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Bit Error Rate (BER) and Eb/No
Measured in exponential notation, the bit error rate (BER) quantifies the performance level of the digital link. A BER of 1 x 10-3 expresses the probability of one bit error occurring in a block of 1,000 bits. A BER of 5.0 x 10-5 is superior to a lower BER of 9.0 x 10-4 because there is a probability that less bit errors will occur. BER also may be expressed as 5E-4 or 3E-3, which is the equivalent to a BER of 5 x 10-4 or 3 x 10-3.
The quantifying measure of a digital satellite link is the Eb/No: the ratio of bit energy to noise density (Figure 2-22). QPSK modulation has the ability to achieve a given BER at a relatively low Eb/No when used for wide-band applications such as satellite communications.
The received Eb/No, which is expressed in decibels (dB), represents the signal-to-noise ratio of the receiving system. Another way to gauge the importance of Eb/No is to realize that as Eb/No increases the number of bit errors decreases. Error correction is used to achieve a given BER at as small a value of Eb/No as possible. The DVB specification calls for a worst-case bit error probability of 1E-11. This equates to not more than one bit error in a 38 Mbit/s data stream every 45 minutes, or no more than one bit error in a 8 Mbit/s digital TV program service every 3.5 hours.
Figure 2-22. A typical example of the relationship of Eb/No to bit error rate (BER).
The quantifying measure of an analog channel is the carrier-to-noise ratio, or C/N. A spectrum analyzer can be used to measure the C/N of the satellite receiving system. This C over N value represents the difference in decibels between the peak carrier and the average noise level hiding under the signal. To do this the technician first measures the carrier peak, and then jogs the antenna away from the satellite until only the noise floor can be measured. The technician also must make one mathematical correction to these numbers, which factors in the bandwidth of the satellite signal as well as the bandwidth of the filter built into the spectrum analyzer.
For example, the following measurement takes into account the performance characteristics of a popular portable spectrum analyzer model. As can be seen on the spectrum analyzer display, the carrier has an amplitude of -54 dB while the noise floor is -72 dB.
In the case of our spectrum analyzer model, the correction factor is equal to the satellite transponder bandwidth divided by the spectrum analyzer filter bandwidth × 1.5. (Other spectrum analyzers will have their own specific C/N measurement procedures, filter bandwidths, and recommended correction factors.) If the satellite transponder bandwidth is 36 MHz and the analyzer bandwidth filter is 8 MHz wide, then the correction factor would equal (36 divided by 8) times 1.55, or 6. 75.
The actual noise equals the noise floor measurement plus the correction factor of 6.75. (Actual noise: -72 dB + 6.75 = -65.25 dB; the C/N is the carrier minus the actual noise (C/N: -65.25 dB - (-54 dB) = 11.25 dB).
The quantifying measure of a digital channel is the bit energy to noise density ratio, or the Eb/No. Essentially, the received Eb/No represents the signal-to-noise ratio that the receiving system achieves. Another way to gauge the importance of Eb/No is to realize that as Eb/No increases, the number of bit errors decreases. Forward error correction is used to achieve a given BER at as small a level of Eb/No as possible.
The Eb/No is the carrier power C divided by the data rate fb. Since data rate and Eb are associated, they must both either include or exclude the forward error correction overhead. As we previously have seen with the formula for the G/T, simple subtraction can be used to solve the equation when all values have already been converted to decibels.
Eb/No = C (dBm) - No (dBm/Hz) - 10log fb.
| Data Test Sets |
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Test Sets We use test sets to send test data across the system where it can either be received and analysed by a compatible test set for one way testing or looped round and sent back to be received and analysed by the same test set. What the test sets are looking for is errors in the received data. Since they know what was originally transmitted they can accurately monitor errors in transmission. Bit Error Rate If you have sent 1,000,000 bits of data and receive 1 error then that is an error rate of 1 in 1 million bits or 1 x E-6. Acceptable error rates start from 1 error in 10 million bits or 1 x E-7. To measure this kind of error rate accurately the tests have to run over time to build up a statistical picture of the errors. 1 error in 24 hours and then 2 million in the next 10 minutes is not a good link but for the first 24 hours is was a superb link. Eb/No & Bit Error Rates Eb/N0 is a specification of the satellite modem which states the size of the signal for a given data rate to give a specified bit error rate. It comprises of the energy per bit in a 1 Hz bandwidth. In order to calculate this we need the data rate. Data Rate = 64 kBps We simply subtract 10 Log this data rate from the measured C/N0 to give the Eb/N0. Eb/N0 = 54 dBc/Hz - 48 = 6 Thus, to find the required C/N0 we simply rearrange: C/N0 = 10 Log Data Rate + Eb/No required C/N0 = 48 + 6 = 54 dBc/Hz The modem manufacturer states the Eb/N0 for a given data rate so you can easily know the required C/N0 to acheive this. |
In any satcom system, there is a need to test the path of the data from end to end to ensure that the bit error rate (amount of errors) is minimal or error free.
