The Internet Encyclopedia (Volume 3)

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RADIOWAVEPROPAGATION 185

is time-varying, then it can cause a rapid variation in the

received signal, resulting in fading.

Absorption

Absorption describes the process where radio energy pen-

etrates a material or substance and gets converted to heat.

Two cases of absorption of radio waves are prevalent.

One occurs when radio waves are incident upon a lossy

medium and the other is due to atmospheric effects. When

the radio wave strikes an object, the incident wave (per-

pendicular wave) propagates into the lossy medium and

the radio energy experiences exponential decay with dis-

tance as it travels into the material. The wave either is

totally dissipated or will reemerge from the material with

a smaller amplitude and continue the propagation. The

skin depth,δ, is the distance for the field strength to be

reduced to 37% of its original value—the energy of the

wave is reduced by 0.37. Particles in the atmosphere ab-

sorb RF energy. Absorption through the atmosphere also

depends on the weather conditions—fair and dry, drizzle,

heavy rain, fog, snow, hail, etc. Usually, the absorption of

RF energy is ignored below 10 GHz.

Doppler Effect

Doppler shift is the change in frequency due to the dif-

ference in path length between two points in space. It is

observed whenever there is relative motion between the

Tx and the Rx. For a mobile moving with a constant ve-

locityv, the received carrier frequencyfcwill be shifted

by the amount

fd=fmcosθ=

vcosθ

λ

=

veff

λ

=

vefffc

c

(2)

where θis the path angle; fm=v/λis the maximum

Doppler frequency fd,atθ= 0 ◦; andveffis the effective

velocity of the mobile (Garg & Wilkes, 1996). The Doppler

shift, bounded by±fm, is related to the phase change    θ

caused by the change in path length. Because each com-

ponent of the received multipath signal arrives from a dif-

ferent direction, each contributes a different value to the

Doppler spreading. This effectively increases the band-

width of the received signal. Depending on the direction

of motion and the source, the frequency can be shifted

up or down, i.e.,±fm. The result of this shift is a random

phase and frequency modulation of the received RF car-

rier, which may necessitate the use of differential phase

and frequency detection techniques.

The above propagation mechanisms strongly influence

system design parameters such as the choice of transmit-

ting and receiving antennas, Tx powers, modulation tech-

niques, and much more. Each of these propagation mech-

anisms contributes to losses in the RF energy and hence

limits system performance. In wireless mobile communi-

cations, propagation losses are commonly classified into

path loss, shadowing, and multipath fading. These losses

are described below.

Path Loss

Path loss (PL) refers to the large-scale envelope fluctuation

in the radio propagation environment, which varies with

the distance between the Tx and Rx. Because the Rx is

located at some distancedfrom the Tx, a loss factor is used

to relate the transmitted power to the received power. For

amplitude fading, an increase indnormally results in an

increase in PL. Different models have been used to model

path loss, but each model obeys the distance propagation

law. In free space, with L=1, PL is expressed as the ratio

of the radiated powerPt, to the received powerPrand is

given by

PL(dB) = 10 log 10

Pt

Pr

=−10 log 10

[

GtGrλ^2

(4π)^2 d^2

]

(3)

Shadowing

Due to topographical variations along the transmission

path, the signal is diffracted and the average power of the

received signal is not constant. Shadowing or large-scale

fading refers to slow variations in the local mean of the

received signal strength. This variation causes shadowing.

The signal is shadowed by obstructions such as buildings

and natural terrain, which leads to gradual variations in

the mean power of the received signal. The effect is a very

slow change in the local mean signal, sayPs. Shadowing is

generally modeled by a lognormal distribution, meaning

thatsd=10 log 10 Psis normally distributed, withsdgiven

in dB (Yacoub, 1993). Shadowing is the dominant factor

determining signal fading.

Multipath Fading

The collective effect of reflection, refraction, diffraction,

and scattering leads to multipath propagation. Due to re-

flection, refraction, and scattering of radio waves along

the channel by manmade structures and natural objects

along the path of propagation, the transmitted signal of-

ten reaches the receiver by more than one path. This re-

sults in the phenomenon known as multipath fading. The

signal components arriving from indirect paths and a di-

rect path (if it exists) combine at the receiver to give a

distorted version of the transmitted signal. These radio

waves are attenuated differently and they arrive with dif-

ferent path gains, time delays, and phases. The resultant

signal may vary widely in amplitude and phase depending

on the distribution of intensity and relative propagation

in time of wave and bandwidth of the transmitted sig-

nal. The number of paths may change drastically when

the mobile unit changes its position depending on the in-

crease or decrease in the number of intervening obsta-

cles. Unlike shadowing, multipath fading is usually used

to describe small-scale fading or rapid fluctuation in the

amplitude of a radio signal over a short period of time

or over short distances. It is affected by rapid changes

in the signal strength over short distances or time in-

tervals and random frequency variations due to varying

Doppler shifts on different multipath signals (Rappaport,

2002).

The loss factor associated with multipath fading is usu-

ally modeled in the channel impulse response. A trans-

mitted impulse will arrive at the Rx as the sum of several

impulses with different magnitudes, delays, and phases.

ForMmultipath, the composite impulse responseh(t,τ)