Tektronix 071-0590-00 user manual Example

BERT Technical Articles

Note that the line through the points in Figure 6 has about the same slope as the dashed lines. This indicates the noise is about Gaussian. As the slope of the plotted line is closer to that of the dashed lines, the noise process is closer to Gaussian, and the extrapolation is more reliable. Departure of the slope from the Gaussian could be due to (a) too few errors measured, leading to inaccurate BER values, (b) the presence of a non-Gaussian noise mechanism such as error bursts, or (c) significant noise in the system before the attenuator. (Noise coming into the receiver with the signal is assumed to be less than that introduced by the first stage in the receiver.)

Whether or not the slope is the expected one, confidence in the extrapolation can always be increased by taking time to plot out the BER-versus-Attenuation curve once down to very low BER. Thus it may take a day or so to test the first system, but subsequent systems can then be tested quickly with the stress-and- extrapolate method.

It is important to measure enough errors that the inaccuracy is low and the extrapolation is valid. Because more than 10,000 errors were measured each time, the inaccuracy of the BER measurement is less than 1% [see Equation (7a)]. This is small enough that the extrapolated results are accurate, even given the magnification effect of extrapolation. To illustrate the importance of measuring enough errors, we will look at an example where measuring too few errors leads to uncertain results.

Example 2

A 1.544-Mbit/s system is stressed with 6 dB of electrical attenuation. In a one-second interval 54 errors are measured––a BER of 54 / 1544000 = 3.5×10−5. But with only 54 errors, the inaccuracy is 14% (see Figure 3 for 68% confidence). Therefore the BER lies between 3.0×10−5 and 4.0×10−5. This uncertainty is indicated by plotting a bar at 6 dB in Figure 6. Then the electrical attenuation is reduced to 4 dB, and 37 errors are measured in 60 seconds. This is a BER of 37 / (60 × 1544000) = 4×10−7. But with 37

errors, the inaccuracy is 16%, and the BER lies between 3.35×10−7 and 4.65×10−7. This is also plotted as a bar in Figure 6. Straight lines passing through the two bars sweep out the gray region shown and

intersect the BER axis anywhere from 2×10−15 to 1.5×10−13.

The large uncertainty of the extrapolated results in this example is mostly due to the few number of errors measured. A good rule is to measure at least 1000 errors for each point. Another guideline is to make the larger attenuation at least 1.5 times the smaller; a greater separation between the two points allows better extrapolation. Also, use as little attenuation as possible so the extrapolation distance is not so great (this involves a trade-off with greater test time).

Stressing can also be used to reduce the time required to show that the unstressed BER is below some specified value. The following example will show how the graph paper provided at the end of the article can be used in this way.

Example 3

A 1.544-Mbit/s system is to have a BER no more than 10−9. This corresponds to an error rate of r = 1544000 × 10−9 = 0.001544 errors per second. For a confidence C = 95% that the BER of the system is less than 10−9, it must test error-free for T = 3 / r = 1943 seconds, or 32 minutes [see Equation (10)]. This test time can be shortened by using stressing.

Suppose a system was just on the limit, with an unstressed BER of the specified 10−9. Make a plot of BER versus Attenuation by starting at BER = 10−9 for Attenuation = 0, and draw a straight line parallel to the dashed lines, as in Figure 7. We see that 3 dB of electrical attenuation would raise a BER of 10−9 to 10−5, or a stressed error rate of rs = 15.44 errors per second. So we stress the system with 3 dB of attenuation and test it for Ts = 3 / rs = 0.194 seconds. If there are no error in that time, then we have 95%

GB1400 User Manual B-39