State-space models are proposed to represent MIMO frequency-selective wireless channels with the motivation of better model approximation performance and consequently more robust channel equalization performance with respect to the mismatch between the order of the channel model and that of the true channel. We develop a simple framework under which the equalizers for state-space channel models can be designed using the existing methods for designing equalizers for FIR models. In particular, a MIMO MMSE-DFE equalizer is developed for state-space models. The performance comparison of a state-space-based receiver and an FIR-based receiver shows that the former provides significantly smaller symbol error rate, and hence is more robust for reduced-order channel models while exhibiting marginally slower but comparable convergence rate. Thus, state-space channel models can be a more robust choice than FIR ones in the presence of model order selection error.

State space models are proposed to represent MIMO frequency-selective wireless channels with the motivation of better model approximation performance and more parsimonious parametrization. We study the MIMO channel approximation error as a function of model order and show that state-space models possess improved performance compared to more standard FIR models. A recursive algorithm, based on the subspace system identification methods, to estimate the state-space channel model using training data is presented. When compared to the FIR-based recursive least squares algorithm, the state-space-based channel estimator shows the ability of providing low-order models of high-quality channel approximation, while preserving comparable convergence rate.

Adaptive quantization is used in many ADPCM systems to improve performance. The authors present an analysis dealing with the effect of adaptive quantizers on the stability of ADPCM systems as compared with ADPCM with nonadaptive quantization. Stability of the system is noted to equate with recovery from encoder internal state discrepancies. A sufficient condition for stability that leads to a relation between adaptation rate and stability is presented. This indicates that a price is paid for adaptation in terms of more stringent restrictions on the predictor to guarantee stability. The theorem further indicates that stability is related to the maximum rate of quantizer step size decrease and can be viewed as a theoretical justification for the shape of the Jayant "one-word memory" multiplier curve for adaptive quantization.>

This paper discusses the problem of designing a frequency tracker using the extended Kalman filter (EKF). The design trade-off between balancing noise rejection and tracking at a maximal slew rate is considered, as are the effect of varying design noise covariance values. The performance penalties for over- and under-design of noise covariances are examined and theoretically supported design guidelines are suggested. These are illustrated via simulation results.>

Discusses the use of a variable bit rate ADPCM system for speech coding. The authors present an ADPCM system, using arithmetic coding and Kalman filtering techniques, that can code signals at very low bit rates, where standard fixed bit rate ADPCM systems fail. The proposed system, at an average bit rate of 16 kbps, produces a reconstructed speech signal that by informal listening tests has been judged to be of significantly higher quality than the LD-CELP 16 kbps speech coding standard. The authors believe that the output quality is comparable to that of LD-CELP at an average rate of around 12 kbps, and the quality at 8 kbps is very promising. Other advantages of the scheme are a reduction in complexity over the LD-CELP standard, and an increase in design flexibility.>

A common nonlinear adaptive quantization problem is posed as a corresponding linear quadratic control problem. Adaptive quantizer algorithms are generated using methods of disturbance rejection in linear systems. Simulation with speech data shows that these algorithms can outperform a previous well-known method. The new approach subsumes and extends previous algorithms in a logical fashion.>

The use of Kalman filtering (KF) techniques in speech coding is investigated. The authors show that the common linear predictor (LP) is a special case of the KF based on an all-pole signal model. They also show that the KF algorithm provides fixed-lag smoothing at no additional complexity. Simulation results reveal that KF based speech coding has significant advantage over the equivalent LP based systems, particularly when used with coarsely quantized measurements.>

The authors present a novel approach to the problem of designing a finite impulse response (FIR) filter of specified length q, which approximates in uniform frequency (L/sub infinity /) norm a given desired (possibly infinite impulse response) filter transfer function. They derive an algorithm-independent lower bound on the achievable approximation error and then present an approximation method which involves the solution of a fixed number of all-pass (Nehari) extension problems and so is called the Nehari shuffle. An upper bound on the approximation error for the algorithm is derived. As this bound is calculable a priori, the length of filter required to satisfy a given maximum error can be found before designing the filter. Examples indicate that the method closely approaches the derived global lower bound. The method is compared with the Parks-McClellan (Remez exchange) algorithm in some examples.>

The authors define the DFE (decision feedback equalizer) system of interest and their finite-error-recovery-time problem. They present their basic result, which establishes that whenever the channel satisfies a simple frequency-domain constraint, the error recovery time of an ideal DFE is always finite. They also include four applications of this theorem, including analysis of a real channel. Convergence rates and explicit bounds, given an exponential overbound on the channel impulse response, are presented. Results of greater practical interest, where the authors relax most of the major idealized assumptions, are also given. The authors present the result for M-ary data and relate the error recovery time bound back to the binary case. A formula for the error probability, given a high signal-to-noise-ratio channel, is provided.>

Adaptive decision-directed equalizers can become locked for long periods onto incorrect equilibria. A test involving data available at the equalizer output is proposed for determining whether an equilibrium is correct or not, up to a fixed overall delay. If an independent sequence of random variables taking values +or-1 is the input to a finite impulse response filter, and the output of the filter is passed through a slicer, then the slicer output is uncorrelated if and only if it is a delayed version of the filter input. An analogous result for M-ary rather than binary data is outlined.>

A decision feedback equalizer (DFE) with correct tap weights operating on a noisy channel is considered. We show how the results concerning a noiseless channel can be extended to yield tight bounds on the stationary error probability performance for the noisy case. The effect of noise on DFE performance is classified according to the noise distribution and the channel parameters.

The detection and tracing of edges of varying diffusion is a problem of importance in image analysis. In particular, it is of interest for the segmentation of meteorological and physiological pictures where the boundaries of objects are possibly not well defined or are obscured to a varying extent by noise. We present an edge detection and line fitting procedure which ascribes a direction, a measure of gradient, and quality of fit to the edge within a square segment of a controlled size or ``scope.'' To detect and fit edges to diffuse objects the scope is adaptively altered based on the confidence of fit to permit tracing of the object's boundary. We discuss predictor-corrector procedures for performing this edge tracing where predicted and calculated lines and confidences are used to generate a better fitting line. The performance of the procedures is demonstrated using both synthetic and satellite meteorological images.

In the study of the behavior of adaptive filtering algorithms, persistence of excitation of the input process arises as a sufficient condition for convergence and, perhaps more importantly, for convergence rate of the parameter estimates. In this paper the underlying nature of the persistence requirement is presented and discussed, relating its normal specification in terms of moment conditions with covariance decays, etc., to sample path properties. Deterministic and stochastic persistence conditions and persistence measures are treated, as well as, persistence conditions for output-error, equation-error, and adaptive control schemes.

The detection and tracing of edges of varying diffusion is a problem of importance in image analysis. In particular, it is of interest for the segmentation of meteorological and physiological pictures where the boundaries of objects are possibly not well defined or are obscured to a varying extent by noise. We present an edge detection and line fitting procedure which ascribes a direction, a measure of gradient and quality of fit to the edge within a square segment of a controlled size or "scope". To detect and fit edges to diffuse objects the scope is adaptively altered based on the confidence of fit to permit tracing of the object's boundary. We discuss predictor-corrector procedures for performing this edge tracing where predicted and calculated lines and confidences are used to generate a better fitting line. The performance of the procedures is demonstrated using both synthetic and satellite meteorological images.