Wiener design of adaptation algorithms with time-invariant gains

A design method is presented that extends least mean squared (LMS) adaptation of time-varying parameters by including general linear time-invariant filters that operate on the instantaneous gradient vector. The aim is to track time-varying parameters of linear regression models in situations where the regressors are stationary or have slowly time-varying properties. The adaptation law is optimized with respect to the steady-state parameter error covariance matrix for time-variations modeled as vector-ARIMA processes. The design method systematically uses prior information about time-varying parameters to provide filtering, prediction, or fixed lag smoothing estimates for arbitrary lags. The method is based on a transformation of the adaptation problem into a Wiener filter design problem. The filter works in open loop for slow parameter variations, whereas a time-varying closed loop has to be considered for fast variations. In the latter case, the filter design is performed iteratively. The general form of the solution at each iteration is obtained by a bilateral Diophantine polynomial matrix equation and a spectral factorization. For white gradient noise, the Diophantine equation has a closed-form solution. Further structural constraints result in very simple design equations. Under certain model assumptions, the Wiener designed adaptation laws reduce to LMS adaptation. Compared with Kalman estimators, the channel tracking performance becomes nearly the same in mobile radio applications, whereas the complexity is, in general, much lower     

Tracking of time-varying mobile radio channels. II. A case study

For pt.I see ibid., vol.49, p.2207-17 (2001). Low-complexity Wiener LMS (WLMS) adaptation algorithms, of use for channel estimation, have been derived in Lindbom et al. (2001). They are here evaluated on the fast fading radio channels encountered in IS-136 TDMA systems, with the aim of clarifying several issues: How much can channel estimation performance be improved with these tools, as compared to LMS adaptation? When can an improved tracking MSE be expected to result in a meaningful reduction of the bit error rate? Will optimal prediction of future channel estimates significantly improve the equalization? Can one single tracker with fixed gain be used for all encountered Doppler frequencies and SNRs, or must a more elaborate scheme be adopted? These questions are here investigated both analytically and by simulation. An exact analytical expression for the tracking MSE on two-tap FIR channels is presented and utilized. With this tool, the MSE performance and robustness of WLMS algorithms based on different statistical models can be investigated. A simulation study then compares the uncoded bit error rate of detectors, where channel trackers are used in decision directed mode in conjunction with Viterbi algorithms. A Viterbi detector combined with WLMS, based on second order autoregressive fading models possibly combined with integration, provides good performance and robustness at a reasonable complexity     

Wiener filter design using polynomial equations

A simplified way of deriving realizable and explicit Wiener filters is presented. Discrete-time problems are discussed in a polynomial equation framework. Optimal filters, predictors, and smoothers are calculated by means of spectral factorizations and linear polynomial equations. A tool for obtaining these equations, for a given problem structure, is described. It is based on the evaluation of orthogonality in the frequency domain, by means of canceling stable poles with zeros. Comparisons are made to previously known derivation methodologies such as completing the squares for the polynomial systems approach and the classical Wiener solution. The simplicity of the proposed derivation method is particularly evident in multistage filtering problems. To illustrate, two examples are discussed: a filtering and a generalized deconvolution problem. A new solvability condition for linear polynomial equation appearing in scalar problems is also presented     

Optimal differentiation based on stochastic signal models

The problem of estimating the time derivative of a signal from sampled measurements is addressed. The measurements may be corrupted by colored noise. A key idea is to use stochastic models of the signal to be differentiated and of the measurement noise. Two approaches are suggested. The first is based on a continuous-time stochastic process as a model of the signal. The second uses a discrete-time ARMA model of the signal and a discrete-time approximation of the derivative operator. Digital differentiators are presented in a shift operator polynomial form. They minimize the mean-square estimation error, and are calculated from a linear polynomial equation and a polynomial spectral factorization. The three obstacles to perfect differentiation, namely a finite smoothing lag, measurement noise, and aliasing effects due to sampling, are discussed     

Tracking of time-varying mobile radio channels .1. The Wiener LMSalgorithm

Adaptation algorithms with constant gains are designed for tracking smoothly time-varying parameters of linear regression models, in particular channel models occurring in mobile radio communications. In a companion paper, an application to channel tracking in the IS-136 TDMA system is discussed. The proposed algorithms are based on two key concepts. First, the design is transformed into a Wiener filtering problem. Second, the parameters are modeled as correlated ARIMA processes with known dynamics. This leads to a new framework for systematic and optimal design of simple adaptation laws based on prior information. The algorithms can be realized as Wiener filters, called learning filters, or as "LMS/Newton" updates complemented by filters that provide predictions or smoothing estimates. The simplest algorithm, named the Wiener LMS, is presented. All parameters are here assumed governed by the same dynamics and the covariance matrix of the regressors is assumed known. The computational complexity is of the same order of magnitude as that of LMS for regressors which are either white or have autoregressive statistics. The tracking performance is, however, substantially improved     

The structure and design of realizable decision feedback equalizers for IIR channels with colored noise

A simple algorithm for optimizing decision feedback equalizers (DFEs) by minimizing the mean-square error (MSE) is presented. A complex baseband channel and correct past decisions are assumed. The dispersive channel may have infinite impulse response, and the noise may be colored. Consideration is given to optimal realizable (stable and finite-lag smoothing) forward and feedback filters in discrete time. They are parameterized as recursive filters. In the special case of transmission channels with finite impulse response and autoregressive noise, the minimum MSE can be attained with transversal feedback and forward filters. In general, the forward part should include a noise-whitening filter (the inverse noise model). The finite realizations of the filters are calculated using a polynomial equation approach to the linear quadratic optimization problem. The equalizer is optimized essentially by solving a system of linear equations Ax=B, where A contains transfer function coefficients from the channel and noise model. No calculation of correlations is required with this method. A simple expression for the minimal MSE is presented. The DFE is compared to MSE-optimal linear recursive equalizers. Expressions for the equalizer in the limiting case of infinite smoothing lags are also discussed.<>     

Simple reinforcement for thin nephrostomy catheters

PURPOSE: Nephrostomy catheters are prone to kinking or damage because the thin, flexible silicone tube is too vulnerable against mechanical stress even when the proximal end is carefully fixed. We developed a simple method to reinforce the outside part of a thin catheter protruding from the skin. MATERIALS AND METHODS: We treated 7 children with nephrostomy catheters or ureteral stents with a diameter of 8F or smaller. After insertion a large plastic tube was wrapped around the small catheter, and fixed to the skin and to the peripheral collection system with adhesive tape. RESULTS: Handling of the catheters improved and there was less need for re-fixation. CONCLUSIONS: Thin nephrostomy catheters can be effectively protected by wrapping them into a larger, outer tube after insertion.     

Digital differentiation of noisy data measured through a dynamicsystem

The design of discrete time differentiating filters, in the presence of colored noise and nonneglectable transducer dynamics, is investigated. The signal and noise are described by autoregressive moving average (ARMA) models, possibly with poles on |z|=1. The mean square error (MSE) optimal filter, based on a discrete time approximation of the derivative operator, is given by a spectral factorization and a linear polynomial equation     

A novel derivation methodology for polynomial-LQ controller design

A simple derivation method for optimization of linear-quadratic (LQ) controllers is presented in the discrete-time polynomial systems framework. A control-law variation, regarded as a potential feedforward from the innovations, is used. Orthogonality is evaluated in the frequency domain by collectively cancelling unstable poles by zeros. The suggested method, summarized as a three-step scheme, is exemplified on a disturbance measurement feedforward and an output feedback problem. It is a simple, more direct alternative to the completing-the-squares approach     

Towards Systems Beyond 3G Based on Adaptive OFDMA Transmission

High data rates, high spectral efficiency, flexibility, and low delays over the air interface will be important features in next-generation wireless systems. The overall challenge will be packet scheduling and adaptive radio transmission for multiple users, via multiple antennas and over frequency-selective wideband channels. This problem needs to be structured to obtain feasible solutions. The basic simplifying assumptions used here are clustering of antennas into cells, orthogonal transmission by use of cyclic-prefix orthogonal frequency-division multiplexing (OFDM) and a time-scale separation view of the total link adaptation, scheduling and intercell coordination problem. Based on these assumptions, we survey techniques that adapt the transmission to the temporal, frequency, and spatial channel properties. We provide a systematic overview of the design problems, such as the dimensioning of the allocated time-frequency resources, the influence of duplexing schemes, adaptation control issues for downlinks and uplinks, timing issues, and their relation to the required performance of channel predictors. Specific design choices are illustrated by recent research within the Swedish Wireless IP program and the EU IST-WINNER project. The presented results indicate that high-performance adaptive OFDM transmission systems are indeed feasible, also for challenging scenarios that involve vehicular velocities, high carrier frequencies, and high bandwidths.