M. Larimore

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.

Modem constellation identification: a performance comparison of two methods

Two algorithms are described for determining the signal constellation quadrature amplitude modulation in use on a (QAM) modulator, one based on Radon transform ideas and the other based on histogramming received signal radius information. The detection performances of the two specific algorithms are compared as a function of the signal-to-disturbance power ratio and the number of samples available. Generally speaking, it is shown that, when the carrier frequency is known with reasonable accuracy, the Radon transform method performs much better than the specific radius- or magnitude-only method tested, in the sense that for the same signal-to-disturbance ratio the former can reliably determine the constellation size and orientation with about one-tenth of the data samples required by the latter. It should be noted, however, that neither of the two algorithms has been optimized, nor have the comparisons taken into account other issues such as the details of particular applications, the relative computational requirements, and the added complexity needed by the Radon transform method to deal with uncertainties in the carrier frequency.<<ETX>>

Convergence rate limitations in certain frequency-domain adaptive filters

It is shown that the transport delay present in the feedback path of a frequency-domain adaptive filter consisting of the combination of a CMA (constant modulus algorithm) with a transmultiplexer reduces the filters maximum attainable convergence rate. An upper bound for the convergence rate is developed in terms of the amount of group delay and hardware pipeline delay present in the adaptive system under analysis. These limitations are shown to be fundamental in nature. They relate directly to the amount of spectral resolution desired in the adaptive filter and not to the particular nonlinear error function employed.<<ETX>>

Some dynamic properties of transmux-based adaptive filters

Frequency-domain Adaptive Filtering This paper examines two aspects of the dynamic behavior of a CMA-directed transmux-based frequency-domain adaptive digital filter used to suppress additive, narrowband interferers of disparate powers. Analysis shows that the ability to power- normalize the bin-level adaptive gains offers the promise of sig- nificant improvements in overdl filter conver ence rate. It is then shown, however, that the the transport day present in the feedback path of the frequency-domain adaptive filter has the result of reducing the lilters maximum attainable convergence rate. An upper bound for the convergence rate was developed in terms of the amount of group delay and hudware pipeline delay present in the adaptive system under analysis. These limitations are shown to be fundemental in nature. They re- late directly to the amount of spectral resolution desired in the adaptive lilter and not the particular nonlinear error function employed.

On the convergence properties of the simple hyperstable adaptive recursive filter (SHARF)

In previous work the authors have developed a class of provably convergent adaptive algorithms for digital IIR filters based on the concept of hyperstability. While this class of adaptive filters offers much promise in practical applications little has been done toward providing the characterization that would allow a designer to select filter order, adaptation constants, and other design parameters. This paper reports on the initial effort toward providing this information through an investigation of the local convergence behavior of SHARF, the simple hyperstable adaptive recursive filter.

Allocation of adaptivity of multistage digital filters

Many communications receivers employ a cascade of two or more filters. They are typically designed and implemented separately, each accomplishing its own specific function. Some are fixed in their spectral characteristics, some are selectable, and some, such as data equalizers, are data-adaptive. The incredible growth in the speed and capability of digital signal processing (DSP) devices allows cost-effective digital implementations of many of these filters. This growing digitization would appear to permit the combination of many heretofore separate functions into the same physical filter realization, leading to yet further savings size, weight, power consumption, and cost. The authors examine the case of a digitally implemented tally implemented demodulator which combines the digital filters used for conversion from real sample to complex-valued samples, predecimation filtering, and adaptive equalization. It is shown that it is feasible to combine these functions into a single adaptive filter, but that computational savings are not always attained and that memory requirements almost always grow.<<ETX>>

Tracking speed requirements for time-varying adaptive channel equalizers

This paper addresses the problem of adaptively equalizing a slowly time-varying linearly dispersive propagation channel. Owing to the time variation, the adaptive filter rarely has exactly the proper impulse response, and the quality of the output signal will almost always be poorer than that of a time-invariant, adaptively equalized channel. In order to gain a fundamental understanding of the underlying mechanisms, this paper examines the signal degradation introduced by the time-varying combination of a propagation channel with a single complex pole and an equalizer with a single adaptable complex zero. The effects on transmission mean squared error (and hence NPR and BER) are quantified in terms of the type of variation in the poles position and the updating strategy of the zero. A set of curves is developed which quantifies the intuitive concept that more rapid updating produces progressively better matching between the channel and the equalizer and hence progressively better signal quality.