Wireless Network Design: Optimization Models and Solution ...

144 Jeff Kennington, Jason Kratz, and Gheorghe Spiride
of WLANs that may be modeled as integer programming problems. One model involves
the assignment of frequencies to a fixed set of APs. Another is to find the
minimum number and location of APs that will provide coverage to a given area.
The most sophisticated model is our new formulation to determine the location,
power, and frequency assignment of a fixed number of APs to maximize the capacity
of a new WLAN. Our formulation is for the static problem with known MD
locations. Research is needed to develop good solution algorithms for this problem.
The dynamic version of this design problem arises when the precise location and
number of MDs requesting service varies by day and time of day. In this case, the
best design is one that maximizes the expected capacity over a large number of potential
MD configurations. Hence, a robust design is preferable for the dynamic case
and research is also needed for this version of the problem.
Appendix A: Attenuation Calculation
Several models are available to determine the attenuation between a pair of locations.
The path loss is the signal attenuation given in dB, and is defined as the difference
between the transmitted power at the source location and the received power
at the destination location. Many factors affect path loss between two locations in a
particular setting, including distance, the presence and nature of obstacles, interference
with other signals or reflected copies of the signal, etc. The presentation that
we follow in this Appendix is based on [16] where path loss (PL) is defined on p.
108, equation 4.5 by
PL = 10log Pt
(A.1)
Pr
where Pt is the transmitted power, and Pr is the received power. This equation can
be rewritten as
− PL
Pr = Pt10 10 (A.2)
Path loss can also be calculated directly between a pair of locations, given in [16]
on p. 161, equation 4.93 by
PL = PL0 + 10nlog d
+ Xσ
d0
(A.3)
where PL0 is the known path loss between locations at a distance of d0, d is the
distance between the source and destination location, n is a constant determined
by the medium of transfer, and Xσ is a random variable representing noise. For
simplicity, the remainder of this description we assume Xσ = 0 and that path loss is
simply a function of distance. In practice, the other factors mentioned earlier would
contribute to path loss, however a detailed presentation is outside of the scope of
this presentation.
Rappaport [16] gives n = 3.27 in Table 4.7 on p. 165, and we use that number.
Rappaport also gives a value for PL0 for a d0 = 1 meter. This value can be calculated