Communications and Network, 2013, 5, 30-36
doi:10.4236/cn.2013.52B006 Published Online May 2013 (http://www.scirp.org/journal/cn)
Terrain Details Effect on Connectivity in Ad hoc
Wireless Networks
Sonja Filiposka, Igor Mishkovski, Blanka Taslamicheska Trajkoska
Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University, Skopje, R. Macedonia
Received 2013
ABSTRACT
In this work, we conduct a research on the effects of the details of the terrain on the path establishment in wireless net-
works. We discuss how the terrain induced variations, that are unavoidably cau sed by the obstruction s and irregularities
in the surroundings of the transmitting and the receiving antennas, have two distinct effects on the network. Firstly, they
reduce the amount of links in the network connectivity graph causing it to behave more randomly, while decreasing the
coverage and capacity of the network. Secondly, they increase the length of the established paths between the nodes.
The presented results show how the terrain oblique influences the layout of the network connectivity graph, in terms of
different network metrics, and gives insight to the appropriate level of details needed to describe the terrain in order to
obtain results that will be satisfyingly accu rate.
Keywords: 3D Terrain Aware Propagation; Network Connectivity Graph; Path Length Distribution
1. Introduction
Propagation models for wireless networks have tradi-
tionally focused on predicting the average received signal
strength at a given distance from the transmitter, as well
as the variability of the signal strength in proximity to a
particular location. Typically, when estimating th e ad hoc
network performances v ery little attention is given to the
terrain [1], and thus, to the propagation model used for
the estimation [2-4]. The nodes are assumed to be scat-
tered on a flat, regular terrain and a simple ground reflec-
tion propagation model is used.
However, radio transmission in a mobile communica-
tions system often takes place over irregular terrain.
Since terrain irregularities can greatly affect and distort
the expected network performances, great care must be
taken when trying to reflect the real-life use of the mod-
eled network. Therefore, the terrain profile of a particular
area needs to be taken into account when estimating the
path loss since the transmission path between the trans-
mitter and the receiver can vary from simple line-of-sight
to one that is obstructed by building s , hillsides or foliage.
In this paper we investigate the influence of th e terrain
detail level on the network connectivity, coverage and
capacity for a typical ad hoc network simulation. Fur-
thermore, we investigate how the different detail level of
the terrain influences the layout of the network connec-
tivity graph, especially in terms of network partitioning,
average path length, node degree distribution and similar
metrics from graph theory. Addition ally, using 3D terrain
wireless simulations in NS-2 we study the influence of
the network connectiv ity graph changes on the multi-hop
path establishment and network performances.
The results from this paper are intended to show how
the terrain can increase the average path length, while
also increasing the overall network performances, be-
cause of the possibility of increased number of parallel
radio transmissions. The results help the user to choose
the appropriate level of details fo r a given terrain in order
to obtain more realistic results with faster simulations.
The rest of this paper is organized as follows: Section
2 is an introduction to terrain aware propagation and the
terrain model. In Section 3 we use metrics from graph
theory to analyze the ch ang es in th e network connectiv ity.
Section 4 presents analyses of the performances of the
case study ad hoc network over 3D terrains with different
detail level. Finally, Section 5 concludes this paper.
2. Terrain Aware Propagation Models
There have been a number of different implementations
of terrain aware radio propagation models, mostly in the
form of a new framework for simulations. Examples
typically include introducing a new realistic simulation
framework, like the case for urban vehicle to vehicle
networks [5], wherein the authors developed a new
simulation tool to evaluate the performance of event dis-
semination protocol in realistic city traffic environment.

S. FILIPOSKA ET AL. 31
Another interesting implementation is the AMADEOS
extension [6] to NS-2 and Glomosim[7]. In addition to
the developed mobility models, it provides a ray-tracing
routine combined with a geometry DXF file that de-
scribes environment characteristics. The algorithm is
based on a 2D ray tracing technique and is more than
seven times slower than the two-ray ground simulations.
The OPNET's Terrain Modeling Module (TMM) [8]
also adds Earth topology, such as mountains, forests and
valleys, as well as user-selectable environmental condi-
tions to the simulated network model. There are several
terrain aware propagation models that are included: the
Longley-Rice model [9], TIREM [10] and the Wal-
fisch-Ikegami model [11]. TMM imports and graphically
displays elevation information from Digital Terrain Ele-
vation Data (DTED) and the US Geological Survey
Digital Elevation Maps (USGS DEM) formats, enabling
accurate calculation of signal strength.
In this paper a similar approach to TIREM is used. The
3D terrain aware propagation model used is a Durkin’s
extension based on knife edge diffraction for the open
source NS-2 [12]that will provid e the users with the abil-
ity to add terrains into triangular irregular network (TIN)
format.
The TIN model is one of the most common vec-
tor-based models of surface. It represents a surface as a
set of contiguous, non-overlapping triangles. Within each
triangle the surface is represented by a plane. The trian-
gles are defined with a set of points called mass points.
These mass points can occur at any location, the more
carefully selected, the more accurate the model of the
surface. A TIN-based model is able to describe features
very well. Although grid based DEMs are easy to handle,
triangulated irregular network models (TINs) have be-
come increasingly popular for the representation of ter-
rain surfaces because of their ability to accommodate
irregularly spaced elevation data. It enables them to adapt
to the variable complexity of the relief and to integrate
structural features (breaklines, ridges, ...) in the terrain
model [15]. A diversity of TIN-based interpretation pro-
cedures is already available today. It has been shown that
many of these procedures have clear advantages over
their grid-based counterparts [16,17].
Since the TIN format needs less data to represent the
terrain, the simulations are a lot faster compared to the
DEM based solutions. TIN also offers another opportu-
nity for the user, i.e. adaptable detail level of the terrain
description by changing the level of mean or max error.
The lower the detail level, i.e. the number of triangles,
the bigger the RSME and max error, but, on the other
hand, the simulations run faster. In order to get a more
clear picture how the RSME and max error change when
the number of triangles is increased, we have generated a
great deal of different representations of one example
TIN terrain. Table 1 summarizes some of the obtained
results for o ne example terrain with size 1000 x 1000 m,
where the mean height is 783.20 m and the standard de-
viation to this value is 19.93 m (hilly terrain).
As it is shown in Table 1 the erro r is rapid ly decreased
with the increased number of triangles up to a certain
point. We discovered that when the max error is less than
1 m, i.e. for more than 4000 triangles, the terrain repre-
sentation is quite acceptable for graph theory analysis or
network simulations. Adding more than 12456 triangles
does not improve the terrain accuracy, because the rep-
resentation is an exact match to th e real life terrain.
3. Graph Connectivity Analysis
In order to investigate the essential properties of ad hoc
networks, such as connectivity and degree distribution,
one needs realistic modeling. This Sectio n is d edicated to
better understan d how the fundamental properties change
in different environment and analyzes the prerequisite for
reliable user application connections in the network.
The analysis of coverage and connectivity in wireless
ad hoc networks modeled using 3D terrains and suitable
propagation model can be addressed using tools and re-
sults from graph theory.
Network connectivity ha s be en an active research top ic
in the scientific community. Hekmatand and Miegh em in
[18] have studied connectivity in wireless ad hoc net-
works when using statistically variable radio signal
power. Barrett et al. in [19] focused on the computation
of the connectivity graph for large networks and explore
approximation alternatives to compute graph connec-
tivity by examining different graph metrics. In [20],
Miorandi and Altman present an analytical procedure for
computing the node isolation probability in presence of
channel randomness. However, in our work instead of
using random statistical variables we analyze the connec-
tivity using radio propagation model that is based on
knife edge diffraction that occurs because of terrain ob-
stacles.
A wireless ad hoc network consists of a number of
wireless nodes scattered over a certain geographic area.
Every node may be connected to other nodes in its vicin-
ity. We assume that connections between nodes are two-
way, undirected links. At any instant in time an ad hoc
Table 1. Statistical data on tin terrain accuracy.
# triang.RSMEmax
error mean error min height max height
12456 0.00 0.00 0.00 741.00 830.33
4000 0.30 0.75 0.21 741.00 830.00
200 2.18 7.31 1.69 741.67 821.67
10 13.39 42.81 10.09 748.00 810.00

S. FILIPOSKA ET AL.
32
network can be considered as a graph with a fixed topol-
ogy. The actual set of connections depends on the geo-
metric distance between nodes. Graphs with distance-
dependent links between nodes and correlated links are
referred to as random geometric graphs [21].
When assuming a flat terrain, the n etwork co nnectivity
graph is a random geometric graph, wherein each node
has a transmission range represented as circle with a
fixed radius. However, when considering the terrain ef-
fect on propagation , this is no long er tru e and pr even ts us
from continuing to use the random geometric graph ap-
proach. When taking into account the terrain features, a
number of nodes will no longer be able to communicate
directly due to obstacles existing between them. How-
ever, in special cases, there could also be newly estab-
lished links because of the effects of the diffraction. Fig-
ure 1 presents the network connectivity graph for 100
uniformly rando mly scattered wireless ad hoc nodes on a
flat terrain. This number of nodes is chosen so that for
the given network area size (1000 x 1000 m) and as-
sumed flat terrain, the randomly scattered nodes always
form a connected graph. Figure 2 shows how the con-
nectivity changes in presence of terrain. The network
connectivity graph is obtained by calculating the radio
coverage of each node in the network by using the terrain
aware propagation model. When comparing the two
connectivity graphs, we observe that the terrain induces a
certain level of ‘localization’ or grouping of the nodes
according to their vertical positioning (height). There are
also two completely ‘dark’ unconnected nodes (node ID
90 - upper left and node ID 82- lower right corner). Fur-
thermore, the network connectivity graph is sensitive to
the number of triangles used to describe the terrain.
We have applied different graph theory metrics in or-
der to measure the changes of the network connectivity
graphs. The results shown in Table 2 confirm that using
a terrain representation with max error less than 1m gives
almost identical results as using maximum number of
triangles (i.e. 12456 triangles). As the number of trian-
gles increases the network density (i.e. the number of
edges and average node degree) decreases. As a conse-
quence, the average and the maximum distance between
the nodes are increased. Please note that these values are
calculated for the reachable nodes only. The most distant
nodes (in terms of number of hops) are always located at
the opposite edges of the terrain, as it is expected. It is
interesting to note that even for a small number of trian-
gles (beginning from 20 in our case) the network is
fragmented in several partitions increasing th e number of
unreachable paths. The number and the structure of the
partitions are strongly influenced by the terrain oblique.
For our example terrain represented with more than 20
triangles the network is partitioned in five clusters (two
of which have only one node, the others have 4, 12 and
the giant componentsize equals to 82 nodes). The only
case in which we did not o bserve network partitio ning is
when using 10 triangles to represent the terrain features;
however, this representation is far from accurate (see
Table 1).
Figure 1. Connectivity graph for an example ad hoc network
on a flat terrain.
Figure 2. Connectivity graph for an example ad hoc network
on a TIN terrain based on 4000 triangles (minheight deep
green –max height white).
Table 2. Connectivity graph ch anges due to terrain effects.
Flat with terrain aware 3D propagation
# triang.
Metric 0 10 200 400012456
# edges 797 605 351 333 339
avg. node degree 0.677 0.708 0.697 0.6280.641
avg. distance 2.839 3.417 4.374 4.4044.460
most distant nodes 5 & 906 & 73 6 & 38 5 & 132 & 29
max distance 6 8 8 10 10
# unreachable pairs 0 0 3010 31143114

S. FILIPOSKA ET AL. 33
In connected graphs there is a natural distance metric
between all pairs of nodes, defined by the length of their
shortest paths. Thus, the more central a node is, the lower
its total distance to all other nodes. Closeness can be re-
garded as a measure of how fast it will take to send in-
formation from one to all other nodes sequentially [18].
Figure 3 shows the closeness centrality value for all the
nodes in the network for the terrain represented with dif-
ferent number of triangles. In the case of flat terrain (i.e.
the number of triangles is 0) the nodes are more central,
i.e. the distance from any node to all other nodes is small.
Whereas, in the case of high resolution terrain descrip-
tion (using 12456 triangles) the nodes are further apart
from each other, i.e. they have greater closeness value.
In Figure 4 we plotted some results in terms of dis-
tance distribution for various numbers of triangles used
to represent the terrain. It can be concluded that in all
cases the prevalent distances in the network are remain-
ing to be 3 and 4 hops long. The introduction of the ter-
rain decreases their frequency while increasing the num-
ber of longer paths. We again confirm that choosing a
terrain that is represented by more than 4000 triangles
(less than 1m max error) does not influence the distance
distribution.
4. Network Performance Analysis
In the previous Section we have analyzed network con-
nectivity graph independen tly from the traffic load in the
network. On the physical layer, connectivity between
nodes is predicted by the radio propagation model.
Whether two connected nodes can communicate with
each other also depends on the interference condition
which is directly linked to parallel communication be-
tween other nodes in the network. Due to interference,
communication between two connected nodes may even
Figure 3. Closeness centrality for the connectivity graph
with a different terrain detail le vel
Figure 4. Distance distribution for the connectivity graph
with a different terrain detail le vel.
become impossible at certain moments. Thus, interfer-
ence can be considered as a capacity-affecting factor.
This Section investigates the changes of the interference
induced network connectivity between the nodes.
The primary objective of our case study simulations is
to understand the impact of the amount of details used to
represent the terrain in a simulation environment for
wireless ad hoc networks. In this Section we investigate
the aspects of traffic throughput, average path length of
the received network traffic, distance distribution for the
received and dropped network traffic and the average
routing load of the nodes for the Durkin’s propagation
model using TIN files with different level of details. For
the case study evaluations made in this paper, we decided
to work with a number of real terrains, but since the ob-
tained result trends are statistically equa l, here we present
the results for the real terrain given in Figure 2.
The terrain is described by a number of TIN files from
10 to 12456 triangles. The complete ad hoc network of
100 nodes all equipped with an IEEE 802.11b radio and a
transmission range of 250 m. The nodes are uniformly
scattered in the terrain area. The routing protocol used is
AODV [23]. The traffic pattern is a completely random
traffic between the nodes with the offered traffic of
3Mbps. We created one scenario for each terrain repre-
sentation with a different detail level based on the num-
ber of triangles. It was crucial that the traffic pattern and
positioning pattern scenarios are defined only once and
are used for all the terrains so that the differences in the
results are exclusively due to the terrain discrepancies.
The results shown here are averaged over the results ob-
tained for 1 0 different generate d scenarios.
On Figure 5 the obtained results for the end-to-end
received traffic (in percentage) when using terrains rep-
resented with a different number of triangles (from 0 to
12456) are show n. When using ter rains that are descr ibed

S. FILIPOSKA ET AL.
34
using more triangles (for which we are sure that the
maximum error is less than 1 m), the obtained results are
converging to the same value. However, it is more inter-
esting to conclude that even for a lesser number of trian-
gles the results can still be taken into consideration with
some skeptics in mind. As it is shown, for terrains with
more than 400 triangles the results fit within a close
range. Given that the simulations are many times faster
when the number of triangles is smaller, with regards to
Table 1, we can conclude that in cases when we need
fast first order approximation we can use terrains that are
generated with a relatively small number of triangles.
When using flat terrain the end-to-end received traffic
is around 8.2%, which is 2 times less compared to the
case when using 12456 triangles to represent the terrain.
This is due to the fact that the obstacles between the
nodes allow multip le parallel transmissions to occur.
The average path length of the received network traffic
for the example ad hoc network is presented in Figure 6.
The presence of the terrain drastically increases the av-
erage path length. However, the amount of detail levels
does not increase it on a large scale. The relative increase
in average path length is equal for the connectivity g raph
(see Table 2) and for the simulated network results,
valuing aro und 60%.
The influence of the increased average path length is
shown in more details in Figure 7, which represents the
distance distribution for the received network traffic for
the example ad hoc network on a different terrain detail
level. Most of the received network traffic for the flat
terrain is due to one hop-direct communication. In the
case of using terrains the amount of one-hop received
traffic decreases, while most of the received traffic is
sent by 2 or 3 hops. Furthermore, for the flat terrain al-
most all of the received traffic is transmitted via less than
6 hops. Another important result is that most of the
dropped traffic occurs at the sender. This means that
Figure 5. Received traffic of the offered traffic for the exam-
ple ad hoc network on a different terrain detail level.
while the packets wait in the qu eue, the sender is not ab le
to find a suitable route to the destination and because of
the high amount of sending traffic the queue keeps in-
creasing and eventually starts to drop packets.
The average node load in terms of forwarded packets
for the example ad hoc network is shown in Figure 8.
We calculate the average node load as the number of
packets one node has forwarded acting as a router in a
multi-hop path. Keep in mind that this does not always
mean that the end-to-end connection was successful. The
packet may have been dropped further along the rou te.
In the case of flat terrain most of the traffic is received
only by one hop and the ad hoc network nodes are under
drastically lesser load compared to the terrain aware
simulation scenarios. However, similar to the case of
average path length and the percentage of received traffic,
the increased amount of detail levels does not induce
more routing load to the nodes on a large scale.
Figure 6. Average Path Length for the received network
traffic on a different terrain detail level.
Figure 7. Distance distribution for the received network
traffic on a different terrain detail level.

S. FILIPOSKA ET AL. 35
Figure 8. Average node load for the received network traffic
on a different terrain detail level.
5. Conclusions
In this paper we have presented an analysis of the influ-
ence of the terrain detail level on the path establishment
in wireless ad hoc network by exploring the changes in
the network connectivity graph. We have also investi-
gated the difference of the obtained results compared to
the behavior of a wireless ad hoc network deployed on a
flat terrain. The main conclusion is that the terrain de-
creases the number of links between the nodes, which
leads to longer paths and network partitioning. However,
this does not necessarily mean lower performance. On
contrary, the obstructions between the nodes can allevi-
ate the interference and, in some cases, improve the net-
work performances. Another goal of this work was to
determine the amount of terrain detail necessary to obtain
satisfyingly accurate results. The results show that when
using relatively small number of triangles to represent
the terrain, the network behavior is close to the most de-
tailed scenario, while the simulation runs several times
faster.
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