Pulse or digital communications – Equalizers – Automatic
Reexamination Certificate
1998-09-17
2002-08-27
Deppe, Betsy L. (Department: 2634)
Pulse or digital communications
Equalizers
Automatic
Reexamination Certificate
active
06442199
ABSTRACT:
TECHNICAL FIELD
This invention refers to a method for stabilizing the operation of fractionally spaced equalizers having a determinate number of taps, associated with which are respective equalization coefficients, used in digital signal receivers, said equalization coefficients being updatable through an algorithm based on the minimization of a proper cost function and stabilized by a proper modification, said modification involving evaluation of a plurality of values to be considered for updating said equalization coefficients.
The invention also concerns a fractionally spaced equalizer and a digital signal receiver incorporating the method.
BACKGROUND OF THE INVENTION
Adaptive equalization is a technique commonly used to compensate the channel distorting effect in a general transmission system. A known technique uses synchronous equalizers obtained through FIR (Finite Impulse Response) filters with variable coefficients time-spaced by an amount equal to the signal interval or to the symbol time.
Performance of such an equalizer depends significantly on the phrase of the symbol synchronism reconstructed during reception. Improved performance can be obtained with the use of the so-called fractionally spaced equalizers (FSE) consisting of an adaptive FIR filter with coefficients time-spaced by a quantity equal to a fraction of the signal interval or to the symbol time. Performance of the fractionally spaced equalizer with a sufficient number of coefficients is practically free from the phrase characteristics of the transmission channel and from the phrase of the symbol synchronism as reconstructed during reception. In a more general way, the fractionally spaced equalizer is able to execute adaptively in only one device both the adaptive filtering and equalization functions, and provide, for instance, the optimum linear receiver. However, a fractionally spaced equalizer has two main drawbacks: first of all the coefficients drift and, secondly, has a low convergence rate. Both these drawbacks are due to the fact that a fractionally spaced equalizer in general allows more configurations than the equalization coefficients, substantially corresponding to the same root-mean-square error. In other words, the root-mean-square error does not change significantly according to certain directions around the point corresponding to the optimum configuration point of the equalization coefficients. Experimental tests have demonstrated that a fractionally spaced equalizer is affected by a long term intrinsic instability due to unavoidable bias taking place in the control circuits. This behaviour leads the equalizer to operate with coefficients having values so high as to cause overflow in the registers or a coefficient saturation, leading to a performance degradation.
Therefore, proper stabilization techniques of the control algorithms are required to maximize the performance of a fractionally spaced equalizer, to prevent the coefficient drift and to increase convergence rate. To this purpose it has been proposed, for instance in the article by R. D. Gitlin, H. C. Meadors, S. B. Weinstein, ‘
The Tap-Leakage Algorithm: An Algorithm for the Stable Operation of a Digitally Implemented Fractionally Spaced Equalizer
’, Bell Sys. Tech. J., vol. 61, no. 8, pp. 1817-1839, Oct. 1982, to change the control algorithm of the fractionally spaced equalizer introducing a predetermined quantity of fictitious white noise. This technique, called ‘tap-leakage’, represents an efficient measure against the drift of equalization coefficients while improving convergence rate.
Namely, if c
k
is the vector of the equalization coefficients at time k and c
k+1
the vector of the equalization coefficients at time k+1, where time increment corresponds to an updating interval, then the updating operation according to the algorithm of the stochastic gradient will be:
c
k+1
=c
k
−&ggr;(
e
k
r
k
*
+&mgr;Qc
) (1)
where &ggr; is a step chosen as a function of the convergence rate to be obtained, &mgr; is a white noise constant, Q is a shaping matrix of the fictitious noise, whereas r
k
*
is the vector of the samples at the equalizer input, and e
k
is an error in a sequence of errors e
k−1
,e
k
,e
k+1
, . . . evaluated according to a certain cost function J among the equalized samples and recognized values.
The cost function J to be minimized can be e.g.:
J=E{|
×(
kT
)−â
k
|
2
} (1a)
where the symbol E{.} shows the mean value operation and â
k
is the recognized signal. Therefore, the cost function J is the mean value of the root-mean-square deviation between the equalized value and the recognized value.
Thus, according to equation (1) the value of the updated equalization coefficients c
k+1
depends on the product e
k
r
*
k
, that is the updating value, as well as on the product &mgr;Qc
k
, which determines a vector I
k+1
which is called of the leakage values, i.e. loss values. It will be in fact:
I
k+1
=&mgr;Qc
k
(2)
Substantially, the function of the leakage value vector I
k+1
is to behave like an additional term controlling the value of the coefficients c
k+1
at every update, so as to avoid their divergence in the long term. The fictitious white noise shaping matrix is a (2L+1)×(2L+1)-element square matrix, and, as is well known in the art, is a Toeplitz-type matrix (see U.S. Pat. No. 5,444,816), having in all only 2N+1 different non-zero values, for some N<L, with some rows having more non-zero values than others, and the non-zero values being centered on the diagonal, corresponding the number of coefficients of the fictitious noise filter to be implemented. (For the definition of a Toeplitz matrix, see e.g. S. Haykin,
Adaptive Filter Theory
, Prentice-Hall, Englewood Cliffs, page 48.) For N=2, the multiplication indicated in
FIG. 2
is as follows;
&LeftBracketingBar;
I
-
5
I
-
4
I
-
3
I
-
2
I
-
1
I
0
I
1
I
2
I
3
I
4
I
5
&RightBracketingBar;
=
μ
&LeftBracketingBar;
q
0
q
1
q
2
q
3
0
0
0
0
0
0
0
q
-
1
q
0
q
1
q
2
q
3
0
0
0
0
0
0
q
-
2
q
-
1
q
0
q
1
q
2
q
3
0
0
0
0
0
q
-
3
q
-
2
q
-
1
q
0
q
1
q
2
q
3
0
0
0
0
0
q
-
3
q
-
2
q
-
1
q
0
q
1
q
2
q
3
0
0
0
0
0
q
-
3
q
-
2
q
-
1
q
0
q
1
q
2
q
3
0
0
0
0
0
q
-
3
q
-
2
q
-
1
q
0
q
1
q
2
q
3
0
0
0
0
0
q
-
3
q
-
2
q
-
1
q
0
q
1
q
2
q
3
0
0
0
0
0
q
-
3
q
-
2
q
-
1
q
0
q
1
q
2
0
0
0
0
0
0
q
-
3
q
-
2
q
-
1
q
0
q
1
0
0
0
0
0
0
0
q
-
3
q
-
2
q
-
1
q
0
&RightBracketingBar;
×
&LeftBracketingBar;
c
-
5
c
-
4
c
-
3
c
-
2
c
-
1
c
0
c
1
c
2
c
3
c
4
c
5
&RightBracketingBar;
where the k dependence (indicating a instant of time) expressly indicated in eq. 2 has here been suppressed.
At present, for every equalization coefficient c
i
k+1
it is known to calculate also its associated leakage value I
i
k+1
at the same instant, independently from the other leakage values. Now, this involves the use of a large number of circuits to calculate each leakage value I
i
k+1
at the same instant. Moreover, the calculated leakage values I
i
k+1
are always relative to the same time instant k preceeding that where equalization coefficients are updated.
The present invention seeks to overcome the above-mentioned drawbacks and provide both a method for stabilizing the operation of fractionally spaced equalizers and a system for stabilizing the operation of fractionally spaced equalizers, whose execution is improved, better performing and more cost effective as compared with the known solutions.
SUMMARY OF THE INVENTION
In this frame, it is the main object of the present invention to provide a method for stabilizing the operation of fractionally spaced equalizers involving a reduced total number of operations for updating the leakage value and, therefore, the equalization coefficients of an adaptive fractionally spaced equalizer.
A further object of the present invention is to provide a method for stabilizing the operation of fractionally spaced equalizers wherein the leakage value c
Della Chiesa Roberto
Leva Angelo
Alcatel
Deppe Betsy L.
Sughrue & Mion, PLLC
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