Telecommunication Principles: The Topic of Modulation


The topic of telecommunications system cannot be studied completely without touching on the topic of modulation, its categorization and ways of usage. Thus, modulation is the telecommunications technique used, as Gaudenzi (2007) argues, to modify the forms of television or radio waves in order to adjust the number of media messages to make their simultaneous transmission possible and convenient. There are different types of modulation in telecommunication systems. Afshar (2005) singles out PWM (Pulse Width Modulation), PAM (Pulse Amplitude Modulation), DM (Delta Modulation), and PCM (Pulse Code Modulation) as the modulation types used in all telecommunication spheres and in any geographical locations but predominantly in North America and Japan (p. 198).

However, Gaudenzi (2007) and Tannenbaum (2003) speak on a wider range of modulation types. Three major areas of use of those types are analog modulation, digital modulation, and spread spectrum (Tannenbaum, 2003, p. 194). The analog modulation techniques are used mainly in electronic telecommunication area and include AM (Amplitude Modulation), SSB (Single Sideband Modulation), QAM (Quadrature Amplitude Modulation), FM (Frequency Modulation), PM (Phase Modulation), and SM (Space Modulation) (Tannenbaum, 2003, p. 214).

Digital modulation types are more modern compared to analog ones and their usage is not limited by any particular telecommunication area. Digital modulation techniques include FSK, ASK, PSK, MSK (Frequency-/Amplitude-/Phase-/Minimum-Shift Keying), OOK (On-off Keying), CPM (Continuous Phase Modulation), PPM (Pulse Position Modulation), TCM (Trellis Coded Modulation), and OFDM (Orthogonal Frequency-Division Multiplexing).

Finally, spread spectrum modulation techniques are mainly used for the purposes of secure telecommunication protected from interferences. The spread spectrum techniques include CSS, DSSS, FHSS, and THSS (Chirp/Direct Sequence/Frequency-Hopping/Time-Hopping Spread Spectrum) (Tannenbaum, 2003, p. 215).


QAM (Quadrature Amplitude Modulation) is a digital modulation technique applied by delivering two different signals at the same time using different channels and modulation channels:

The two modulation inputs (analog or digital) are applied to two separate balanced modulators (BM) each of which are supplied with the sin or cos carriers, i.e., modulator #1 is supplied with the sin carrier and modulator #2 is supplied with the cos carrier. The outputs of both modulators are algebraically summed; the result of which is now a single signal to be transmitted, containing the I & Q information (Williamson, 2006).

PSK (Phase- Shift Keying) is, on the other hand, is the technique that involves modifying the reference signal and demands a special demodulator able of decoding the reference signal and putting it in accordance with the received signal (Williamson, 2006). The main advantage of QAM over PSK is the need of the specialized technology to operate the latter and ease of QAM operation. The disadvantage of QAM in this case is the same but from the viewpoint of security, as PSK is harder to decode, therefore it is more difficult to interfere with and spy on (Tannenbaum, 2003, p. 189).

Packet and Circuit Switching

The packet switching method is the process when “no specific path is used for data transfer. Instead, the data is chopped up into small pieces called packets and sent over the network” (Topipguide, 2009). As contrasted, circuit switching is the process when “a connection called a circuit is set up between two devices, which is used for the whole communication” (Topipguide, 2009). Drawing from this, the main advantage of the packet switching over the circuit one is the fact that packet switching allows simultaneous communication between multiple telecommunication devices, while circuit switching if used with multiple devices might cause failure of them all even if one or two actually fail (Topipguide, 2009). The examples of home telephone stations and corporate multiple telephones illustrate this difference brightly.

However, the possibility of loss of the chopped data pieces in transit is the main disadvantage of the packet switching technique. According to Topipguide (2009), data might get lost or be delivered in a wrong order if operated by the packet switching and this fact limits the use of packet switching to precisely developed and supervised operations like IT development, scientific telecommunications, etc.

Telecommunications Congestion

The area of telecommunications is not deprived of issues and obstacles on the way of its development. One of the main obstacles that are difficult to fight is the so called congestion, i. e. “The condition that arises when a system or network experiences a level of offered calling activity or message traffic that exceeds its capacity” (Tannenbaum, 2003, p. 109). Fighting congestion is thus a difficult task because it develops from a positive factor which is the growth of demand for telecommunication services. However, the imbalance in demand and an organization’s capacities leads to congestion, which in its turn slows down the data transmission and results in delays of service deliveries (Burstein, 2009).

The main congestion management techniques, as Tannenbaum (2003) and Afshar (2005) argue, include the creation of specialized buffers for temporary storage of the delayed data, establishing substitute minor routes that might fight congestion if the main data transmission routes are busy (Tannenbaum, 2003, p. 138), and the development of special routers, i. e. software packages that would report the potential congestion conditions and allow the organization to allocate its effort in the direction necessary to prevent congestion (Afshar, 2005, p. 129).

Effect of Multiplexing in Communications Systems

The technique of multiplexing is often used in telecommunications for the purposes of increasing the capacities of transmission channels: “Multiplexing is the process where multiple channels are combined for transmission over a common transmission path” (TBI, 2009). Based on the type of combination of channels multiplexing can be either Frequency Division (FDM) or Time Division Multiplexing (TDM) (TBI, 2009).

As the titles tell, the FDM combines channels into an aggregate where these channels are still separated by their different frequency, while TDM benefits from time-based division of channels united into an aggregate. The TDM is also subdivided into three types including Conventional, Statistical, and Cell-Relay/ATM Time Division Multiplexing types (TBI, 2009). The effects of multiplexing on telecommunications development are mainly positive as multiplexing allows saving time and transmission channels and facilitates the delivery of multiple signals thus satisfying requirements of wider audiences.

Telephone Network Issues

Given the telephone network that connects two end offices through the intermediate switching point by the 1 MHz full duplex trunk, we can calculate that the total number of phones possible to place in each of the end offices will amount to 25,000 telephones. To calculate this, we need to realize that in an office a telephone is used to make four calls per 8-hour shift with the average call lengths amounting to 6 minutes and the percentage of long distance calls totals 10%. Accordingly, 4/10 = 0.4 long distance calls are made daily by a telephone in each office. Drawing from this, the time spent for long distance calls totals 0.4 * 6 = 2.4 minutes spent daily on long distance calls from every telephone in each of the offices. Given the 480-minute working day, we have 480/2.4 = 200 slots that every office must have. The number of telephones needed is calculated from the slots number for two offices and the 1 MHz trunk capacity that equals 125 Kbps: 400 * 125 = 50,000 telephones which gives the figure of 25,000 telephones for each office.

Audio Signals and Uniform Quantization Levels

If there is an audio signal with spectral components in the range 300 to 3000 Hz, and the sampling rate of 7,000 samples per second used to generate a PCM signal, the creation and transmission of such a sound will need the number of uniform quantization levels. This number is calculated using the following equation given that the SNR = 30 DB:

SNRDB = 10log102n + 1.76 DB = 6.02n + 1.76 DB, when SNRDB = 30 DB, n = 5 bits

SNRDB = 6.02*5 + 1.76 = 32

Accordingly, the generation of the PCM signal and the sound with the above stipulated spectral components will involve 32 uniform quantization levels. Drawing from this, the data rate (DR) required for the process discussed is calculated by multiplying the sampling rate of the signals and the bit rate observed:

DR = 7,000 * 5 = 35,000 bps

Thus, the number of uniform quantization levels required for generating a PCM signal is 32, while the data rate needed for the same procedure amounts to 35,000 bits per second.

Spectral Efficiency of Bandwidth Utilization

Voice Channels

To calculate the spectral efficiency with respect to modulation efficiency in Erlangs/MHz/Km2, it is necessary to use the following formula:

ηm = (Total traffic carried by the system) / (Bandwidth) (Total Coverage Area)

Accordingly, to dispose of all the data needed for this calculation, it is first of all necessary to find out the voice channels used per cell, total traffic carried per cell in Erlangs/cell and Erlangs/km2, the numbers of calls/hour/cell & calls/hour/km2 and users/ hour/cell & users. Starting with the first point, i. e. the number of voice channels involved, it is first necessary to know the number of 30 kHz channels and control channels involved. The number of 30 kHz channels equals the available bandwidth of 12.5 MHz multiplied by 1000 and divided by 30:

30 kHz Channels = (12.5 * 1000)/30 = 416

Given the number control channels involved equaling 21, the number of voice channels will be 416 – 21 = 395. To calculate the number of these channels per cell, the total voice channels number should be divided by the figure of frequency reuse factor:

Voice Channels per Cell = Voice Channels’ Total/ Frequency Reuse Factor = 395/7 = 56 voice channels per cell.

Total Traffic per Cell

The calculation of the total traffic per cell demands further inquiries about the total number of cells, total coverage area, area of each cell implemented, the percentage of the call blocking probability, and the use of Erlang-B formula at the final stage. Thus, the total number of cells used in an area equals the total coverage area divided by the area of a cell:

Total Cell Number = 4000/8 = 500 cells.

Accordingly, given that the number of cells is 500 and the percentage of the call blocking probability is 2%, it is possible to calculate that the total traffic carried per cell, which will equal 45.9 Erlangs/cell. This amount is converted in Erlangs/km2 through dividing the Erlangs/cell figure by the area of a cell:

Erlangs/ km2 = 45.9/8 = 5.74 Erlangs/ km2

Calls/Hour/Cell & Calls/Hour/km2

The calculation of the following two factors involves further calculations. Thus, to see the rate of the calls/hour/cell rate observed in the given conditions, it is necessary to multiply the Erlangs/cell figure (Ec) by the number of seconds in an hour, i. e. 3600 seconds (H). The second step in this manipulation is to divide the figure obtained after multiplication by the average holding time of a call (Ta):

Calls/hour/cell rate = (Ec * H) / Ta

Calls/hour/cell rate = (45.9*3600)/100 = 1652.4 calls per hour

At the same time, the calculation of the number of calls/hour/km2 involves the consideration of the area of a cell implemented by the network. To obtain the calls/hour/km2 figure it is necessary to divide the calls/hour/cell rate by the area of a cell:

Calls/hour/km2 = 1,652.4 calls per hour / 8 km2 = 206.6

Drawing from these figures, the calculation of the overall efficiency of modulation for the ways the system utilizes its bandwidth in for a particular installation becomes even more possible. The only two factors to be considered further are the figures of users/ hour/cell and users/hour/channel rates.

Users/ Hour/Cell & Users/Hour/Channel

Accordingly, the figure of the first rate, i.e. users/ hour/cell rate, is calculated in the relation of calls/hours/cell rate and the average number of calls per unit during a busy hour (Ca):

Users/ Hour/Cell = calls/hours/cell rate / Ca

Users/ Hour/Cell = 1,652.4 / 1.2

Users/ Hour/Cell = 1,377

To inquire more about the nature of the process in its development, the number of calls per user, per cell, and per hour is to be calculated through the process of dividing the user/hour/cell rate figure by the previously calculated number of voice channels per cell:

Users/ Hour/Channel = Users/ Hour/Cell / Number of Voice Channels per Cell

Users/ Hour/ Channel = 1,377 / 56 = 24.6 users are reported to averagely call in a given cell during a given hour.

System Modulation Efficiency

Thus, when all the prior calculations are carried out and it is possible to see all the data needed for the calculation of the overall efficiency with which the system under consideration utilizes bandwidth for a particular installation, the very efficiency of modulation in this process can finally be calculated in Erlangs/MHz/Km2. The formula for this final manipulation is as follows:

ηm = (Total traffic carried by the system) / (Bandwidth) (Total Coverage Area)

Now that all the components of the formula can be observed and calculated, the following equation will assist is calculating the efficiency of modulation:

ηm = (Erlangs/cell * Number of Cells) / (Total coverage area * Bandwidth)

ηm = (45.9*500) / (4000*12.5) = 22,950 / 50,000 = 0.459 Erlangs/MHz/Km2, which is a rather high efficiency that allows considering all important above stipulated factors in the process of the telecommunication network operation.

Reference List

Afshar, A 2005, Principles of semiconductor network testing, Elsevier.

Burstein, D 2009, British Telecom: “Congestion Problem? No!”, Fastnetnews. Web.

Gaudenzi, R 2007, ESA develops new modulation patent for DVB-S2, ESA Telecom. Web.

Modiano, E 2009, Quantization, Eytan Modiano AA Dept., pp. 1 – 16.

Tannenbaum, A 2003, Computer Networks, Prentice Hall PTR.

TBI 2009, Multiplexing Techniques, TBI Telecom. Web.

Topipguide 2009, Circuit Switching and Packet Switching Networks, Switching Networks. Web.

Williamson, L 2006, Quadrature Amplitude Modulation, QAM. Web.

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