Transmission of Digital Signals
8.2.1 Transmission Coding
Binary signals cannot normally be transmitted over long distances directly. They must first be coded into a form that guarantees the following parameters:
1. A constant dc level along the transmission path 2. A suitable shaped energy spectrum
3. An adequate timing information content
Many coding structures offer additional desirable features such as the detection of errors, a reduction in the transmission bandwidth, and so on. These possibilities will be examined in Chap. 9.
The simplest transmission code that can satisfy the criteria identified above is the alternate mark inversion (AMI), or bipolar code. The conversion process interprets each binary (logical 1) pulse as a positive or negative mark, taken alternately, while the binary logical zero condition continues to be transmitted as such. The code translation is self-evident from Fig. 8-4.
The transmitted marks may occupy a full time slot (Fig. 8-4c), in which case they are referred to as full baud, or non return to zero (NRZ) pulses. It is more usual however to employ return to zero (RZ) pulses as shown in Fig. 8-4d. The choice between the two schemes is dependent on the energy spectrum exhibited by the code and the consequent difficulty of extracting timing information (clock) from the transmitted line signal. Typically an equal mark/space ratio is used in the case of RZ transmission, although this is not absolutely necessary. (Optical systems based on laser emitters typically employ a 10 to 30 percent mark/space ratio to increase the lifetime of the laser.)
The energy spectra, assuming a random binary input signal, is shown for an AMI coded RZ and a binary line signal in Fig. 8-5. The chosen line code should ideally have a negligible energy at low frequencies; otherwise, physically large components will be required within the equalization circuitry. Furthermore, the attenuation intro-duced by the cable will be very small at low frequencies, and consequently overloading can occur at the repeater inputs if a significant energy level is permitted. Some
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Fig. 8-3 Block schematic of a digital-regenerative reader (cable transmission medium). The power feeding and supervision circuits have not been identified (see Sees. 8.7.1 and 8.7.3).
(a)
(b)
(c) Positive
Transmission of Digital Signals 179
Time slot locations
Clock signal
Binary signal
Nonreturn to zero (NRZ) AMI signal
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Return to zero (RZ) AMI signal mark(d)
Fig. 8-4 Alternate mark inversion (AMI) coding of a binary plus clock signal.
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0.4
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Frequency (i.e., signalling rate)
Fig. 8-5 Relative energy spectra of binary and AMI signals. Random signals are assumed in both plots.
equipments overcome this problem by deliberately increasing the low-frequency attenu-ation by using a high-pass network.
The line code must be chosen such that a sufficient number of transitions, or zero crossings occur. These will be used to stimulate the timing information (clock) extraction circuits.
The AMI code has an equal number of positive and negative marks, and conse-quently guarantees a constant dc level. The absence of a dc component is important for several practical reasons, which are listed below.
180 Transmission
1. The decision threshold at which a mark is considered present or absent will ideally be linear. This cannot be so if the dc level is variable.
2. If an automatic gain control (AGe) is included within the repeater input cir-cuitry, it will most likely use the pulse height as a control reference. A varying dc level causes the pulses to be displaced.
3. The transmission cable usually supplies a dc current to the dependent repeaters, in addition to carrying the message signal. In this case a constant dc level is most important.
The first two drawbacks can be overcome by adopting a more complex circuitry solution. However, the problem of power feeding (3) is much more difficult to solve.
The judicious choice of a transmission code is a most important part of any digital communication system. Distance, information rate, and the complexity of the cir-cuitry required to implement the code will influence the selection. The following example demonstrates this fact.
Conventional practice within telephone exchanges is to keep multiplex and L TAs separate. Consequently, distances of up to 200 m between the multiplexer and LTA are not unknown. In this case a line code that is simple to implement, but requires
Typically a resonant tank circuit, tuned to the peak energy of the coded line signal, is employed. The line signal must first be rectified to produce unipolarity marks, the originally transmitted clock
!C.
Consequently the extracted timing signal will have a frequency!c
at the moment of stimulation, and will thereafter drift toward a new frequency h. The extent of the drift will be dependent on the separation between marks, the values hand!C,
and the Q of the tank circuit. This effect results in an extracted clock that exhibits a continually varying phase, and is commonly known as pattern-induced jitter (see Chap. 10).8.2.3 Regeneration
Let us consider the impairments that occur when a perfectly shaped pulse is transmit-ted over a cable. The pulse will be attenuatransmit-ted, dispersed, and subjectransmit-ted to the effects of random noise. In addition the effect of interference from other cables, that is crosstalk, must be taken into account.
Crosstalk and noise interference problems must be considered in relation to the
Transmission of Digital Signals 181
AMI signal
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pulse amplitude, which is in turn a function of the cable attenuation. The limiting situation largely determines the maximum acceptable repeater separation.
Pulse spreading, due to the effect of dispersion, will in the extreme cause intersymbol interference as shown in Fig. 8-7. Fortunately, however, digital signals are quantized both in amplitude and time; a fact that is exploited within the regeneration process by detecting the presence or absence of pulses at specified instants in time only.
Consequently the level of the line signal outside the sampling instants may be conve-niently ignored.
In theory the regeneration process can provide an almost error-free transmission performance. This ideal may be approached in practice by setting severe limits on the permitted amount of signal degradation before regeneration is deemed necessary.
182 Transmission
Fig. 8-7 Dispersion of the transmitted pulse by the transmission medium.
In this case it is necessary to consider the performance requirement of each regenerator section (i.e., regenerative repeater, plus the preceding length of cable) in isolation.
Let us suppose that the likelihood of a single error occurring in each regenerator section is 10-12, and that a particular transmission path comprises 50 sections. In this case the probability of an error for the complete system will be 50 X 10-12 (see Sec. 8.4.5; this is an approximation). It is interesting to analyze the effect of a localized reduction in the transmission quality.
Let us assume that the possibility of an error increases from 10-12 to 10-7 in one
This example shows that the performance of a digital transmission system is dependent on the weakest link.
It is interesting to compare the above analysis to the case of analog FDM transmis-sion. We shall consider here signal-to-noise ratio, rather than error probability, as a measure of analog transmission quality.
The signal-to-noise ratio (SIN) and error probability P. can be shown, for gaussian noise, to be related by the curve defined in Fig. 8-13 (see Sec. 8.4.3). being shared between all others in the case of analog transmission.
8.2.4 Equalization
Equalization serves two purposes within a digital transmission system. In the first place it provides compensation for those cable parameters that are strongly fre-quency dependent. Secondly, it facilitates simple shaping of the transmitted pulses.
Coaxial and symmetric pair cables can be shown to exhibit the following frequency dependence:
a
=
a+ bv'F +
cF dB/km (8.5)Transmission of Digital Signals 183
where a = attenuation, per unit length
a = constant; typical valuel = almost zero b
=
constant; typical value=
8.64c = constant; typical value = 0.05 F= transmission frequency, MHz
degrees of phase shiftlkm where
/3
= phase variation, per unit lengthL
=
characteristic impedance of the cable C = characteristic capacitance of the cable(8.6)
The above equations are valid at high frequencies, when the ac and dc resistances become comparable. This typically occurs at frequencies above 200 kHz.
The value of constants a and c in Eq. (8.5) is very small. Consequently, unless very high transmission rates are involved, say above 100 MHz, it is possible to ignore the linear term. The attenuation in this case may be considered proportional to the square root of F.
Ideally the equalization circuitry will exhibit a frequency dependence which is the exact inverse of that recorded for the cable. In practice, however, it is necessary to compensate for variations of attenuation with frequency almost exactly, while providing only a limited amount of phase distortion correction.
The regenerator decision circuitry does not require a perfectly rectangular waveform;
a near sinusoidal pulse shape is quite satisfactory. Such a pulse requires less band-width, and this implies a lower level of noise within the input amplification circuitry.
Consequently there would appear to be merit in choosing a pulse shape that keeps noise to a minimum (low bandwidth) yet remains well defined at the decision instants.
Normally the equalization process is performed in two stages. A preequalizer generates a suitable pulse shape, and provides initial compensation for the transmission medium. Further pulse shaping and final compensation for the medium occurs at the postequalizer, situated at the distant end of the 'transmission path. This approach is usually simpler to analyze compared to designing an equalizer that performs the sections, since it implies a transfer function of variable slope.
Eq. (8.5) makes it clear that the equalization of varying cable lengths would be difficult to perform within a single unit. Consequently a two-stage approach is to be recommended. The first stage, the line build out (LBO) unit, functions as a variable length cable simulator, duplicating the frequency-attenuation/phase transfer characteristic for a specified length of cable. The second stage contains an equalizer with a transfer function related to a predetermined reference length of cable. Thus the transfer functions of the actual cable correspond to that of the LBO, plus equalizer.
The LBO units within early equipments were made in a range of fixed values.
These were then selected appropriately during the installation of each repeater.
1 Values refer to a high-quality symmetric-pair cable and have been obtained from: J. Doerner and R.
Pospischil "Communications Engineering," Siemens Review, special issue, vol. XLI, 1974, p. 281.
184 Transmission
This was a time-consuming and expensive process. Furthermore, if an incorrect value of LBO was selected by mistake, the result would be a difficult to identify, degraded performance of the repeater.
Current repeater designs employ automatic line build out (ALBO) units that can compensate for a wide range of attenuations. These devices quantize the level of the received pulses using a peak detector, and switch different passive elements, plus various amplification stages, in and out of circuit as required. In this way the transfer function of the circuit can be modified and equated to different cable lengths automati-cally.
The practical realization of an ALBO circuit is much more difficult than the above description would suggest, especially if a large attenuation range is required. For example, in the United Kingdom the ALBO must compensate for a 37-dB attenuation range (first-order line equipment), and this is extremely difficult to achieve. Further-more, special attention must be paid to the effects of crosstalk when such high amplifier gains are involved.
Unless special precautions are taken the ALBO will move to its most sensitive range when the line signal fails. In this case if the crosstalk from other digital signals has any significant level, the ALBO will amplify them, and pass them as a valid input to the regenerator. This chain of events is very serious since the terminal alarm equipment will not be aware that a fault has occurred.
The problems described above closely correspond to those encountered in the devel-opment of analog FDM transmission systems. However, in the digital case, high linearity assumes less importance compared to good transient response.