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How to Measure the Bit Error Rate to a Given Confidence Level

Blog Post created by stmichel Employee on Jul 4, 2018

One of the most important ways to determine the quality of a digital transmission system is to measure its Bit Error Ratio (BER). The BER is calculated by comparing the transmitted sequence of bits to the received bits and counting the number of errors. The ratio of how many bits received in error over the number of total bits received is the BER. This measured ratio is affected by many factors including: signal to noise, distortion, and jitter.

BER Equation

The most obvious method of measuring BER is to send bits through the system and calculate the BER. Since this is a statistical process, the measured BER only approaches the actual BER as the number of bits tested approaches infinity. Fortunately, for most cases we need only to test if the BER is less than a predefined threshold. The number of bits required to accomplish this will only depend on the required confidence level and BER threshold. The confidence level is the percentage of tests that the system’s true BER is less than the specified BER. Since we cannot measure an infinite number of bits and it is impossible to predict with certainty when errors will occur, the confidence level will never reach 100%.

To calculate the confidence level (CL), we use the equation:

CL Equation

For our purposes, we will only be concerned with the case where there are zero errors detected. To calculate the BER when there are errors detected and for a mathematical explanation of the origins of these equations, see Total Jitter Measurement at Low Probability Levels, Using Optimized BERT Scan Method. This equation can be rearranged to calculate the number of bits required for a given BER and confidence level (CL).

N490xA Nbits Equation

As an example, if our specified BER is 10-12 and we require a typical confidence level of .95 (95%), the required number of bits to test without any errors is 3x1012. Once we have tested this many bits without error, we can be sure that our actual BER is less than 10-12. Whether the actual BER is 10-12, 10-15 or 3.1x10-14 is unimportant. Again, note that this value is independent of the data rate that the bits are being tested at. To determine the test time required, the number of bits to be tested is simply divided by the bit rate (bits/second). Resulting in the equation:

time equation

At a standard 95% confidence level, we can substitute 0.95 in for CL and obtain a very usable function:

A table of test times at 95% confidence level is given for popular standard bit rates and bit error ratios assuming every single bit/symbol is compared.

 PCI Express 5Gb/s
NRZ
PCI Express 16 Gb/s
NRZ
IEEE 802.3 bj 25.78125 Gb/s
NRZ
IEEE 802.3 bs 26.5625 Gbd
PAM-4
IEEE 802.3 bs 53.125 Gbd
PAM-4
10-15~ 165 hrs~ 51 hrs~ 32 hrs~ 31 hrs~ 16 hrs
10-12~ 10 min~ 3.1 min~ 1.9 min~ 1.9 min~ 1 min
10-9~ 59 secs~ 19 secs~ 12 secs~ 11 secs~ 6 secs
10-6~ 2 µsec~ 0.7 µsec~ 0.4 µsec~ 0.4 µsec~ 0.2 µsec

1. For PAM-4 coded signals, the corresponding symbol error ratio

Table 1. The table shows how long it takes to confirm a target BER with a 95% confidence level for various popular bit rates and interface standards.

For this example, we will simply choose Accumulation end = Full Duration and Accumulation Duration = Fixed Time and set the Accumulation fixed time to 10 seconds.

To measure BER to a given confidence level with J-BERT M8020A or a M8040A high-performance BERT, there are a few things you need to do.

  1. Set up the Error Detector for your configuration. This may include Differential/Normal transmission and/or clock data recovery or line coding.
  2. To start the BER test, open the M8070A system software for BER measurements and select in the menu bar “measurements”.
  3. Set the M8046A under the acquisition parameters, you may choose which

- analyzer hardware to select,
- accumulation end and duration,
- “pass/fail” for a target BER and confidence level,
- “number of bits”, and
- “Full Duration” for selecting a measurement time.

.

Acquisition parameters for the Bit Error Rate (BER) measurement

Figure 1. You can adjust the acquisition parameters for the BER measurement

 

To start and view your results, go to the measurement menu and select “Error Ratio”. Hit the green arrow to start the accumulation the J-BERT M8020A or M8040A will perform the test for 10 seconds. . As you can see in Figure 2, we injected a BER of 10-6 four times button. Now you may view the results. In this example, we measured a data rate of 5 Gb/s for 10 seconds, resulting in a bit count of 50.1 M bits. We measured an Error Count of 4020 bits, resulting in an Error Ratio (BER) of 8.02 * 10-8. According to our calculations above in Table 1, we would need to measure zero errors for ~1 minute at this data rate to ensure a BER of less than 10-11.

 

Error ratio result display in M8070A

Figure 2: Error ratio result display in M8070A

M8040A 64 Gbaud high-performance BERT (Bit Error Ratio Tester)

Figure 3: Keysight M8040A 64 Gbaud high-performance BERT (Bit Error Ratio Tester) for simplified and accurate test of 400 GbE PAM-4 & NRZ devices.

 

BERT M8020A high-performance BERT (Bit Error Ratio Tester)

Figure 4: Keysight J-BERT M8020A high-performance BERT (Bit Error Ratio Tester) for accurate receiver characterization of single- and multi-lane devices running up to 16 or 32 Gb/s. 

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