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 xe2x80x9c1xe2x80x9d (there is a signal pulse) and xe2x80x9c0xe2x80x9d (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 xe2x80x9c1xe2x80x9d after receiving is xcexc1, standard deviation is "sgr"1, a mean value of the signal level of xe2x80x9c0xe2x80x9d after receiving is xcexc0, 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                                            ⁢                                              xe2x80x83                                                                              )                                            +                              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                ⁢                                  xe2x80x83                                ⁢                π                                              ⁢                                    ∫              x              ∞                        ⁢                                          ⅇ                                  -                                                            β                      2                                        2                                                              ⁢                              xe2x80x83                            ⁢                              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., xe2x80x9cMargin Measurements in Optical Amplifier Systemxe2x80x9d, 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                        ⁢                          xe2x80x83                        -                          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 1a is compared with a level 1b of the threshold value by the amplitude comparator 12, and the comparative output 2a is sampled by the data flip-flop (D-FF) 14 in accordance with the time of the clock signal 1c. According to the signal 3a which has been sampled, the bit error rate measuring section 20 measures a bit error rate and outputs a bit error rate 4a. The bit error rate 4a is accommodated in the memory 30 together with the threshold value level 1b. 
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 (D1,BER(D1)), (D2,BER(D2)), (D3,BER(D3)), . . . , and (DN,BER(DN)), the number of which is N, wherein xcexc0xe2x89xa6D1 less than D2 less than D3 . . .  less than DNxe2x89xa6xcexc1. At first, in n=1, 2, 3, . . . , N, the minimum value BERmin of BER(Dn) is found.
Next, an inverse function erfcxe2x88x921( ) 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), erfcxe2x88x921 (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 xcexc0xe2x89xa6DN less than  less than xcexc1.                               BER          ⁡                      (            D            )                          ≈                              1            2                    ⁢                      erfc            ⁡                          (                                                D                  -                                      μ                    0                                                                    σ                  0                                            )                                                          (        4        )            
Further, the following Formula 5 is obtained from Formula 4.
D≈"sgr"0erfcxe2x88x921{2BER(D)}+xcexc0xe2x80x83xe2x80x83(5)
Therefore, from data (erfcxe2x88x921(2BER(DN)),DN) (n=1, 2, 3, . . . ) accommodated in the memory 30 in step 60, a mean value xcexc0 of the level xe2x80x9c0xe2x80x9d 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 xcexc1 of the level xe2x80x9c1xe2x80x9d 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 (2xc3x97mxc3x97N), 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.
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 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 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 by the method of least squares when data obtained in the first and the second step are utilized.
According to a fourth 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 when a standard deviation of input data of level xe2x80x9c0xe2x80x9d and a standard deviation of input data of level xe2x80x9c1xe2x80x9d are equal to each other in the signal level distribution of input data; 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 by solving simultaneous linear equations of two variables when data obtained in the first and the second step are utilized.
According to the invention, the mean value and standard deviation of the input signal level are calculated from the measured bit error rate distribution by conducting a difference calculation between the data of measurement of the bit error rate without using the inverse function of the complementary error function. Accordingly, it is possible to reduce the number of times of calculation. Therefore, the measurement of the Q-value can be quickly carried out.
In order to accomplish the second object of the present invention, according to a fifth aspect of the invention, there is provided a device of measuring a Q-value according to a mean value and standard deviation of a signal level distribution of input data comprising: an input data discrimination means for sampling input data by a plurality of threshold levels which are a little different from each other; a bit error rate measuring means for measuring a bit error rate of input data according to a sampling output of the input data discrimination means; and a calculation means for taking in bit error rates of input data measured by the bit error rate measuring means, for calculating a difference between the bit error rates and for calculating a difference between the thus calculated difference data.
According to a sixth aspect of the invention, there is provided a device of measuring a Q-value according to the fifth aspect of the invention, wherein the calculation means calculates a difference between the error rates of input data, further calculates a difference between the calculated difference data, and calculates a mean value and standard deviation of the signal level distribution of input data by utilizing the difference data and also by utilizing the data obtained when the difference data is subjected to difference calculation.
According to a seventh aspect of the invention, there is provided a device of measuring a Q-value according to claim 5, wherein the calculation means calculates a difference between the error rates of input data, further calculates a difference between the calculated difference data, and calculates a mean value and standard deviation of the signal level distribution of input data by the method of least squares by utilizing the difference data and also by utilizing the data obtained when the difference data is subjected to difference calculation.
According to an eighth aspect of the invention, there is provided a device of measuring a Q-value according to a mean value and standard deviation of a signal level distribution of input data comprising: an input data discrimination means for sampling input data by a plurality of threshold levels which are a little different from each other; a bit error rate measuring means for measuring a bit error rate of input data according to a sampling output of the input data discrimination means; and a calculation means for taking in bit error rates of input data measured by the bit error rate measuring means, 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 when a standard deviation of input data of level xe2x80x9c0xe2x80x9d and a standard deviation of input data of level xe2x80x9c1xe2x80x9d are equal to each other in the signal level distribution of input data, for calculating a difference between the obtained difference data, and for calculating a mean value and standard deviation of the signal level distribution of input data by solving simultaneous linear equations by utilizing the difference data and also by utilizing the data obtained when the difference data is subjected to difference calculation.
According to the invention, the method of measuring a Q-value of the present invention is used. Accordingly, it is possible to reduce the number of times of calculation. Therefore, the measurement of the Q-value can be quickly carried out.
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