Wireless Network Design: Optimization Models and Solution ...

6 Optimization Based WLAN Modeling and Design 133
Fig. 6.3 Frequency Assignment Using Three APs with a 60 Degree Antenna at each Star cf. [10]
Mishra et al. [13] describe an environment where multiple APs are operational
and mobiles scan the wireless medium and associate with the AP having the
strongest signal, and the channel assignment can be changed dynamically. The APs
are capable of selecting the best channel from {1,...,k} for operation. Generally, k
is 11 and channel overlap is permitted.
Let G = [V,E] denote a graph, where V is the set of APs and E denotes pairs
of APs that are close enough to cause interference if the assigned channels overlap.
Let Wi j∀(i, j) ∈ E be the weight associated with link (i, j). The authors generally
use the total number of clients associated with the two APs as the edge weight. A
channel assignment is a mapping C : V → {1,...,k}. Given such a mapping, Ii j is
defined as the interference caused by the assignment of C(i) to AP i and C( j) to AP
j. Interference is a function of the distance between the network components (MDs
and APs) as well as obstacles between the devices. If there is no overlap in frequency
bands, then Ii j is 0. Using this notation, 3 versions of the channel assignment model
are defined in [13].
The first version minimizes the maximum weighted interference:
Minimize max(Wi jIi j) ∀(i, j) ∈ E
The second version minimizes the sum of the weighted interference: