Error detection/correction and fault detection/recovery – Pulse or data error handling – Error count or rate
Reexamination Certificate
2002-10-21
2003-08-19
Ton, David (Department: 2133)
Error detection/correction and fault detection/recovery
Pulse or data error handling
Error count or rate
C714S705000
Reexamination Certificate
active
06609220
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method and device of measuring a Q-value. More particularly, the present invention relates to a method and device for measuring a Q-value in which the Q-value is calculated from a bit error rate distribution.
2. Description of the Related Art
In a digital receiver, an input signal level is compared with a threshold value at each discrimination time in a discrimination decision circuit, and “1” (there is a signal pulse) and “0” (there is no signal pulse) are determined as data showing the existence of a signal pulse. A signal level received by this digital receiver sways by the influence of noise. Therefore, a distribution of the signal level can be expressed by a probability density function. As shown in
FIG. 4
, marks are defined as follows. A mean value of the signal level of “1” after receiving is &mgr;
1
, standard deviation is &sgr;
1
, a mean value of the signal level of “0” after receiving is &mgr;
0
, and standard deviation is &sgr;
0
. In this case, it is assumed that the probability density function is a Gaussian distribution. At this time, a threshold value level in the discrimination decision circuit is represented by D. Then, a bit error rate BER (D) is given by the following Formula 1.
BER
(
D
)
=
1
2
{
erfc
(
μ
1
-
D
σ
1
)
+
erfc
(
D
-
μ
0
σ
0
)
}
(
1
)
In this case, erfc( ) is a complementary error function and defined by the following Formula 2.
erfc
(
x
)
=
1
2
π
∫
x
∞
ⅇ
-
β
2
2
ⅆ
β
(
2
)
However, in a region in which bit error rate BER(D) is low, it is actually difficult to detect an error in a predetermined measurement time. For example, as shown in [Neal S. Bergano et al., “Margin Measurements in Optical Amplifier System”, IEEE PHOTONICS TECHNOLOGY LETTERS, Vol.5, No.3, March 1993], a ratio of signal to noise (SNR) of a system is evaluated by a Q-value. The Q-value is defined by the following Formula 3.
Q
=
μ
1
-
μ
0
σ
1
-
σ
0
(
3
)
In order to calculate the Q-value by a bit error rate distribution of input data sampled when threshold value level D is changed as described above, conventionally, it is necessary to conduct a calculation in which an inverse function is used.
FIG. 5
is a view showing an arrangement of a conventional Q-value measurement device in which the Q-value is calculated by the bit error rate distribution. In
FIG. 5
, the Q-value measurement device includes: a discriminating section
10
, bit error rate measurement section
20
, memory
30
, and calculating section
40
. The discriminating section
10
includes an amplitude comparator
12
and a data flip-flop (D-FF)
14
. The Q-value is measured by this device as follows. A level of the input signal
1
a
is compared with a level
1
b
of the threshold value by the amplitude comparator
12
, and the comparative output
2
a
is sampled by the data flip-flop (D-FF)
14
in accordance with the time of the clock signal
1
c
. According to the signal
3
a
which has been sampled, the bit error rate measuring section
20
measures a bit error rate and outputs a bit error rate
4
a
. The bit error rate
4
a
is accommodated in the memory
30
together with the threshold value level
1
b.
On the other hand, the calculating section
40
calculates a Q-value by the procedure shown in FIG.
6
. In this case, a row of data of the bit error rates accommodated in the memory
30
is (D
1
,BER(D
1
)), (D
2
,BER(D
2
)), (D
3
,BER(D
3
)), . . . , and (DN,BER(DN)), the number of which is N, wherein &mgr;
0
≦D
1
<D
2
<D
3
. . . <DN≦&mgr;
1
. At first, in n=1, 2, 3, . . . , N, the minimum value BERmin of BER(Dn) is found.
Next, an inverse function erfc−1( ) of the complementary error function is developed in series by degree m (step
52
). While n is being increased from 1 (steps
54
and
62
), erfc−1 (2BER(DN)) is calculated (step
56
) until the bit error rate becomes BER(DN)=BERmin (step
58
). Then, it is accommodated in the memory
30
together with DN (step
60
). In the above case, it is utilized that Formula 1 can be approximated to Formula 4 in the case where &mgr;
0
≦DN<<&mgr;1.
BER
(
D
)
≈
1
2
erfc
(
D
-
μ
0
σ
0
)
(
4
)
Further, the following Formula 5 is obtained from Formula 4.
D≈&sgr;
0
erfc
−1
{2BER(D)}+&mgr;
0
(5)
Therefore, from data (erfc−1(2BER(DN)),DN) (n=1, 2, 3, . . . ) accommodated in the memory
30
in step
60
, a mean value &mgr;
0
of the level “0” and standard deviation &sgr;
0
in the input data are determined by the method of least squares (step
64
).
In the same manner as that described above, in steps
66
to
78
, a mean value &mgr;
1
of the level “1” and standard deviation &sgr;
1
in the input data are determined. Finally, by Formula 3, which is a defining formula of the Q-value, the Q-value is calculated (step
80
).
As described above, by the conventional Q-value measuring device, a calculation of sum of products is conducted by a plurality of times at the maximum, the number of which is (2×m×N), in the two loops in the flow shown in FIG.
6
.
In the above conventional Q-value measurement device, in order to enhance the accuracy of measurement, when the inverse function of the complementary error function is subjected to series development, it is necessary to increase the degree m of series development, and further in order to judge the existence of an input signal, it is necessary to reduce the interval of the threshold value level D, that is, it is necessary to increase N. Therefore, the following problems may be encountered in the conventional Q-value measurement device. When the accuracy of measurement of the Q-value is enhanced, the number of times for the calculation of a sum of products, which is necessary for the measurement of the Q-value, is remarkably increased, and it takes time to calculate the Q-value.
SUMMARY OF THE INVENTION
The present invention has been accomplished to solve the above problems. It is a first object of the present invention to provide a method of measuring a Q-value in which the Q-value can be measured by a small number of times of calculation without directly using the inverse function of the complementary error function.
It is a second object of the present invention to provide a device of measuring a Q-value by which the Q-value can be quickly measured when the Q-value measurement method of the present invention is carried out.
In order to accomplish the first object of the present invention, according to a first aspect of the invention, there is provided a method of measuring a Q-value according to a mean value and standard deviation of a signal level distribution of input data comprising: a first step for calculating a difference between bit error rates of input data sampled by a plurality of threshold values which are a little different from each other; and a second step for further calculating a difference between the difference data obtained in the first step.
According to a second aspect of the invention, there is provided a method of measuring a Q-value according to a mean value and standard deviation of a signal level distribution of input data comprising: a first step for calculating a difference between bit error rates of input data sampled by a plurality of threshold values which are a little different from each other; a second step for further calculating a difference between the difference data obtained in the first step; and a third step for calculating a mean value and standard deviation of the signal level of input data when data obtained in the first and the second step is utilized.
According to a third aspect of the invention, there is provided a method of measuring a Q-value according to a mean value and standard deviation of a signal level distribution of input data comprising: a first step for calcula
Ando Electric Co. Ltd.
Ton David
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