In this chapter we will look at the lowest layer depicted in the hierarchy of Fig. 1-24. It defines the mechanical, electrical, and timing interfaces to the network. We will begin with a theoretical analysis of data transmission, only to discover that Mother (Parent?) Nature puts some limits on what can be sent over a channel.
Then we will cover three kinds of transmission media: guided (copper wire and fiber optics), wireless (terrestrial radio), and satellite. This material will provide background information on the key transmission technologies used in modern networks.
The remainder of the chapter will be devoted to three examples of communication systems used in practice for wide area computer networks: the (fixed) telephone system, the mobile phone system, and the cable television system. All three use fiber optics in the backbone, but they are organized differently and use different technologies for the last mile.
The Theoretical Basis for Data Communication
Information can be transmitted on wires by varying some physical property such as voltage or current. By
representing the value of this voltage or current as a single-valued function of time, f(t), we can model the
behavior of the signal and analyze it mathematically. This analysis is the subject of the following sections.
Fourier Analysis
In the early 19th century, the French mathematician Jean-Baptiste Fourier proved that any reasonably behaved
periodic function, g(t) with period T can be constructed as the sum of a (possibly infinite) number of sines and
cosines:
where f = 1/T is the fundamental frequency, an and bn are the sine and cosine amplitudes of the nth harmonics (terms), and c is a constant. Such a decomposition is called a Fourier series. From the Fourier series, the function can be reconstructed; that is, if the period, T, is known and the amplitudes are given, the original function of time can be found by performing the sums of Eq. (2-1).
A data signal that has a finite duration (which all of them do) can be handled by just imagining that it repeats the entire pattern over and over forever (i.e., the interval from T to 2T is the same as from 0 to T, etc.).
The an amplitudes can be computed for any given g(t) by multiplying both sides of Eq. (2-1) by sin(2pkft) and then integrating from 0 to T. Since only one term of the summation survives: an. The bn summation vanishes completely. Similarly, by multiplying Eq. (2-1) by cos(2pkft) and integrating between 0 and T, we can derive bn. By just integrating both sides of the equation as it stands, we can find c. The results of performing these operations are as follows:
Bandwidth-Limited Signals
To see what all this has to do with data communication, let us consider a specific example: the transmission of the ASCII character ''b'' encoded in an 8-bit byte. The bit pattern that is to be transmitted is 01100010. The lefthand part of Fig. 2-1(a) shows the voltage output by the transmitting computer. The Fourier analysis of this signal yields the coefficients:
Figure
2-1.
(a) A binary signal and its root-mean-square Fourier amplitudes.
(b)-(e) Successive
approximations to the original signal.
The root-mean-square amplitudes,
, for the first few terms are shown on the right-hand side of Fig. 2-
1(a). These values are of interest because their squares are proportional to the energy transmitted at the corresponding frequency.
No transmission facility can transmit signals without losing some power in the process. If all the Fourier components were equally diminished, the resulting signal would be reduced in amplitude but not distorted [i.e., it would have the same nice squared-off shape as Fig. 2-1(a)]. Unfortunately, all transmission facilities diminish different Fourier components by different amounts, thus introducing distortion. Usually, the amplitudes are transmitted undiminished from 0 up to some frequency fc [measured in cycles/sec or Hertz (Hz)] with all frequencies above this cutoff frequency attenuated. The range of frequencies transmitted without being strongly attenuated is called the bandwidth. In practice, the cutoff is not really sharp, so often the quoted bandwidth is from 0 to the frequency at which half the power gets through.
The bandwidth is a physical property of the transmission medium and usually depends on the construction,
thickness, and length of the medium. In some cases a filter is introduced into the circuit to limit the amount of
bandwidth available to each customer. For example, a telephone wire may have a bandwidth of 1 MHz for short
distances, but telephone companies add a filter restricting each customer to about 3100 Hz. This bandwidth is
adequate for intelligible speech and improves system-wide efficiency by limiting resource usage by customers.
Now let us consider how the signal of Fig. 2-1(a) would look if the bandwidth were so low that only the lowest
frequencies were transmitted [i.e., if the function were being approximated by the first few terms of Eq. (2-1)].
Figure 2-1(b) shows the signal that results from a channel that allows only the first harmonic (the fundamental, f)
to pass through. Similarly, Fig. 2-1(c)-(e) show the spectra and reconstructed functions for higher-bandwidth
channels.
Given a bit rate of b bits/sec, the time required to send 8 bits (for example) 1 bit at a time is 8/b sec, so the frequency of the first harmonic is b/8 Hz. An ordinary telephone line, often called a voice-grade line, has an artificially-introduced cutoff frequency just above 3000 Hz. This restriction means that the number of the highest harmonic passed through is roughly 3000/(b/8) or 24,000/b, (the cutoff is not sharp).
For some data rates, the numbers work out as shown in Fig. 2-2. From these numbers, it is clear that trying to send at 9600 bps over a voice-grade telephone line will transform Fig. 2-1(a) into something looking like Fig. 2-
1(c), making accurate reception of the original binary bit stream tricky. It should be obvious that at data rates much higher than 38.4 kbps, there is no hope at all for binary signals, even if the transmission facility is completely noiseless. In other words, limiting the bandwidth limits the data rate, even for perfect channels. However, sophisticated coding schemes that make use of several voltage levels do exist and can achieve higher data rates. We will discuss these later in this chapter.
