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Abstract—We present a distributed energy-efficient Inter-Cell
Interference Coordination (ICIC) scheme for multi-cell HetNets
(Heterogeneous Networks) in the downlink. This novel scheme
aims to maximize the user fairness performance of the overall
system as well as minimizing the total average transmit power at
the base station side. We consider a realistic power model to
characterize the power consumed (including circuit and
transmitted power) at the base station side. We define an energy
efficient performance metric in bits/Joule and the user fairness
as the 5
th
percentile of the average user throughput. The
proposed scheme is divided into the following three stages:
dominant interferences classification, inter-cell radio resource
restriction and intra-cell power control. In order to satisfy the
complexity requirements associated with multi-cell networks, we
simplify, relax and decompose the original problem into a main
master problem and multiple sub-problems. Our simulation
results show the proposed scheme significantly increases both
the user fairness and the energy efficiency (EE) of the overall
network.
Keywords — Bits per Joule, Energy Efficiency, Inter-Cell
Interference Coordination, Dual Decomposition, User Fairness,
OFDMA.
I. I
NTRODUCTION
A recent analysis has shown that the average energy
consumption in cellular basestations can reach up to 60% of
the total network consumption [1]. Another study on the
cellular energy consuption has shown that the coupling link
between transmit power and the power consumption of the
cellular system is almost linear [2]. Furthermore, the increase
of communication devices over recent years gives an
ever-increasing demand for higher data rates leading to higher
energy consumption. However, the need to supply this high
demand leads to higher frequency reuse across the cells,
inevitably to higher levels of inter-cell interference and thus
low cell-edge user experience.
In the near future a mass of supplementary networks are
expected to overlay the main network in order to eliminate the
‘dead zones’, mainly indoors. Moreover, different types of
cells (e.g. macro, micro, pico, femto), also known as HetNets
(Heterogeneous Networks), are anticipated to satisfy the
unprecedented demand for bandwidth-hungry services and
radio coverage. However, their heterogeneity will cause
higher inter-cell interference and power consumption if their
operation is not coordinated. Thus, investigation of
energy-aware interference coordination techniques is urgently
required.
Although the idea of energy efficiency (EE) has begun to
draw attention in the literature, minimizing the total average
transmit power in interference-limited multi-cell scenarios
has not yet been fully investigated [3]. Most existing studies
in the literature focus on a single-cell OFDMA network [4].
Additionally, the concept of interference-aware
energy-efficient radio resource management (RRM) is very
limited [5]. We have observed that user fairness is becoming
increasingly important as a number of papers try to address
this pertinent issue [6] [7]. However, these studies can provide
only a proportional user fairness at the cost of overall
throughput. Furthermore, all these studies try to perform EE
with user fairness only through a power control algorithm.
In this paper, we present an energy-efficient scheme in a
multi-cell interference-limited system that can also extend the
minimum achievable data-rate at the user-side. Extending the
minimum data-rate is necessary particularly in indoor
multi-cell networks where high-levels of interference may
exist. Although an intra-cell power control technique may
reduce the transmit power and as well the inter-cell
interference the gain to the deprived users is limited. This
limitation is significant in closed-access dense femtocells
where femto-users may not be linked to their nearest
femtocell. In order to extend further the date-rate of a user in a
disadvantaged position, we employ the concept of
interference avoidance/coordination.
Interference avoidance through Inter-Cell Interference
Coordination (ICIC) [8] is a promising and effective inter-cell
(RRM) technique. The concept of ICIC is to provide
favorable interference conditions across sets of deprived user
equipments (UEs) that are severely impacted by the inter-cell
interference. By applying specific radio resource restrictions,
dominant interference can be mitigated, less overall power
can be transmitted and higher spectral efficiency (SE) can be
achieved by those UEs. Additionally, as the channel quality of
those UEs is improved, an eNB (evolved Node B) may
transmit less power via an intra-cell power control to further
increase the EE. The inter-cell resource restriction may be
managed through fixed, adaptive, or real-time coordination to
ease the complexity involved and signaling overhead through
an inter-cell communication link.
This paper investigates an energy-efficient ICIC scheme in
an interference-limited multi-cell HetNet consisting of
macrocell and femtocells. We extend a semi-centralized
multi-cell ICIC scheme from our previous work [9] with an
emphasis on user fairness and EE of the overall network. For
performance evaluation, we compare the performance of our
scheme with an energy efficient algorithm which is user
fairness aware [5] [7]. Our main performance metrics are the
total sector throughput per joule including transmit and circuit
Distributed Energy-efficient Inter-Cell Interference
Coordination (ICIC) in multi-cell HetNets
C. Kosta, B. Hunt, A. Quddus, and R. Tafazolli
CCSR, University of Surrey, Guildford, UK
{C.Kosta, B.Hunt, A.Quddus, R.Tafazolli}@surrey.ac.uk
power and user fairness defined as 5
th
percentile of the user
average throughput. For convenience in overall performance,
total cell throughput is also considered.
This paper is organized as follows: In Section II a general
description of our system model is given. In Section III, we
describe our distributed energy efficient ICIC scheme.
Simulation results and comparisons of the proposed scheme
are given in Section IV. This paper is concluded in Section V.
II. S
YSTEM
M
ODEL
A multi-user radio interface based on OFDM (Orthogonal
Frequency Division Multiplexing) has been standardized in
the downlink for next generation mobile systems, i.e.
OFDMA (Orthogonal Frequency Division Multiple Access).
In our system model, two sub-frames (or timeslots) are
considered in scheduling, well known as a transmission time
interval (TTI). Each of the resource blocks (RBs) consists of
12 subcarriers in the frequency domain and 7 OFDM symbols
in the time domain. In addition, we assume that our system
uses orthogonal reference sequences (RS) and that the served
users can look for different sources of interference and
estimate their levels separately [10]. The SINR estimated by
UE k connected with i on RB n not including the interfering
source eNB j
∈
G
i,m
is expressed as:
,
,
,
,
,
γ
≠
∉
⋅
=⋅ +
∑
i
k n
i
s k n
i g
k n j
t k n w
j i
j G
P H
P H N
. (1)
Here, H
k,n
is the channel gain that UE k experiences on RB n.
P
t
is the power allocated per RB and N
w
stands for the average
thermal noise power in each RB. The super-indexes i and j in
(1) represent the serving and interfering link, respectively.
G
k,,n
, denotes an index to represent the subset of possible
in-group sources of interference. For example, the in-group
possibilities of interfering sources of eNB ‘α’ and eNB ‘β’
are: {}, {a}, {b} and {a, b}. The {} denotes the possibility
that eNB ‘α’ and eNB ‘β’ do not interfere whereas the {a, b}
denotes that both eNBs may interfere.
For simplicity, we define f ( ) as an adaptive modulation
and coding function that converts the SINR to an achievable
data rate as:
(
)
,,
, ,
i
i
i g i g
k n k n
r f
γ
=
. (2)
For studies not related with the component-wise EE
improvements, it has been shown that a linear approximation
model may be considered realistic [2]. Therefore, we use a
linear power model to calculate the total power consumed as
follows,
T c t
P P b P
= + ⋅
, (3)
where P
c
is the total power circuit consumption, b the
amplifier coefficient loss and P
t
as the total transmit power.
We define EE in bits/Joule, where the ‘bits’ are the data
information that have been successfully transmitted over the
wireless channel and the ‘Joule’ is the total energy consumed
by an eNB.
III. P
ROPOSED
E
NERGY
-E
FFICIENT
S
CHEME
Our proposed scheme is divided into three stages, i.e. the
dominant interference classification, the inter-cell resource
restriction (or inter-cell power control), and the intra-cell
power control. In the 1
st
stage our algorithm selects a
scheduling list of best users for possible inter-cell restrictions
for each RB (or group of RBs), while in the 2
nd
stage it
optimally decides the inter-cell restrictions in conflict. This
modification allows fast execution over the RBs, while
keeping the optimality gap to a minimum. Finally, based on
these radio resource restrictions our algorithm can further
minimize the average transmit power while maintaining
channel radio quality in the 3
rd
stage.
A. Dominant interferences classification
In a typical cellular system, cell-edge UEs experience both
low channel reception from the desired cell and severe
inter-cell interference from cells close-by. Therefore, to
extend their minimum achievable data rates, we restrict the
major interferences on such UEs. Interestingly, by applying
radio resource restrictions to the dominant interferers, less
power is transmitted, to some extent higher overall throughput
can be seen, and thus less transmit power is observed. Since
the only way to reduce transmit power is by restricting
dominant interference, our ICIC algorithm thrives in
mitigating as many interferers as possible in the first stage. In
order to further minimize the power consumption across the
network we employ intra-cell power control afterwards.
With the help of RS, dominant interferences can be
classified to each UE on an RB basis. The rationale behind
mitigating the dominant interferences is as follows. First, in
downlink LTE systems up to six major interferences are
expected to be identifiable and measurable [10]. Second, a
higher improvement on the user achievable data-rate can be
seen only by mitigating the dominant interference. Therefore,
we investigate the mitigation of dominant interferences in
order to increase the data rate achieved by a set of
disadvantaged UEs. This can be seen as a local problem that
prepares a scheduling list of UEs according to the radio
channel and the interference conditions.
Let us consider the IDs of the first, second and third
dominant interfering eNBs with indices ‘a’, ‘b’, and ‘c’
respectively. The interfering eNB in-group possibilities of
interest are: {}, {a}, {a, b} and {a, b, c}. For simplicity, each
possibility is denoted by m ∈ {1, 2, 3, 4}. Other, interfering
eNB in-group possibilities ({b} and {a, c}) are not of interest
since they provide insignificant performance improvement
accounting for the computational complexity and signaling
involved.
An inter-cell utility matrix is estimated as:
2
,
,
1
1
= ( 1)
⋅
− + ⋅
64444744448
14243
U
m
k n
m
k n
k T
U
r
U
d M m P
, (4)
were M denotes the total number of interfering eNB in-group
possibilities. Here, we define the user demand d
k
as the
average throughput of UE k divided by the average
throughput across all UEs. The U1 in (4) models a
network-wide SE (bits/sec) with an emphasis on user fairness.
Based on the following observation the U2 in (4) may model a
power saving scheme network-wide. Consider an
interference-limited cellular system with a total of M eNBs.
Now consider the case when the active configuration on a
specific RB is increased from 1 to M. This means that only
one eNB transmits out of M eNBs. Then, the exact expression
given in (4) will also have at least an M-fold increase (r
m
>
r
1
).
With respect to the M-eNBs case, the U2 in (4) may simulate
an EE metric.
Once the utility matrix is calculated, the scheduling UE
list
m
n
I
, on each configuration m and RB n is given by:
,
arg max{ }
m m
n k n
k
I U
=
. (5)
B. Inter-cell resource restrictions
The inter-cell resource restriction problem can decide
which configuration in which cell is to be set. Given that the
user-allocation problem is decoupled in this stage, each
decision is taken independently across all RBs. An optimal
solution of which configuration an eNB should transmit to
each RB is reached via the formulated linear problem as
follows:
, ,
1
maximize ;
i
i
i
f
M
i m i m
i m
f
U
ρ
=
⋅
∑
∑∑
6447448
1442443
(6a)
,
,
,
,
1 1
subject to {0, 1}
i m
i
j
j m
M M
i m
i m
m m
j G
xx
G
ρ
ρ
= =
∈
+ ∈
∑ ∑ ∑
14243 1442443
. (6b)
For notational convenience, we use a generalized form G
i,m
to denote the eNBs involved in each interfering scenario. The
binary variable ρ
i,m
denotes whether it is beneficial for the
eNB i to transmit on configuration m (ρ
i,m
= 1) or not (ρ
i,m
= 0).
Furthermore, the term x
i
denotes that an eNB is allowed to
transmit with one configuration only. In a similar way, this
inter-relationship is propagated to x
j
for each eNB j within the
restricted interfering eNB group G
i,m
and therefore to variable
ρ
j,m
. The denominator | G
i,m
| under the variable ρ
j,m
normalizes
the term x
j
to 1. The significance of the denominator here is to
allow more than one candidate (eNB j) to transmit (x
j
=1) in
the case when the eNB i does not transmit (x=0). Both x
i
& x
j
indicate that if the RB n is not restricted it can be allocated to
one UE, or if the RB n is restricted it can then benefit more
than one candidate.
One main challenge associated with problems belonging to
the class of binary linear programming is that they require an
extensive search path so that they can be solved. Prolonged
extensive search of a linear problem can be reduced by
introducing a number of tighter constraints or cuts [11].
In order to reduce the complexity involved with the
scalability of the problem we may reformulate (6b) to this,
,
, ,
1 1
subject to {0, 1}
i m
ij
M M
i m j m
m m
j G
hh
ρ ρ
= =
∈
+ ∈
∑ ∑ ∑
14243 14243
. (6c)
Now the constraint (6c) of the reformulated problem is a
special case, i.e. problem with totally unimodular matrix
specifications [12], whose relaxed solution is also the optimal
solution to the initial problem. This means that there is a small
integrality gap
1
between the reformulated problem and its
relaxation. Linear programming relaxation is a problem that
arises when binary variables are replaced with real variables
belonging to interval [0 1]. For instance, the constraint in (6b)
can be assumed as,
, ,
, [0, 1];
i m j m
ρ ρ
∈ (6d)
[0, 1];
ji
h h
+ ∈ (6e)
and round the final solution to its nearest integer (0 or 1).
Thus, binary optimization problems with totally unimodular
matrix specifications can be relaxed [13] and solved in
polynomial time. However, a direct implication of
substituting the equation (6b) with (6e) is that the
reformulated problem does not benefit more than one of the
eNB candidates that are requesting resource restrictions.
C. Intra-cell power control
We employ intra-cell power control as a final stage in order
to minimize the total average transmit power. An intra-cell
utility matrix is calculated as:
( )
,
,
1
=
P ( )
⋅
k n
k n t
k T t
r
U P
d P
(7a)
Here, a constrained optimization problem can be formulated
and solved independently in each eNB as follows:
(
)
,
maximize ;
k n t
U P
(7b)
min max
subject to [ , ]
∈ =
t
P C C P P
. (7c)
where P
min
and P
max
are the minimum and maximum that an
eNB may transmit on a RB, respectively. However, an
optimal P
t
* only exists if U
k,n
(P
t
) is strictly quasi-concave in
P
t
. In order to achieve this, let us redefine the operating
mapping function by assuming a log-transformed rate region
[14] as follows,
,
, 2
1.5
log 1
(5 BER)
k n
k n
r B L
L In
γ
= + = −
⋅
. (8)
Here, R is the maximum amount of data that can be conveyed
in terms of SINR, B is the allocated bandwidth and L is the
SNR gap to data-rate, which is linked via a particular target bit
error rate (BER). The rate region R is now convex with a
unique optimal P
t
*.
The power can be updated at step s by using a projected
subgradient method as,
1
Integrality gap is defined as the maximum ratio between the solution
quality of the binary/integer problem and of its relaxation.
[
]
( 1) ( ) ( )
+ =℘ + ⋅
t t
P s P s a g s
. (9)
where ℘[ ] is the projection on C, g(s) is the subgradient of
U
k,n
at P
t
(s) and α >0 is a small iterative step size. Generally, if
the iteration step size a is sufficiently small as s→∞ the power
gap between the P
t
and its optimal P
t
* will converge to zero.
D. Dual Decomposition
In order to satisfy the complexity requirements set by the
next generation multi-cell networks we may break down the
relaxed ICIC problem into a number of independent
sub-problems via dual decomposition [15] as follows,
(
)
( , ) 1
( , )
i i i j
i
i i i i
i i
L f h h
L
ρ λ λ
ρ λ λ
= − + −
= +
∑
∑ ∑
(10)
where λ
i
> 0 is the Lagrange multiplier or dual variable
associated with the constraint (6e). The main network
problem is now reformulated as,
maximize g(λ)= ( )
i i
i
g
ι
λ λ
+
∑ ∑
; (11a)
subject to , 0
i
λ λ
≥
, (11b)
where
(
)
*
( ) ( , )
i i i i
g L
ι
λ ρ λ λ
=
. The
(
)
*
i i
ρ λ
is the optimal
primal variable of the independent sub-problem L
i
and is
unique due to strict concavity of the log-transformed f
i
which
can be calculated as,
(
)
(
)
*
[0,1]
argmax 1
i
i i i i i j
f h h
ρ
ρ λ λ
∈
= − + −
. (12)
Since the solution in equation (13) is unique, the following
subgradient method may be used
[ ]
λ( 1) λ( )
i i i
s s g
β
+
+ = − ⋅
(13)
where [ ]
+
is the projection on the non-negative orthant and β
is a positive iterative step size. The network problem forwards
to all involved eNBs regarding the updated value of λ. In a
similar way, if the iteration step size β is sufficiently small as
s→∞ the duality gap between the relaxed problem and its dual
will converge to zero.
IV. S
IMULATION
S
TUDY
P
ERFORMANCE
The simulation study is performed in the downlink using
the freely available LTE-based system-level simulator [16] in
order to evaluate the performance of the novel scheme. Apart
from the outdoor eNB network, a closed-access low-power
HeNB (Home eNB) network is implemented to simulate a
HetNet scenario with numerous small-cells. However, to
avoid excessive interference from HeNB to eNB network, an
e-ICIC mechanism is used, namely, a high-interference
indicator (HII) is performed on allocated RBs in conflict [17].
Table 1 gives the main simulation parameters used in this
paper.
Table 2 and Table 3 show the performance of the proposed
scheme compared with a number of reference schemes in
macro and femto cells, respectively. We observe bits/Joule as
the performance energy-efficiency and the 5
th
percentile point
of CDF of UE throughput (i.e. the throughput of deprived
users) in Kbps as the user fairness performance of the system.
Furthermore, for convenience in overall performance, the
sector/cell throughput is also shown in the same table.
Moreover, as a baseline reference scheme we show the
performance of reuse-1 scheme under a proportional fairness
scheduler (
R
EUSE
-1
PF
) were no intra-cell power control is
employed. As expected, the
R
EUSE
-1
PF
scheme shows
minimum performance in user fairness and EE since full
power is transmitted to all RBs. A state-of-the-art energy
efficient user fairness scheme is displayed as ‘
R
EF
’,
where its
performance gain is relatively satisfactory over the baseline.
However, this gain is lower in the case of femtocells due to
severe interference conditions which may exist in an
unplanned deployment. Our candidates are displayed with the
notation I
CIC
-X, where X denotes the total number of
dominant interferers which can be mitigated. The option ‘EE’
denotes the proposed utility, the option ‘R
ELAXED
-
D
UAL
’
denotes the relaxed version of proposed ICIC algorithm and
the option ‘SE’ denotes the U1 utility in (4), which aims to
increase SE rather than EE. The percentage in parenthesis
shows the relative gain/loss with respect to the baseline
scheme (
R
EUSE
-1
PF
). The
R
EF
scheme has a near optimal
performance in the macro EE, however the macro user
fairness is limited. The candidate ‘I
CIC
-1’ can increase
significantly the user fairness without losing its
competiveness in other metrics. However, we can observe that
T
ABLE
1.
M
AIN
S
YSTEM
S
IMULATION
P
ARAMETERS
Parameter Assumption or Value
Outdoor scenario deployment 2-tier tri-sectorized sites (19-
sites)
with a total of 57 eNBs
Indoor (Home) scenario
deployment
Block type: 5x5 grid, 10% HeNBs
House dimensions: 10x10 m
2
eNB Inter-Site Distance (ISD) 500 m
Total bandwidth 10 MHz
Total Resource Blocks (RB) 50 RBs
Total bandwidth per RB 180 KHz
Total eNB/HeNB transmit power
46 dBm / 10 dBm
Average eNB/HeNB circuit power
100 W / 0.05 W
Outdoor path loss model L = 128.1 + 37.6 log
10
(R), R[KM]
Indoor path loss model L = 127 + 30 log
10
(R), R[KM]
External wall penetration loss 30dB
Outdoor/Indoor Shadowing’s
standard deviation 8 dB / 10 dB
\ 50 m / 3 m
Fast fading models ITU models [18]
User noise figure/ Thermal noise 9 dB / −174 dBm
Simulation time 500 TTIs
Num of UEs per sector area 10
HeNodeB blocks per sector area 1
HeNodeB deployment/
activation ratio 0.15 / 1.0
Power amplifier coefficient loss
eNB/HeNB 5 / 20
the ‘I
CIC
-1’ can significantly increase all performance metrics
in femto cells due to the mitigation of strong interferences.
Subsequently, ‘I
CIC
-2’ and ‘I
CIC
-3’ are better candidates to
increase further the overall performance of the system. In
terms of EE, there are huge potential savings by employing a
power efficient scheme in HetNets since there is high
coupling link between transmit power and the power
consumption of the system. We note that an interference
aware scheme becomes a necessity in femtocells where indoor
eNBs can be deployed in an ad hoc manner and are subject to
movement or switched on/off at any time. We observe that the
performance degradation in sector throughput of the ‘I
CIC
-X
R
ELAXED
-
D
UAL
’ candidates is increased when the number of
total interferers which can be mitigated is increased. This
performance degradation is due to the higher number of
candidates which are limited by the relaxed problem. In the
case of femtocells, the scalable candidate ‘I
CIC
-1 R
ELAXED
D
UAL
’
can outperform the reference scheme in all
performance metrics.
V. C
ONCLUSION
In this paper we have proposed a distributed
energy-efficient ICIC scheme for the emerging multi-cell
OFDMA networks, based on an ICIC distributed framework.
The novel ICIC scheme can increase not only the
energy-efficiency in bits/Joule of the overall network but can
also extend the user fairness defined as the 5
th
percentile of
user throughput. In order to satisfy the on-going research
demand in finding distributed solutions regarding the
inter-cell complexity involved with the associated problem,
we simplify, relax and decompose the proposed scheme into
multiple sub-problems in a way that does not lose its
competiveness. Through a simulation study using a HetNet
scenario, we show that the proposed scheme can outperform a
state-of-the-art reference scheme in all performance metrics,
particularly in ad hoc deployments such as femtocells. It has
also been observed that dynamic ICIC schemes are more
favorable in femtocells due to the existence of nearby strong
interferers which may degrade the user experience
significantly.
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T
ABLE
2.
P
ERFORMANCE IN
M
ACROCELLS
(
GAIN
/
LOSS
)
S
CHEME
S
ECTOR
T
HROUGHPUT
IN MBPS
5
TH
–
ILE
U
SER
T
HROUGHPUT IN
KBPS
EE
IN
KB
ITS
/J
OULE
R
EUSE
-1
PF 14.5 288 58
R
EF
[5]
&
[7]
15.0 (3%) 403 (40%) 234 (303%)
I
CIC
-1
E
E
15.3 (6%) 500 (73%) 230 (296%)
S
E
15.5 (7%) 429 (49%) 216 (273%)
R
ELAXED
-
D
UAL
14.7 (1%) 505 (75%) 235 (305%)
I
CIC
-2
E
E
15.1 (4%) 573 (99%) 250 (330%)
S
E
15.9 (9%) 495 (72%) 224 (286%)
R
ELAXED
-
D
UAL
13.2 (-9%) 578 (100%) 253 (335%)
I
CIC
-3
E
E
14.7 (1%) 624 (117%) 262 (351%)
S
E
16.0 (11%) 548 (90%) 231 (299%)
R
ELAXED
-
D
UAL
12.0 (-17%) 611 (112%) 284 (389%)
T
ABLE
3.
P
ERFORMANCE IN
F
EMTOCELLS
(
GAIN
/
LOSS
)
S
CHEME
C
ELL
T
HROUGHPUT
IN
M
BPS
5
TH
–
ILE
U
SER
T
HROUGHPUT IN
K
BPS
EE
IN
M
BITS
/J
OULE
R
EUSE
-1
PF 17.87 50.21 71
R
EF
[5]
&
[7]
15.27 (-15%)
90 (80%) 130 (81%)
I
CIC
-1
E
E
18.66 (4%) 790 (1474%) 178 (149%)
S
E
19.83 (11%) 707 (1310%) 172 (140%)
R
ELAXED
-
D
UAL
18.07 (1%) 780 (1455%) 179 (150%)
I
CIC
-2
E
E
16.27 (-9%) 1000 (1893%) 190 (166%)
S
E
19.44 (9%) 1166 (2224%) 181 (154%)
R
ELAXED
-
D
UAL
15.17 (15%) 978 (1848%) 185 (158%)
I
CIC
-3
E
E
14.72 (-18%)
1302 (2495%) 186 (160%)
S
E
19.36 (8%) 1463 (2815%) 185 (158%)
R
ELAXED
-
D
UAL
11.74 (-34%)
1274 (2438%) 164 (129%)
