Eeng360 1 Chapter 1 INTRODUCTION  Propagation of Electromagnetic Waves  Information Measure  Channel Capacity and Ideal Communication Systems Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University

Eeng360 2 Frequency Bands  Regulations specify, modulation type, bandwidth, power, type of information and etc. that a user can transmit over designed frequency bands.  Frequency assignments and technical standards are set internationally by International Telecommunication Union (ITU).  Each nation of ITU retains sovregnity over spectral usage and standards adopted in its territory.  Each nation is expected to abide by the overall frequency plan adopted by ITU.

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Eeng360 6 Propagation of Electromagnetic Waves  The propagation characteristics of electromagnetic waves used in wireless channels are highly dependent on the frequency.  Based on carrier frequency EM wave propagations can be classified as: GROUND-WAVE PROPAGATION SKY-WAVE PROPAGATION Line of Sight (LOS) PROPAGATION

Eeng360 7 Ionized Regions Above Earth. Ionization of air is caused by UV rays from the sun. Ionized air shows different properties at different levels (Density and pressure). Speed of the wave differs with the changing properties. Dominant regions are named as D, E, F 1 and F 2.

Eeng360 8 GROUND-WAVE PROPAGATION  Dominant mode of propagation for frequencies below 2 MHz.  Diffraction of the wave causes the wave to propagate along the surface of the earth.  This propagation mode is used in AM Radio Broadcasting.  Diffraction of waves in “D” layer helps propagation along the surface of earth.

Eeng360 9 SKY-WAVE PROPAGATION  Dominant mode of propagation for EM waves in the frequency range of 2 MHz to 30 MHz.  Long coverage is obtained by reflection of wave at the ionosphere and at the Earth’s boundary.  This mode is used in HF band International Broadcasting (Shortwave Radio).  Sky-wave propagation is caused primarily by reflection from the F layer (90 to 250 miles in altitude).

Eeng  The refraction index of the ionosphere can be approximated as Where, n -- Refractive index, N -- Free electron density (number of electrons/m 3 ) ( ~ /m 3 ) f -- Frequency of the wave (Hz).  Refractive index will change gradually with the altitude.  Traveling waves will gradually bend according to Snell’s law. n r Sin φ r = n i Sin φ i  Waves will be bent back to earth. Ionosphere acts as a reflector. Transmitting station will have coverage areas along the surface of earth. SKY-WAVE PROPAGATION

Eeng LINE-OF SIGHT (LOS) PROPAGATION  Dominant mode of propagation for EM waves above 30 MHz.  Since the frequency is high, f 2 >> 81 N so that n ≈ 1 ( Free Space)  This mode can be used in Satellite Communications.  The disadvantage of LOS is that the signal path has to be above the horizon and the receiver antennas need to be placed on tall towers so that they can see each other.

Eeng LOS Calculations  Let’s assume d = Distance to the horizon; h = Antenna height... r = Effective radius of earth Where h << r  Effective radius of earth = 4/3 * real radius Effective radius of earth r = 4/3 * 3960 = 5280 miles Converting feet to mile Example: For a television station with an h=1000 ft tower, d = √(2000) = 44.7 miles. The transmitter will cover an area of 44.7 miles around.

Eeng Measuring Information  Definition: Information Measure (I j ) The information sent from a digital source (I j ) when the jth massage is transmitted is given by: where P j is the probability of transmitting the j th message. Messages that are less likely to occur (smaller value for Pj) provide more information (large value of Ij). The information measure depends on only the likelihood of sending the message and does not depend on possible interpretation of the content. For units of bits, the base 2 logarithm is used; if natural logarithm is used, the units are “nats”; if the base 10 logarithm is used, the units are “hartley”.

Eeng Measuring Information  Definition: Average Information (H) The average information measure of a digital source is, –where m is the number of possible different source messages. –The average information is also called Entropy. Definition: Source Rate (R) The source rate is defined as, –where H is the average information –T is the time required to send a message.

Eeng Measuring Information-Example1.1  Find the information content of message that consists of a digital word 12 digits long in which each digit may take on one of four possible levels. The probability of sending any of the four levels is assumed to be equal, and the level in any digit does not depend on the values taken on by pervious digits. Answer: Possible combinations of 12 digits ( # of possible messages) = 4 12 Because each level is equally likely, all different words are equally likely.

Eeng Channel Capacity & Ideal Comm. Systems  For digital communication systems, the “Optimum System” may defined as the system that minimize the probability of bit error at the system output subject to constraints on the energy and channel bandwidth.  Is it possible to invent a system with no error at the output even when we have noise introduced into the channel? Yes under certain assumptions !.  According Shannon the probability of error would approach zero, if R< C Where R - Rate of information (bits/s) C - Channel capacity (bits/s)  B - Channel bandwidth in Hz and  S/N - the signal-to-noise power ratio Capacity is the maximum amount of information that a particular channel can transmit. It is a theoretical upper limit. The limit can be approached by using Error Correction

Eeng Channel Capacity & Ideal Comm. Systems ANALOG COMMUNICATION SYSTEMS In analog systems, the OPTIMUM SYSTEM might be defined as the one that achieves the Largest signal-to-noise ratio at the receiver output, subject to design constraints such as channel bandwidth and transmitted power. Question: Is it possible to design a system with infinite signal-to-noise ratio at the output when noise is introduced by the channel? Answer: No! DIMENSIONALITY THEOREM for Digital Signalling: Nyquist showed that if a pulse represents one bit of data, noninterfering pulses can be sent over a channel no faster than 2B pulses/s, where B is the channel bandwidth.

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