ap-5-11.dvi


Acta Polytechnica Vol. 51 No. 5/2011

Topology Control with Anisotropic and Sector Turning Antennas in
Ad-hoc and Sensor Networks

V. Černý

Abstract

During the last several years, technological advances have allowed the development of small, cheap, embedded, inde-
pendent and rather powerful radio devices that can self-organise into data networks. Such networks are usually called
ad-hoc networks or, sometimes, depending on the application field, sensor networks. One of the first standards for
ad-hoc networks to impose itself as a fully industrial framework for data gathering and control over such devices is IEEE
802.15.4 and, on top of it, its pair network architecture: ZigBee. In the case of multiple radio devices clamped into
a small geographical area, the lack of radio bandwidth becomes a major problem, leading to multiple data losses and
unnecessary power drain from the batteries of these small devices. This problem is usually perceived as interference. The
deployment of appropriate topology control mechanisms (TC) can solve interference. All of these algorithms calculate
TC on the basis of isotropic antenna radiation patterns in the horizontal plane.

Keywords: ad-hoc network simulation, interference, antenna radiation patterns,mobile network simulation, Omnet++,
topology control, interference, sector antennas, rotating antennas, wireless networks, anisotropic antennas, sensor net-
works.

1 Introduction
Event simulators such as Omnet++ were developed
inorder to study interferencewithout thedeployment
of large and sometimes expensive networks. How-
ever, these simulators lack the proper radio propaga-
tion characteristics that are crucial for understanding
the interference phenomenon. The widely-used ra-
dio propagationmodel is isotropic (in the horizontal
planewe can imagine it as a circlewith the transmit-
ter in the center). This radio pattern is very hard to
achieve in the real world. In addition, this model is
unusable for simulating the radio patterns of sector
antennas.
Classical TC is based on graph theory alone,

and does not take into account antenna radiation
patterns, propagation, receiver sensitivity or any
other radio-related characteristics. Such algorithms,
e. g. Relative Neighbourhood Graph [1], Gabriel
Graph [1], Yao Graph [1], Minimal Spanning Tree,
XTC, ITC [2], etc. are based on the following as-
sumptions: all nodes are situatedonaflat surface, no
radio propagation model is involved (coverage being
determined on geometric properties only), antennas
areperfect emitters (isotropic radiopattern), and the
receiver is a perfect receiver with no minimal sen-
sitivity threshold. Power regulation is modeled by
varying (with infinitely fine increments and with no
maximal limit) the radius of the circle that defines
the radiation pattern. Such simplified models are
easy to test, but they are very far removed from real-

ity. To obtainmore realistic output it is necessary to
involve new transmitter properties in our simulation.

2 A better antenna
simulation model

For our simulation we do not need the whole 3D an-
tenna propagation pattern because we work only in
the horizontal plane, hence flat pattern is sufficient.
The modeling is performed by sampling the signal
power around the modeled transmitter. The correct-
ness of such a model can by adjusted by changing
the size of the sampling step. All measured received
power values are recomputed to gain values [3].
In order to obtain an antenna model that is easy

to understand and adapt, the radiation pattern for
each antenna is defined inOmnet++as anXMLfile.
Eachsimulatednodecanbe coupledwithoneormore
modeled antennas; in this way, studies of spatial di-
versitycanbeperformedeasily,with little ornomod-
ification to the model itself. Below is a sample code
of an antenna radiation pattern:

<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE antenna SYSTEM "Antenna.dtd">
<antenna>
<angle min="0" max="10" gain="0.76" />
<angle min="10" max="20" gain="0.26" />
...
</antenna>

24



Acta Polytechnica Vol. 51 No. 5/2011

The code was shortened due to the length of the
file. This slicing into 10-degree sectors gives good re-
sults for reasonable amounts of run time and for the
algorithm. The radiation pattern for the above an-
tenna (using the complete set of data) is provided in
Figure 1 and Figure 2.

Fig. 1: Gain distribution
pattern of a rubber-duck
antenna measured in the
antenna chamber

Fig. 2: Gain distribution
pattern of a rubber-duck
antenna in Omnet++

3 TC algorithms with
anisotropic antennas

This section contains the adapted (towards anisotro-
py) versions of the classical topology control algo-
rithms.

3.1 ARNG — Anisotropic Relative
Neighbourhood Graph

The subgraph G′ = ARN G(G) = (V, E′) obtained
from graph G, where E′ is:

E(G)′ = {(p, q) ∈ V × V |u ∈ V \ {p, q}, (1)
u �∈ σ(p) ∩ σ(q)}

Where σ(p) and σ(q) are the irregular shapedcov-
erage areas of the communication nodes, defined as
the zonewhere the signal receivedbyanantennahav-
ing gain0dBiwill be at least theminimal power level
Pmin, when p respectively q acts as a transmitter, Fi-
gure 4.

Fig. 3: Step condition in
RNG

Fig. 4: Step condition in
ARNG

3.2 AGG — Anisotropic Gabriel
Graph

The subgraph G′ = AGG(G) = (V, E′) obtained
from graph G, where E′ is:

(p, q) ∈ E′if fΓp,q ∩ V \ {p, q} ∩ σ(p)∩ σ(q)= ∅ (2)

Γp,q = D

(
p + q
2

,
δ(p, q)
2

)
(3)

Put into words, the zone represented by the in-
tersection of the disc centred in the middle of the
segment (p, q) andwith as its diameter the Euclidian
distance between p and q, intersectedby the irregular
coverage areas of p and q must be empty in order for
the edge (p, q) to be included in the E′ set, Figure 6.

Fig. 5: Step condition in
GG

Fig. 6: Step condition in
AGG

3.3 AYG — Anisotropic Yao Graph

The subgraph G′ = AY G(G) = (V, E′) obtained
from graph G, where E′ is:

(p, q) ∈ E′if f δ(p, q) ≤ (4)
≤ ( min

v∈Cp,q\{p,q}
{δ(p, v)})∧ (q ∈ σ(p))

Put into words, in each sector around node p
we choose to connect to the closest node q that lies
within the irregular coverage area of node p; even
though node r is in the same sector closer to p than
q, node p will not connect to it if r is outside the cov-
erage area of p, Figure 8 (the arrow represents the
node to connect to, and not an oriented edge).

Fig. 7: Step condition in
YG

Fig. 8: Step condition in
AYG

3.4 Examples of simulated networks

Table 1 presents the differences between classical and
anisotropic structures for a network containing auni-
form randomplacement of 50 communication nodes.
For the anisotropic simulations, the chosen antenna
type was rubber-duck; this is motivated by the fact
that it has the radiation pattern closest to the ideal
dipole. It can be clearly seen that even in this case
there are (minor) differences.

25



Acta Polytechnica Vol. 51 No. 5/2011

Table 1: Comparison between classical and anisotropic
topology control algorithms

Type Isotropic Anisotropic

RNG

GG

YG

4 Particular case: high gain
sector turning antennas

A sector turning antenna “i” is defined as a touple
ST Ai(x, y, G1, G2, ϕ, θ, P , A, Pmin, Pmax, P rmin,
P imin, Δθmin,ΔPmin), by the following parameters
〈in brackets is the measure unit〉:
• coordinates in plane: x 〈m〉, y 〈m〉;
• gains: G1 〈dBi〉, G2 〈dBi〉; with G2 > G1;
• opening of the main lobe: ϕ 〈deg〉;
• rotation of the symmetry axes of the main
lobe towards north (azimuth/azimuthal angle):
θ〈deg〉;

• power injected in the antenna: P 〈dBm〉;
• antenna aperture: A 〈m2〉;
• minimal and maximal power levels: Pmin〈dBm〉
and Pmax〈dBm〉, respectively;

• minimal power threshold required for proper
data reception: P rmin〈dBm〉;

• minimal power threshold beyondwhich interfer-
ence is registered: P imin〈dBm〉;

• azimuth angle resolution: Δθmin〈deg〉, with the
condition Δθmin ≤ ϕ (in order to cover all the
area around the antenna through rotation);

• power resolution: ΔPmin〈dBm〉;
• i is the index to keep a record of the antennas in
the network.
In this model, parameters x, y, G1, G2, ϕ, A,

Pmin, Pmax, P rmin, P imin,Δθmin andΔPmin arefixed
(antennas do notmove in a plane and do not modify

the radiation lobe parameters, the limit power levels
or theminimal variation intervals for power or turn).

a) b) c)
Fig. 9: Example of a 2.4 GHz sector antenna. 1a – real
antenna; 1b – radiation pattern; 1c – simulated radiation
pattern

a) b) c)
Fig. 10: Example of a Ferimex sector antenna. 1a – real
antenna; 1b – radiation pattern; 1c – simulated radiation
pattern

a) b) c)
Fig. 11: Example of a Yaggi-Uda lobe antenna. 1a – real
antenna; 1b – radiation pattern; 1c – simulated radiation
pattern

4.1 n-Sector turning antenna

A n-sector turning antenna is an extended ST A,
a touple: nST Ai(x, y, G[], ϕ[], θ, P, A, Pmin, Pmax,
P rmin, P imin,Δθmin,ΔPmin), where all the parame-
ters excepting G[] and ϕ[] have the same definition
as in the STAdefinition. G[] represents the gain vec-
tor G[] = G1, G2, . . . , Gn−1, Gn, Gn−1, . . . , G2, G1,
where G1 < G2 < Gn and ϕ[] represents the open-
ings vector ϕ[] = ϕ1, . . . , ϕn, where ϕj is the angle
opening of the zone having gain Gj. This type of
antenna mimics the behaviour of lobe-antennas such
as Yaggi-Uda antennas (Figure 11).

4.2 Network composed of turning
sector antennas

A cluster composed of sector turning antennas is
defined by a touple K(nk, Xk, Yk, xk, yk, ST A[k]),
where:
• geographical extent of cluster: Xk 〈m〉, Yk 〈m〉;
• geographical coordinates of the centre: xk 〈m〉,

yk 〈m〉;

26



Acta Polytechnica Vol. 51 No. 5/2011

• number of antennas nk 〈〉;
• ST A1, ST A2, . . . , ST Ank component antennas.
All the parameters defining a cluster remain con-

stant (clusters do not change positions or number of
components).
A network composed of clusters of sector turning

antennas is definedas a touple N(X, Y, n, k, K[k], Q),
by the following parameters:
• geographical extentof thenetwork: X〈m〉, Y 〈m〉;
• n 〈〉 number of antennas;
• k 〈〉 number of clusters;
• K1, K2, . . . , Kk component clusters;
• a property Q that has to be satisfied;
• nk[1]+ nk[2]+ . . . + nk[k] = n.
A network consisting in a single cluster will have

k =1, Xk[1]= X, Yk[1]= Y and nk[1]= n —like for
example a uniform distribution of nodes over the en-
tirefield. Differentnodeplacementsweretested: ran-
domplacement—nodes are placed randomlyaround
the geographic network centre (defined by coordi-
nates [X/2, Y /2]) and cluster placement — the cen-
tre of each cluster is chosen randomly around the
network centre and the nodes composing one cluster
are placed randomly around the centre of the respec-
tive cluster. All the parameters defining a network
remain constant (the number of clusters in the net-
work, positions of the clusters, etc.). For network N,
let us define an evaluating metric E, which will be
detailed in the next paragraph.
Symmetricnetwork: network N is definedas sym-

metric, thus all the nodes in the network have the
same shared parameters (G1, G2, ϕ, A, Pmin, Pmax,
P rmin, P imin,Δθmin andΔPmin, which is allwith the
exception of power and rotation of the main lobe to-
wards north). Such a network canmodel for example
a city-wide radio network which consists of identical
sector antennasand inwhichareallocatedavery lim-
ited number of radio channels. The operator of this
network will be interested to connect the entire net-
work (if possible) with low interference rather than
low power (because the antennas — in such a net-
work — are powered from the electric grid).
Applying TC to network N translates to finding

an assignment of power and azimuth to north (P and
θ) for each antenna in the network, such that the
property Q is achieved (if possible) and the value
of evaluation E is improved towards other methods.
Classical TC is reduced to finding just a power level
assignment (P) for each node in the network such
that property Q is fulfilled while E is evaluated.

5 Connectivity and
interference

This section defines the connectivity between two
nodes and the methods for measuring interference in
the network.

5.1 Connectivity between two nodes

In the horizontal plane (which in our case corre-
sponds to the magnetic H-plane of all antennas), in
the far field, an ideal dipole radiator l 〈m〉 in length,
which is fed an alternative current with frequency
f 〈Hz〉 and intensity I 〈A〉 will generate a power den-
sity (measuredbythe time-averagedPoyntingvector)
at distance r 〈m〉 from the radiator Pdens 〈W/m2〉
given by:

Pdens =
1
2

(
Il

2rλ

)2
η (5)

where η 〈Ω〉 =120π is the impedanceof the free space
and λ 〈m〉 = c/f is the radio signalwavelength (c be-
ing the speed of light) [3]. In our case λ =0.12244m
(for f =2450 MHz).
Considering the emitter antennaas ST A1 and the

receiver as ST A2, the receiving antenna captures the
power density on the whole aperture (A), thus in-
ducing power Pind 〈W〉 equal to the power density
multiplied by the aperture of the receiver. However
this does not take into account antenna gains; the
received power Precv 〈dBm〉, with the gain contribu-
tion, becomes [3]:

Precv 〈dBm〉 = Pind 〈dBm〉 + G12 〈dBi〉+ (6)
G21 〈dBi〉 − F SP L 〈dB〉

where Pind had to be converted fromWtodBm, G12
is the gain of the emitter facing towards the receiver,
G21 is the gain of the receiver towards the emitter,
and FSPL is the free space path loss of the connec-
tion [3]. In order to have communication between
ST A1 and ST A2 it is required that Precv ≥ P rmin.
Thus, the minimal power density level that must

be created by antenna ST A1 to communicate to
ST A2 can be computed as:

Pdens 〈W ·m−2〉 =
10

P rmin−G12−G21
10

A
(7)

byconvertingdBmtoWandwhere A 〈m2〉 =3λ2/8π
is the aperture of the receiver (dipole-based sector
antenna).
The power that must be injected into the emit-

ter ST A1 can be calculated by integrating the power
density Pdens over the whole surface that is the 3D
radiation pattern of the antenna. Thus P 〈W〉 =
Pdens 〈W/m

2〉S〈m2〉. In the case of dipole-based sec-
tor antennas or lobe antennas (like Yaggi-Uda), the
radiation surface is S = 8πr2/3 and in the case of
an ideal antenna (the radiation pattern of which is a
perfect sphere) is S =4πr2, with r in this case being
the distance between the two antennas.
In this paper theminimal receive levelwas chosen

at P rmin = −46.511 dBm, based on the XBee Series

27



Acta Polytechnica Vol. 51 No. 5/2011

2 modules specification (however it can be chosen at
any other value, depending on the used network de-
vices) and the required antenna gainswere chosen on
the basis of various sector and Yaggi-Uda antennas.

6 Interference in the network
Based on the radio parameters, six interference es-
timations are defined (for node, edge, maximal and
average cases); interference is the metric E that will
be evaluated for each network.
For module ST A1, let us define the radio cover-

age interference of the node as the number of other
nodes that receive from ST A1 a radio signal stronger
than P imin:

Rcov(ST A1)=∣∣∣∣∣ {ST Ax ∈ N \ ST A1;Precv(ST A1 → ST Ax) ≥ P imin}
∣∣∣∣∣ (8)

where Precv(ST A1− > ST Ax) designates the power
induced by node ST A1 at the ST Ax node.
For bi-directional communication between ST A1

and ST A2, let us define the radio coverage interfer-
ence of thewhole link ST A1−ST A2 as thenumber of
other nodes that receive a radio signal stronger than
P imin from either ST A1 or ST A2:

Rcov(ST A1 − ST A2)=∣∣∣∣∣∣∣∣∣∣

{ST Ax ∈ N{ST A1;ST A2};
Precv(ST A1 → ST Ax) ≥ P imin}
∪{ST Ay ∈ N{ST A1;ST A2};

Precv(ST A2 → ST Ay) ≥ P imin}

∣∣∣∣∣∣∣∣∣∣
(9)

For the whole network, let us define the maximal
andaverage radio interference values, basedon either
nodes (vertices) or links (edges in a graph represent-
ing the network):

RIV Cov(N)= max
ST Ax∈N

(RCov(ST Ax) (10)

RIECov(N)=

max
ST Ax−ST Ay

(Rcov(ST Ax − ST Ay)) (11)

RiavgV cov(N)=
1
n

∑
ST Ax

Rcov(ST Ax) (12)

RIAvgEcov(N)=
1
n

∑
ST Ax−ST Ay

Rcov(ST Ax − ST Ay) (13)

where n is the number of all nodes in the network.
In all the simulated networks P imin was chosen at
−55 dBm, based on theXBee specification (it can be
chosen at other values, depending on the used net-
work devices). The E estimation in this paper was
chosen as RIAvgECov. From (5) it can be seen that

the radio signal decreases with the square of the dis-
tance from the emitter — corresponding to the free-
space propagation model.

7 TC with sector turning
antennas

Twoalgorithmsare presented in this paper: MaxDis-
tanceMinimise (MDistM) and axDegreeMinimise
(MDegM). The two algorithms do not require global
information about the network (each node relies on
localnodediscovery); eachof the twoalgorithmscon-
sists in two stages/steps: discovery and configura-
tion; because the discovery phase is common it will
be presented only once. If global information about
the network is available in the form of geographical
coordinates of the antennas, the first step (discovery)
can be skipped.

7.1 Node Discovery

This phase assumes that each antenna is randomly
oriented at initial azimuthal angle θi and it requires
one complete turn in the azimuthal plane in order
to perform a full discovery. It is also required that
a neighbour antenna should not be identified more
than once. For this purpose, the antennas exchange
Hellomessages that contain: a unique id (antenna in-
dex i), current azimuth θ (read froman internal com-
pass, for example) — based on this the receiver can
determine whether the sender is using the strongest
radiation lobe. The algorithm requires 360/Δθmin
rotation steps to complete.

Node Discovery (all nodes execute in parallel):
• set power level to maximum P = Pmax;
• while θ < θi +360 execute:

• exchange Hello packets;
• identify neighbours reachable with azimuth

θ;
• θ = θ +Δθmin;

• build a neighbour table NT containing: neigh-
bour id., possible azimuths θ that each neigh-
bour can be reached with, and the power level
that each neighbour was listened to;

• exclude fromNT the cases when a neighbour can
be seen only if both antennas are oriented with
the strongest lobe towards each other. These
neighbours are very distant and they will be dis-
connected;

7.2 MaxDistanceMinimise (MDistM)

This algorithmisbasedonthe fact that linksbetween
distant nodes can be achievedby orienting a stronger
lobe of radiation in the desired direction, without in-
creasing the power injected into the emitter. The

28



Acta Polytechnica Vol. 51 No. 5/2011

algorithm requires maximum (Pmax − Pmin)/ΔPmin
steps of power adjustment to complete.
MaxDistanceMinimise (all nodes execute in

parallel):
• determine the most distant neighbour (MDN)
from the NT (MDN is the node that has the low-
est received signal over all registered entries in
NT);

• calculate the azimuth θx to reach the MDN;
• set power level to maximum P = Pmax;
• while θ < θx execute: θ = θ +Δθmin;
• while P < Pmin execute:

• exchange Hello messages;
test connectivity with neighbours in NT;

• if no nodes missing P = P −ΔPmin;
• else P = P +ΔPmin and end while cycle;

• while P > Pmin execute:
• exchange NT tables with neighbours;
• test connectivity with neighbours through
intermediate nodes (acting as relays);

• if no nodes missing P = P −ΔPmin;
• else P = P +ΔPmin and end while cycle.

• Result: (θx, P) for each node.

7.3 MaxDegreeMinimise (MDegM)

This algorithm is based on the fact that in clus-
tered networks it is desired that the main radia-
tion lobe will be used to create intercluster links,
while the weak lobe will be used to create intra-
cluster links. The algorithm requires maximum
(Pmax − Pmin)/ΔPmin steps of power adjustment to
complete.
The degree of a transmitter node in one direction

θ is adapted from graph theory, and is defined as the
number of other nodes that can receivea signal above
P rmin fromthe transmitter if themain radiation lobe
of the transmitter has azimuthal angle θ.
MaxDegreeMinimise (all nodes execute in par-

allel):
• from NT calculate the azimuth θx that corre-
sponds to the direction for which the transmitter
has the highest degree;

• set power level to maximum P = Pmax;
• while θ < θx execute: θ = θ +Δθmin;
• while P > Pmin execute:

• exchange Hello messages;
• test connectivity with neighbours in NT;
• if no nodes missing P = P −ΔPmin;
• else P = P +ΔPmin and end while cycle;

• while P > Pmin execute:
• exchange NT tables with neighbours;
• test connectivity with neighbours through
intermediate nodes (acting as relays);

• if no nodes missing P = P −ΔPmin;
• else P = P +ΔPmin and end while cycle.

Result: (θx, P) for each node.

8 Power level adjustment
The algorithms MDistM and MDegM presented in
the previous sections make use of linear power de-
crease, which is the standard approach for having
power adjustments implemented in hardware. How-
ever faster results can be achieved if the power levels
are adjusted exponentially:
PowAdj:
• set power level to maximum P = Pmax;
• base b =2; exponent e =1;
• while P > Pmin execute:

• ΔP =
Pmax
be

• exchange NT tables with neighbours;
• test connectivity with neighbours through
intermediate nodes (acting as relays);

• if no nodes missing P = P −ΔP;
• else P = P +ΔPmin and end while cycle;
• e = e +1.

9 Simulation results
For the simulations, we chose a squared flat play-
ground of 180 × 180 m on which 20 or 50 nodes
(equipped with STA or nSTA, uniform networks —
all nodes have one type of antenna only) were placed
indifferent configurations: uniformrandomandclus-
tered. A cluster placement is defined by choosing the
number of clusters (2 to 10) and their geometric sizes
(5 to25m): the centres of the clusters areplaced ran-
domly around the playground centre and the nodes
of each cluster are placed within the borders of the
cluster randomly around the centre of the cluster.
The following experiments were performed for

both 20 and 50 nodes, uniform or clustered, STA or
nSTA:
• sector opening (ϕ) variation: the gains G1 and

G2 aremaintained constant, while ϕ is increased
from 10◦ to 350◦;

• gain (G2) variation: the gain G1 and the sec-
tor opening ϕ aremaintained constant, while the
gain G2 is increased from 2 dBi to 20 dBi;

• sector openings for nSTA with 5 to 10 gain
zones in the gain vector, ranging from 1.5 dBi
to 20 dBi.
In order to compare the interference results, we

used the same simulator as in [1], the same configu-
rations for node distributions and wave propagation.
In the following graphs we compare the results ob-
tained by applying anisotropic TC (ARNG, AGG,
AYG — without antenna turning) with results ob-
tained by antenna turning. Finally, the total power
need per network is estimated for all the methods in
order to keep the network connected. Eachpresented
result is an average over 100 simulations of the same
type; a total of 52000 networks were simulated for
this paper.

29



Acta Polytechnica Vol. 51 No. 5/2011

a) Interference (0y),
uniform distribution

b) Total power (0y − dBm),
uniform distribution

c) Interference (0y),
cluster distribution

d) Total power (0y − dBm),
cluster distribution

Fig. 12: 50 nodes STA gain increment for sector ϕ =10◦, G1 =1.5 dBi, G2 =2 . . .20 dBi (0x)

a) Interference (0y),
uniform distribution

b) Total power (0y − dBm),
uniform distribution

c) Interference (0y),
cluster distribution

d) Total power (0y − dBm),
cluster distribution

Fig. 13: 50 nodes STA sector increment ϕ =10◦ . . .350◦ (0x) for gains G1 =3.5 dBi, G2 =7 dBi

a) Interference (0y),
uniform distribution

b) Total power (0y − dBm),
uniform distribution

c) Interference (0y),
cluster distribution

d) Total power (0y − dBm),
cluster distribution

Fig. 14: 50 nodes STA sector increment ϕ =10◦ . . .350◦ (0x) for gains G1 =3.5 dBi, G2 =12 dBi

a) Interference (0y),
uniform distribution

b) Total power (0y − dBm),
uniform distribution

c) Interference (0y),
cluster distribution

d) Total power (0y − dBm),
cluster distribution

Fig. 15: 50 nodes STA sector increment ϕ =10◦ . . .350◦ (0x) for gains G1 =3.5 dBi, G2 =20 dBi

30



Acta Polytechnica Vol. 51 No. 5/2011

a) Interference (0y),
uniform distribution

b) Total power (0y − dBm),
uniform distribution

c) Interference (0y),
cluster distribution

d) Total power (0y − dBm),
cluster distribution

Fig. 16: 50 nodes nSTA sector increment n = 5, ϕ1 = ϕ2 = ϕ3 = ϕ4 = 10
◦, ϕ5 = 20

◦
. . .70◦ (0x), G1 = 2 dBi,

G2 =4 dBi, G3 =8 dBi, G4 =16 dBi, G5 =20 dBi

a) Exponential node chain and solution to have
lower interference: introduction of auxiliary nodes

b) Solution with sector antennas: no auxiliary
nodes required, zero additional interference. Note
that in this image the radiation pattern is
correlated to power not coverage— thus a link can
exist even when a node is not located inside the
radiation pattern

Fig. 17: Exponential node chain

10 Conclusions
As is shown in Figures 12–16, MDistM and MDegM
have better behaviour (lower interference and power
need) for clusterdistributions than foruniformdistri-
bution: this is explained by the fact that a high-gain
lobe tends to create intercluster links and a resid-
ual lobe tends to create intracluster links. Another
consideration is the decrease in power needwhen the
main lobe widens (Figures 13–15b and d).
Another example architecture is the exponential

node chain—all nodes placed on the same axeswith
distances increasing exponentially (Figure 17a. on
axes 0x) [4]; in this case, the use of isotropic an-
tennas yields huge interference values (this being in
fact a counterexample for lownode degreeTC,which
does not ensure low interference). However, the node
topology can be elegantly solved by using STA (Fi-
gure 17b.), where each antenna has gain G2 = 2G1,
which proves that antenna behavior opens new hori-
zons for TC.

Nodeswhich take advantage of using the newTC
with STA are capable to create networks that need
less energy consumption. As it can be seen, the net-
works created in such a way model very well WiFi
infrastructure networks for metropolitan areas (for
example, networks composed by turning high-gain
antennas placed on tops of building roofs). What
it is presented in this paper is a networkwhich is ca-
pable to automatically connect and reconnect in case
of a failure (due to the removal of one communication
node for example).
The principle described in this paper is interest-

ing because it can be improved, for example by com-
bining TC with smart antennas [3]. Different TC
methods which take into account slightly different
parameters as an input will generate slightly differ-
ent results, suitable for different real-world scenari-
ous. How to precisely choose what is best for each
scenario is a subject for future improvement in this
area.

31



Acta Polytechnica Vol. 51 No. 5/2011

References

[1] Wagner, D., Wattenhofer, R.: Algorithms for
Sensor and Ad Hoc Networks — Advanced Lec-
tures, ISSN 0302-9743, Springer, 2007, pp. 85–90.

[2] Janecek, J., Moucha, A.: Comparison of local
interference-aware topology control algorithms,
Proceedings of the 19th IASTED International
Conference on Parallel and Distributed Comput-
ing and Systems, 2007. ISBN 978-0-88986-704-8.

[3] Balanis,C.: AntennaTheory—Analysis andDe-
sign. 3rd ed., Wiley, 2005, pp. 154–162. ISBN
0-471-66782-X.

[4] Burkhart, M., von Rickenbach, P., Watten-
hofer, R., Zollinger, A.: Does Topology Con-

trolReduce Interference?,MobiHoc ’04: Proceed-
ings of the 5th ACM international symposium on
Mobile ad hoc networking and computing, 2004,
pp. 9–19.

About the author

Viktor ČERNÝ was born in Prague in 1982 and
was awardedhismaster degree in 2009. Currently he
is a PhD student in computer science atFELCVUT.

Viktor Černý
E-mail: cernyvi2@fel.cvut.cz
Dept. of Computer Science and Engineering
Faculty of Electrical Engineering
Czech Technical University
Technická 2, 166 27 Praha, Czech Republic

32