Base Station Placement in WLANs - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 180

or

d
d

PL d ( ) = PL d ( ) 10 log + n

. (8.2)

0

.

0

where. d .is.the.reference.distance;. d is.the.distance.between.the.base.station.
and. terminal;. n . is. the. path. loss. ex po nent. indicating. the. rate. at. which. the.
path. loss. increases. with. distance;.

PL d . is. the. reference. path. loss. due. to.
free-space.propagation.from.the.base.station.to.a.1-m.reference.distance.that.
is.equal.to. 10

( )

0

( )

π
λ ;. n .is.the.reference.path.loss.exponent;.and.λ.is.the.
wavelength.of.the.frequency.used.
Since.the.reference.distance. d .is.chosen.as.1.m.and.the.reference.path.loss.
exponent. n .is.equal.to.2.for.the.free-space.environment.[16,.19],

4 d

n log

0

0

4 π

λ

.

PL d = ( ) 20 log

(8.3) 0

.

For. the. obstructed. environment. in. factories,. the. path. loss. exponent n . is.
selected. as. 2. [16,19].. Moreover,. because. physical. obstructions. lie. directly.
between.the.base.station.and.terminal,.an.additional.term,.the.penetration.
loss,.has.to. be .added.to. Equation.(8.2) . to.account.for.the.total.average.path.
loss..Then,. PL ( ) .is.finally.modified.as

J

4 π

λ

∑ +

( )

PL d ( ) = 20 log 20 log d + N L

i i

i = 1

. (8.4)

J

4 π

λ

d

∑

= 20 log + N L

i i

.

i = 1

where. J is. the. total. number. of. different. types. of. obstructing. objects;. i is.
the. type. of. obstructing. objects;. N i . is. the. number. of. obstructing. objects.
with.type i ;.and. L i .is.the.penetration.loss.caused.by.an.obstructing.object.
of.type i. i .

8.3 MathematicalFormulation
In. this. multiobjective. base. station. placement. problem,. the. mathematical.
model. used. in. Tang,. Man,. and. Kwong. [19]. was. applied;. the. notations. are.
listed.in . Table 8.1 .