الفهرس 
EFFECT OF FINITE WORD LENGTH ON THE STEADY STATE PERFORMANCE OF THE LMS ALGORITHM AND ITS SIGNED VARIANTSOnly 14 pages are availabe for public view
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Abstract
Nabil Roneh Yousef Effect of Finite Wordlength on the Performance of
Adaptive Filters. Master of Science dissertation, Ain Shams University, 1997.
In adaptive filtering applications dealing with high speed data
communications, the baud interval may not be long enough to enable the
execution of one iteration of the adaptive filter coefficients according to the
conventional least mean square (LMS) algorithm. This has initiated the need
of multiplication-free adaptive digital signal processing algorithms. These
algorithms include the signed regressor algorithm (SRA) and the sign
algorithm (SA). The analyses of these algorithms are available only for the
infinite precision implementation of the algorithms. However, in digital
implementation, signals and adaptive filter coefficients are quantized to
finite· wordlengths. This results in a steady state excess quantization error at
the output of the adaptive filter. This error has not yet been analyzed in
literature. The present thesis has four main contributions inthis context. In
the first contribution, the thesis provides roundoff error analyses of the SRA
and the SA in a stationary environment with Gaussian data. Expressions are
derived for the steady state excess quantization mean square error of both
algorithms. It is shown that the steady state excess quantization mean square
error is a decreasing function of both the filter coefficients and data
wordlengths. For both algorithms, it is found that there exists an optimum
step size that minimizes the excess quantization mean square error.
Expressions for this optimum step size are derived for each algorithm. The
second contribution is the study of the transient behavior of the SRA, and
the SA. Expressions for the convergence times of the algorithms are derived.
It is found that effects of roundoff errors are minor at the beginning of
convergence and they become effective only when the algorithm approaches
its steady state. In the third contribution, the thesis analyzes the adaptation
stopping and slow-down phenomena in the SRA and the SA. It is found that
stopping takes place in the SRA when data and noise have bounded ..
ABSTRACT
Nabil Roneh Yousef Effect of Finite Wordlength on the Performance of
Adaptive Filters. Master of Science dissertation, Ain Shams University, 1997.
In adaptive filtering applications dealing with high speed data
communications, the baud interval may not be long enough to enable the
execution of one iteration of the adaptive filter coefficients according to the
conventional least mean square (LMS) algorithm. This has initiated the need
of multiplication-free adaptive digital signal processing algorithms. These
algorithms include the signed regressor algorithm (SRA) and the sign
algorithm (SA). The analyses of these algorithms are available only for the
infinite precision implementation of the algorithms. However, in digital
implementation, signals and adaptive filter coefficients are quantized to
finite· wordlengths. This results in a steady state excess quantization error at
the output of the adaptive filter. This error has not yet been analyzed in
literature. The present thesis has four main contributions inthis context. In
the first contribution, the thesis provides roundoff error analyses of the SRA
and the SA in a stationary environment with Gaussian data. Expressions are
derived for the steady state excess quantization mean square error of both
algorithms. It is shown that the steady state excess quantization mean square
error is a decreasing function of both the filter coefficients and data
wordlengths. For both algorithms, it is found that there exists an optimum
step size that minimizes the excess quantization mean square error.
Expressions for this optimum step size are derived for each algorithm. The
second contribution is the study of the transient behavior of the SRA, and
the SA. Expressions for the convergence times of the algorithms are derived.
It is found that effects of roundoff errors are minor at the beginning of
convergence and they become effective only when the algorithm approaches
its steady state. In the third contribution, the thesis analyzes the adaptation
stopping and slow-down phenomena in the SRA and the SA. It is found that
stopping takes place in the SRA when data and noise have bounded
distributions such as the uniform distnbution, while the slow-down takes
place when they follow unbounded distributions, such as the Gaussian
distribution. Surprisingly, it is found that neither stopping nor slow-down
takes place in the case of the SA. The fourth contribution is the proposal of
an algorithm that reduces the effect of finite wordlength on the performance
of the adaptive filter. Expressions are derived for the steady state mean
square error and the convergence time of the proposed algorithm. It is found
that the proposed algorithm possesses higher resistance to roundoff errors
than that of the conventional algorithm. The analytical findings of the thesis
are supported by computer simulations.