20-07-2012, 03:12 PM
On Multihop Distances in Wireless Sensor Networks with Random Node Locations
101.On Multihop Distances in Wireless Sensor Networks with Random Node Locations.pdf (Size: 2.48 MB / Downloads: 33)
INTRODUCTION
METHODS providing information on the distribution of
the euclidean distance between nodes in wireless
sensor networks (WSN) are regarded as versatile tools for
protocol parameter tuning and performance modeling.
Therefore, internode distance estimation is of profound
importance for various WSN applications. For instance,
when urgent data are disseminated from a source node via
broadcast, it is critical to estimate the covered distance as a
result of a sequence of data forwards. Similarly, estimation
of the hop distance between two network locations is
equivalent to estimating the minimum number of hops,
which leads to maximization of the distance covered in
multihop paths. Furthermore, hop distance estimation is
closely related with transmission delay estimation and
minimization of multihop energy consumption.
GREEDY MAXIMIZATION OF MULTIHOP EUCLIDEAN DISTANCE
Network Model
WSNs considered in this study consist of sensors with
circular communication ranges of radius R. Node locations
are static and uniformly distributed with a planar density
. Hence, the number of points n that can be found in a
given area A has a Poisson distribution given by
pnðnÞ ¼ ðAÞneA
n! . It is assumed that nodes can receive every
packet transmitted within their communication ranges.
Definition of Maximum Multihop Euclidean Distance
In a 2D network of randomly located nodes, there exists
only one node with the maximum distance that can be
reached in a given number of hops. Due to spatially random
node locations, the position of this node as well as its
distance to the source node is random. However, analytical
computation of the maximum euclidean distance in N hops
involves considering all nodes in the previous hops and
recursively reaches the source node of the multihop
propagation, which becomes intractable even for small
instances. Hence, we propose a greedy method of maximization
of the euclidean multihop distance. By selecting
locally maximally distant nodes, the multihop propagation
intends to reach further distances to the source node.
Approximation Accuracy for Different Angles
Before moving to the performance analysis of the derived
approximation expressions, the effect of on the accuracy
of the derived expressions is evaluated. Fig. 11a illustrates
the average percent error in E½dN. For each value of , the
error of E½dN approximation decreases with increasing
node density and settles to a value less than 0.2 percent,
except for ¼ =6 which requires a larger node density to
stabilize. One obvious observation is the decreasing amount
of percent error in E½dN approximation for larger angles,
which shows that our approximation is more accurate when
single hops cover larger angular ranges.
The choice of a large angle, however, causes instability in
the approximation of the standard deviations shown in
Fig. 11b. Despite the decrease in the percent error, the
percentage error of dN has a noticeable incline when ¼
5=12 for node densities larger than ¼ 0:001 nodes=m2.
The increasing error for large angles is due to the multiplication
of the two approximated values of E½di1ri and
cosi in (13). Although these two terms are approximated
with high accuracies of the order of 2.5 and 0.62 percent,
respectively, their multiplication creates significant terms
when and are large.