in the theory of hyperstability, a concept historically associated with the analysis of closed-loop nonlinear time-varying control systems. Exploiting this theory yields HARF, a hyperstable adaptive recursive filtering algorithm which has provable convergence properties. A simplified version of the algorithm, called SHARF, is then developed which retains provable convergence at low convergence rates and is well suited to real-time applications. In this paper both HARF and SHARF are described and some background into the meaning and utility of hyperstability is given, in addition, computer simulations are presented for two practical applications of IIR adaptive filters: noise and multi-path cancellation.

Fractionally spaced equalization using CMA: robustness to channel noise and lack of disparity

In the noise-free case, the fractionally spaced equalization using constant modulus (FSE-CM) criterion has been studied previously. Its minima were shown to achieve perfect equalization when zero-forcing (ZF) conditions are satisfied and to be able to still achieve fair equalization when there is lack of disparity. However, to our best knowledge, the effect of additive channel noise on the FSE-CM cost-function minima has not been studied. In this paper, we show that the noisy FSE-CM cost function is subject to a smoothing effect with respect to the noise-free cost function, the result of which is a tradeoff between achieving zero forcing and noise enhancement. Furthermore, we give an analytical closed-form expression for the loss of performance due to the noise in terms of input-output mean square error (MSE). Under the ZF conditions, the FSE-CM MSE is shown to be mostly due to output noise enhancement and not to residual intersymbol interference (ISI). When there is lack of disparity, an irreducible amount of ISI appears independently of the algorithm. It is the lower equalizability bound for given channel conditions and equalizer length-the so-called minimum MSE (MMSE). The MMSE lower bound is the sum of the MMSE and of additional MSE mostly due to noise enhancement. Finally, we compare the FSE-CM MSE to this lower bound.

The Pros and Cons of Compressive Sensing for Wideband Signal Acquisition: Noise Folding versus Dynamic Range

Compressive sensing (CS) exploits the sparsity present in many signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors and any associated communication links. This paper examines the use of CS in the design of a wideband radio receiver in a noisy environment. We formulate the problem statement for such a receiver and establish a reasonable set of requirements that a receiver should meet to be practically useful. We then evaluate the performance of a CS-based receiver in two ways: via a theoretical analysis of its expected performance, with a particular emphasis on noise and dynamic range, and via simulations that compare the CS receiver against the performance expected from a conventional implementation. On the one hand, we show that CS-based systems that aim to reduce the number of acquired measurements are somewhat sensitive to signal noise, exhibiting a 3 dB SNR loss per octave of subsampling, which parallels the classic noise-folding phenomenon. On the other hand, we demonstrate that since they sample at a lower rate, CS-based systems can potentially attain a significantly larger dynamic range. Hence, we conclude that while a CS-based system has inherent limitations that do impose some restrictions on its potential applications, it also has attributes that make it highly desirable in a number of important practical settings.

Practical blind demodulators for high-order QAM signals

Abstract This paper examines the problem of demodulating time-dispersed digitally modulated signals, with particular emphasis on the use of ‘blind’ algorithms for initializing the demodulator in the absence of explicit training by the transmitter. It is shown that the absence of training leads to coupling between the various control loops operating in the demodulator. This coupling impacts the architecture of the demodulator, limiting the array of choices available to the designer. This paper describes a blind demodulator design which has proven practical, and illustrates several implementations of the design. The paper closes with a list of open theoretical questions, which, if answered, can lead to the next generation of blind demodulators.

Convergence behavior of the constant modulus algorithm

An adaptive filter algorithm has been developed and introduced [1] for use with constant envelope waveforms, e.g., FM communication signals. It has proven capable of suppressing additive interferers as well as equalization, without the need for a priori statistical information. In this paper, aspects of dynamic convergence behavior are discussed, with conclusions supported by simulation.

SHARF convergence properties

A class of stable algorithms for adapting infinite impulse response (IIR) digital filters based on the concepts of nonlinear stability theory prominent in the control literature is emerging. While this class of adaptive filters offers much promise in practical applications, little has been done toward providing a characterization that would guide selection of design parameters such as adaptation constants and error smoothing coefficients. This paper focuses on the simplest well-behaved member of this class of adaptive recursive filters, SHARF. Progression from a local linearization of the nonlinear parameter estimate convergence behavior, through an idealized eigenvalue/eigenvector analysis of the parameter estimate time-varying recursion, to Lyapunov function establishment for the full output and parameter error system reveals the exponential, local, nongradient descent convergence character of SHARF and provides initial insight into the effects of adaptation constants and error smoothing coefficients on these characteristics.

Observed misconvergence in the constant modulus adaptive algorithm

Practical application of the constant modulus algorithm (CMA) has demonstrated a number of circumstances in which CMA fails to converge, or, equally bad from a practical standpoint, converges to a solution which fails to equalize the input signal. The authors describe several situations in which misconvergence occurs, suggesting that a firmer analytical understanding is needed of the behavior of blind algorithms in the presence of cyclostationary and/or quasi-periodic, nonwhite inputs. While this analytical understanding is not yet established, the practical experience reported should be directly useful to those designing new digital communications systems. An example presented, is the use of CMA to equalize quadrature amplitude modulation (QAM) signals used to broadcast high-definition television signals.<<ETX>>

A globally convergent approach for blind MIMO adaptive deconvolution

We address the deconvolution of MIMO linear mixtures. The approach is based on the construction of a hierarchical family of composite criteria involving CM criterion and second order statistics constraint. Although, the criteria are based on fourth order statistics, we give a complete proof of convergence of this structure. We show that each cost function leads to the restoration of one single source. Moreover the approach is naturally robust with respect to the channels order estimation. An adaptive algorithm is derived for the simultaneous estimation of all sources.

&#947;-LMS and its use in a noise-compensating adaptive spectral analysis technique

The application of an adaptive prediction error filter to autoregressive spectral analysis has been proposed by Lloyd Griffiths and is in use for the measurement of the frequencies of sinusoids It is well known that additive observation noise can bias these frequency estimates, thus limiting the useful applications of Griffiths technique to low noise environments. In the limit of white observation noise this paper develops a modified adaptive algorithm which incorporates a priori or measured noise power information so that the generated frequency estimates are unbiased. Unlike other bias removal techniques recently discussed, this technique can work with multiple sinusoids. The performance of this algorithm will be demonstrated through computer simulations and its convergence behavior will be discussed.