Fixed-Point Implementation of Fast QR-Decomposition Recursive Least-Squares Algorithms (FQRD-RLS): Stability Conditions and Quantization Errors Analysis

The fast QR-decomposition based recursive least-squares (FQRD-RLS) algorithms offer RLS-like convergence and misadjustment at a lower computational cost, and therefore are desirable for implementation on a fixed-point digital signal processor (DSP). Furthermore, the FQRD-RLS algorithms are derived f...

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Bibliographic Details
Published in:Circuits, systems, and signal processing Vol. 32; no. 4; pp. 1551 - 1574
Main Authors: Shoaib, Mobien, Alshebeili, Saleh
Format: Journal Article
Language:English
Published: Boston Springer US 01.08.2013
Springer Nature B.V
Subjects:
Algorithms
Circuits and Systems
Electrical Engineering
Electronics and Microelectronics
Engineering
Error analysis
Errors
Fixed points (mathematics)
Instrumentation
Least squares method
Mathematical analysis
Mathematical models
Propagation
Quantization
Signal processing
Signal,Image and Speech Processing
Stability
Systems stability
QR-decomposition
Stability analysis
Quantization error
Fixed-point
Fast algorithms
ISSN:0278-081X, 1531-5878
Online Access:Get full text
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Summary:The fast QR-decomposition based recursive least-squares (FQRD-RLS) algorithms offer RLS-like convergence and misadjustment at a lower computational cost, and therefore are desirable for implementation on a fixed-point digital signal processor (DSP). Furthermore, the FQRD-RLS algorithms are derived from QR-decomposition based RLS algorithms that are well known for their numerical stability in finite precision. Hence, these algorithms are often assumed numerically stable, although there is no rigorous analysis addressing the stability of such algorithms in finite precision. In this paper, we derive the conditions that guarantee stability of the FQRD-RLS algorithms, and also derive mathematical expressions for the mean-squared quantization error (MSQE) of internal variables of the FQRD-RLS algorithms at steady state. The objective is to quantify the propagation error due to quantization effects. The derived MSQE expressions have been verified by comparisons with fixed-point computer simulations.
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ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-012-9526-7