DATA RATE AND BANDWIDTH RELATIONSHIP

The data communication channel is the most important facility in the whole communication process. The greater the bandwidth of a channel, the higher the cost of the facility. Thus, a given bandwidth must be used as efficiently and prudently as possible. For a given level of noise, the maxi-mum data rate is determined by the bandwidth of the channel. A given channel has a limited bandwidth determined by the physical properties of the medium. Data rate through a channel is determined by available band-width, number of levels present in the signal, and also the amount of noise present, i.e., quality of the channel.

The Nyquist bit rate for a noiseless channel and the Shannon capacity for a noisy channel are the two yardsticks for determining the maximum data rate through a channel. The maximum theoretical data rate, in bps, is given by 2 × B × log₂L, where B is the bandwidth and L is the number of levels in the signaling element. Thus, for a given bandwidth, if the number of levels is increased, the corresponding bit rate would increase. Although it is true theoretically, data retrieval at the receiver would be more and more difficult because of presence of so many levels. As per Shannon, the channel capacity, in presence of noise, is given by B × log₂(1 + SNR). SNR is the signal-to-noise ratio at the receiver where the received signal is processed and the bits are retrieved. This formula does not contain the number of levels present in the signal element. Thus, channel capacity increases with either bandwidth or signal strength. However, with increasing signal strength, nonlinearities in the system also increases as also the intermodulation noise. Again, since the noise is assumed to be white, the greater the bandwidth, more noise would get into the system. This effectively decreases the SNR with increasing bandwidth.

Data Communication 13

1.12 MULTIPLEXING

Bandwidth is one of the most precious resources in communication, and its judicious use is seemingly the main challenge to the communication engineers. If a low bandwidth (narrow bandwidth) signal occupies a link whose bandwidth is high, then the link’s resources are woefully utilized.

A communication engineer’s task is to utilize the available bandwidth as fully as possible. Multiplexing is used to utilize the bandwidth of a link most efficiently and effectively.

1.12.1 introduCtion

Multiplexing is the transmission of multiple signals simultaneously over a single link. Although they share the same medium for transfer of information, they do not necessarily occur at the same time or occupy identical bandwidth.

Metallic wires, coaxial cables, satellite microwave, optical fiber, etc., may act as the transmission medium. At the receiver, demultiplexing is done to retrieve the original signals. Figure 1.7 shows the basic principle of operation of a mul-tiplexer–demultiplexer (MUX–DEMUX) system. They are connected by a single link through which n channels transmit their information. A multiplexer combines the input signals into a single stream (many-to-one) while a demulti-plexer (one-to-many) separates the signals into individual ones.

1.12.2 tyPes

There are three basic multiplexing schemes. These are frequency division multiplexing (FDM), wavelength division multiplexing (WDM), and time division multiplexing (TDM). Of these, the FDM and WDM techniques are used for analog signals, while TDM is used for digital signals. Apart from the above, another multiplexing technique called space division multiplexing (SDM) is sometimes used, which is rather not a very sophisticated one. In this,

Medium

Receiver n Receiver 2 Receiver 1 Demultiplexer

Multiplexer

Sender 1

Sender 2

Sender n

FIGURE 1.7 Schematic of MUX–DEMUX system. (Available at www.comsci.

liu.edu/~jrodriguez/cs154fl08/Slides/Lecture5.pdf.)

individual cables are allocated for individual signals, which are then put within the same trench. The trench itself is considered to be the transmission medium.

An example of SDM is the local telephone system. Here, each telephone is connected to the central office by a local loop not shared by any other subscriber. The SDM technique is not considered to be a true multiplexing scheme and, hence, its demultiplexing is not necessary in the way it is done for FDM, WDM, or TDM techniques.

1.12.3 FdM

Frequency division multiplexing (FDM) is a technique in which the avail-able bandwidth in a communication link is divided into a series of nonover-lapping frequency subbands, each of which carries the modulated version of the original signal. Cable television uses a single cable to transmit many channels for viewing using FDM technique. Other uses of FDM are hand-ling multiple telephone calls through high-capacity trunk lines, communi-cation satellites that transmit different channel data for both uplinking and downlinking purposes.

An FDM scheme and its subsequent demultiplexing is shown in Figure 1.8. The multiplexer section consists of a low-pass filter, modulator, and band-pass filter for each channel.

In the demultiplexer side, the same three are present in the reverse order. Each input signal is modulated by separate distinct carrier frequencies.

The modulated carriers consist of a narrow band of frequencies, called the

Message

FIGURE 1.8 FDM MUX–DEMUX system.

Data Communication 15

passbands, centered around the carrier frequency of each individual channel.

The input signal information is contained in these passbands. The carrier fre-quencies of each individual channels are so chosen that their passbands do not overlap, minimizing chances of interference. Figure 1.9 shows six channels with the carrier frequency of the first channel fixed at 200 kHz and the sixth channel at 1300 kHz with a guard band of 20 kHz between any two channels.

1.12.4 WdM

Wavelength division multiplexing (WDM) is, in a sense, identical to FDM.

However, in this case, optical signals of different wavelengths (i.e., of differ-ent colors) are used and sdiffer-ent via a single optical cable. Optical signals have very high frequencies, unlike FDM. Multiplexing ensures that the very high bandwidth associated with optical fibers is effectively utilized. Figure 1.10 shows how a multiplexer combines several different wavelengths and the combined signal is demultiplexed at the receiving end. The methodology applied here is that a prism can bend a beam of light, which depends on the angle of incidence and also the frequency. SONET uses WDM technology in which more than one optical cable is used for MUX–DEMUX purposes.

Of late, dense WDM (DWDM) is used, which uses many channels with very less spacing between them, thereby enhancing efficiency even more.

200 400 600 800 1000 1200 1400

Guard band = 20 kHz

kHz

1 2 3 4 5 6

FIGURE 1.9 Different carrier frequencies with guard band in between. (Available at www.comsci.liu.edu/~jrodriguez/cs154fl08/Slides/Lecture5.pdf.)

Beam of light being carried by optical fiber

λ₁ λ₁

λ₂

λ₂

λ₃

λ₃

λ_n λ_n

Prism

FIGURE 1.10 Schematic of WDM system. (Available at www.comsci.liu.edu/

~jrodriguez/cs154fl08/Slides/Lecture5.pdf.)

1.12.5 tdM

Time division multiplexing (TDM) is a digital communication process that allows several signals from different sources to time share the resources of a link. In TDM, the whole bandwidth of the link is utilized at any instant of time by a single signal, while the total bandwidth is always shared by the communicating signals in FDM. In TDM, all signals have their own precise clocks to send data that needs proper synchronization. The differ-ent channels have their own scheduling for data transfer. The receiver can extract the channel signals by proper clocking and synchronization with the individual channels. Proper redesigning entails TDM to be adaptive in nature to any load changes. The concept of time division multiplexing is shown in Figure 1.11. It shows n channels that send data one after the other, utilizing the full bandwidth of the link.

1.12.5.1 Synchronous TDM

In synchronous TDM, data from different sources are divided into fixed time slots, in which a slot may contain a single bit, a byte of data, or a pre-defined amount of data. As shown in Figure 1.12, data from the first source is sent in the first time slot, followed by data from the second source in the second time slot. This is continued until data from the last source is sent.

Then the system repeats itself. Thus, in the first four time slots, data A₁ from source 1, data B₁ from source 2, no data from source 3, and data D₁ from source 4 are fed into the multiplexer. In this sequence, the next set of data from the four sources are sent, following the same logic. It should be noted here that even if some source does not have any data to be sent at any given instant of time, because of preallocation, that time is simply wasted.

For Figure 1.12, four time slots are wasted—one for source 2, two for source 3, and one for source 4. In a particular case when a channel does not have any data to be sent for a considerable time, underutilization of the channel takes place, leading to a less efficient system. Statistical TDM

Multiplexer Demultiplexer

Sender 1

Sender 2

Sender n

Medium Data flow

3 2 1 n 3 2 1

Receiver 1

Receiver 2

Receiver n

FIGURE 1.11 TDM MUX–DEMUX system. (Available at www.comsci.liu.

edu/~jrodri guez/cs154fl08/Slides/Lecture5.pdf.)

Data Communication 17

addresses this problem by skipping slot allocation for a source if it does not have any data in that particular time slot.

1.12.5.2 Statistical TDM

To overcome the shortcomings of synchronous TDM, statistical TDM uti-lizes only those slots that do have data, skipping those slots that do not have data at the times they are to send their data on the channel. Referring to Figure 1.13, one slot for source 2, two slots for source 3, and one slot for source 4 are skipped because they are empty. The scheme must have an identifier to indicate and identify the particular receiver, since the tra-ditional multiplexing scheme is not used here for the sake of improved channel utilization.

1.12.6 Variable data rate

Thus far, the discussions on TDM centered on the assumption that all the sources involved in data transmission has the same data rate—which is not always the case. There are different approaches to overcome such data rate

Data flow

FIGURE 1.12 Synchronous TDM system. (Available at www.comsci.liu.edu/

~jrodriguez/ cs154fl08/Slides/Lecture5.pdf.)

FIGURE 1.13 Statistical TDM system. (Available at www.comsci.liu.edu/

~jrodriguez/cs154fl08/Slides/Lecture5.pdf.)

variations. These are multilevel multiplexing, multislot multiplexing, and pulse stuffing technique, which are discussed below.

1.12.7 MultileVel MultiPlexing

Multilevel multiplexing is employed when most of the lines have higher data rates and fewer ones slower data rates, with the data rates of the lat-ter an integral multiple of the former. The slower ones are multiplexed so that the data rate of the multiplexed output is equal to the other ones.

Figure 1.14 shows a two-level multiplexing scheme with the two 20 kbps lines combined by the first multiplexer. The second multiplexer effectively combines four input lines. The output frame is a 160 kbps line. It should be noted that demultiplexing at two levels are needed to get back the original five lines—two of 20 kbps and three of 40 kbps.

1.12.8 Multislot MultiPlexing

Multislot multiplexing is employed when most of the lines have slower data rates and fewer ones faster data rates, with the data rates of the former an integral multiple of the latter. Figure 1.15 shows the 50 kbps line divided

40 kbps Communications and Networking, 4th Edition, Special Indian Edition. Tata McGraw Hill Companies Inc., New Delhi, India, p. 174, 2006.)

25 kbps

Input with a data rate of 50 kbps has two time slots in each frame

D C B A A

FIGURE 1.15 Multislot multiplexing scheme. (From B. A. Forouzan. Data Communications and Networking, 4th Edition, Special Indian Edition. Tata McGraw Hill Companies Inc., New Delhi, India, p. 174, 2006.)

Data Communication 19

into two 25 kbps lines so that the reduced rate is equal to the other three.

The 50 kbps line is allocated two time slots in the output data frame of 125 kbps rate.

1.12.9 Pulse stuFFing MultiPlexing

The above two schemes fail when data rates of the sources are not an integral multiple of each other. In this scheme, extra bits are added to the slower data rate sources so that ultimately their data rates become equal to the faster ones. This scheme is also called bit padding or bit stuffing and is shown in Figure 1.16.