Energy-Efficiency-Aware Upgrade of Network Capacity

TLDR: This work investigates the conditions under which a network upgrade does not deteriorate its energy efficiency, and considers two ways of upgrading a network: either by adding equipment with the same technology or by deploying equipment with another technology, typically more recent and more efficient.

Abstract: Energy efficiency of a network, defined as the number of bits transmitted per unit of consumed energy, increases with the traffic load for a constant network capacity. This comes from the fact that energy is composed of two components: a fixed one, consumed by the network regardless of the traffic load, and a variable one, which depends on the traffic load. And so, when traffic load increases, the fixed component gets amortized. However, a network upgrade, namely adding more equipment in the network to fit traffic increase, comes typically with a higher increase in capacity than traffic, at least for a while after the upgrade, as traffic previsions are based on relatively long term projections. Thus, the power consumption of the network would increase faster than the traffic, and energy efficiency would then decrease. We investigate in this work the conditions under which a network upgrade does not deteriorate its energy efficiency. We consider two ways of upgrading a network: either by adding equipment with the same technology or by deploying equipment with another technology, typically more recent and more efficient. We discuss in both cases the number of equipment to be added so that to preserve the network's energy performance.

Figures

TABLE I ENODEB PARAMETERS

Fig. 5. Maximum number of sites in the upgraded network (LTE-A sites) to avoid degrading the network’s energy efficiency

Fig. 6. Right proportions of LTE sites in the upgraded network, case with no traffic increase

Fig. 7. Right proportions of LTE sites in the upgraded network, case with 23% traffic increase

Fig. 1. Power model of a network’s equipment.

Fig. 2. Sign of the derivative of the energy-per-bit

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Energy-eciency-aware upgrade of network capacity
Wilfried Yoro, Mamdouh El Tabach, Taouk En-Najjary, Azeddine Gati,
Tijani Chahed
To cite this version:
Wilfried Yoro, Mamdouh El Tabach, Taouk En-Najjary, Azeddine Gati, Tijani Chahed. Energy-
eciency-aware upgrade of network capacity. IEEE WCNC, Mar 2017, San Francisco, United States.
pp.1 - 6, �10.1109/WCNC.2017.7925952�. �hal-01528461�

Energy-efficiency-aware Upgrade of Network
Capacity
Wilfried Yoro
∗
, Mamdouh El Tabach
∗
, Taoufik En-Najjary
∗
, Azeddine Gati
∗
, Tijani Chahed
†
∗
Orange Labs, Chatillon, France
†
Institut Mines-Telecom, Telecom SudParis, UMR CNRS 5157 SAMOVAR, Evry, France
Email: {wilfried.yoro, mamdouh.eltabach, taoufik.ennajjary, azeddine.gati}@orange.com
tijani.chahed@telecom-sudparis.eu
Abstract—Energy efficiency of a network, defined as the num-
ber of bits transmitted per unit of consumed energy, increases
with the traffic load for a constant network capacity. This comes
from the fact that energy is composed of two components: a
fixed one, consumed by the network regardless of the traffic load,
and a variable one, which depends on the traffic load. And so,
when traffic load increases, the fixed component gets amortized.
However, a network upgrade, namely adding more equipment in
the network to fit traffic increase, comes typically with a higher
increase in capacity than traffic, at least for a while after the
upgrade, as traffic previsions are based on relatively long term
projections. Thus, the power consumption of the network would
increase faster than the traffic, and energy efficiency would then
decrease. We investigate in this work the conditions under which
a network upgrade does not deteriorate its energy efficiency. We
consider two ways of upgrading a network: either by adding
equipment with the same technology or by deploying equipment
with another technology, typically more recent and more efficient.
We discuss in both cases the number of equipment to be added
so that to preserve the network’s energy performance.
Index Terms—Energy efficiency, Network densification, Wire-
less network
I. INTRODUCTION
Internet traffic is growing exponentially over years, mainly
due to the democratization of smartphones and tablets and the
increase of content. According to Cisco [1], overall IP traffic
will grow at a compound annual growth rate (CAGR) of 23
percent from 2014 to 2019. To face this situation, Internet
providers upgrade their networks so as to keep up and/or
improve the users Quality of Experience (QoE).
Energy efficiency of a network is defined as the number
of transmitted bits per unit of consumed energy. At constant
network capacity, energy efficiency increases with the traffic
load of the network. This is due to the fact that the energy
consumption of a network consists of two components: a fixed
one, consumed by the network infrastructure regardless of the
traffic, and a variable one, which is proportional to the traffic
load. When the traffic increases, the fixed component of energy
gets amortized, and hence the network’s energy efficiency gets
improved.
When the network is upgraded, new equipment are added in
order to fit traffic increase, based on long term previsions. This
typically comes with a higher increase in capacity than traffic,
at least for a while after the upgrade operation. Thus, the power
consumption of the network could increase faster than the
traffic, and energy efficiency could decrease consequently. So,
the energy efficiency of the network has upward and downward
trends, that is, it decreases after an upgrade then increases with
traffic load until the next upgrade operation.
A network upgrade improves the energy efficiency of the
network when it is operated at full load. In fact, newer
technologies are typically more energy efficient than older
ones as they come with better software, algorithms, etc. On
the field however, the network is not operated at full load,
i.e., maximum capacity, and so the newer technologies are not
necessarily more energy efficient. For instance, deploying a 4G
network along side with the existing 3G network may result
in a less efficient network since the traffic is shared between
the two technologies.
Several works in the literature investigated the network
upgrade topic (we will report on some of them in section II).
These works introduce different techniques for networks
densification, but there is still work to do on how to prevent
a capacity upgrade from degrading the energy performance of
the network. This paper is a contribution in that direction.
We specifically focus on the two ways mostly used for
upgrading the network capacity: either by adding equipment
with the same technology, for instance adding 4G sites in a 4G
network, or by deploying equipment with another technology,
typically more recent and more efficient, for instance adding
LTE-A sites in a LTE network. In each case, we determine the
number of equipment to be added so as the upgrade preserves
the network’s energy efficiency.
The remainder of this paper is organized as follows. In
section II, we review some literature related to densification
of networks. In section III, we introduce our models for
assessing the energy efficiency of a mobile access network.
In section IV, we discuss the impact of different techniques
of network upgrade on the energy efficiency. Section V shows
some applications of our model, run on a real dataset taken
from an operational European network. Section VI eventually
concludes the paper.
II. RELATED WORK
In [2], Mugume et al. investigate with stochastic geometry
tools the impact of small cells deployed by users on the
spectral and energy efficiency of mobile networks. The authors
define three scenarios according to the ratio of networks’ base

stations versus users’ base stations. The authors recommend
to densify the network so as to avoid a low value of that ratio.
Yunas et al. [3] propose a new approach for network
densification. The authors state that the majority of data
traffic, approximately 65 − 70% is generated by indoor users.
Therefore, it is more spectral and energy efficient to densify
the network with indoor small cells mainly, while maintaining
some outdoor coverage for high-speed outdoor users. The
authors propose the distributed antenna system (DAS) for
outdoor hotspots coverage.
According to Andrews et al. in [4], densification of wireless
networks for enabling data rate increase by spatial reuse is
reaching a fundamental limit. Even though the standard path
loss model shows that the SINR becomes density-independent
starting from a given value of density, when considering the
dual slope path loss model instead, the authors come out
with a SINR decreasing monotonically with density in dense
networks. There is therefore a densification limit.
Litjens et al. in [5] assess the energy efficiency improvement
of future mobile networks. The energy efficiency of mobile
networks in 2010 and 2020 are compared, considering all rel-
evant scenarios aspects. The results show an energy efficiency
improvement factor of about 793 in 2020 over 2010.
III. MODELING THE ENERGY PER BIT.
A. Modeling the energy-per-bit of the network
The energy-per-bit of the network, which we denote by α , is
the amount of energy consumed by the network per transmitted
bit. Let ∆t denote the observation time of the network’s traffic
and energy consumption; ∆t = t
2
− t
1
, with t
1
and t
2
the
initial and final instants of observation, respectively.
α(R, C) =
R
t
2
t
1
P (t)dt
P
N
i=1
v
i
(1)
with R the mean traffic rate (in units of (Mega)bits per sec-
ond), C the network capacity (also in (Mega)bits per second),
v
i
the traffic volume of service i (in units of (Giga)bits), N the
number of services in the network and P (t) the instantaneous
power consumption of the network, which consists, as stated
earlier, of a constant component (independent of the load) and
a variable one (load-dependent).
According to [6], the power model of a network equipment
is a linear function of its traffic rate, as depicted in Fig. 1. We
deduce that:
P (t) = P
0
+ ρ(t)(P
max
− P
0
) (2)
where P
0
is the network’s idle power, ρ(t) =
R(t)
C
is the
network’s load at time t and P
max
is the network’s maximum
power.
In addition,
N
X
i=1
v
i
= R × ∆t (3)
So,
α(R, C) =
1
∆t
R
t
2
t
1
P
0
+ ρ(t)(P
max
− P
0
)dt
R
(4)
Fig. 1. Power model of a network’s equipment.
.
α(R, C) =
P
0
R
+ ρ
P
max
− P
0
R
(5)
where ρ =
1
∆t
R
t
2
t
1
ρ(t)dt, the mean load over ∆t.
Moreover,
ρ =
R
C
(6)
And so, Eqn. (5) becomes,
α(R, C) =
P
0
R
+
P
max
− P
0
C
(7)
B. Evolution of the network’s energy efficiency with the traffic
rate
As stated earlier, the network’s energy efficiency typically
increases proportionally to the traffic rate R, when the num-
ber of equipment is constant, i.e., when the network is not
upgraded. This intuition is mathematically proved, as follows.
∂α(R, C)
∂R
= −
P
0
R
2
(8)
The network energy-per-bit decreases with the traffic rate
as
∂α(R,C)
R
< 0.
And so, a traffic rate increase improves the network energy
efficiency as long as this increase does not call for a network
upgrade. When a network upgrade is however operated, this
rule might be upset, and we study next the impact of an
upgrade on the energy efficiency of the network.
IV. UPGRADE OF THE NETWORK
As stated above, we consider in this investigation that
a network upgrade can be achieved either by adding new
equipment with the same technology or by replacing existing
equipment by newer ones, implementing more recent and
typically more energy-efficient technologies.
A. Upgrading the network with the same technology
The network’s capacity and power consumption are function
of the number of equipment, denoted by K. Upgrading the
network can improve its energy efficiency if the energy-per-
bit (inverse of the energy efficiency) of the network is not
an increasing function of the number of equipment, i.e., the
derivative of the energy-per-bit (α) with respect to K should
not be positive. We then study the sign of the derivative
of the energy-per-bit in order to determine the limit value
of the number of equipment, i.e., the value of K, beyond

Fig. 2. Sign of the derivative of the energy-per-bit
which the derivative is positive. When the number of network’s
equipment is lower than this limit value, the network upgrade
is able to preserve the network’s energy performance.
From Eqn. (7), the derivative of α with respect to K is:
∂α(R, C)
∂K
=
1
R
∂P
0
∂K
+
∂P
max
∂K
−
∂P
0
∂K
C
−
(P
max
− P
0
)
∂C
∂K
C
2
(9)
In the case the network’s capacity is a linear function of
the number of equipment K, the variation of the energy-per-
bit versus the number of equipment is a parabola, as depicted
in Fig. 2. The limit value of K corresponds to the number of
equipment for which the derivative of α is equal to zero.
B. Upgrading the network with a new technology
We consider in this section that the network upgrade results
from a new technology, denoted by T . The network’s capacity
and power consumption are function of the deployed technol-
ogy. We keep the same reasoning as with the case of upgrading
the network with the same technology. Energy efficiency varies
with the technology as follows,
∂α(R, C)
∂T
=
1
R
∂P
0
∂T
+
∂P
max
∂T
−
∂P
0
∂T
C
−
(P
max
− P
0
)
∂C
∂T
C
2
(10)
The derivative of the capacity or power versus the technol-
ogy T indicates the increase of the capacity or power when
the new technology is deployed in the network. Here too, we
study the sign of the derivative and find the limit value of the
number of network’s equipment.
It is worth to note that unlike the network upgrade with the
same technology case, where the parabola is always opened
upward, since
∂P
0
∂K
is always positive because the idle power
consumption of the network increases with the number of
network’s equipment, in the case of a network upgrade with a
new technology, the parabola can open upward or downward
since
∂P
0
∂T
can be positive or negative as the new technology
can increase or decrease the idle power of the network. When
the parabola opens downward, i.e., when the new technology
decreases the idle power of the network, there is no limit
value of K beyond which the derivative of the energy-per-
bit is always positive, this means that it is always possible
to upgrade the network while preserving its energy efficiency
when the new technology decreases the network’s idle power.
When the parabola opens upward, there is a limit value of K
beyond which the network upgrade cannot preserve the energy
efficiency, since the derivative is always positive beyond this
value.
V. APPLICATIONS TO 4G ACCESS NETWORK
We consider a real, operational 4G access network com-
posed of 10000 eNodeBs and an average traffic rate of 10
Gbps. Tab. I summarizes the parameters of the network’s
equipment. Column 3 gives the typical mean values of the
maximum power, idle power and capacity of an eNodeB. We
consider that the uplink represents 20% of the total traffic,
based on [7] and on measurements carried out on the above-
mentioned real operator network, and 13% of the total power
consumption [6], [8].
A. Energy efficiency of a mobile access network
Let us consider that the network’s equipment have the same
mean capacity and mean power. Then, the total mean capacity
of the network is the mean capacity of an equipment multiplied
by the number of equipment in the network. It applies also
to the total power of the network. Hence, P
max
= KP
bs
max
,
P
0
= KP
bs
0
and C = KC
bs
where P
bs
max
, P
bs
0
and C
bs
are respectively the mean maximum power, idle power and
capacity of a single base station. The network capacity is
then a linear function of the number of network equipment
K. In the sequel, we use the terms base station and site
interchangeably.
The energy-per-bit of the network is (after simplification of
Eqn. (7)),
α(R, K) =
P
bs
max
− P
bs
0
C
bs
+ P
bs
0
K
R
(11)
Eqn. (11) shows that the energy efficiency of the network
(inverse of the energy-per-bit) is proportional to the traffic
and inversely proportional to the number of sites. But the
network’s energy efficiency cannot be increased indefinitely
as the traffic should not exceed a threshold R
threshold
, at a
constant network’s capacity. We have from Eqn. (6):
R
threshold
= KC
bs
ρ
threshold
(12)
with ρ
threshold
a given network load threshold obeying to
operational constraints.
Eqns. (11) and (12) yield the lower bound of the network
energy-per-bit at a constant number of sites, termed α
min
.
α
min
=
P
bs
max
− P
bs
0
C
bs
+
P
bs
0
C
bs
ρ
threshold
(13)
Let z denote the proportion of traffic increase. The capacity
upgrade does not degrade the network energy efficiency if:
K
f
− K
i
K
i
≤ z (14)
where K
f
and K
i
are respectively the number of sites in the
upgraded and initial networks.

TABLE I
ENODEB PARAMETERS
Parameters Definition Typical values
K Number of network equipment
P
bs
max
(W att) Maximum power 528
P
bs
0
(W att)
Idle power 333
C
bs
(Mbps)
Base station capacity 72 DL, 12 UL
R
Traffic rate
Eqn. (14) results from the resolution of α(R
f
, K
f
) ≤
α(R
i
, K
i
), i.e., the energy-per-bit of the upgraded network
should be lower than or equal to the energy-per-bit of the
initial network. Hence, the maximum number of sites that
can be added in the network in order to preserve its energy
efficiency is proportional to the traffic increase z. As a result, if
there is no traffic increase, i.e., z = 0, the operator should not
add LTE sites in the network otherwise its energy efficiency
would be degraded. However to keep up with a traffic increase,
the operator should add at most z% of new LTE sites in his
network. It is worth to note that this limit does not take into
consideration spectral efficiency constraints, and it is up to the
network designer to consider both our results along with other
network constraints in the upgrade policy.
The access network has different characteristics in the
uplink and downlink, so all the above expressions should
be considered separately in both directions. The network we
investigated has an uplink-energy-per-bit of 200 µJ/bit, i.e.,
the uplink radio resources consume on average 200 µJ per
transmitted bit. According to [6], the observed traffic for
uploading a 5-MB photo to Facebook in normal quality using
a smartphone with Wifi and 4G technologies is about 1.1 MB,
because Facebook compresses photos heavily in user browser
before sending them to Facebook servers. Uploading a 5-MB
photo to Facebook in normal quality costs about 0.5 Wh. If
the operator sets the maximum acceptable load of the network
to 50%, then this cost can be reduced to 0.02 Wh, since the
lower bound on the uplink energy-per-bit would be 9.3 µJ/bit,
that is, 96% of energy gain. Hence, using the network even
only at half of its capacity allows significant energy savings,
unlike the actual operation of networks which are most of the
time under-loaded, about 10% on average for the investigated
network.
The results are similar in the downlink direction.
B. LTE network swap
We discuss in this section the conditions under which a swap
operation does not degrade the energy efficiency of the net-
work. A swap consists in replacing the sites of the network by
newer, more efficient ones. We propose to investigate the swap
of LTE sites by LTE-A sites. Typically the energy efficiency
of network’s equipment improves with the technology. Thus,
an LTE base station is less energy efficient than an LTE-A
base station at full operating load. But in practice, networks
are typically underloaded, and so an LTE-A network is not
necessarily more energy efficient than an LTE network. Hence
Fig. 3. Limit value of the number of network’s equipment
Fig. 4. Energy efficiency of the upgraded network (LTE-A network)
the need to study the conditions for a swap operation not to
degrade the network energy efficiency.
Let x denote the power consumption ratio of an LTE-A site
versus an LTE site. We consider values of x between 0.5 and
1.5 depending on the network configuration. When x = 1,
then an LTE-A site consumes as much power as an LTE site.
1) Replacing LTE sites by an equal number of LTE-A sites:
Let us consider first a simple scenario where the network
operator makes a swap operation consisting in replacing the
LTE sites by an equal number of LTE-A sites, at constant
traffic.
The study of the sign of the derivative of the energy-per-bit
shows that when an LTE-A site does not consume more power
than an LTE site, the swap operation increases the capacity of
the network without deteriorating its energy efficiency. In fact,
replacing the LTE sites by less energy-consuming LTE-A sites,
at constant traffic, can only improve the energy efficiency of
the network.
If an LTE-A site consumes more power than an LTE site,
the study of the sign of the derivative of the energy-per-bit
shows that the swap operation increases the network’s capacity
but decreases its energy efficiency, although an LTE-A site is
more energy-efficient than an LTE site at full operating load.
In fact, replacing the LTE sites by more energy-consuming
LTE-A sites, at constant traffic, can only degrade the energy
efficiency of the network. This result is corroborated by Fig. 3
which shows that the number of network’s equipment (10000)
is greater than the limit values.
Fig. 4 shows the energy efficiency (inverse of the energy-
per-bit) of the upgraded network (LTE-A network), as a
function of x, the power consumption ratio of an LTE-A site
versus an LTE site. We note clearly that the LTE-A technology
degrades the energy performance of the network when an LTE-

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Energy-efficiency-aware upgrade of network capacity" ?

This comes from the fact that energy is composed of two components: a fixed one, consumed by the network regardless of the traffic load, and a variable one, which depends on the traffic load. However, a network upgrade, namely adding more equipment in the network to fit traffic increase, comes typically with a higher increase in capacity than traffic, at least for a while after the upgrade, as traffic previsions are based on relatively long term projections. The authors investigate in this work the conditions under which a network upgrade does not deteriorate its energy efficiency. The authors consider two ways of upgrading a network: either by adding equipment with the same technology or by deploying equipment with another technology, typically more recent and more efficient. The authors discuss in both cases the number of equipment to be added so that to preserve the network ’ s energy performance. 

Q2. What are the future works in "Energy-efficiency-aware upgrade of network capacity" ?

In the future, the authors would like to consider the following perspectives. Further investigations will tackle the case of mobile networks that do not fit this linearity condition. First, it is worth to note that the numerical applications contained in this paper are limited to a mobile network whose capacity is a linear function in the number of radio sites, or which can be approximated as such. It may be worthy to investigate the impact of other network topologies, for instance a Heterogeneous Network ( HetNet ) comprising micro sites, as well as the impact of their model on the QoS performance of the network. 

Q3. What is the way to preserve the energy efficiency of the network?

However when an LTE-A site consumes more power, i.e., x > 1, the only way to preserve the energy efficiency of the network is when θ = 1, i.e., when the network is not upgraded. 

Q4. How much energy does the network consume?

The network the authors investigated has an uplink-energy-per-bit of 200 µJ/bit, i.e., the uplink radio resources consume on average 200 µJ per transmitted bit. 

Q5. What is the sign of the derivative of the energy-per-bit?

The study of the sign of the derivative of the energy-per-bit shows that when an LTE-A site does not consume more power than an LTE site, the swap operation increases the capacity of the network without deteriorating its energy efficiency. 

Q6. What is the result of the study?

The authors showed that when the new technology decreases the idle power component of the network, a network upgrade can always improve or at least keep the energy efficiency of the network. 

Q7. What is the energy efficiency of an LTE site?

If an LTE-A site consumes more power than an LTE site, the study of the sign of the derivative of the energy-per-bit shows that the swap operation increases the network’s capacity but decreases its energy efficiency, although an LTE-A site is more energy-efficient than an LTE site at full operating load. 

Q8. How many LTE sites should be kept in the upgraded network?

For instance, in the case where an LTE-A site consumes 0.4 more energy than an LTE site, i.e., x = 1.4, the operator should keep at least 40% of LTE sites in the upgraded network, given 23% of traffic increase. 

Q9. What is the effect of upgrading a network?

In addition, the authors showed that a network loaded even at only half of its capacity allows significant energy savings, on the order of 95% for a photo upload on Facebook, for the network considered in this work. 

Q10. What is the energy-per-bit of the network?

The energy-per-bit of the network is (after simplification of Eqn. (7)),α(R,K) = P bsmax − P bs 0Cbs + P bs0K R (11)Eqn. (11) shows that the energy efficiency of the network (inverse of the energy-per-bit) is proportional to the traffic and inversely proportional to the number of sites. 

Q11. What is the value of the derivative of the energy-perbit?

When the parabola opens downward, i.e., when the new technology decreases the idle power of the network, there is no limit value of K beyond which the derivative of the energy-perbit is always positive, this means that it is always possible to upgrade the network while preserving its energy efficiencywhen the new technology decreases the network’s idle power. 

Q12. What is the main reason for densification of mobile networks?

it is more spectral and energy efficient to densify the network with indoor small cells mainly, while maintaining some outdoor coverage for high-speed outdoor users. 

Q13. What is the purpose of this paper?

it is worth to note that the numerical applications contained in this paper are limited to a mobile network whose capacity is a linear function in the number of radio sites, or which can be approximated as such. 

Q14. How much energy is used to power the network?

using the network even only at half of its capacity allows significant energy savings, unlike the actual operation of networks which are most of the time under-loaded, about 10% on average for the investigated network. 

Q15. What is the energy efficiency of the upgraded network?

Fig. 4 shows the energy efficiency (inverse of the energyper-bit) of the upgraded network (LTE-A network), as a function of x, the power consumption ratio of an LTE-A site versus an LTE site. 

Q16. What is the energy efficiency of the upgraded network?

Fig. 4 shows the energy efficiency (inverse of the energyper-bit) of the upgraded network (LTE-A network), as a function of x, the power consumption ratio of an LTE-A site versus an LTE site. 

Q17. What is the energy efficiency of the network when an LTE site consumes more power than an?

The authors note clearly that the LTE-A technology degrades the energy performance of the network when an LTE-A site consumes more power than an LTE site, since the LTEA network’s energy efficiency is lower than the LTE network’s energy efficiency for x > 1.2) Replacing LTE sites by a different number of LTEA sites: 

Q18. what is the energy efficiency of the upgraded network?

By resolving the inequality α(Rf ,Kf ) ≤ α(Ri,Ki), i.e., the energy-per-bit of the upgraded network should be lower than or equal to the energy-per-bit of the initial network, the authors get:(1− x)(1− y)KfC bsP bs0zRi θ2 + ((( xKf z −Ki) 1− y Ri+ (1− x)yKfzRi )CbsP bs0 + (y − x)(P bs max − P bs 0 ))θ+ (( xKf z −Ki) yCbsP bs0 Ri + (x− y)(P bsmax − P bs 0 )) ≤ 0(16)where θ is the proportion of LTE sites in the upgraded network. 

Q19. What is the way to upgrade a network?

The authors considered two techniques for network upgrade: either by adding sites with the same technology or by adding sites implementing another technology, typically more recent and more efficient. 

Q20. What is the reason why the network is not upgraded?

This result is also logical since replacing an LTE site by a more energy-consuming LTE-A site at constant traffic can only degrade the network’s energy efficiency.