ANALOG AND DIGITAL DATA TRANSMISSION

ANALOG AND DIGITAL DATA TRANSMISSION

In transmitting data from a source to a destination, one must be concerned with the

nature of the data, the actual physical means used to propagate the data, and what

processing or adjustments may be required along the way to assure that the received

data are intelligible. For all of these considerations, the crucial question is whether

we are dealing with analog or digital entities.

The terms analog and digital correspond, roughly, to continuous and discrete,

respectively. These two terms are used frequently in data communications in at

least three contexts:

Data

Signaling

Transmission

We can define data as entities that convey meaning. Signals are electric or electromagnetic

encoding of data. Signaling is the act of propagating the signal along a

suitable medium. Finally, transmission is the communication of data by the propagation

and processing of signals. In what follows, we try to make these abstract concepts

clear by discussing the terms analog and digital in these three contexts.

Data

The concepts of analog and digital data are simple enough. Analog data take on

continuous values on some interval. For example, voice and video are continuously

varying patterns of intensity. Most data collected by sensors, such as temperature

and pressure, are continuous-valued. Digital data take on discrete values; examples

are text and integers.

The most familiar example of analog data is audio or acoustic data, which, in

the form of sound waves, can be perceived directly by human beings. Figure 2.10

shows the acoustic spectrum for human speech. Frequency components of speech

may be found between 20 Hz and 20 kHz. Although much of the energy in speech

is concentrated at the lower frequencies, tests have shown that frequencies up to

600 to 700 Hz add very little to the intelligibility of speech to the human ear. The

dashed line more accurately reflects the intelligibility or emotional content of

speech.

Another common example of analog data is video. Here it is easier to characterize

the data in terms of the viewer (destination) of the TV screen rather than the

original scene (source) that is recorded by the TV camera. To produce a picture on

the screen, an electron beam scans across the surface of the screen from left to right

and top to bottom. For black-and-white television, the amount of illumination produced

(on a scale from black to white) at any point is proportional to the intensity

of the beam as it passes that point. Thus, at any instant in time, the beam takes on

an analog value of intensity to produce the desired brightness at that point on the

screen. Further, as the beam scans, the analog value changes. The video image,

then, can be viewed as a time-varying analog signal.

Figure 2.11a depicts the scanning process. At the end of each scan line, the

beam is swept rapidly back to the left (horizontal retrace). When the beam reaches

the bottom, it is swept rapidly back to the top (vertical retrace). The beam is turned

off (blanked out) during the retrace intervals.

To achieve adequate resolution, the beam produces a total of 483 horizontal

lines at a rate of 30 complete scans of the screen per second. Tests have shown that

this rate will produce a sensation of flicker rather than smooth motion. However,

the flicker is eliminated by a process of interlacing, as depicted in Figure 2.11b. The

electron beam scans across the screen starting at the far left, very near the top. The

beam reaches the bottom at the middle after 241 1/2 lines. At this point, the beam is

quickly repositioned at the top of the screen and, beginning in the middle, produces

an additional 241% lines interlaced with the original set. Thus, the screen is

refreshed 60 times per second rather than 30, and flicker is avoided. Note that the

total count of lines is 525. Of these, 42 are blanked out during the vertical retrace

interval, leaving 483 actually visible on the screen.

A familiar example of digital data is text or character strings. While textual

data are most convenient for human beings, they cannot, in character form, be easily

stored or transmitted by data processing and communications systems. Such systems

are designed for binary data. Thus, a number of codes have been devised by

which characters are represented by a sequence of bits. Perhaps the earliest common

example of this is the Morse code. Today, the most commonly used code in the

United States is the ASCII (American Standard Code for Information Interchange)

(Table 2.1) promulgated by ANSI. ASCII is also widely used outside the United

 

States. Each character in this code is represented by a unique 7-bit pattern; thus, 128

different characters can be represented. This is a larger number than is necessary,

and some of the patterns represent "control" characters (Table 2.2). Some of these

control characters have to do with controlling the printing of characters on a page.

Others are concerned with communications procedures and will be discussed later.

ASCII-encoded characters are almost always stored and transmitted using 8 bits per

character (a block of 8 bits is referred to as an octet or a byte). The eighth bit is a

parity bit used for error detection. This bit is set such that the total number of binary

1s in each octet is always odd (odd parity) or always even (even parity). Thus, a

transmission error that changes a single bit can be detected.

Signals

In a communications system, data are propagated from one point to another by

means of electric signals. An analog signal is a continuously varying electromagnetic

TABLE 2.2 ASCII control characters. (Continued on next page.)

Format control

BS (Backspace): Indicates movement of the printing

mechanism or display cursor backward one

position.

HT (Horizontal Tab): Indicates movement of the

printing mechanism or display cursor forward to

the next preassigned 'tab' or stopping position.

LF Fine Feed): Indicates movement of the printing

mechanism or display cursor to the start of the next

line.

VT (Vertical Tab): Indicates movement of the printing

mechanism or display cursor to the next of a

series preassigned printing lines.

FF (Form Feed): Indicates movement of the printing

mechanism or display cursor to the starting position

of the next page, form, or screen.

CR (Carriage Return): Indicates movement of the

printing mechanism or display cursor to the starting

position of the same line.

Transmission control

SOH (Start of Heading): Used to indicate the start of

a heading, which may contain address or routing

information.

STX (Start of Text): Used to indicate the start of the

text and so also indicates the end of the heading.

ETX (End of Text): Used to terminate the text that

was started with STX.

EOT (End of Transmission): Indicates the end of a

transmission, which may have included one or more

'texts' with their headings.

ENQ (Enquiry): A request for a response from a

remote station. It may be used as a 'WHO ARE

YOU' request for a station to identify itself.

ACK (Acknowledge): A character transmitted by a

receiving device as an affirmation response to a

sender. It is used as a positive response to polling

messages.

NAK (Negative Acknowledgment): A character

transmitted by a receiving device as a negative

response to a sender. It is used as a negative

response to polling messages.

SYN (Synchronous/Idle): Used by a synchronous

transmission system to achieve synchronization.

When no data are being sent, a synchronous transmission

system may send SYN characters continuously.

ETB (End of Transmission Block): Indicates the end

of a block of data for communication purposes. It

is used for blocking data where the block structure

is not necessarily related to the processing format.

Information separator

FS (File Separator)

GS (Group Separator)

RS (Record Separator)

US (United Separator)

Information separators to be used in an optional

manner except that their hierarchy shall be FS

(the most inclusive) to US (the least inclusive).

wave that may be propagated over a variety of media, depending on spectrum;

examples are wire media, such as twisted pair and coaxial cable, fiber optic cable,

and atmosphere or space propagation. A digital signal is a sequence of voltage

pulses that may be transmitted over a wire medium; for example, a constant positive

voltage level may represent binary 1, and a constant negative voltage level may

represent binary 0.

In what follows, we look first at some specific examples of signal types and

then discuss the relationship between data and signals.

Examples

Let us return to our three examples of the preceding subsection. For each example,

we will describe the signal and estimate its bandwidth.

Miscellaneous

NUL (Null): No character. Used for filling in time

or filling space on tape when there are no data.

BEL (Bell): Used when there is need to call human

attention. It may control alarm or attention devices.

SO (Shift Out): Indicates that the code combinations

that follow shall be interpreted as outside of the

standard character set until an SI character is

reached.

SI (Shift In): Indicates that the code combinations

that follow shall be interpreted according to the

standard character set.

DEL (Delete): Used to obliterate unwanted characters,

for example, by overwriting.

SP (Space): A nonprinting character used to separate

words, or to move the printing mechanism or display

cursor forward by one position.

DLE (Data Link Escape): A character that shall

change the meaning of one or more contiguously

following characters. It can provide supplementary

controls or permit the sending of data characters

having any bit combination.

DCl, DC2, DC3, DC4 (Device Controls): Characters

for the control of ancillary devices or special terminal

features.

CAN (Cancel): Indicates that the data that precede it

in a message or block should be disregarded (usually

because an error has been detected).

EM (End of Medium): Indicates the physical end of

a tape or other medium, or the end of the required

or used portion of the medium.

SUB (Substitute): Substituted for a character that is

found to be erroneous or invalid.

ESC (Escape): A character intended to provide code

extension in that it gives a specified number of

continuously following characters an alternate

meaning.

In the case of acoustic data (voice), the data can be represented directly by an

electromagnetic signal occupying the same spectrum. However, there is a need to

compromise between the fidelity of the sound, as transmitted electrically, and the

cost of transmission, which increases with increasing bandwidth. Although, as mentioned,

the spectrum of speech is approximately 20 Hz to 20 kHz, a much narrower

bandwidth will produce acceptable voice reproduction. The standard spectrum for

a voice signal is 300 to 3400 Hz. This is adequate for voice reproduction, it minimizes

required transmission capacity, and it allows for the use of rather inexpensive

telephone sets. Thus, the telephone transmitter converts the incoming acoustic

voice signal into an electromagnetic signal over the range 300 to 3400 Hz. This signal

is then transmitted through the telephone system to a receiver, which reproduces

an acoustic signal from the incoming electromagnetic signal.

Now, let us look at the video signal, which, interestingly, consists of both analog

and digital components. To produce a video signal, a TV camera, which performs

similar functions to the TV receiver, is used. One component of the camera

is a photosensitive plate, upon which a scene is optically focused. An electron beam

sweeps across the plate from left to right and top to bottom, in the same fashion as

depicted in Figure 2.11 for the receiver. As the beam sweeps, an analog electric signal

is developed proportional to the brightness of the scene at a particular spot.

Now we are in a position to describe the video signal. Figure 2.12a shows three

lines of a video signal; in this diagram, white is represented by a small positive voltage,

and black by a much larger positive voltage. So, for example, line 3 is at a

medium gray level most of the way across with a blacker portion in the middle.

Once the beam has completed a scan from left to right, it must retrace to the left

edge to scan the next line. During this period, the picture should be blanked out (on

both camera and receiver). This is done with a digital "horizontal blanking pulse."

Also, to maintain transmitter-receiver synchronization, a synchronization (sync)

pulse is sent between every line of video signal. This horizontal sync pulse rides on

top of the blanking pulse, creating a staircase-shaped digital signal between adjacent

analog video signals. Finally, when the beam reaches the bottom of the screen,

it must return to the top, with a somewhat longer blanking interval required. This is

shown in Figure 2.12b. The vertical blanking pulse is actually a series of synchronization

and blanking pulses, whose details need not concern us here.

Next, consider the timing of the system. We mentioned that a total of 483 lines

are scanned at a rate of 30 complete scans per second. This is an approximate number

taking into account the time lost during the vertical retrace interval. The actual

US. standard is 525 lines. but of these about 42 are lost during vertical retrace.

Finally, we are in a position to estimate the bandwidth required for the video

signal. To do this, we must estimate the upper (maximum) and lower (minimum)

frequency of the band. We use the following reasoning to arrive at the maximum

frequency: The maximum frequency would occur during the horizontal scan if the

scene were alternating between black and white as rapidly as possible. We can estimate

this maximum value by considering the resolution of the video image. In the

vertical dimension, there are 483 lines, so the maximum vertical resolution would be

483. Experiments have shown that the actual subjective resolution is about 70 percent

of that number, or about 338 lines. In the interest of a balanced picture, the

horizontal and vertical resolutions should be about the same. Because the ratio of

width to height of a TV screen is 4:3, the horizontal resolution should be about

413 X 338 = 450 lines. As a worst case, a scanning line would be made up of 450

elements alternating black and white. The scan would result in a wave, with each

cycle of the wave consisting of one higher (black) and one lower (white) voltage

level. Thus, there would be 450/2 = 225 cycles of the wave in 52.5 ps, for a maximum

frequency of about 4 MHz. This rough reasoning, in fact, is fairly accurate.

The maximum frequency, then, is 4 MHz. The lower limit will be a dc or zero frequency,

where the dc component corresponds to the average illumination of the

scene (the average value by which the signal exceeds the reference white level).

Thus, the bandwidth of the video signal is approximately 4 MHz - 0 = 4 MHz.

The foregoing discussion did not consider color or audio components of the

signal. It turns out that, with these included, the bandwidth remains about 4 MHz.

Finally, the third example described above is the general case of binary digital

data. A commonly used signal for such data uses two constant (dc) voltage levels,

one level for binary 1 and one level for binary 0. (In Lesson 3, we shall see that

this is but one alternative, referred to as NRZ.) Again, we are interested in the

bandwidth of such a signal. This will depend, in any specific case, on the exact shape

of the waveform and on the sequence of Is and 0s. We can obtain some understanding

by considering Figure 2.9 (compare Figure 2.8). As can be seen, the greater

the bandwidth of the signal, the more faithfully it approximates a digital pulse

stream.

Data and Signals

In the foregoing discussion, we have looked at analog signals used to represent analog

data and digital signals used to represent digital data. Generally, analog data are

a function of time and occupy a limited frequency spectrum; such data can be represented

by an electromagnetic signal occupying the same spectrum. Digital data

can be represented by digital signals, with a different voltage level for each of the

two binary digits.

As Figure 2.13 illustrates, these are not the only possibilities. Digital data can

also be represented by analog signals by use of a modem (modulator/demodulator).

The modem converts a series of binary (two-valued) voltage pulses into an analog

signal by encoding the digital data onto a carrier frequency. The resulting signal

occupies a certain spectrum of frequency centered about the carrier and may be

propagated across a medium suitable for that carrier. The most common modems

represent digital data in the voice spectrum and, hence, allow those data to be prop

agated over ordinary voice-grade telephone lines. At the other end of the line, the

modem demodulates the signal to recover the original data.

In an operation very similar to that performed by a modem, analog data can

be represented by digital signals. The device that performs this function for voice

data is a codec (coder-decoder). In essence, the codec takes an analog signal that

directly represents the voice data and approximates that signal by a bit stream. At

the receiving end, the bit stream is used to reconstruct the analog data.

Thus, Figure 2.13 suggests that data may be encoded into signals in a variety

of ways. We will return to this topic in Lesson 4.

Transmission

A final distinction remains to be made. Both analog and digital signals may be

transmitted on suitable transmission media. The way these signals are treated is a

function of the transmission system. Table 2.3 summarizes the methods of data

transmission. Analog transmission is a means of transmitting analog signals without

regard to their content; the signals may represent analog data (e.g., voice) or digital

data (e.g., binary data that pass through a modem). In either case, the analog signal

will become weaker (attenuated) after a certain distance. To achieve longer distances,

the analog transmission system includes amplifiers that boost the energy in

the signal. Unfortunately, the amplifier also boosts the noise components. With

amplifiers cascaded to achieve long distances, the signal becomes more and more

distorted. For analog data, such as voice, quite a bit of distortion can be tolerated

and the data remain intelligible. However, for digital data, cascaded amplifiers will

introduce errors.

Digital transmission, in contrast, is concerned with the content of the signal. A

digital signal can be transmitted only a limited distance before attenuation endangers

the integrity of the data. To achieve greater distances, repeaters are used. A

repeater receives the digital signal, recovers the pattern of 1s and Os, and retransmits

a new signal, thereby overcoming the attenuation.

The same technique may be used with an analog signal if it is assumed that the

signal carries digital data. At appropriately spaced points, the transmission system

has repeaters rather than amplifiers. The repeater .recovers the digital data from

the analog signal and generates a new, clean analog signal. Thus, noise is not cumulative.

The question naturally arises as to which is the preferred method of transmission;

the answer being supplied by the telecommunications industry and its customers

is digital, this despite an enormous investment in analog communications

facilities. Both long-haul telecommunications facilities and intrabuilding services

are gradually being converted to digital transmission and, where possible, digital

signaling techniques. The most important reasons are

Digital technology. The advent of large-scale integration (LSI) and very largescale

integration (VLSI) technology has caused a continuing drop in the cost

and size of digital circuitry. Analog equipment has not shown a similar drop.

Data integrity. With the use of repeaters rather than amplifiers, the effects of

noise and other signal impairments are not cumulative. It is possible, then, to

transmit data longer distances and over lesser quality lines by digital means

while maintaining the integrity of the data. This is explored in Section 2.3.

Capacity utilization. It has become economical to build transmission links of

very high bandwidth, including satellite channels and connections involving

optical fiber. A high degree of multiplexing is needed to effectively utilize

such capacity, and this is more easily and cheaply achieved with digital (timedivision)

rather than analog (frequency-division) techniques. This is explored

in Lesson 7.

Security and privacy. Encryption techniques can be readily applied to digital

data and to analog data that have been digitized.

Integration. By treating both analog and digital data digitally, all signals have

the same form and can be treated similarly. Thus, economies of scale and convenience

can be achieved by integrating voice, video, and digital data.

TRANSMISSION IMPAIRMENTS

With any communications system, it must be recognized that the received signal will

differ from the transmitted signal due to various transmission impairments. For analog

signals, these impairments introduce various random modifications that degrade

the signal quality. For digital signals, bit errors are introduced: A binary 1 is trans- - formed into a binary 0 and vice versa. In this section, we examine the various

impairments and comment on their effect on the information-carrying capacity of a

communication link; the next lesson looks at measures to compensate for these

impairments.

The most significant impairments are

Attenuation and attenuation distortion

Delay distortion

Noise

Attenuation

The strength of a signal falls off with distance over any transmission medium. For

guided media, this reduction in strength, or attenuation, is generally logarithmic and

is thus typically expressed as a constant number of decibels per unit distance. For

unguided media, attenuation is a more complex function of distance and of the

makeup of the atmosphere. Attenuation introduces three considerations for the

transmission engineer. First, a received signal must have sufficient strength so that

the electronic circuitry in the receiver can detect and interpret the signal. Second,

the signal must maintain a level sufficiently higher than noise to be received without

error. Third, attenuation is an increasing function of frequency.

The first and second problems are dealt with by attention to signal strength

and by the use of amplifiers or repeaters. For a point-to-point link, the signal

strength of the transmitter must be strong enough to be received intelligibly, but not

so strong as to overload the circuitry of the transmitter, which would cause a distorted

signal to be generated. Beyond a certain distance, the attenuation is unacceptably

great, and repeaters or amplifiers are used to boost the signal from time

to time. These problems are more complex for multipoint lines where the distance

from transmitter to receiver is variable.

The third problem is particularly noticeable for analog signals. Because the

attenuation varies as a function of frequency, the received signal is distorted, reducing

intelligibility. To overcome this problem, techniques are available for equalizing

attenuation across a band of frequencies. This is commonly done for voice-grade

telephone lines by using loading coils that change the electrical properties of the

line; the result is to smooth out attenuation effects. Another approach is to use

amplifiers that amplify high frequencies more than lower frequencies.

An example is shown in Figure 2.14a, which shows attenuation as a function

of frequency for a typical leased line. In the figure, attenuation is measured relative

to the attenuation at 1000 Hz. Positive values on the y axis represent attenuation

greater than that at 1000 Hz. A 1000-Hz tone of a given power level is applied to

the input, and the power, Plooo, is measured at the output. For any other frequency

f, the procedure is repeated and the relative attenuation in decibels is

The solid line in Figure 2.14a shows attenuation without equalization. As can

be seen, frequency components at the upper end of the voice band are attenuated

much more than those at lower frequencies. It should be clear that this will result in

a distortion of the received speech signal. The dashed line shows the effect of equalization.

The flattened response curve improves the quality of voice signals. It also

allows higher data rates to be used for digital data that are passed through a modem.

Attenuation distortion is much less of a problem with digital signals. As we

have seen, the strength of a digital signal falls off rapidly with frequency (Figure

2.6b); most of the content is concentrated near the fundamental frequency, or bit

rate, of the signal.

Delay Distortion

Delay distortion is a phenomenon peculiar to guided transmission media. The distortion

is caused by the fact that the velocity of propagation of a signal through a

guided medium varies with frequency. For a bandlimited signal, the velocity tends

to be highest near the center frequency and lower toward the two edges of the band.

Thus, various frequency components of a signal will arrive at the receiver at different

times.

This effect is referred to as delay distortion, as the received signal is distorted

due to variable delay in its components. Delay distortion is particularly critical for

digital data. Consider that a sequence of bits is being transmitted, using either analog

or digital signals. Because of delay distortion, some of the signal components of

one bit position will spill over into other bit positions, causing intersymbol interference,

which is a major limitation to maximum bit rate over a transmission control.

Equalizing techniques can also be used for delay distortion. Again using a

leased telephone line as an example, Figure 2.14b shows the effect of equalization

on delay as a function of frequency.

Noise

For any data transmission event, the received signal will consist of the transmitted

signal, modified by the various distortions imposed by the transmission system, plus

additional unwanted signals that are inserted somewhere between transmission and

reception; the latter, undesired signals are referred to as noise-a major limiting

factor in communications system performance.

Noise may be divided into four categories:

Thermal noise

Intermodulation noise

Crosstalk

Impulse noise

Thermal noise is due to thermal agitation of electrons in a conductor. It is

present in all electronic devices and transmission media and is a function of temperature.

Thermal noise is uniformly distributed across the frequency spectrum and

hence is often referred to as white noise; it cannot be eliminated and therefore

places an upper bound on communications system performance. The amount of

thermal noise to be found in a bandwidth of 1 Hz in any device or conductor is

 

The noise is assumed to be independent of frequency. Thus, the thermal noise,

in watts, present in a bandwidth of W hertz can be expressed as

When signals at different frequencies share the same transmission medium,

the result may be intermodulation noise. The effect of intermodulation noise is to

produce signals at a frequency that is the sum or difference of the two original frequencies,

or multiples of those frequencies. For example, the mixing of signals at

frequencies fi and fi might produce energy at the frequency fi + f2. This derived signal

could interfere with an intended signal at the frequency fi + f2.

Intermodulation noise is produced when there is some nonlinearity in the

transmitter, receiver, or intervening transmission system. Normally, these components

behave as linear systems; that is, the output is equal to the input, times a constant.

In a nonlinear system, the output is a more complex function of the input.

Such nonlinearity can be caused by component malfunction or the use of excessive

signal strength. It is under these circumstances that the sum and difference terms

occur.

Crosstalk has been experienced by anyone who, while using the telephone,

has been able to hear another conversation; it is an unwanted coupling between signal

paths. It can occur by electrical coupling between nearby twisted pair or, rarely,

coax cable lines carrying multiple signals. Crosstalk can also occur when unwanted

signals are picked up by microwave antennas; although highly directional,

microwave energy does spread during propagation. Typically, crosstalk is of the

same order of magnitude (or less) as thermal noise.

All of the types of noise discussed so far have reasonably predictable and reasonably

constant magnitudes; it is thus possible to engineer a transmission system to

cope with them. Impulse noise, however, is noncontinuous, consisting of irregular

pulses or noise spikes of short duration and of relatively high amplitude. It is generated

from a variety of causes, including external electromagnetic disturbances,

such as lightning, and faults and flaws in the communications system.

Impulse noise is generally only a minor annoyance for analog data. For example,

voice transmission may be corrupted by short clicks and crackles with no loss of

intelligibility. However, impulse noise is the primary source of error in digital data

communication. For example, a sharp spike of energy of 0.01-second duration

would not destroy any voice data, but would wash out about 50 bits of data being

transmitted at 4800 bps. Figure 2.15 is an example of the effect on a digital signal.

Here the noise consists of a relatively modest level of thermal noise plus occasional

spikes of impulse noise. The digital data are recovered from the signal by sampling

the received waveform once per bit time. As can be seen, the noise is occasionally

sufficient to change a 1 to a 0 or a 0 to a 1.

Channel Capacity

We have seen that there are a variety of impairments that distort or corrupt a signal.

For digital data, the question that then arises is to what extent these impairments

limit the data rate that can be achieved. The rate at which data can be transmitted

over a given communication path, or channel, under given conditions, is

referred to as the channel capacity.

There are four concepts here that we are trying to relate to one another:

Data rate. This is the rate, in bits per second (bps), at which data can be communicated.

Bandwidth. This is the bandwidth of the transmitted signal as constrained by

the transmitter and by the nature of the transmission medium, expressed in

cycles per second, or hertz.

Noise. The average level of noise over the communications path.

Error rate. The rate at which errors occur, where an error is the reception of

a 1 when a 0 was transmitted, or the reception of a 0 when a 1 was transmitted.

The problem we are addressing is this: Communications facilities are expensive,

and, in general, the greater the bandwidth of a facility, the greater the cost.

Furthermore, all transmission channels of any practical interest are of limited bandwidth.

The limitations arise from the physical properties of the transmission

medium or from deliberate limitations at the transmitter on the bandwidth to prevent

interference from other sources. Accordingly, we would like to make as efficient

use as possible of a given bandwidth. For digital data, this means that we

would like to get as high a data rate as possible at a particular limit of error rate for

a given bandwidth. The main constraint on achieving this efficiency is noise.

To begin, let us consider the case of a channel that is noise-free. In this environment,

the limitation on data rate is simply the bandwidth of the signal. A formulation

of this limitation, due to Nyquist, states that if the rate of signal transmission

is 2W, then a signal with frequencies no greater than W is sufficient to carry the

data rate. The converse is also true: Given a bandwidth of W, the highest signal rate

that can be carried is 2W. This limitation is due to the effect of intersymbol interference,

such as is produced by delay distortion. The result is useful in the development

of digital-to-analog encoding schemes and is derived in Lesson 4A.

Note that in the last paragraph, we referred to signal rate. If the signals to be

transmitted are binary (two voltage levels), then the data rate that can be supported

by W Hz is 2W bps. As an example, consider a voice channel being used, via

modem, to transmit digital data. Assume a bandwidth of 3100 Hz. Then the capacity,

C, of the channel is 2W = 6200 bps. However, as we shall see in Lesson 4, signals

with more than two levels can be used; that is, each signal element can represent

more than one bit. For example, if four possible voltage levels are used as

signals, then each signal element can represent two bits. With multilevel signaling,

the Nyquist formulation becomes

where M is the number of discrete signal or voltage levels. Thus, for M = 8, a value

used with some modems, C becomes 18,600 bps.

So, for a given bandwidth, the data rate can be increased by increasing the

number of different signals. However, this places an increased burden on the

receiver: Instead of distinguishing one of two possible signals during each signal

time, it must distinguish one of M possible signals. Noise and other impairments on

the transmission line will limit the practical value of M.

Thus, all other things being equal, doubling the bandwidth doubles the data

rate. Now consider the relationship between data rate, noise, and error rate. This

can be explained intuitively by again considering Figure 2.15. The presence of noise

can corrupt one or more bits. If the data rate is increased, then the bits become

"shorter" so that more bits are affected by a given pattern of noise. Thus, at a given

noise level, the higher the data rate, the higher the error rate.

All of these concepts can be tied together neatly in a formula developed by

the mathematician Claude Shannon. As we have just illustrated, the higher the data

rate, the more damage that unwanted noise can do. For a given level of noise, we

would expect that a greater signal strength would improve the ability to correctly

receive data in the presence of noise. The key parameter involved in this reasoning

is the signal-to-noise ratio (SIN), which is the ratio of the power in a signal to the

power contained in the noise that is present at a particular point in the transmission.

Typically, this ratio is measured at a receiver, as it is at this point that an attempt is

made to process the signal and eliminate the unwanted noise. For convenience, this

ratio is often reported in decibels:

This expresses the amount, in decibels, that the intended signal exceeds the noise

level. A high S/N will mean a high-quality signal and a low number of required

intermediate repeaters.

The signal-to-noise ratio is important in the transmission of digital data

because it sets the upper bound on the achievable data rate. Shannon's result is that

the maximum channel capacity, in bits per second, obeys the equation

where C is the capacity of the channel in bits per second and W is the bandwidth of

the channel in hertz. As an example, consider a voice channel being used, via

modem, to transmit digital data. Assume a bandwidth of 3100 Hz. A typical value

of S/N for a voice-grade line is 30 dB, or a ratio of 1000:l. Thus,

This represents the theoretical maximum that can be achieved. In

practice,however, only much lower rates are achieved. One reason for this is that

the formula assumes white noise (thermal noise). Impulse noise is not accounted

for, nor are attenuation or delay distortion.

The capacity indicated in the preceding equation is referred to as the errorfree

capacity. Shannon proved that if the actual information rate on a channel is less

than the error-free capacity, then it is theoretically possible to use a suitable signal

code to achieve error-free transmission through the channel. Shannon's theorem

unfortunately does not suggest a means for finding such codes, but it does provide

a yardstick by which the performance of practical communication schemes may be

measured.

The measure of efficiency of a digital transmission is the ratio of CIW, which

is the bps per hertz that is achieved. Figure 2.16 illustrates the theoretical efficiency

 

of a transmission. It also shows the actual results obtained on a typical voice-grade

line.

Several other observations concerning the above equation may be instructive.

For a given level of noise, it would appear that the data rate could be increased by

increasing either signal strength or bandwidth. However, as the signal strength

increases, so do nonlinearities in the system, leading to an increase in intermodulation

noise. Note also that, because noise is assumed to be white, the wider

the bandwidth, the more noise is admitted to the system. Thus, as W increases,

SIN decreases.

Finally, we mention a parameter related to SIN that is more convenient for

determining digital data rates and error rates. The parameter is the ratio of signal

energy per bit to noise-power density per hertz, Eb/No. Consider a signal, digital or

analog, that contains binary digital data transmitted at a certain bit rate R. Recalling

that 1 watt = 1 joulels, the energy per bit in a signal is given by Eb = STb, where

S is the signal power and Tb is the time required to send one bit. The data rate R is

just R = l/Tb. Thus,

The ratio EbINo is important because the bit error rate for digital data is a (decreasing)

function of this ratio. Given a value of EbINo needed to achieve a desired error

rate, the parameters in the preceding formula may be selected. Note that as the bit

rate R increases, the transmitted signal power, relative to noise, must increase to

maintain the required EbINo.

Let us try to grasp this result intuitively by considering again Figure 2.15. The

signal here is digital, but the reasoning would be the same for an analog signal. In

several instances, the noise is sufficient to alter the value of a bit. Now, if the data

rate were doubled, the bits would be more tightly packed together, and the same

passage of noise might destroy two bits. Thus, for constant signal and noise strength,

an increase in data rate increases the error rate.

Example