Antennas and Propagation
The notes in this document are based almost entirely on Chapter 5 of the textbook [Sta05]. Rappaport’s text is also a good reference for wireless signal propagation [Rap95].
An antenna is an electrical conductor or a system of conductors that radiates/collects (transmits or receives) electromagnetic energy into/from space. An idealized isotropic antenna radiates equally in all directions. The directivity of an antenna is captured by its beam width; it is the angle within which power radiated is at least half of that in the most preferred direction (that is, half of the maximum power).
Antenna gain is the power output, in a particular direction, compared to that produced in any direction by an idealized omnidirectional antenna. If f is the carrier frequency and Ae is the eﬀective area of the antenna, then the antenna gain is given by 4πAe f 2
where c is the speed of light. The eﬀective area of an antenna depends on the size and shape of the antenna. The eﬀective area of an idealized isotropic antenna is 1, by deﬁnition. G=
Wireless transmissions propagate in three modes: ground-wave, sky-wave, and line-of-sight. Ground wave propagation follows the contour of the earth, while sky wave propagation uses reﬂection by both earth and ionosphere. Finally line of sight propagation requires the transmitting and receiving antennas to be within line of sight of each other. Which of these propagation modes dominates depends on the frequency of the underlying signal.
Examples of ground wave and sky wave communication are AM radio and international broadcasts such as BBC. Above 30 MHz, neither ground wave nor sky wave propagation operates and the communication is through line of sight.
If h is the height of a transmitting (resp., receiving) antenna in meters, then the distance to the receiver (resp., transmitter) for line-of-sight transmission should be at most √
d = 3.57 h kms.
This can be proved using elementary geometry. Since microwaves are bent or refracted by the atmosphere, the “eﬀective” line of sight is, in fact, larger than the true line of sight. We introduce an adjustment factor K to capture the refraction eﬀect and obtain √
d = 3.57 Kh kms.
If the two antenna have heights h1 and h2 meters, then the distance between them for LOS propagation should be at most √
3.57 K ( h1 + h2 ) kms.
There are four classes of limitations that aﬀect electromagnetic wave transmissions. Attenuation. The strength of signal falls with distance over transmission medium. The extent of attenuation is a function of distance, transmission medium, as well as the frequency of the underlying transmission. Even in free space, with no other impairment, the transmitted signal attenuates over distance simply because the signal is being spread over a larger and larger area. For an ideal isotropic antenna, the ratio between the transmitted power Pt and the received power Pr for a separation distance of d is given by
where λ, f , and c are the wavelength, frequency, and the speed of the signal. One can express the above ratio in terms of antenna gains and eﬀective areas of the antennas by applying the appropriate formulae.
Distortion. Since signals at diﬀerent frequencies attenuate to diﬀerent extents, as the above formula indicates, a signal comprising of components over a range of frequencies gets distorted; i.e., the shape of the received signal changes. A standard method of resolving this problem (and recovering the original shape) is to amplify higher frequencies and thus equalize attenuation over a band of frequencies.
Dispersion. Dispersion is the phenomenon of spreading of a burst of electromagnetic energy during propagation. It is especially prevalent in wireline transmissions...