Capacity Analysis of Heterogeneous Wireless Networks under SINR
Interference Constraints
W. Mansouri
1
, K. Mnif
1
, F. Zarai
1
, M. S. Obaidat
2
and L. Kamoun
1
1
LETI laboratory, University of Sfax, Sfax, Tunisia
2
Computer Science and Software Engineering Department, Monmouth University, West Long Branch, NJ, 07764, U.S.A.
Keywords: Heterogeneous Wireless Networks, LTE, WLAN, Capacity, Interference.
Abstract: Next Generation Wireless Networks (NGWNs) are expected to be heterogeneous, which integrate different
Radio Access Technologies (RATs) such as 3GPP’s Long Term Evolution (LTE) and Wireless Local Area
Networks (WLANs) where a transmission is supported if the signal-to-interference-plus-noise ratio (SINR)
at the receiver is greater than some threshold. In this paper, we analyze the interference in heterogeneous
wireless networks and determine the capacity by taking into consideration the class of traffic of each call
and considering both intra-network interference and inter-network interference. This analysis allows us to
simplify the estimation of capacity under SINR interference constraints in different wireless networks.
1 INTRODUCTION
Wireless networks are rapidly evolving, and are
playing an increasing role in the lives of people
throughout the world and ever-larger numbers of
people are relying on the technology directly or
indirectly (Nicopolitidis et al., 2003). Coexistence of
heterogeneous wireless networks appears as an
important issue in the NGWNs due to the
interference from different radio access
technologies, which may cause degradation of
Quality of Service (QoS). The interworking between
different wireless access networks has been a hot
research and development area in the past few years
(Yongqiang and Weihua, 2008). Heterogeneous
wireless interworking refers to the integration and
interoperability of wireless networks with different
access technologies, which present distinct
characteristics in terms of mobility management,
security support and Quality of Service (QoS)
provisioning (Zarai and al., 2006). Such works
studied the effects of interference in wireless
networks (Deepti and al., 2011) and in
heterogeneous wireless networks like (Kyuho and
al., 2011) and (Robert and al., 2012). They develop a
model for the composite interference distribution.
In (Christelle et al., 2008), the capacity is
presented as the amount of bandwidth that can be
divided with equity to each user. In (Piyush and
Kumar, 2000), (Jangeun and Mihail, 2003), the
capacity is defined as the maximum bandwidth that
can be allocated to each user. The study of the
capacity may have different goals. For an operator,
the aim is to increase the number of users served
while ensuring a better quality of service. For a user,
ameliorating the capacity is obtaining more amount
of bandwidth to increase its end-to-end data rate. In
general, capacity planning is to make sure that the
resources will be available to meet future demands
(Obaidat and Boudriga, 2010). The need to increase
system capacity in wireless networks has driven the
research in the field over the past years (Deepti et
al., 2011), (Ismail, 2011) and (Weng-Chon and
Kwang-Cheng, 2011). In (Weng-Chon and Kwang-
Cheng, 2011), the authors propose to deploy some
more powerful wireless nodes called helping nodes
in order to improve the capacity of homogeneous ad
hoc networks. The authors, in (Deepti et al., 2011),
study the capacity estimation problem using the
SINR as a model for interference and propose
algorithms to approximate the throughput capacity
of wireless network. In this paper, we address the
problem of computation of the total capacity in
heterogeneous networks and study the interference
in such wireless networks and estimate their
throughput capacity.
The remainder of this paper is organized as
follows. Related work of this research is
summarized in Section 2. Section 3 describes our
233
Mansouri W., Mnif K., Zarai F., S. Obaidat M. and Kamoun L..
Capacity Analysis of Heterogeneous Wireless Networks under SINR Interference Constraints.
DOI: 10.5220/0004515402330239
In Proceedings of the 10th International Conference on Signal Processing and Multimedia Applications and 10th International Conference on Wireless
Information Networks and Systems (WINSYS-2013), pages 233-239
ISBN: 978-989-8565-74-7
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
contribution for the interference model. In Section 4
we present the capacity analysis in heterogeneous
wireless networks. Simulation results are provided in
Section 5. Finally, Section 6 concludes the paper and
gives suggestions for future works.
2 RELATED WORKS
In (Weiwei and Lianfeng, 2010), the authors propose
a method to determine the total capacity in
heterogeneous wireless networks. They begin by
presenting the system model, which is composed of
N RATs with overlapping coverage in a given area,
where resources are jointly managed. They define
the system capacity as the maximum number of
users that can be admitted while satisfying the
required QoS constraints. The authors model the
heterogeneous system as a multi-dimensional
Markov chain. The proposed method takes into
consideration the handoff calls when calculating the
maximum number of users. The authors consider the
loss probability and the average throughput of
admitted users as a required QoS level.
Several research works have focused on
analyzing the capacity of a given network such as
(Abdellatif et al., 2010) and (Ismail, 2011). In
(Ismail, 2011), investigating the capacity and
fairness of heterogeneous networks with range
expansion and inter-cell interference coordination
(ICIC) is provided. The proposed method is limited
to macrocell and picocell. In (Weng-Chon and
Kwang-Cheng, 2011), Pan and Yuguang investigate
the capacity of heterogeneous wireless networks
with general network settings. They proposed to
analyze the throughput capacity of regular and
random heterogeneous wireless networks assuming
that the helping nodes are regularly placed and
uniformly and independently placed respectively.
3 INTERFERENCE MODEL
We use the signal to interference and noise ratio
(SINR) model of interference as described in (Deepti
et al., 2011). The set of links that can simultaneously
communicate successfully is denoted asE
e
u
,v
∶i1,…,k. For anye
∈E, the
interference at receiver v
due to all other
communications is defined as following:
I
v
,
,
(1)
WherePe
, d and α denotes the power level with
which node u
transmits, the Euclidean distance
between nodesu
, v
and the path-loss exponent,
respectively.
3.1 Interference in LTE
In LTE, the overall transmission power is uniformly
distributed among the subcarriers allocated to the
same user. As defined in (Liying et al., 2011), the
transmission power P
,
of each subcarrier for user i
is calculated is given by: P
,
where P
is the
overall transmission power and K
is the number of
resource block (RB) in the set K
, which represents
the consecutive RBs assigned to useri. Then the
signal to interference and noise ratio in the m
th
subcarrier corresponding to user i is written as
follows:
SINR
,
P
,
G
,
G
θ
IP
(2)
Here, G
,
is the channel gain from user i to its
enhanced-NodeB (eNB),Gθ is the antenna gain,
P
is the power of Additive White Gaussian Noise
(AWGN) and I is the power of interference, which is
given by: II
I
where I
is the intra-
cell interference power and I
is the inter-cell
interference. As defined in (Pan and Yuguang,
2010), I
1αP
with α∈0,1denotes the
average channel multipath orthogonality factor and
P
denotes the intra-cell transmit power. In the case
of LTE, α1 and henceI
0. In the
Orthogonal Frequency Division Multiple Access
(OFDMA) systems, such interference is limited to
inter-cell interference, as users within a given cell
use sub-carriers which are orthogonal to each other
(AbdulBasit, 2009).
3.2 Interference in WLAN
There have been many studies about the interference
in WLAN (Sandra et al., 2011). They mainly focus
on analyzing the effects of interference in those
networks by determining the SINR. The SINR
received by user i from WLAN access point AP
is
given by (Kemeng et al., 2007):
SINR
,
P
G
,
∑
P
G
,
∈
P
(3)
Where P
is the transmitting power ofAP
, G
,
is
the channel gain from user i to itsAP
and P
is the
noise power at the receiver.
WINSYS2013-InternationalConferenceonWirelessInformationNetworksandSystems
234
4 CAPACITY ANALYSIS IN
HETEROGENEOUS WIRELESS
NETWORKS
In this section, we develop a mathematical
expression for the total capacity of wireless
heterogeneous networks taking into consideration
the SINR interference constraints.
4.1 Architecture Overview
Most of the researchers mainly focus on
interworking between WLAN and cellular networks.
The well deployed cellular networks and WLANs
will both be included along with other wireless
access networks such as wireless mesh networks
(WMNs), which consist of dedicated nodes called
mesh routers that relay the traffic generated by mesh
clients over multi-hop paths. In this paper, we
consider an interworking of WMNs with WLAN and
4G cellular networks (LTE) as shown in Fig.1.
Figure 1: LTE/WLAN/WMN interworking architecture.
4.2 Capacity Analysis
In this section, we evaluate the system capacity of
heterogeneous networks by taking into consideration
the interference and the type of service. We consider
intra-network interference and inter-network
interference as proposed in (Tracy, 2003), (Weng-
Chon and Kwang-Cheng, 2011). Our architecture is
composed of N heterogeneous wireless networks.
For a networki,1iN, the total interference
consists of intra-network interference and inter-
network interference denoted as I
and I
,
respectively.
We consider a typical node (reference node located
at the origin and it is representative for all other
nodes) as defined in (Weng-Chon and Kwang-
Cheng, 2011). Let AN
denote the number of active
nodes in the networki. The intra-network
interference is given by:
I
G
P
d
(4)
Where G
is the channel gain from node k to the
typical node in the networki, P
is the transmitting
power in the networki, d
is the distance between
node k and the typical node in network i andα is the
path-loss exponent. The channel gain is modeled by
G
s
d
where s
is the shadow fading
factor with standard deviation values between 6-12
dB (Ayyappan and Dananjayan, 2008) depending on
the environment.
The inter-network interference is defined as the
total interference caused by the other coexisting
networks. For example, the interferenceI
caused by
network j presents the interference from active nodes
in network j to the typical node in networki. Then
the total inter-network interference is given by:
I
I
(5)
Where I
∑
G
P
d
Here, G
is the channel gain from node k to the
typical node in the networki, P
is the transmitting
power in the networkj, d
is the distance between
node k in the network j and the typical node in
network i andα is the path-loss exponent.
In this paper, we consider two types of traffic
(real time and non real time traffic). Real time (RT)
applications such as Voice over Internet Protocol
(VoIP) require a limited delay and cannot tolerate a
delay higher than this limit. Non real time
applications (NRT) are not sensitive to delay and
delay variation (jitter) such as data traffic, and e-
mail traffic.
We consider a service area covered by multiple
networks (RATs). Let Rbe the set of RATs,
RR
,R
,…,R
,…R
. We assume that each
RAT R
1iN) has a number of users of class c
called N
i
where c is the class of service in the
RAT R
, c 1,2,…,C and has a required SINR of
class c denoted SINR
,,
. We also consider
SINR
,
jas the SINR of user j of class c in RAT i.
The total number of users in the considered area is
denoted asN
.
CapacityAnalysisofHeterogeneousWirelessNetworksunderSINRInterferenceConstraints
235
Since, the considered area is covered by N
heterogeneous wireless networks and each network
is transmitting at different power level and has
different bandwidth, power consumption, received
signal strength and cost, the comparison of SINR of
user j in different Radio Access Technologies
(RATs) in order to select a candidate RAT is not
possible. We propose to compare the ratio of
received SINR and the requested SINR. S
,
j
is
defined as follows:
S
,
j
SINR
,
j
SINR
,,
(6)
Where SINR
,
j
is the SINR of user j1jN
)
of class c1cC) in RAT R
1iN) and
SINR
,,
represents the required SINR of class c
in the RAT R
. If the termS
,
j
1, then the
received SINR satisfied the requested SINR and then
the user can have a communication with the base
station or the access point ofRATi. If S
,
j
1
then the user cannot have a communication with this
RAT.
In order to determine the capacity of the
heterogeneous wireless networks, we begin by
calculating the number of users of each class of
service connected to each network (RAT). We use
the term S
,
j
to determine the RAT of each user
and then calculate the number of users.
For each user, we find out a set r of RATs at
which S
,
j
is maximum as follows:
r argmax
∈
S
,
j
, S
,
j
1
(7)
The set r of RATs can be composed of one or more
than one
RAT. If rr
then the number of users
in the RAT r
is given by:
N
r
N
r
1
(8)
Where N
r
is the number of users of class service
c in the RATr
. If the set r is composed of more
than one element rr
,r
,…,r
then we propose
another criterion for selecting RAT from the set r. In
this case the user selects a RAT as the one that is
physically nearest to it. We find out the nearest RAT
(the distance between the user and the base station or
access point) as follows:
r
argmin
∈
d
(9)
Here d
is the distance between user j and the base
station or the access point of RATi wherei ∈ r.
The number of users is given by Eq.(8):
N
r
N
r
1
As mentioned in (Abdellatif et al., 2010), the
bandwidth for the real time calls is calculated as
follows:
B
E
N
⁄
WT
⁄
E
N
⁄
(10)
WhereE
is the energy per bit transmitted for RT
calls, N
is the density of the white noise and T
is
the transmission rate of RT calls. W is the spread-
spectrum bandwidth.
Following the Shannon’s formula, the capacity
C
,
[in bps] for user j connected to RATi is given
by:
C
,
c B
,
log
1
,
1jN
i, 1cC
(11)
Here, N
i and B
,
are the maximum number of
real time (RT) or non real time (NRT) calls of
RAT(i) that can be served simultaneously and the
bandwidth for calls of class c, respectively.G
,P
, d
and α are the channel gain from node j to the base
station or access point in the networki, the
transmitting power in the networki, the distance
between node j and the base station or the access
point in the networkiandαis the path-loss
exponent, respectively.
The sum capacity of all users of class c
connected to RATi is given by:
C
c B
,
log
1
(12)
Then, the total capacity of all the users in RATi is
as follows:
(13)
5 PERFORMANCE EVALUATION
Existing network simulators (NS2, OPNET, etc.) do
not provide appropriate support for the simulation of
heterogeneous wireless networks with end-to-end
communication between nodes using different
wireless technologies simultaneously and vertical
handovers. In this paper, we use Matlab to
implement our own network simulator that allows
the modelling of heterogeneous networks at a
simplified level.
WINSYS2013-InternationalConferenceonWirelessInformationNetworksandSystems
236
5.1 Simulation Parameters
We simulate the heterogeneous wireless networks by
three networks which have 7, 7, and 6 nodes in
WLAN, WMNs and LTE, respectively.
The scope of
each node in WMN and WLAN is about 50 meters
(Philippe, 2010). In this paper, we consider two
classes of services (RT and NRT).We assume that
the mean arrival rate of new calls follows a Poisson
process with parameter λ
1
= 0.12 calls/s (Wei, 2007)
for the voice service and λ
2
=0.001 calls/s (Kemeng
et al., 2007) for the data service.
The simulation parameters are summarized in the
following table. Those parameters are selected based
on popularly deployed WMNs (Valarmathi and
Malmurugan, 2012); (Yin and Liu, 2002), cellular
networks (LTE) (Liying and al., 2011), (Jan and al.,
2009); (Giuseppe et al., 2010); (Sayandev, 2012)
and WLANs (Weiwei and Lianfeng, 2010);
(Kemeng et al. 2007); (Tracy, 2003):
Table 1: Main simulation parameters.
LTE WMN WLAN
Bandwidth 10MHz 10MHz 22MHz
Path loss exponent α 3 3 3
Data rate 100 Mbps 2 Mbps 11Mbps
Transmit power 46 dBm 20 dBm 20 dBm
Thermal noise power
N
(36 PRBs)
-121 dBm
per PRB
-96 dBm -96 dBm
Radius 500 m 50 m 50 m
SINRreq
Voice -4 dB 12 dB 5.5 dB
Data -4 dB 9 dB 5.5 dB
Packet size
Voice 60 bytes
Data 1500 bytes
Movement speed 1 m/s
Transmission rate for RT
callsT
12.2 kbps
Transmission rate for
NRT callsT
64 kbps
Energy per bit transmitted
E
RT
/N
0
= 4.57 dB,
E
NRT
/N
0
= 4.69 dB
Handoff deadline 32 ms
Simulation time 30 minutes
5.2 Performance Evaluation
In this section, we consider that the size of the
heterogeneous network is expressed in terms of the
number of users. The users are in an arbitrary
topology around the base stations or the access
points of the overlapped areas. Figures 2 and 3 plot
the results obtained of two different classes of
application RT and NRT, respectively. We estimate
the capacity of those classes in different RATs
where RAT 1, RAT 2 and RAT 3 are LTE, WMN
and WLAN, respectively.
Figure 2: RATs capacity for RT calls.
Fig. 2 shows that the capacities of RT
connections vary between 1 and 290 (bps).
Comparing the results in Figures 2 and 3, we note
that the capacity of NRT traffic is greater than the
RT traffics (between 6 and 980 bps). NRT
applications are greedy and attempt to inject packets
whenever permitted by TCP’s congestion window.
In this work, we consider intra-network interference
and inter-network interference. The inter-network
interference is defined as the total interference
caused by the other coexisting networks and the
intra-network represents the total interference caused
by other nodes transmitting in the same time inside
the network.
Figure 3: RATs capacity for NRT calls.
When we introduce an interference in the
considered area, the power of signals arriving from
the base station or the access point of the network
will be influenced by the sources of interference that
use the same frequency and the SINR value of the
CapacityAnalysisofHeterogeneousWirelessNetworksunderSINRInterferenceConstraints
237
considered network will be decreased and then the
capacity will be influenced. As a result of the
different types of interference, the majority of calls
coming on the overlapped areas will be served by
the suitable RAT selected by the user according to
the proposed SINR ratio among all available ones to
make his connection. In Fig. 4, we plot the total
capacity versus the number of users with varying the
networks. The total capacity of each RAT represents
the sum of the real time capacity and the non real
time capacity.
Figure 4: Total Capacity versus number of users.
6 CONCLUSIONS
In this paper, we have estimated the total capacity in
heterogeneous wireless networks (LTE, WMNs, and
WLANs) in terms of SINR interference constraints.
A novel mathematical and simple expression for the
total capacity of wireless heterogeneous networks,
which considers the intra-network and inter-network
interference, is derived. The capacity experienced by
a user is dependent on its distance from the access
point or base station. It is also dependent on the
number of stations in each ring of the RAT. Our
strategy takes into consideration both the signal
strength and the interference power to select a target
network in the integrated wireless environment and
then determine the number of users in each in order
to estimate the total capacity of the heterogeneous
wireless networks. Studying the problem of capacity
optimization in the heterogeneous networks would
be an interesting extension of this work.
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