Michael G. Larimore

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.

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.

A globally convergent approach for blind MIMO adaptive deconvolution

We discuss the blind deconvolution of multiple input/multiple output (MIMO) linear convolutional mixtures and propose a set of hierarchical criteria motivated by the maximum entropy principle. The proposed criteria are based on the constant-modulus (CM) criterion in order to guarantee that all minima achieve perfectly restoration of different sources. The approach is moreover robust to errors in channel order estimation. Practical implementation is addressed by a stochastic adaptive algorithm with a low computational cost. Complete convergence proofs, based on the characterization of all extrema, are provided. The efficiency of the proposed method is illustrated by numerical simulations.

Understanding the topology of a telephone network via internally-sensed network tomography

The ability to determine the topology of worldwide telephone networks offers the promise of substantially improving their operating efficiency. This paper explores the problem of identifying the topology of a telephone network using observations made within the network. Using tomographic methods inspired by medical imaging, we consider measurements made by transmitting probes (e.g., phone calls) between network endpoints. In general, these measurements alone do not suffice to reconstruct a unique network, and in fact, there are many network topologies from which the set of measurements could have been generated. We propose a topology reconstruction algorithm based on correlating measurements collected at different internal nodes, and identify conditions under which correctness of the inferred topology is guaranteed.

A real-arithmetic implementation of the constant modulus algorithm

An earlier paper [1] presented the Constant Modulus Algorithm, an adaptive filtering algorithm which can be employed to remove interference and equalize propagation anomolies that impair communications via constant envelope signals, such as FM and QPSK. The technique presented in that paper employs complex waveforms and a FIR adaptive filter with complex coefficients so that signal properties such as the instantaneous amplitude (modulus) can be measured. Even so many practical applications of such equalization or interference reduction involve real signals and adaptive filters implemented with real rather than complex arithmetic. This paper presents a version of the constant modulus algorithm (CMA) which employs real signals and real arithemtic. The algorithm is developed in an evolutionary form from the version based on complex arithmetic. A key technical result is that certain error terms can be highly simplified due to the smoothing intrinsic to a gradient search algorithm.

Hyperstability and adaptive filtering

Recently, results from the area of system identification concerning the concept of system hyperstability have been applied to the analysis of adaptive filtering configurations. In particular, this analysis tool has allowed the development of a family of convergent adaptive recursive digital filtering algorithms, where the use of conventional gradient analysis techniques had proven insufficient. This correspondence provides a somewhat informal explanation of hyperstability analysis as might be useful to the adaptive signal processing community, and clarifies its implications and limitations.

Recursive linear prediction for clock synchronization

An interest in the application of communication techniques to the recovery of information from magnetic recording has lead to an investigation of clock synchronization for these channels. The work presented here demonstrates a means of extracting clocking information using a lattice linear predictor on a received digital data stream, such as seen from a recording channel. The lattice linear predictor accurately follows the transient behavior of the digital symbols and isolates the symbols to form a sync signal suitable for driving a phase-locked-loop. The supression of noise using this technique enables the bandwidth of the locked oscillator to be sufficient to allow rapid tracking of the varying data rate associated with magnetic readback signals.

Suppression of FM adjacent channel interference

Within current RF allocations, increases in communication traffic have resulted in a trend toward spectral crowding. Effects of adjacent channel interference have traditionally been minimized by geographically isolating channel assignments, or by over-spacing channel centers, inefficiencies which will be unacceptable for future needs. As a result of increased density of communication signals, future receiver hardware will require digital signal processing techniques for suppressing adjacent channel interference. Over the last few years, there have been research efforts aimed at solutions for this type of interference, especially in FM communications Of specific interest here is a mathematical structure developed in [7] addressing suppression of such interfering components after discrimination, where bandwidth reduction results in savings in computation requirements. Initial attempts to apply adaptive filtering techniques to this structure indicated that fundamental problems existed with the formulation. In this paper, this technique is closely scrutinized, and we demonstrate that significant baseband improvements are unlikely for general modulating signals, contrary to published claims.