A block floating-point treatment to the LMS algorithm: efficient realization and a roundoff error analysis

An efficient scheme is presented for implementing the LMS-based transversal adaptive filter in block floating-point (BFP) format, which permits processing of data over a wide dynamic range, at temporal and hardware complexities significantly less than that of a floating-point processor. Appropriate...

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Bibliographic Details
Published in:IEEE Transactions on Signal Processing Vol. 53; no. 12; pp. 4536 - 4544
Main Authors: Mitra, A., Chakraborty, M., Sakai, H.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.12.2005
Institute of Electrical and Electronics Engineers (IEEE)
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive filters
Algorithm design and analysis
Algorithms
Applied sciences
Block floating-point arithmetic
Blocking
Convergence
Detection, estimation, filtering, equalization, prediction
Dynamic range
Error analysis
Errors
Exact sciences and technology
Filtering
Floating point arithmetic
Format
Hardware
Information theory
Information, signal and communications theory
least mean square methods
Least squares approximation
overflow
Regression analysis
Roundoff error
Roundoff errors
Signal and communications theory
Signal, noise
Studies
Telecommunications and information theory
Transversal filters
Overflow(computer arithmetics)
Filtering
Error estimation
least mean square methods
Rounding error
Processing time
Data processing
Adaptive filter
Steady state
Implementation
Mean square error
Quantization noise
overflow
Algorithm performance
Block floating-point arithmetic
roundoff errors
Transverse filter
Convergence rate
Floating point
Least mean squares methods
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:An efficient scheme is presented for implementing the LMS-based transversal adaptive filter in block floating-point (BFP) format, which permits processing of data over a wide dynamic range, at temporal and hardware complexities significantly less than that of a floating-point processor. Appropriate BFP formats for both the data and the filter coefficients are adopted, taking care so that they remain invariant to interblock transition and weight updating operation, respectively. Care is also taken to prevent overflow during filtering, as well as weight updating processes jointly, by using a dynamic scaling of the data and a slightly reduced range for the step size, with the latter having only marginal effect on convergence speed. Extensions of the proposed scheme to the sign-sign LMS and the signed regressor LMS algorithms are taken up next, in order to reduce the processing time further. Finally, a roundoff error analysis of the proposed scheme under finite precision is carried out. It is shown that in the steady state, the quantization noise component in the output mean-square error depends on the step size both linearly and inversely. An optimum step size that minimizes this error is also found out.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2005.859342