Signal-to-noise ratio

Signal integrity is the cornerstone of effective fiber optic communication. In this sphere, two metrics stand paramount: Bit Error Ratio (BER) and Q factor. These indicators help engineers assess the performance of optical networks and ensure the fidelity of data transmission. But what do these terms mean, and how are they calculated?

What is BER?

BER represents the fraction of bits that have errors relative to the total number of bits sent in a transmission. It’s a direct indicator of the health of a communication link. The lower the BER, the more accurate and reliable the system.

ITU-T Standards Define BER Objectives

The ITU-T has set forth recommendations such as G.691, G.692, and G.959.1, which outline design objectives for optical systems, aiming for a BER no worse than 10⁻¹² at the end of a system’s life. This is a rigorous standard that guarantees high reliability, crucial for SDH and OTN applications.

Measuring BER

Measuring BER, especially as low as 10⁻¹², can be daunting due to the sheer volume of bits required to be tested. For instance, to confirm with 95% confidence that a system meets a BER of 10⁻¹², one would need to test 3×10¹² bits without encountering an error — a process that could take a prohibitively long time at lower transmission rates.

The Q Factor

The Q factor measures the signal-to-noise ratio at the decision point in a receiver’s circuitry. A higher Q factor translates to better signal quality. For a BER of 10⁻¹², a Q factor of approximately 7.03 is needed. The relationship between Q factor and BER, when the threshold is optimally set, is given by the following equations:

The general formula relating Q to BER is:

A common approximation for high Q values is:

For a more accurate calculation across the entire range of Q, the formula is:

Practical Example: Calculating BER from Q Factor

Let’s consider a practical example. If a system’s Q factor is measured at 7, what would be the approximate BER?

Using the approximation formula, we plug in the Q factor:

This would give us an approximate BER that’s indicative of a highly reliable system. For exact calculations, one would integrate the Gaussian error function as described in the more detailed equations.

Graphical Representation

The graph typically illustrates these relationships, providing a visual representation of how the BER changes as the Q factor increases. This allows engineers to quickly assess the signal quality without long, drawn-out error measurements.

Concluding Thoughts

Understanding and applying BER and Q factor calculations is crucial for designing and maintaining robust optical communication systems. These concepts are not just academic; they directly impact the efficiency and reliability of the networks that underpin our modern digital world.

References

https://www.itu.int/rec/T-REC-G/e

Q is the quality of a communication signal and is related to BER. A lower BER gives a higher Q and thus a higher Q gives better performance. Q is primarily used for translating relatively large BER differences into manageable values.

Pre-FEC signal fail and Pre-FEC signal degrade thresholds are provisionable in units of dBQ so that the user does not need to worry about FEC scheme when determining what value to set the thresholds to as the software will automatically convert the dBQ values to FEC corrections per time interval based on FEC scheme and data rate.

The Q-Factor, is in fact a metric to identify the attenuation in the receiving signal and determine a potential LOS and it is an estimate of the Optical-Signal-to-Noise-Ratio (OSNR) at the optical receiver. As attenuation in the receiving signal increases, the dBQ value drops and vice-versa. Hence a drop in the dBQ value can mean that there is an increase in the Pre FEC BER, and a possible LOS could occur if the problem is not corrected in time.

The Quality of an Optical Rx signal can be measured by determining the number of “bad” bits in a block of received data. The bad bits in each block of received data are removed and replaced with “good” zero’s or one’s such that the network path data can still be properly switched and passed on to its destination. This strategy is referred to as Forward Error Correction (FEC) and prevents a complete loss of traffic due to small un-important data-loss that can be re-sent again later on. The process by which the “bad” bits are replaced with the “good” bits in an Rx data block is known as Mapping. The Pre FEC are the FEC Counts of “bad” bits before the Mapper and the FEC Counts (or Post FEC Counts) are those after the Mapper.

The number of Pre FEC Counts for a given period of time can represent the status of the Optical Rx network signal; An increase in the Pre FEC count means that there is an increase in the number of “bad” bits that need to be replaced by the Mapper. Hence a change in rate of the Pre FEC Count (Bit Erro Rate – BER) can identify a potential problem upstream in the network. At some point the Pre FEC Count will be too high as there will be too many “bad” bits in the incoming data block for the Mapper to replace … this will then mean a Loss of Signal (LOS).

As the normal number of Pre FEC Counts are high (i.e. 1.35E-3 to 6.11E-16) and constantly fluctuate, it can be difficult for an network operator to determine whether there is a potential problem in the network. Hence a dBQ value, known as the Q-Factor, is used as a measure of the Quality of the receiving optical signal. It should be consistent with the Pre FEC Count Bit Error Rate (BER).

The standards define the Q-Factor as Q = 10log[(X1 – X0)/(N1 – N0)] where Xj and Nj are the mean and standard deviation of the received mark-bit (j=1) and space-bit (j=0) ……………. In some cases Q = 20log[(X1 – X0)/(N1 – N0)]

For example, the linear Q range 3 to 8 covers the BER range of 1.35E-3 to 6.11E-16.

Nortel defines dBQ as 10xlog10(Q/Qref) where Qref is the pre-FEC raw optical Q, which gives a BER of 1E-15 post-FEC assuming a particular error distribution. Some organizations define dBQ as 20xlog10(Q/Qref), so care must be taken when comparing dBQ values from different sources.

The dBQ figure represents the dBQ of margin from the following pre-FEC BERs (which are equivalent to a post-FEC BER of 1E-15). The equivalent linear Q value for these BERs are Qref in the above formula.

Pre-FEC signal degrade can be used the same way a car has an “oil light” in that it states that there is still margin left but you are closer to the fail point than expected so action should be taken.

BER and Q Factor