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Journal of Computer Applications, Vol – II, No.2, April-June 2009 Page No. 24
OPTIMIZATION ALGORITHMS FOR ACCESS POINT
DEPLOYMENT IN WIRELESS NETWORKS
S.F.Rodd,
Asst. Prof., Dept. of ISE,
GIT. Belgaum.
Email ID : sfrodd@git.edu
M.M.Math,
Asst. Prof. & Head,
Dept. of ISE, GIT, Belgaum.
Anand H. Kulkarni,
Asst. Prof. Dept. of ISE,
GIT, Belgaum.
Abstract
Wireless Local Area Networks (WLANs) have
become very popular as they provide mobility for the
nodes and the convenience with which such networks
can be setup. However, there are important design
considerations while setting up such networks. This
paper focuses on the issues in the design of wireless
networks and discusses several proposed techniques.
The important issues are node coverage, co-channel
interference, signal strength and the desired
bandwidth at the nodes. Several solutions have been
proposed to address these issues and these solutions
are based on Discrete gradient optimization
algorithm[1], Genetic Algorithmic approach[8] and
Global Optimization technique[4]. In this paper we
review these three techniques and propose a new
search technique based on Heuristic approach.
Keywords
Access Points, Global Optimization, Signal
Coverage, Heuristic.
1. Introduction
Wireless Local Area Networks have become
common place at home and office environments as
they provide mobility to the users and also they can
be setup with very little effort. Mobile Adhoc
Networks do not even require any additional
infrastructure for forming a network. To setup a
WLAN all that is required are a few Access
Points(APs) that are strategically located. These
Access Points have an Omni-directional antenna that
sends wireless signals uniformly in all directions.
However, it is no easy task to decide on the number
and locations where these APs have to be fixed in an
indoor environment so as to provide not only
coverage but ensure minimum signal strength at all
node points, requisite bandwidth, in the presence of
obstructions, reflections and signal interference.
Design of this nature is very complex and needs
proper modeling and formulating the problem as an
optimization problem with several constraints.
The indoor environment may consist of several
compartments, nodes spread across the entire floor
area. The nodes are assumed to be fixed in their
position and the access points when they radiate
energy, the energy loss as a function of distance, loss
due to obstruction and signal interference from
reflected energy is to be considered while modeling
the network. The amount of signal attenuation as a
result of obstruction depends on the material used in
the obstruction. If the node is place inside a partition
made of aluminum or glass material, the typical
value of absorption coefficient is 0.7. On the other
hand if a wall made of bricks and coated with cement
then the absorption coefficient depends on the
thickness of the wall. The walls and ceilings acting as
reflecting surfaces, the effective signal strength at the
nodes depends on the reflection coefficient and the
phase with which the direct and reflected signals
meet the receiver.
This paper is organized as follows. In section 2,
we present the basic mathematical model, followed
by that a refined model that accounts for attenuation
due to obstruction and interference due to reflection.
Section 3 describes the three different algorithms to
solve this optimization problem. In section 4 we
describe the new Heuristic Search Technique(HST).
In section 5 we discuss the results of simulation and
compare with respect to signal strength, coverage and
bandwidth. Finally, the conclusions are given in
section 5.
2. Mathematical Model
The mean path loss Pth as a function of distance
is given by
Pth(d) = Pth(d0) + 10nlog10 (d/d0) --- 2.1
Where d is the distance from the access point and the
first term Pth(d0) the constant loss at a reference
distance. The distance d0 is typically 1 meter. The
multiplication factor n has a value equal to 2 in free
space. The first term can be computed using the
following formula
Pth(d0) = 20 log 10 ( 4 π d0/ λ ) --- 2.2
Where λ is the wavelength of the radiated RF energy.
The path loss at a distance d in the presence of soft
and hard partitions can be written as
Pth(d) = Pth(d0) + 20 log10 (d/d0)+ A_SP[db] +
A_HP[db] +A_OR_GDREF --- 2.3
where, A_SP and A_HP are the attenuation due to
soft and hard part itions. A__OR_GDREF is the
factor that accounts for Attenuation or Gain due to
reflections from the surrounding walls and ceiling. In
the design of a WLAN with N nodes and M Access
Points the Objective function is to minimize the loss
at the nodes, so as to obtain a signal strength slightly
Journal of Computer Applications, Vol – II, No.2, April-June 2009 Page No. 25
greater than the required minimum. This can be
formulated as under. Let us designate the path loss at
node i due to access point j as PL_ni_aj. Therefore
the total path loss due to all the access points at a
given access point must satisfy the following
constraints.
3. Solutions of the Model
3.1 Descent Gradient Method
Let y=f(x) have a maximum at xmax. Pick an
arbitrary value for x, say x1. Compute f'(x1). If the
slope of y is positive at x1, i.e. f'(x1) > 0, then xmax > x1
lies to the right of x1. Likewise if f'(x1) < 0, then xmax
< x1 lies to its left. Thus we know the direction in
which x1 should be updated in order to approach xmax.
In fact this direction is given by f'(x1). So we can use
the update rule:
x1 = x1 + ηf’(x1) --- 2.6
where ηis a positive constant. If η is sufficiently
small, and there is indeed a maximum for f, the above
update rule will converge to it after a finite number of
iterations. As applied to the current problem of
deploying APs, the next AP position to be selected
would be in a direction where the objective function
has the steepest gradient.
3.2 Genetic Solution
In this approach, the entire floor area is divided
into cells of appropriate size and the nodes and APs
are placed inside these cells. In genetic approach, an
initial population has to be created by randomly
placing the APs across the grid structure. Genetic
operations such as mutation, crossover are then
applied to these initial genes to generate the next
generation genes. An appropriate fitness function for
this problem domain is used to decide on the fitness
of the gene to get promoted to the next generation.
This process is repeated until a satisfactory solution
is obtained. The problem with this approach is that
the convergence of the method is very slow and
depends on the
min ∑ PL_ni_aj – PLmax>=0
M
min ∑ PL_ni_aj – PLmax>=0
j = 1 --- 2.4
where, PL is the Maximum acceptable path loss at
any node. The PLmax is calculated as under:
PLmax = Pt-Rth
Where, Pt is the transmitted power and Rth is the
receiver threshold. A feasible solution (a1,a2,….aM)
exists only if
N M
∑ ( min ∑ PL_ni_aj – PLmax ) = 0 --- 2.5
i =1 j = 1
parameters like the initial population, mutation
probability, crossover point etc.
3.3 A Global Optimization(AGOP) technique
Global Optimization technique is designed to
solve unconstrained and continues optimization
problems. The problem can be formulated as :
f(x) : Rn Æ R such that x ∈ B where B is a
given Box constraint.The AGOP must be given an
initial set of points x say Ω = x1,x2,x3…..xq ⊂ Rn.
Suppose x* be a point in Rn that has the smallest
value for the objective function that is, f(x*)<= f(x)
for all x ⊂ Ω. A possible approach has been
developed for finding a possible descent direction at
point x*. An inexact search along this direction
provides a new point xq+1. A local search around
this point is then carried out. This is done using local
variation method. This is an efficient local
optimization method that does not directly use
derivatives and can be applied to non-smooth
functions. The set is augmented with this new value
and the whole process is again repeated. The process
is terminated when v is approximately 0 or a
prescribed number of iterations are carried out The
solution returned would be the value x*.
4. Heuristic Approach
The idea here is, to divide the floor area into a
grid. The cell size should be large enough to occupy
an access point and a receiver. The method begins
with random locations of the APs. It then
heuristically, estimates the signal strengths at the
receivers by moving in the four diagonal directions.
The cell that shows the best signal strength is chosen
as the next AP position.
Fig 4.1 - Heuristic Search Technique : Circles
Æ
Nodes Rectangles
Æ
Access Points
If the two diagonal positions show almost
equal signal strength then the AP is moved on a
horizontal line that lies between these to diagonal
positions. Only one AP is moved at a time and each
AP is moved in turn until the desirable signal strength
and coverage is obtained. The process can be best
described with the following algorithm.
A
A
A
Journal of Computer Applications, Vol – II, No.2, April-June 2009 Page No. 26
4.1 Heuristic Algorithm
1. Read the floar Area.
2. Draw a grid.
3. Compute the number of Access Points(APs).
4. Lay the receivers and APs.
5. For each Access Point APi do the following :
Estimate the Pathloss according to the eq. by
moving the AP diagonally
6. Decide the direction of movement using the above
described technique.
7. Check if desired results are obtained if not repeat
step 5 else Goto step 8.
8. Print Solution and Stop.
5. Conclusion
In this paper we have presented a model to
design a Wireless LAN of strategically deploying the
Access Points so as to network the nodes in a given
area taking into account signal degradation,
obstructions and reflections. We have formulated the
design problem as an optimization problem with the
important constraints. Three techniques have been
presented to solve the design problem namely,
Discrete Gradient Method, Genetic Approach and
Global Optimization Technique. Though all of these
provide satisfactory solutions however, they either
suffer from high computational complexity, slower
convergence and implementation difficulties. In this
paper a new technique namely, Heuristic Search
Technique is also discussed which is much simpler to
implement and provides faster and accurate solution.
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