2,793 research outputs found
Stochastic Analysis of LMS Algorithm with Delayed Block Coefficient Adaptation
In high sample-rate applications of the least-mean-square (LMS) adaptive
filtering algorithm, pipelining or/and block processing is required. In this
paper, a stochastic analysis of the delayed block LMS algorithm is presented.
As opposed to earlier work, pipelining and block processing are jointly
considered and extensively examined. Different analyses for the steady and
transient states to estimate the step-size bound, adaptation accuracy and
adaptation speed based on the recursive relation of delayed block excess mean
square error (MSE) are presented. The effect of different amounts of pipelining
delays and block sizes on the adaptation accuracy and speed of the adaptive
filter with different filter taps and speed-ups are studied. It is concluded
that for a constant speed-up, a large delay and small block size lead to a
slower convergence rate compared to a small delay and large block size with
almost the same steady-state MSE. Monte Carlo simulations indicate a fairly
good agreement with the proposed estimates for Gaussian inputs.Comment: 13 pages, 8 figure
An affine combination of two LMS adaptive filters - Transient mean-square analysis
This paper studies the statistical behavior of an affine combination of the outputs of two LMS adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor is restricted to the interval . The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the MSE. First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSD's of either filter
Stochastic analysis of an error power ratio scheme applied to the affine combination of two LMS adaptive filters
The affine combination of two adaptive filters that simultaneously adapt on the same inputs has been actively investigated. In these structures, the filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying parameter for combining the filter outputs. A recently proposed scheme based on the ratio of error powers of the two filters has been shown by simulation to achieve nearly optimum performance. The purpose of this paper is to present a first analysis of the statistical behavior of this error power scheme for white Gaussian inputs. Expressions are derived for the mean behavior of the combination parameter and for the adaptive weight mean-square deviation. Monte Carlo simulations show good to excellent agreement with the theoretical predictions
Adaptive Mixture Methods Based on Bregman Divergences
We investigate adaptive mixture methods that linearly combine outputs of
constituent filters running in parallel to model a desired signal. We use
"Bregman divergences" and obtain certain multiplicative updates to train the
linear combination weights under an affine constraint or without any
constraints. We use unnormalized relative entropy and relative entropy to
define two different Bregman divergences that produce an unnormalized
exponentiated gradient update and a normalized exponentiated gradient update on
the mixture weights, respectively. We then carry out the mean and the
mean-square transient analysis of these adaptive algorithms when they are used
to combine outputs of constituent filters. We illustrate the accuracy of
our results and demonstrate the effectiveness of these updates for sparse
mixture systems.Comment: Submitted to Digital Signal Processing, Elsevier; IEEE.or
Performance Analysis of l_0 Norm Constraint Least Mean Square Algorithm
As one of the recently proposed algorithms for sparse system identification,
norm constraint Least Mean Square (-LMS) algorithm modifies the cost
function of the traditional method with a penalty of tap-weight sparsity. The
performance of -LMS is quite attractive compared with its various
precursors. However, there has been no detailed study of its performance. This
paper presents all-around and throughout theoretical performance analysis of
-LMS for white Gaussian input data based on some reasonable assumptions.
Expressions for steady-state mean square deviation (MSD) are derived and
discussed with respect to algorithm parameters and system sparsity. The
parameter selection rule is established for achieving the best performance.
Approximated with Taylor series, the instantaneous behavior is also derived. In
addition, the relationship between -LMS and some previous arts and the
sufficient conditions for -LMS to accelerate convergence are set up.
Finally, all of the theoretical results are compared with simulations and are
shown to agree well in a large range of parameter setting.Comment: 31 pages, 8 figure
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