Information Technology Reference

In-Depth Information

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

(radio packet reception)

=

=

1 if

rR

≤

p

(radio packet reception)

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

radiated power intensity

effective receiver

æ

öæ

ö

æ

Received power

ö

ç

÷ç

÷

=

at receiver

´

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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