Digital Transmission Systems: Eye Diagram and Bit Error Ratio

Let's take a look and evaluate existing methods for assessing signal quality.

Eye diagram analysis

An eye diagram is a convenient (and ingeniously simple!) graphical method for assessing the quality of a digital signal. It is the result of the superposition of all possible pulse sequences over a period of time equal to two clock intervals of the linear signal.

The simplest example is a diagram for a ternary (logical levels of -1, 0, +1) linear signal with a raised cosine pulse shape of the regenerator input signal. The eye diagram's eye-opening area (or just "opening") is clearly visible, within which the signal identification operation should be carried out for each of the two designated levels. The horizontal lines marked as '-1', '0', and '+1' correspond to the pulse amplitudes with no interference, and the vertical lines at each clock interval T correspond to the correct identification moments.

The decision-making process is represented by two crosses in each "opening" of the eye diagram. The vertical segment of each cross determines the moment of decision, and the horizontal segment represents its level. Error-free regeneration of the digital signal is guaranteed if there is a certain area within the proximity of each cross within which the signal is recognized.

Interference leads to a reduction in this area compared to the ideal case. The minimum distance between the centers of the crosses and the edges of the "eye" serves as a measure of the interference protection margin. The margin decreases due to distortions in the pulse shape and imperfections in the decision-making process. The first reason leads to a decrease in the "opening" of the eye diagram, and the second leads to a movement of the decision point along the edges of the eye. Distortions arising as a result of these two reasons are usually divided into amplitude and time, corresponding to the vertical and horizontal shifts of the decision point. For the convenience of further explanation, we assume that the decision point remains put and the 'opening' decreases.

The degree of 'squinting' of the eye diagram is determined by the resulting distortions caused by intersymbol interference, echo signals, changes in the amplitude of pulses at the output of the regenerator, and errors in the thresholds of trigger devices. The result of these influences is ∆A, the vertical component of eye-diagram distortion. It is the value for the edges of the ideal eye diagram to be shifted.

Time distortions of the eye diagram ∆T, including the discrepancy between the decision moments and their static values and jitter, are usually taken into account in the horizontal shift of the "eye" edges.

Obviously, to compensate for the deterioration of the real eye diagram compared to the ideal one, the signal-to-noise ratio must be increased by ∆S/N = 20×lg(H/h) dB, where H and h stand for the vertical "opening" of the ideal and real eye diagram, respectively.

Bit error ratio

The error rate is a key quality parameter in Digital Transmission Systems (DTS). There are many error metrics; let's describe a few. The simplest is the bit error ratio (BER) or jitter, which is relevant for VoIP telephony or inter-network gateways. This is a reminder that BER should be understood as the ratio of corrupt bits to the total number transmitted.

It should be noted that BER depends on the number of bits transmitted. For example, a long sequence of identical symbols can cause low-frequency amplitude modulation and a persistent jitter, resulting in increased errors. Standard test sequences are used to ensure a correct comparison of different transmission systems, and each standard transmission speed has its own test sequence. Their properties are close to Gaussian noise but have a certain loop period. Therefore, they are called not just random but pseudo-random sequences (PRS) or pseudo-random bit sequences (PRBS).

It should be emphasized that the BER estimate will only be absolutely accurate if the number of bits transmitted is infinite. Strictly speaking, when their number is limited, we do not get the probability of an event BER, but its estimate BERT. Surely, the confidence level (CL) of this estimate, also called the confidence interval (CI), depends on the number of errors caught and on the total number of transmitted bits N.

This is confirmed by the data in the table below, which shows the required values of the normalized duration NxBER depending on the number of registered errors E and the confidence level CL of the estimate: the greater the number of registered errors and the confidence level CL of the estimate, the greater the number of bits that must be transmitted.

A typical BER measurement scheme involves a BER tester test bit (character) sequence generator, a test object (regenerator, DTS section, etc.), and a BER tester error detector.

The BER tester generator forms test signals fed to the input of the object under test. The signal generator under test is also the signal source for the error detector of the BER tester.

The tested object can be geographically co-located with the BER tester or be at a remote spot. In any case, the test object must be taken out of service, and the signal from its output must be directed to the receiver input of the BER tester. As telecom specialists call it, a measuring loop must be organized.

The error detector receives a test signal from the output of the object under test or generates an exact copy of this signal autonomously. The generator test signal is compared bit by bit with the signal coming from the object's output under test. The detector records each signal difference as a bit error.

An error detector ensures the necessary in-phase of the two indicated signals by providing the required delay of the signal from the generator output. Signal phasing is usually performed during the calibration of the BER tester.

The test signals of BER testers are standardized. As noted above, the information signal in BER testers is simulated in the form of so-called pseudo-random sequences (PRS or PRBS). They are formed in accordance with standard algorithms and differ in the number of generated symbols M = 2k–1, where k is an integer.

BER tester generators provide the ability to create custom test sequences, usually called codewords.

A clear disadvantage of BER is the need to take the tested object out of service (OoS), which is acceptable when equipping or rebuilding the facility and is inconvenient if the DSL is already in operation. More than that, BER is quite good for assessing the impact of single noise occurrences caused by Gaussian processes, such as self- and transient noise. At the same time, in any real communication system, there are packets of such errors (also called serial errors). Therefore, without knowledge of the time structure of errors in the communication system, it is impossible to effectively localize damage and accumulate adequate information about the quality of the design and installation of equipment. In fact, the BER parameter alone is not enough to correctly assess the performance of a DSL. More adequate quality indicators of DSLs are needed, taking into account the interference structure, with the ability to monitor them during normal operation of the communication system ('In Service Monitoring,' ISM), such as recommendations G.821 and G.826.