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Fundamental of Digital Transmission | Analog or Digital

Basically there are two ways in which information of any type can be transmitted over telecommunication media – analog or digital. Analog means that the amplitude of the transmitted amplitude signal varies over a continuous range. Digital transmission means that a stream of on/off pulses are sent on the transmission media. The pulses are referred to as bits. Examples of analog signals are human voice, hi–fi music, temperature reading, etc. While that of digital are data, telegraphy signals.

Telecommunication systems started with the transmission of digital signals. In fact, non–electric signalling systems date back over 2000 years. The Greek General Polybius is known to have used a scheme based on an array of 10 torches in 300 B.C. and Roman armies made extensive use of a form of samaphore signalling. Claude Chappe, Sommering, Wheatstone and Cook were all experimenting with different kinds of Telegraphy till it was perfected by Mores. In all this, only written message was transmitted and message was converted to a coded signal to match the characteristics of a transmission line. Gary, Bandot and others developed other codes which were mainly used in Telegraph network. Thus, we can say, by 1972 most of the basic techniques of digital transmission had been discovered.

In 1876, Alexander Graham Bell invented the Telephone and as means of communication, the telephone was fast, personal and convenient. It needed no training in the use of codes and so made electrical communications directly accessible to the general public. Thus, telephone began to dominate the development of communications. Telephony involves the transmission of analog signals and when a practical amplifying service appeared in the form of the thermionic valve, this also proved suitable for dealing with analog signals. Hence, after 1880, the developing Telecom networks were basically designed to handle analog transmissions and to an increasing extent, the digital transmission in the form of telegraphy had to be adopted to fit in with the characteristics of these networks. By 1950s, the world’s communications systems were based entirely on analog transmission.

However, interest in the digital transmission received an impetus after the publications of classic papers of Nyquist and Shannon. With the invention of pulse code modulation by Reeves in 1938, the basic principles for digitizing analog speech signals were established. However, the technical means for transmitting digitized speech signals were not available at that time. It was not until the transistor came into use that indications of the economic advantages of digital techniques as compared to analog methods became apparent. LSI and VLSI techniques that are now available have made digital communications far more economical as compared to analog methods became apparent.

LSI and VLSI techniques that are now available have made digital communications far more economical  as compared to analog systems. Digital transmission systems are gaining more acceptance in view of : (1) introduction of digital switching systems, (2) the need to transmit non voice signals which are increasingly becoming important instead of the plain old Telephone service, and (3) the introduction of new media like optical fibres, waveguide which are more suitable for digital transmission systems, will be introduced in the network and by the turn of the century, most of the countries would have gone completely digital.

Advantages of Digital Communication

• Fig 1 shows the qualitative representation of the signal to noise ratio along a transmission line. In both analog and digital systems the signal power P is subject to line attenuation which can be compensated by repeaters. However, a main difference exists in the accumulated noise power N. In the transmission of analog signals, this power Na is amplified in linear repeaters by the same factor as the useful signal and the noise contributions from the individual repeater section accumulate. In the digital transmission on the other hand, the signal is practically achieved of the noise Nd with the aid of regenerative repeaters. Residual noise may only become effective in the form of digital errors and jitter due to regeneration, reshaping and retiming (3 Rs.) carrier out section by section, only the digital errors are accumulated while the noise is not. The need to recognize only the presence or absence of a pulse makes the system highly immune from noise. Thus, the transmission quality is almost independent of distance and method of transmission involved. This is of particular value in transmission paths subject to extreme interference such as for instance in space flights or in communications with interplanetary probes.

• Compatibility of different media : Cables, radio links, switching equipment can be interconnected without decoding the digital signals by means of relatively cheap interface equipment which contributes little or no impairment to the signal. There is thus no need to take any consideration of the particularities of the original signal.
• Compatibility of different traffic : Any digital media of suitable capacity can carry encoded speech, telephone signalling, telegraphy, digital data, encode visual information or an arbitrary mixture there of. The desperate requirements of these signals can be handled in the terminals and have no mutual interference between different types of traffic. The introduction of ISDN is thus possible.
• Multiplexing, demultiplexing, branching of digital signals produce no additional interference as noise in analog communications. Hence, these can be done as often as necessary. Moreover, all bits are subject to same interference and hence all TDM channels are treated equally, i.e. there are no channels of inferior quality as for instance in FDM transmission certain channels at the edges of the tranmission bands.
• Level fluctuations occurring during transmission have no effect on the primary signal recovered in the receiver. In FDM, however, sophisticated equipments are required to maintain the level more or less constant.
• Economies in certain applications : PCM is inherently cheaper than the FDM and the investment needed can be made progressively as the traffic growth justifies it. Economies can be achieved by combining services already of a digital nature. Digital signals can be switched by digital exchanges without demodulation.
• Possibility of novel facilities : The digital mode lends itself to such things as cryptography, storage and various forms of digital processing not accomplished otherwise.
• Applicability to other transmission media : Optical fibre waveguides multiple access satellites appear to be more suited digital than to analog information.
• Applicability to extremely difficult transmission paths.
• Simpler equipment : There is no need of complicated filter and analog amplifiers for various ranges.
• Easy repeatability of design.

Main Obstacles to Digitalisation

• Spectrum width : For example the bandwidth required for 2700 channels is 12 MHz in the case of analog systems where as band width required in the case of 1920 channels is as much as 140 MHz. Thus, band width required is very large in the case of digital signals, this results consequently :
• Less efficient use of carrier capacity in terms of telephone channels;
• Working at very high frequencies;
• Need of multi–level modulation for radio transmission;
• Voice interpolation required for satellite communication;
• Higher sensitivity to selective transmissions caused by propagation.
• Different transmission of TV signals : Digital transmission of TV signals requires a very wideband if redundancy reduction is not used which, however, involve higher cost and quality problems for moving images.
• Reliability and power consumption : For the same transmitted signals, digital transmission equipments are in general more complex than analog ones.

Eqpt.	Analog	Digital
Line repeaters (12 MHz Vs 140 Mb/s)	2 W	4 W
1+1 Radio repeater (1800 FDM Vs 140 Mb/s)	200 W	600 W

Means to overcome digital transmission limits:

• Evolution of high frequency components and technology
• Hybrid circuits
• High speed integrated circuits
• FET’s amplifiers (for radio transmission)
• Introduction of large scale integrated components (LSI, VLSI)
• Use of microprocessor (for functions such as adaptive combination, voice interpolation etc.).
• increased circuit compactness (TV encoding, Signal processing, etc.).
• reduced power consumption.

Pulse Transmission

Channel Capacity or Information Rate

In general, the capacity of a channel for information transfer is proportional to its bandwidth. Two major theories that relate to the amount of data that can be transmitted based upon the bandwidth of a medium are the Nyquist Relationship and Shannon’s Law. Prior to discussing these theories, it is important to understand the difference between bit and baud due to the confusion that dominates the use of these terms.

Bit versus baud

The binary digit or bit is a unit of information transfer. In comparison, the term baud defines a signalling change rate, normally expressed in terms of signal changes per second.

In a communications system, the encoding of one bit per signal element results in equivalency between bit and baud. That is, an information transfer rate of X bits per second is carried by a signalling change rate of X baud, where each baud signal represents the value of one bit. Now, suppose our communications system was modified so that two bits are encoded into one signal change. This would result in the baud rate being half the bit rate, which obviously makes bit and baud non–equivalent. The encoding of two bits into one baud is known as dibit encoding.

Nyquist relationship

In 1928, Harry Nyquist developed the relationship between the bandwidth and the baud rate on a channel as

B = 2W

where B is the baud rate and W the bandwidth in Hz.

The Nyquist relationship was based upon a problem known as intersymbol interference which is associated with band–limited channels. If a rectangular pulse is input to a band–limited channel, the bandwidth limitation of the channel results in a rounding of the corners of the pulse. This rounding results in the generation of an undesired signal in which the leading and trailing edges formed due to signal rounding can interfere with both previous and subsequent pulses. This signal interference is illustrated in Fig.3.

Pulse response through a band–limited channel. The bandwidth limitation of a channel causes the leading and trailing edges of a pulse to interfere with other pulses as the signal change exceeds twice the bandwidth of a channel. This condition is called intersymbol interference.

The Nyquist relationship states that the rate at which data can be transmitted prior to intersymbol interference occurring must be less than or equal to twice the bandwidth in Hz. Thus, an analog circuit with a bandwidth of 3000 Hz can only support baud rates at or under 6000 signaling elements per second.

Since an oscillating modulation technique such as amplitude, frequency or phase modulation halves the achievable signaling rate, a twisted pair telephone circuit supports a maximum signaling rate of 3000 baud.

Shannon’s law

In 1948, Claude E. Shannon presented a paper concerning the relationship of coding to noise and calculated the theoretical maximum bit rate capacity of a channel of bandwidth W Hz. The relationship developed by Shannon is given by

C  =  W log₂ (1+S/N)

where

C  = capacity in bits per second,

W = bandwidth in Hz,

S =  Signal power at the receiver input

N = power of thermal noise =  No.W

Bit Baud Rate, Symbols

We wish to transmit f_b bits/s in a baseband channel having a bandwidth of B Hz. In most applications, the transmission system is considered to be more cost effective, if, in a given bandwidth, more bits/sec can be transmitted. If fb, the transmission rate, is normalized to a Bandwidth B = 1 Hz, then the system efficiency can be characterized in terms of transmitted bits per second per Hz (b/s/Hz).

Nyquist theorem on minimum Bandwidth transmission systems states that it is possible to transmit fs independent symbols in a channel (low pass filter) having a bandwidth of only B = fn = fs/2 Hz.

If the digital signal changes at a rate of N bits/sec, then the modulated phase would change at a rate of N/2 symbols/sec. This rate of change of symbols is known as the Baud–rate (R).

Nyquist Criteria, Roll Off Factor

Give an ideal low pass change of Bandwidth B_o Hz, it is possible to transmit independent binary symbols through the channel at the maximum rate R_b = 2 B_o bits/sec. Equivalently, given a bit rate R_b = 1/T_b, the Bandwidth B_o = 0.5 R_b defines the minimum transmission bandwidth acceptable for distortion-less transmission. The Bandwidth B_o so defined is called Nyquist Bandwidth.

For practical usefulness, however, the minimum Bandwidth Solution has to be modified. It is done by (1) permitting a channel Bandwidth B in excess of the Nyquist Bandwidth B_o, and (2) introducing transition region shaped as one–half of a raised–cosine. The width of the transition region is controlled by the role off factor x, defined as excess bandwidth (i.e. the amount by which the channel Bandwidth B exceeds the Nyquist Bandwidth B_o) divided by the Nyquist Bandwidth itself.

In the raised cosine solution, flexibility exists in the selection of the transmitting and receiving filters. This flexibility can be exploited to provide noise immunity. In particular, given a base-band channel of transfer function H(f) and a message source of known waveform, we can optimize the transfer function H_T(f) of the transmitting filter and the transfer function H_R(f) of the receiving filter, so that the following 3 requirements are jointly satisfied.

• ISI is Zero.
• Probability of symbol error is minimized.
• Constant power is transmitted.
• Nyquist BW required has been defined as equal to half the symbol rate, i.e. N.BW = R/2

Thus, for a 140 Mb/s signal, the symbol rate = 70 Mb/s if QPSK is employed. The minimum BW needed for transmitting so many symbols without ISI is 35 MHz. This is the one sited filter Bandwidth. The total RF BW would include both sides of the spectrum and be equal to 70 MHz. This is the theoretical minimum BW.

If 16 PSK is used, then Baud rate = 35 MB/s.

Nyquist BW  =  17.5 MHz.

Total channel BW  =  35 MHz.

What is Inter Symbol Interference (ISI) ?

Intersymbol interference is interference between adjacent symbols due to pulse spreading by band-limited channels.

Because of the delay (as the bandwidth of the channel is finite) the delayed version of waveform of one sampling interval will extend into the next sampling interval leading to ISI.

Suppose that binary information is transmitted using a pulse type waveform. A 1 Volt pulse is used to send a 1 and 0 Volt pulse for a binary 0. When this waveform goes through the system, it gets distorted. Among other effects, any sharp corners of the wave are rounded, since the system cannot pass infinite frequency. Therefore, the values in previous sampling intervals affect the value within the present interval. If for example, we send a long string of 1s, we would expect the channel output to eventually settle to a constant 1. Similarly, if we send a long string of 0’s, the output should eventually settle towards 0. If we alternate 1’s and 0’s, the output might resemble a sine wave, depending upon the frequency cut off of the channel.

Therefore, if we examine a single interval in which a binary 1 is being transmitted, the output waveform within that interval will depend upon the particular sequence that preceded the interval in question. If we now plot all possible waveforms within the interval, including those for a 1 and those for a 0 in the interval, we get a pattern that resembles a picture of an eye.

The following figure (Fig.6) shows some representative transmitted waveforms and the resulting receiver waveform. The eye pattern is sketched.

The eye pattern is, therefore, the superposition of many waveforms within one sampling interval, the components of this composite waveform being the signals due to all possible preceeding data strings. The number of individual waveforms contributing to the eye pattern depends upon the memory of the system. For example, if the system transient response extends over six sampling intervals, the particular pattern of six most recent bits determines the waveform within the interval.