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Early attempts simply aimed to improve the realism with which a point-to-point
communication model has been implemented [ 1-3 ].
Numerous publications, both in the radio engineering [ 4-6 ] and wireless networking
communities [ 13, 15 ], have identified the need to move away from conceptually
simple mathematical models of the wireless channel. Starting from the simplest of
such models, it is widely accepted that the unit disk graph (UDG) model, much
favored by theoreticians in the computer science community, results in algorithms
and predictions that deviate significantly from reality as verified by experiments. Our
definition of the UDG model is taken to be
p
=
=
1 if
rR
p
0 if
rR
>
where p denotes probability, r is the distance between two radio nodes, and R is a
notional coverage radius, possibly specific to each transmitting node, but more
frequently identical for all nodes in a wireless peer-to-peer network.
7.2
Review of Basic Radio Wave Propagation Mechanisms
and Models
By definition, the received power by an antenna can be expressed as
æ
öæ
ö
æ
ö
ç
÷ç
÷
=
´
antenna aperture area
ç
÷
ç
÷ç
÷
è
in Watts
ø
2
2
è
in Watts/metre
øè
in metre
ø
The principle of reciprocity can be applied to a pair of antennas to show that, the
ratio of the gain to the effective aperture area is a universal constant for all antennas
of a given frequency, f (in Hz), and wavelength,
λ = (in m), where c (in ms −1 )
is the speed of light. This universal constant can be explicitly computed for a simple
dipole to give
cf
G
A
4
π
λ
=
2
e
The law of conservation of energy between two antennas situated in free-space
(vacuum) then takes the following form:
æ
2
ö
ì
æ
1
ö
ü
G
λ
π
P
= í
(
PG
)
rx
ýç
÷
ç
÷
rx
tx
tx
4
π
d
2
4
è
ø
î
þ è
ø
where the last term on the right-hand side is the receiving antenna effective aperture,
the term in the curly brackets is the radiated power intensity at the receiving antenna;
the first term in the curly brackets is the effective, isotropically radiated power

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