Wireless Network Design: Optimization Models and Solution ...

6 Optimization Based WLAN Modeling and Design 131
between an AP and a MD must be no more than 120 feet. The optimal solution used
4 APs located at the following grid points: (50,50),(150,50),(50,150),(200,150)
as illustrated in Figure 6.2. Note that all MD grid points are covered, but there is a
small area near (125,250) that is not covered. A finer grid could be used to eliminate
this dead spot.
Fig. 6.1 The Site With a Superimposed Grid
A more detailed coverage-oriented model has been developed by Bahri and
Chamberland [2]. They developed an optimization model for AP placement, AP
transmit power, and frequency assignment. The sets and variables used to describe
their model may be found in Table 6.3. The objective is to minimize the required total
number of APs to be installed that guarantee coverage. Their model is a nonlinear
integer mathematical program that is shown to be NP-hard. The authors propose using
a tabu search algorithm to obtain a solution. Attenuation factors are based on an
adaptation of the Hata formula ([6]). Their algorithm was empirically evaluated on
a 10-floor building with several hundreds of stations. They compare their solutions
to lower bounds obtained by relaxing a subset of the difficult constraints.
6.2.3 Channel Assignment
Leung and Kim [10] present a heuristic procedure for frequency assignment that is
closely related to frequency assignment models for cellular networks. They demonstrate
their procedure on a clover-leaf hexagon served by APs with an antenna hav-