What is the way to adapt the FT algorithm to the structure?

From the structure adaptation point of view, an ideal variable tap-length algorithm should converge fast to the optimum tap-length with high accuracy and have the tap-length remain unchanged after the optimum length is reached.

How many times is the step-size of the NLMS algorithm set?

For all experiments in this example, the step-size of the NLMS algorithm is set as 0.8, the initial tap-length, and a time varying scenario is considered,or n 10000, and W (z) = W (z) for 5000 n < 10000.

How many tap-length learning curves are used in the FT algorithm?

For clarity of exposition, all tap-length learning curves in this section are obtained based on one typical simulation run, and all MSE learning curves are averaged by passing through a rectangular window with size of 50.

How is the FT algorithm more robust to the optimum tap-length?

Although this problem can be overcome by increasing the step-size , this phenomenon indicates that the FT algorithm is more robust to then 4000, and W (z) = W (z) for 2000 n < 4000.local minima than the GD algorithm.

Open AccessJournal Article10.1109/TSP.2005.849170

An LMS style variable tap-length algorithm for structure adaptation

Q: What have the authors contributed in "An lms style variable tap-length algorithm for structure adaptation" ?

In this paper, at first, the authors carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvanges relative to the other. Then, the authors propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length ( FT ).

Q: Why is the optimum tap length always higher than the MMSE?

Due to adaptation noise, the steady-state MSE is always higher than the MMSE, and the authors may have sometimes, although the MMSE is a strict nonincreasing function of.

Q: What is the accumulated squared error of each segment?

An exponential smoothing window with forgetting factor is used to track the so-called accumulated squared error (ASE) of each segmentASE (6)where is the segment index and is obtained from (3) with , which is the output error from the th segmentat time instant .

Q: What is the main advantage of the GD algorithm over the SF algorithm?

The main advantage of the GD algorithm over the SF algorithm is that the former can freely choose the step-size param-eter of , whereas the latter must have , which implies that the tap-length in the SF algorithm has to be changed by each time.

Q: How many tap-length learning curves are used in the FT algorithm?

For clarity of exposition, all tap-length learning curves in this section are obtained based on one typical simulation run, and all MSE learning curves are averaged by passing through a rectangular window with size of 50.

Q: How is the FT algorithm more robust to the optimum tap-length?

Although this problem can be overcome by increasing the step-size , this phenomenon indicates that the FT algorithm is more robust to then 4000, and W (z) = W (z) for 2000 n < 4000.local minima than the GD algorithm.

Yu Gong, +1 more

- 01 Jul 2005

- IEEE Transactions on Signal Processing

- Vol. 53, Iss: 7, pp 2400-2407

127

TL;DR: This paper proposes an improved variable tap-length algorithm using the concept of the pseudo fractionaltap-length (FT), which not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms.

Abstract: Searching for the optimum tap-length that best balances the complexity and steady-state performance of an adaptive filter has attracted attention recently. Among existing algorithms that can be found in the literature, two of which, namely the segmented filter (SF) and gradient descent (GD) algorithms, are of particular interest as they can search for the optimum tap-length quickly. In this paper, at first, we carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvantages relative to the other. Then, we propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length (FT). Updating the tap-length with instantaneous errors in a style similar to that used in the stochastic gradient [or least mean squares (LMS)] algorithm, the proposed FT algorithm not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms. Both performance analysis and numerical simulations are given to verify the new proposed algorithm.

AI Agents for this Paper

Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps

Most frequently asked questions

1. What have the authors contributed in "An lms style variable tap-length algorithm for structure adaptation" ?

In this paper, at first, the authors carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvanges relative to the other.. Then, the authors propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length ( FT ).

2. Why is the optimum tap length always higher than the MMSE?

Due to adaptation noise, the steady-state MSE is always higher than the MMSE, and the authors may have sometimes, although the MMSE is a strict nonincreasing function of.

3. What is the accumulated squared error of each segment?

An exponential smoothing window with forgetting factor is used to track the so-called accumulated squared error (ASE) of each segmentASE (6)where is the segment index and is obtained from (3) with , which is the output error from the th segmentat time instant .

4. What is the main advantage of the GD algorithm over the SF algorithm?

The main advantage of the GD algorithm over the SF algorithm is that the former can freely choose the step-size param-eter of , whereas the latter must have , which implies that the tap-length in the SF algorithm has to be changed by each time.

Fig. 4. Learning curves of N(n), where W (z) = W (z) for n < 2000 or

Fig. 5. MSE learning curves corresponding to Fig. 4.

Fig. 3. Learning curves of N(n), where W (z) = W (z) and the step-size for the NLMS algorithm is deliberately set as small as 0.05.

Fig. 1. Block diagram of the adaptive system modeling.

TABLE I PARAMETERS FOR THE VARIABLE TAP-LENGTH ALGORITHMS

Citations

•Journal Article•10.1109/TSP.2008.2010600

The Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes

Clive Cheong Took, +1 more

- 01 Apr 2009

- IEEE Transactions on Signal Processing

TL;DR: The analysis shows that QLMS operates inherently based on the so called ldquoaugmentedrdquo statistics, that is, both the covariance and pseudocovariance of the tap input vector x are taken into account.

...read moreread less

330

Journal Article•10.1109/TASLP.2013.2297016

Feedforward Active Noise Control With a New Variable Tap-Length and Step-Size Filtered-X LMS Algorithm

Dah-Chung Chang, +1 more

- 01 Feb 2014

- IEEE Transactions on Audio, Speech, and ...

TL;DR: In the online secondary path modeling ANC system, simulation results show that the new algorithm with different kind of variable step sizes can provide significant improvements of convergence rate and noise reduction ratio, compared to the fixed-tap-length FxLMS algorithms.

...read moreread less

Journal Article•10.1016/J.SIGPRO.2008.11.008

An improved variable tap-length LMS algorithm

Ning Li, +3 more

- 01 May 2009

- Signal Processing

TL;DR: An improved variableTap-length LMS algorithm that can obtain both a fast convergence rate and a small steady-state error of the tap-length and also provides a guideline for the parameter choice.

...read moreread less

Journal Article•10.1109/TSP.2010.2101066

Adaptive Volterra Filters With Evolutionary Quadratic Kernels Using a Combination Scheme for Memory Control

Marcus Zeller, +3 more

- 01 Apr 2011

- IEEE Transactions on Signal Processing

TL;DR: This paper proposes a new paradigm for adaptive Volterra filtering using a time-variant size of the quadratic kernel memory in order to optimally identify any unknown transversal second-order nonlinear system.

...read moreread less

•Journal Article•10.1109/LSP.2006.887784

A New Variable Tap-Length LMS Algorithm to Model an Exponential Decay Impulse Response

Yonggang Zhang, +4 more

- 19 Mar 2007

- IEEE Signal Processing Letters

TL;DR: Simulation results show the proposed algorithm has a faster convergence rate as compared with the fixedTap-length LMS algorithm and is robust to the initial tap-length choice.

...read moreread less

...

Expand

References

Journal Article•10.1016/0967-0661(96)82838-3

Adaptive Filter Theory

Steve Rogers

- 01 Nov 1996

- Control Engineering Practice

TL;DR: A guide to using artificial intelligence in the filmmaking process, as well as practical suggestions for improving the quality and efficiency of existing and new approaches.

...read moreread less

12.6K

•Book

Adaptive Filters Theory and Applications

Behrouz Farhang-Boroujeny

- 04 Jan 1999

TL;DR: This comprehensive book is both a valuable student resource and a useful technical reference for signal processing engineers in industry.

...read moreread less

1.1K

Journal Article•10.1109/78.806077

Blind channel approximation: effective channel order determination

A.P. Liavas, +2 more

- 01 Dec 1999

- IEEE Transactions on Signal Processing

TL;DR: The derived criterion provides a "maximally stable" decomposition of the range space of an "over-modeled" data covariance matrix into signal and noise subspaces and provides useful estimates, leading to sufficiently good blind approximation/equalization of measured real-world microwave radio channels.

...read moreread less

153

Proceedings Article•10.1109/ACSSC.1998.751442

Blind channel approximation: effective channel order determination

A.P. Liavis, +2 more

- 01 Nov 1998

...read moreread less

142

Journal Article•10.1109/26.650219

Tap-selectable decision-feedback equalization

S. Ariyavisitakul, +2 more

- 01 Dec 1997

- IEEE Transactions on Communications

TL;DR: In this article, an adaptive tap assignment technique for improving the performance of a previously reported reduced-complexity decision-feedback equalizer (DFE) for broadband band wireless systems is presented.

...read moreread less

119

...

Expand

An LMS style variable tap-length algorithm for structure adaptation

Chat with Paper

AI Agents for this Paper

Most frequently asked questions

1. What have the authors contributed in "An lms style variable tap-length algorithm for structure adaptation" ?

2. Why is the optimum tap length always higher than the MMSE?

3. What is the accumulated squared error of each segment?

4. What is the main advantage of the GD algorithm over the SF algorithm?

5. What is the way to adapt the FT algorithm to the structure?

6. How many times is the step-size of the NLMS algorithm set?

7. How many tap-length learning curves are used in the FT algorithm?

8. How is the FT algorithm more robust to the optimum tap-length?

Figures

Citations

The Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes

Feedforward Active Noise Control With a New Variable Tap-Length and Step-Size Filtered-X LMS Algorithm

An improved variable tap-length LMS algorithm

Adaptive Volterra Filters With Evolutionary Quadratic Kernels Using a Combination Scheme for Memory Control

A New Variable Tap-Length LMS Algorithm to Model an Exponential Decay Impulse Response

References

Adaptive Filter Theory

Adaptive Filters Theory and Applications

Blind channel approximation: effective channel order determination

Blind channel approximation: effective channel order determination

Tap-selectable decision-feedback equalization

Related Papers (5)

LMS algorithm with gradient descent filter length

Linear equalisers, with dynamic and automatic length selection

Performance analysis of the deficient length LMS adaptive algorithm

Structure adaptation of linear MMSE adaptive filters

Convergence analysis of a deficient-length LMS filter and optimal-length sequence to model exponential decay impulse response