Coverage Analysis of
Heterogeneous Wireless Network with
n
–
Interacted Transmission Nodes
Shuvabrata Bandopadhaya
1
,
Saroj Kumar Dora
2
1,2
Silicon Institute of Technology, Bhubaneswar, India
1
s
huva_bandopadhaya@rediffmail.com,
2
skdora1988@gmail.com
Abs
tract:
–
In this paper, statistical analysis for coverage of
H
eterogeneous Networks
(
HetNet
)
with
n
–
interacted
transmission nodes has been carried out.
T
he successful
commercial implementation of HetNet needs improvement of
coverage probability
that
is lin
early related to the effective
signal
–
to
–
interference
–
plus
–
noise
–
ratio (SINR)
at the user end.
However, for practical implementation of both the coverage
probability improvement strategies,
i
nterference cancellation
(IC) and network cooperation (NC),
the s
ervicing transmission
node has to interact with (
n
–
1) transmission nodes with
subsequent strongest signals. The network complexity and
latency linearly increase with the value of
n
.
The analysis
in the
paper
provide
s
the guidance for choosing the optimum v
alue of
n
.
Key
Term
s
:
H
eterogeneous Networks (HetNet)
, Coverage
Poisson point process
,
Interference cancellation
,
Network Cooperation
,
interference factor
.
I.
I
NTRODUCTION
Due to
exponential growth in mobile data demand due
to proliferation of data
–
thirsty applica
tions
and non
–
uniform
user density
,
the cellular networks are forced to deploy
h
eterogeneous Network
(Het
Net). Several
low power
classes of transmission nodes associated with
picocells
and
femtocells are deployed
along with long range traditional
macro ba
se stations (BSs)
making a significant increase in
transmitter
density
[1
]
–
[
4]
.
scarcity of available
spectrum, to achieve maximum throughput, the HetNet goes
for
universal frequency reuse with simultaneous use of total
available spectrum by all co
–
existing tiers making the
system interference limited [
5
]
–
[
6
]. In such type of
networks
,
the strength of the interference signal at the user
terminal is much higher than the thermal noise power that
significantly reduces the coverage probability.
By deploy
ing the demand specific transmission nodes,
the network topology deviates from conventional hexagonal
grid to a random one
,
that can be modeled with a stochastic
point process. The point process that captures almost all
network properties is Poiss
on point p
rocess (PPP)
[
7
]
–
[
9
A
d
dimensional point process
is said to be PPP if and
only if
the
number of points in a closed set
is a
Poisson random variable
[
10
]. A HetNet of
k
tier
can be
visualized as a set of
same
number of
independent
homogeneous
PPPs with different densities
[
11
]
.
Though huge improvement in throughput is promised,
the successful commercial implementation of HetNet needs
significant improvement of coverage probability i.e. the
probability of
signal
–
to
–
interference
–
plus
–
noise
–
ratio (SINR)
SINR and coverage probability for single
–
tier network is
given in [12] and the references therein and for multi
–
tier
networks in [
11
], [13]
–
[14].
The improvem
ent of the
coverage probability is linearly related to the effective SINR
at the user
end
. The
strategies
proposed
in literature to
improve the SINR are broadly classified as network
cooperation and interference cancelation
[15
]
–
[
20]
.
With
network cooperat
ion,
significant improvement in SINR is
achieved by combining signals of „
n
‟
strongest transmitters
to serve single user [15].
In [16], Laplace technique has
probability under stochastic geometry
–
bas
ed cooperation
strategies.
The implementation challenges of this strategy lie
in cooperation between different transmitting nodes of
different tiers.
With i
nterference cancellation based
strategies
, a user being served by the strongest transmitting
node
ca
n eliminate the
(
n
–
1)
subsequent
strongest interfering
signals.
S
ignificant improvement in coverage probability
has been registered with the application of the interference
cancellation strategy in HetNet [19
–
20].
Howe
v
e
r,
for
practical implement
ation of
both
the
coverage probability improvement strategies, the servicing
transmission node has to interact with
(
–
1) transmission
nodes with
subsequent strongest signals. The interaction
process involves exchange of channel state information
(CSI)
among
n
inte
racting transmission nodes. This process
brings tremendous additional complexity and latency in the
network.
The choice of the value of
n
is critical for network
designing that
involves the trade
–
off between coverage
performance and network complexity.
In
this paper
,
statistical
analysis
for coverage
of
HetNet
with
n
–
interacted transmission nodes
has been carried out.
The
analysis
includes
both
classes of
coverage probability
d
X
d
improvement
strategies
that
provide
the guidance for
choosing the optimum value
of
n
.
The organization of the
paper is as given: section II provides the
coverage analysis
of HetNet
,
section III discuses
on
heterogeneous wireless
network with
n
–
interacted transmission nodes
,
the
simulation results ar
e given in section IV
and section V
concludes the paper.
II.
C
OVERAGE ANALYSIS
Consider a
k
–
tire HetNet
is
being deployed on a torus of
.
Let
be the set of
k
independent homogeneous
Poisson point processes where the
i
th element is a PPP
of intensity
, that defines the spatial
locations of the transmission nodes of the
i
th tier, where
.
is the transmitted power for
i
th tier. The
power received at the mobile user wi
th spatial location
due to
is given by,
,
(1)
where,
A
is the propagation constant,
is the path loss
exponent,
which
is a set of random variables
following a zero mean log
–
normal distribution representing
shadowing experienced between the transmitting nodes of
i
th
tier and user mobile and
is the random fading
variable between node at
and the user mobile
,
.
An
open access
network is considered where
the user terminal selects the transmitting node having
strongest average signal strength
irrespective of tiers. The
tier index is therefore being re
moved in further analysis. A
node
qualifies as the serving node if
(2)
and all other nodes are interfering nodes. Hence the signal
power and interference power expe
rienced by the user
mobile at the downlink respectively are
and
.
With the additive thermal noise
power as
W
,
the SINR can be formulated as
,
(3)
where
is constant termed as interference factor.
For system with no interference,
. In the given
interference limited network, the contribution of the thermal
noise is marginal and hence can
be neglected. Hence the
signal to interference ratio (SIR) is given as
. (4)
The coverage probability for the user in the network with a
given SIR threshold (
T
h
)
, which is equivalent to the
complementary cumulative distribution function (CCDF) of
received SIR, is defined as
. (5)
III.
H
ETNET WITH
n
–
INTERACTED TRANSMISSION
NODES
The coverage probability impro
vement strategies in
HetNet aim
to improve
the effecti
ve
SIR of the system
by
eliminating
the
effect of the strongest interfering signals.
Hence
the servicing node
,
having strongest signal
,
has to
interact with (
n
–
1) nodes of
subsequent signal strength. As
both
coverage probability improvement and system
complexity increases with the value of
n
, a trade
–
off is
necessary.
Let the order of interference power received at
the user terminal be
such
that
if
.
The collaborative power of
n
–
1
interacting transmission nodes
is
.
(6)
(A)
Interference c
ancellation
: With
n
–
interference
cancellation (
n
–
IC) strategy, (
n
–
1) strongest interfering
signals are cancelled using success
ive interference
cancellation technique. Hence the modified SIR is expressed
as
.
(7
)
H
ere
and
are
the signal power and
interference
power
respectively
for
n
–
IC
strategy
,
where
.
(8)
From equation (4) and (7
),
the
i
nterference fa
ctor
for
n
–
IC
strategy is given as
,
(
9
)
2
G
(
)
N
j
i
j
i
X
X
)
(
i
l
k
i
,..,
2
,
1
(
)
i
T
U
X
(
)
i
j
X
(
)
(
)
(
)
(
)
(
)
b
U
i
j
i
jU
X
i
T
i
j
R
X
X
h
S
AP
X
i
j
)
(
)
(
)
(
i
i
j
X
X
S
S
(
)
i
jU
h
(
)
1
]
[
i
jU
h
E
j
X
)]
(
[
max
arg
0
j
R
X
X
E
X
j
G
)
(
0
X
S
R
(
)
(
)
S
X
I
i
j
X
j
R
G
I
W
S
SINR
x
1
,
0
x
0
x
I
S
SIR
x
]
Pr[
)
(
Th
SIR
Th
Pc
(
)
(
)
(
)
,
,
,
3
2
1
X
X
X
R
R
R
(
)
(
)
j
R
i
R
X
X
j
i
1
1
)
(
)
(
n
j
j
R
X
n
Pw
IC
n
IC
n
IC
n
I
S
SIR
IC
n
S
IC
n
I
)
(
n
Pw
I
I
S
S
IC
n
IC
n
I
n
Pw
I
n
Pw
I
I
I
IC
n
IC
n
)
(
1
)
(
x
The improved coverage probability with the given strategy
is given as
. (
10
)
(B) Network Cooperation
:
With
n
–
network cooperation (
n
–
NC) strategy, subsequent (
n
–
1) strong signal combines with
the strongest signal
and provide the service
to the user
collaboratively
.
Hence the modified SIR is expressed as
.
(
1
1
)
H
ere
and
are
the signal power and
interference
power respectively
for
n
–
N
C
strategy
,
where
.
(12)
From equation (4) and (
11
),
the
i
nterference fa
ctor
for
n
–
N
C
strategy is given as
.
(13)
The improved coverage probability with the given strategy
is given as
. (1
4
)
IV.
S
IMULATION RESULT & ANALYSIS
In this section, a 3
–
tier HetNet has been simulated and
analyzed.
The transmitt
ing
power for macro
–
cell
(tier 1)
,
pico
–
cell
(tier 2)
and femto
–
cell
(tier 3)
tiers
we
re taken as
50W, 2W, 0.
2W respectively [
21
].
The transmission
nodes
of each tier we
re taken from
an
independent homog
eneous
PPP with
.
T
he user terminal
was
considered to be
located at the origin.
The
standard
deviation for shadowing vector (
) is taken as 2dB. F
igure
1 and figure 2 show
s
the
coverage probability
V
s
SIR
threshold performance with path loss exponent
=
3
and
5
respectively. In simulation, the performance of the
conventional 3 tier HetNet with no
interaction
with other
nodes
is being compared with
networks having
n
–
IC and
n
–
NC strategies;
t
he values of
n
are taken as 2 and 3.
The
network was being
simulated around
times.
A
significant improvement in coverage probability has been
observed with both the strategies
taken together
over the
conventional network. The coverage probability increases
with increase of the value of
n
. The
n
–
NC
strategy
outperforms the
n
–
IC
strategy at all points
as it introduces a
diversity gain in the system
.
Fig. 1
Coverage Probability Vs SIR Threshold performance with
ath loss
exponent
=
3
Fig.
2 Coverage Probability Vs SIR Threshold performance with
Path loss
exponent
= 5
The figure 3 shows the graph of i
nterference factor
(
)
Vs
n
umber of interacted transmitting nodes
(
n
) for both
strategies with
= 3 and 5.
With both the values of pat
h
loss exponent,
n
–
NC out performs
n
–
IC.
For
all case the
value of
de
creases with increase in
n
. However the graphs
become almost flat for
n
� 6
,
i.e. no significant
improvement in coverage probability can be achieved in the
cost of ad
ditional complexity.
]
Pr[
)
(
Th
SIR
Th
Pc
IC
n
IC
n
NC
n
NC
n
NC
n
I
S
SIR
NC
n
S
NC
n
I
)
(
)
(
n
Pw
I
I
n
Pw
S
S
NC
n
NC
n
S
n
Pw
I
n
Pw
n
Pw
S
n
Pw
I
I
S
NC
n
)
(
1
)
(
1
)
(
)
(
x
]
Pr[
)
(
Th
SIR
Th
Pc
NC
n
NC
n
3
2
1
25
.
0
5
.
0
l
l
l
s
4
10
x
-10
-8
-6
-4
-2
0
2
4
6
8
10
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Coverage Probability
SIR Threshold in dB
Conventional Network
With n-IC :n=2
With n-NC : n=2
With n-IC :n=3
With n-NC : n=3
-10
-8
-6
-4
-2
0
2
4
6
8
10
0.4
0.5
0.6
0.7
0.8
0.9
1
Coverage Probability
SIR Threshold in dB
Conventional Network
With n-IC :n=2
With n-NC : n=2
With n-IC :n=3
With n-NC : n=3
Fig. 3 Interference factor Vs Number of interacted transmitting nodes
(
= 3 & 5)
V.
C
ONCLUSION
The coverage probability of HetNet with
n
–
interacted
transmission nodes
has been
carried out statistically.
With
both
the
strategies
,
n
–
IC and
n
–
NC, the
interference
factor
reduces with increase in the value of
n.
However,
for
n
�
6
,
the rate of dec
rease is marginal
and
hence the
h
igher values
of
n
are not
advisable
keeping implementation feasibility in
mind.
Same analysis for
closed access
networks, which
is
very popular in corporate
networks,
may be considered as
future direction o
f
research.
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2
3
4
5
6
7
8
9
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Number of Interacted Transmiting Nodes (n)
Interference Factor (
z
)
n-IC:
b
=3
n-NC:
b
=3
n-IC:
b
=5
n-NC:
b
=5
b