1:00, SPTM-P9.1
STOCHASTIC ANALYSIS OF THE AFFINE PROJECTION ALGORITHM FOR GAUSSIAN AUTOREGRESSIVE INPUTS
N. BERSHAD, D. LINEBARGER, S. MCLAUGHLIN
ABSTRACT This paper studies the statistical behavior of the Affine Projection (AP) algorithm for mu = 1 for Gaussian Autoregressive inputs. This work extends the theoretical results of Rupp [3] to the numerical evaluation of the MSE learning curves for the adaptive AP weights. The MSE learning behavior of the AP(P+1) algorithm with an AR(Q) input (Q < P) is shown to be the same as the NLMS algorithm (mu = 1) with a white input with M-P unity eigenvalues and P zero eigenvalues and increased observation noise. Monte Carlo simulations are presented which support the theoretical results.

1:00, SPTM-P9.2
ANALYSIS OF THE ADAPTIVE FILTER ALGORITHM FOR FEEDBACK-TYPE ACTIVE NOISE CONTROL
H. SAKAI, S. MIYAGI
The feedback-type active noise control (ANC) system uses only one microphone to provide necessary signals for adjusting the adaptive filter. Due to the complicated nature of the whole adaptive filter structure there have been no theoretical results about its convergence properties. In this paper, first a stationary point of the adaptive filter using the filtered-X LMS algorithm is obtained by the averaging method combined with the frequency domain technique. Then the local convergence condition is derived. This is a counterpart of the well-known 90 degrees condition for the feedforward-type ANC. Finally, the convergence condition is explicitly given for a simple example and its validity is shown by some simulations.

1:00, SPTM-P9.3
EVALUATION AND DESIGN OF VARIABLE STEP SIZE ADAPTIVE ALGORITHMS
C. LOPES, J. BERMUDEZ
This paper presents a new methodology for evaluation and design of variable step size adaptive algorithms. The new methodology is based on a learning plane, which combines the evolutions of both the step size and the mean square error. It includes both transient and steady-state behaviors and can be used to compare performances of different algorithms against an optimum trajectory in the learning plane. The new technique can also be used for algorithm optimization in system identification applications.

1:00, SPTM-P9.4
CONVERGENCE ANALYSIS OF THE NLMS ALGORITHM WITH M-INDEPENDENT INPUTS
P. SCALART
In most adaptive identification applications, a finite impulse response (FIR) filter is employed with coefficients that are computed using the normalized least mean square (NLMS) algorithm. In this paper, the convergence behavior of the NLMS algorithm is analyzed using a simple model of the input signal vectors. Explicit expressions of the learning curve and misadjustement are derived and compared with those previously established for the NLMS algorithm. Comparisons between theoretical and experimental results are given to validate our approach.

1:00, SPTM-P9.5
LOCAL STABILITY ANALYSIS AND SYSTOLIC IMPLEMENTATION OF A SUBSPACE TRACKING ALGORITHM
F. XU, A. WILLSON
We discuss the DPASTd algorithm for signal subspace tracking. Our analysis shows that, under a sufficient condition on the step size, the DPASTd algorithm is locally stable even though delayed updating is applied. A pipelined realization of the algorithm and the corresponding systolic architecture are also proposed and a method for reciprocal computation is discussed. We also present simulation results to validate the algorithm.

1:00, SPTM-P9.6
MULTIPLE ENVIRONMENT OPTIMAL UPDATE PROFILING FOR STEEPEST DESCENT ALGORITHMS
M. MILISAVLJEVIC
In this paper, the methods for use of prior information about multiple operating environments, in improving adaptive filter convergence properties are discussed. More concretely, the gain selection, profiling and scheduling in steepest descent algorithms are treated in detail. Work presented in this paper is an extension of prior work in [1]. Two flavors of optimization are discussed: average descent rate optimization and maximization of the minimum descent rate. It is demonstrated, just as in the case of single channel optimization, with no additional complexity a substantial increase of convergence rate of steepest descent algorithms can be achieved. Finally, performance of the method is analyzed on the adaptive linear equalizer design for local area networks.

1:00, SPTM-P9.7
STABILITY ANALYSIS OF THE SEQUENTIAL PARTIAL UPDATE ALGORITHM
M. GODAVARTI, A. HERO III
Partial updating of LMS filter coefficients is an effective method for reducing the computational load and the power consumption in adaptive filter implementations. The Sequential Partial Update LMS algorithm is one popular algorithm in this category. In \cite{Douglas} a first order stability analysis of this algorithm was performed on wide sense stationary signals under the restrictive assumption of small step size parameter $\mu$. The necessary and sufficient condition derived on $\mu$ for convergence in the mean was identical to the one for guaranteeing stability in the mean of LMS. In \cite{Godavarti2} first order sufficient conditions were derived for stability without the aforementioned small $\mu$ assumption. The sufficient region of convergence derived was smaller than that of regular LMS. In this paper, we establish that for stationary signals the sequential algorithm converges in mean for the same values of the step size parameter $\mu$ for which the regular LMS does. In other words, we show that the conclusion drawn in \cite{Douglas} holds without the restrictive assumption of small $\mu$. We also derive sufficient conditions for stability on $\mu$ for cyclo-stationary signals.

1:00, SPTM-P9.8
ADAPTATION WITH CONSTANT GAINS: ANALYSIS FOR SLOW VARIATIONS
L. LINDBOM, M. STERNAD, A. AHLEN
Adaptation laws with constant gains, that adjust parameters of linear regression models, are investigated. The class of algorithms includes LMS as its simplest member. Closed-form expressions for the tracking MSE are obtained for parameters described by ARIMA processes. A key element of the analysis is that adaptation algorithms are expressed as linear time-invariant filters, here called learning filters, that work in open loop for slow parameter variations. Performance analysis can then easily be performed for slow variations, and stability is assured by stability of these learning filters. http://www.signal.uu.se/Publications/abstracts/r002.html

1:00, SPTM-P9.9
TRANSIENT ANALYSIS OF ADAPTIVE FILTERS
T. AL-NAFFOURI, A. SAYED
This paper develops a framework for the mean-square analysis of adaptive filters with general data and error nonlinearities. The approach relies on energy conservation arguments and is carried out without restrictions on the probability distribution of the input sequence. In particular, for adaptive filters with diagonal matrix nonlinearities, we provide closed form expressions for the steady state performance and necessary and sufficient conditions for stability. We carry out a similar study for long adaptive filters that employ error nonlinearities relying on a weaker form of the independence assumption. We provide expressions for the steady-state error and bounds on the step size for stability by exploiting the Cramer-Rao bound of the underlying estimation process.

1:00, SPTM-P9.10
MEAN-SQUARE ANALYSIS OF NORMALIZED LEAKY ADAPTIVE FILTERS
A. SAYED, T. AL-NAFFOURI
In this paper, we study leaky adaptive algorithms that employ a general scalar or matrix data nonlinearity. We perform a mean-square analysis of this class of algorithms without imposing restrictions on the probability distribution of the input. In particular, we derive conditions on the step-size for stability, and provide closed form expressions for the steady-state performance.

1:00, SPTM-P9.11
FILTER TRANSITIONS IN ADAPTIVE IIR APPROXIMATE FILTERING
R. ADHIKARY, S. NAWAB
The effects associated with the switching of filter orders in an incrementally adaptive IIR approximate filtering technique are evaluated in the context of speech signals. Through listening experiments, we have found that the perceptual quality of the speech at the filter output is sensitive to the initial conditions used in initiating a transition to a higher filter order. If zero initial conditions are used there is a significant crackling sound due to error bursts at points where switches to higher order filters take place. If output samples from the pre-transition filter are used as initial conditions for the post-transition filter, the amplitude of the error bursts are found to decrease significantly. An analysis is presented to account for these observations.

1:00, SPTM-P9.12
ITERATIVE WIENER DESIGN OF ADAPTATION LAWS WITH CONSTANT GAINS
M. STERNAD, A. AHLEN, L. LINDBOM
We present a method for optimizing adaptation laws that are generalizations of the LMS algorithm. Time-varying parameters of linear regression models are estimated in situations where the regressors are stationary or have slowly time-varying properties. The parameter variations are modeled as ARIMA-processes and the aim is to use such prior information to provide high performance filtering, prediction or fixed lag smoothing estimates for arbitrary lags. The method is based on a novel signal transformation that recasts the algorithm design problem into a Wiener design. http://www.signal.uu.se/Publications/abstracts/r001.html