Bit per Joule Efficiency of Cooperating
Base Stations in Cellular Networks
Albrecht J. Fehske, Patrick Marsch, and Gerhard P. Fettweis
Vodafone Stiftungslehrstuhl, Technische Universität Dresden
Email: {albrecht.fehske, marsch, fettweis}@ifn.et.tu-dresden.de
Abstract—Energy consumption is lately receiving increased
interest, and research efforts to assess the energy efficiency
of cellular communication networks are made. This paper
addresses the tradeoffs between gains in cell throughput that
can be expected from coordinated multi point transmission and
reception technologies and the increased energy consumption
that they induce in cellular base stations. We explicitly consider
effective transmission rates, taking into account the additional
pilot, control and feedback overhead required for CoMP schemes,
and determine the bit per Joule efficiency of network models
for common propagation parameters under varying network
densities and cooperation cluster sizes.
I. I NTRODUCTION
The ever increasing demand and ubiquitous availability of
wireless communications services comes at the price of a
considerable carbon footprint of the mobile communications
industry. While the footprint of the overall communications
sector is expected to less than double between 2010 and
2020, the corresponding figures of the mobile sector are
expected to almost triple during the same period, ramping
up to about 235 Mto CO2 e an amount that corresponds
to more than one third of the overall emissions (including
industrial production, transport, households, etc.) of the UK.
For operators, the electricity need of their networks becomes
increasingly important. Currently, over 80% of the electrical
power in mobile telecommunications accounts to the radio
access network (RAN), i.e., the radio base station sites. In
mature western markets, already today the energy cost due to
network operation amount to about one percent of earnings
before interest and tax (EBIT), and a further increase by a
factor between two and three can be expected until 2020 [1].
In developing countries, the ratio of energy cost and EBIT is
much worse not only due to lower revenue per user but also
due to the use of diesel powered sites, where inefficiency of
the generators and high diesel transporting cost often prohibit
provision of wireless services. Here, energy efficient base
station equipment will be a key enabler for use of alternative
energy sources that allow for much lower operational cost and
feasible business models.
The growing importance of ubiquitous connectivity for
social and economical interaction renders a further growth
of the mobile communications sector inevitable. Ecologically
sustainable and economically feasible wireless services, however, can only be provided with increasingly energy efficient
radio access technologies.
Improvements can in principle be achieved in two ways.
Firstly, by optimization of individual sites, e.g., through the use
of more efficient and load adaptive hardware components as
well as software modules. Secondly, by improved deployment
strategies, effectively lowering the number of sites required
in the network to fulfill certain performance metrics such as
coverage and spectral efficiency. In principle, gains achieved
in one area are complimentary to gains achieved in the other.
When it comes to increasing data rates in cellular systems,
there are in principle two research paths that are being pursuit.
On the one hand, higher rates can be offered through network
densification, i.e., an increased number of radio access points
per unit area. On the other hand high efforts have recently been
dedicated to coordinated multi point (CoMP) technologies
which allow base stations to jointly process, send, and receive
user data.
While both concepts are able to achieve both an increased
sum rate as well as a more uniform distribution of user rates
in the cell, they incur different costs in terms of consumed
energy. Naturally, densification increases the network’s energy
need due to increased number of radio access points and tradeoffs between gains in cell throughput and increased energy
consumption have been investigated, e.g., in [2], [3]. CoMP
schemes in up and downlink require additional backhaul connections between cooperating sites as well as additional signal
processing at the base stations. Required energy consumption
due to application of these technologies is so far not addressed.
In this paper we investigate the tradeoffs between gains in the
average cell throughput obtained from CoMP schemes and
increased power dissipation of base stations.
Similar investigations with respect to base station densification and CoMP are conducted in [4], where spectral
efficiencies of increasingly dense networks cooperative networks are compared. However, the [4] only considers downlink
communication and no direct relation to energy consumption
has been drawn. In addition to a comprehensive study of uplink
and downlink rates we also consider the effective data rates
by explicitly modeling the pilot and control channel overhead
required for CoMP schemes as in [5]. We also provide a
simple extension to energy consumption models for cellular
base stations to cover energy consumption of backhauling
links.
The remainder of the paper is organized as follows. In
Section II we introduce the system model including the
transmission equations and effective rates calculations. In
where Ptx , Prx , r, and λ denote transmit and receive power,
propagation distance, and path loss exponent, respectively.
The parameter r0 specifies a reference distance where signal
strength is known. We assume the parameter K to be composed of three factors, i.e.,
K = K(r, φ) = U · V · W (r, φ).
(a) Cooperation size three
(b) Cooperation size seven
Fig. 1: Cellular network layout of co-localized base stations
for two cooperation sizes.
Section III we describe the energy consumption model for
base stations. Section IV provides the main results obtained
from system level simulations and Section V concludes the
paper.
(2)
Factor U incorporates the impact of user terminal and base
station antenna heights, carrier frequency, and propagation
environment. Propagation loss due to outdoor-to-indoor propagation is captured in the factor V . The antenna pattern
depending on the relative location of transmitter and receiver
is modeled by the term W (r, φ). For simulative investigations,
we employ the propagation parameter values specified in [8]
presented in the Appendix.
In order to capture the fast fading component of the channel
we sample a channel coefficient from a Rayleigh distribution
for each transmit and receive antenna pair in the setup.
B. Transmission Equations
II. S YSTEM M ODEL
In this paper, we model a network as a setup of Nbs cellular
base stations, co-located in groups of three at a regular grid
of N3bs sites characterized by the inter site distance D. We
assume the BSs to be equipped with two transmit and receive
antennas each. We further assume the user terminals to be
equipped with a single transmit and receive antenna. We use
the terms cell or sector to refer to the hexagonal shaped region
served by a single BS. For given inter site distance D, the cell
2
size A calculates as A = 2D√3 .
Depending on the scenario under study up to Nc BSs
are allowed to jointly transmit and receive user data. We
assume all base stations to be connected by a full mesh
of backhaul links allowing them to exchange information as
further detailed in Section III.
CoMP techniques are able to significantly increase sum and
cell edge throughputs in a cellular system [6], [7], however,
they introduce a certain amount of overhead into the the
system, which can be categorized as
• Additional pilots
• Additional backhauling
• Additional signal processing
Modeling gains and energy needs involved in CoMP schemes
is the concern of the following sections.
A. Propagation Model
Deterioration of signal quality is commonly assumed to
be due to three different causes: path loss, slow fading, also
referred to as shadowing, and fast fading. In this work we
mainly concentrate on the effects of path loss and fast fading
and include the effects of slow fading as a margin in the link
budget. We employ a signal propagation model as follows
−λ
r
Prx = K ·
· Ptx
(1)
r0
We consider an OFDM system and observe a single subcarrier for uplink and downlink transmission. All observed effects
are than translated to a full system through simple scaling.
1) Uplink: Assuming that each BS has assigned exactly
one UE to the observed subcarrier and each UE’s signal is
received at a cluster of Nc cooperating BSs, we can state the
uplink transmission equation for each OFDM symbol as
1
1
y = V H H H Px/2 x + GH Pu/2 u + n ,
(3)
where x ∈ CNc ×1 , y ∈ CNc ×1 , V ∈ C2Nc ×Nc , H ∈ CNc ×2Nc ,
u ∈ C(Nbs −Nc )×1 , and n ∈ C2Nc ×1 model transmitted and
received symbol vectors of UEs inside the cooperation cluster,
the receive filter matrix, the channel matrix, the symbol vector
of UEs outside the cluster, and an additive noise term with
E[nnH ] = σn2 , respectively. The matrices H ∈ CNc ×2Nc and
G ∈ C(Nbs −Nc )×2Nc contain the channel coefficients between
the receiving BS antennas and the terminals that are processed
by the cluster BS and those that are not, respectively. We
assume E[xxH ] = I and E[uuH ] = I, i.e., the powers of
the signals from cluster and non-cluster users are assumed to
be contained in the diagonal matrices Px and Pu , respectively.
We assume V to be an MMSE filter matrix. The average
achievable rate in bits per channel use per cell can then be
bounded as
rul ≤ 1/Nc log2 I + (Φi + Φn )−1 · H H Px H ,
(4)
where the term Φi = V H GH Pu GV denotes the covariance
matrix of the signals coming from interfering UEs outside the
cluster while Φn = σn2 V H V denotes the covariance matrix of
the filtered noise.
2) Downlink: The transmission equation for Nc BSs transmitting jointly to Nc users can be stated as
y = HW x + LT u + n,
(5)
where W ∈ C2Nc ×Nc and T ∈ C2(Nbs −Nc )×Nc denote the
transmit filters of the BSs inside and outside the cluster, respectively. The matrix L ∈ CNc ×2(Nbs −Nc ) contains the channel coefficients from all BSs outside the considered cluster
to the cluster UEs. In analogy to the uplink receive filter we
assume an MMSE transmit filter W to be applied jointly to
all cooperating antennas, i.e.
W =
−1
p
tr(Φi + Φn )
β · HH H +
I
.
Nc · Pdl
(6)
The term Pdl denotes the maximum transmit power per BS and
the factor β = Nc Pdl/tr(W W H ) ensures that this limit is kept after application of the filter. The matrices Φi = Pdl · LT T H LH
and Φn = σn2 I refer to the interference coming from BS
outside the cluster and the additive noise, respectively. For
simplicity, the transmit filter T at all other BS is assumed to
be 1/2 in all elements, i.e., to map half the symbol energy to
each of the two transmit antennas of each BS. The average
downlink rate in bits per channel use per cell for a cluster of
Nc cooperating base stations can now be stated as
Nc
1 X
rdl ≤
log2
Nc i=1
where
σi2 =
1 + PNc
H 2
w hi i
H
2
j6=i |wj hi |
Nc · Pdl
·
2
2(Nbs −Nc )
X
+ σi2 + σn2
|lj 1|2
!
(7)
r̃dl = rdl · 1 − ρ · 3Nc − δ
C. Effective Transmission Rates
While equations (4) and (7) state the achievable rates per
channel use, a certain amount of rate has to be invested into
signalling overhead due to pilots and CSI feedback.
1) Uplink: Uplink pilot overhead scales linearly with the
number of cooperating BSs, as orthogonal pilots are needed
for all UEs in the cluster to enable joint detection. If downlink
CoMP is performed, CSI must be fed back in the uplink.
Since CSI needs to be generated per transmit antenna, the CSI
feedback rate scales linearly with the total number of downlink
transmit antennas within a cluster. Thus, for Nc cooperating
BSs the achievable rate per channel use reduces on average to
(9)
Here, the term ρ models the average pilot density in time and
frequency, which is governed by the average coherence time
and frequency expected by the system. The term q denotes
the amount of feedback bits employed to feed back CSI of
acceptable quality. It becomes clear from equation (9) that
there is an upper limit on the cluster size Nc , since at some
point the effective uplink rate will be zero.
(10)
D. Backhauling
As stated above, application of CoMP schemes requires
information exchange between all sites involved, where the
rate of exchange depends on the cluster size. In this work we
are not directly concerned with backhaul data rates, but rather
look at the amount of additional energy that is required to
provide a certain backhaul rate.
1) Uplink: In order to jointly detect Nc user signals received at Nc BSs, we need to forward the sampled received
signals to one master site, where processing is performed. The
average required backhaul in bits per channel use and cell can
be calculated as
gul =
denotes the received power from interfering BS outside the
cluster.
where δ models the average control overhead.
(8)
j=1
r̃ul = rul · (1 − ρ · Nc ) − 2Nc · ρ · q.
2) Downlink: Similar to the uplink case, the achievable
downlink rate per channel use is degraded due to pilots, where
we need both orthogonal pilots such that the terminals can
estimate and feed back the channel matrix as well as precoded
pilots for equalization and decoding. Given 2 transmit and
one receive antenna at BS and UE, respectively, we need 3Nc
orthogonal pilot sequences. In addition, some OFDM symbols
are reserved for control information of various kinds and the
effective downlink rate is given by
(Nc − ξc ) · 2 · z
Nc
(11)
where z denotes the number of quantization bits applied to
each complex symbol. We have to consider that cooperating
BSs which are co-located do not require backhaul infrastructure. This is taken care of by the term ξc , which denotes the
maximum number of cells within the cooperation cluster being
located at the same site. Only the remaining cooperating cells
need then forward quantized signals to this site. Note that we
assume that not only data, but also pilot symbols are quantized
and forwarded, such that an additional exchange of channel
knowledge among BSs is not required. The detected data are
then forwarded into the system by the master site. Since this
distribution effects primarily the backbone, i.e, connection of
the BSs to the core network, rather than the BS themselves,
it is not considered here.
2) Downlink: In the downlink, the CSI feedback decoded
centrally in the uplink has to be distributed among the cooperating BSs. The overall backhaul effort in bits per channel
use and cell can be stated as
gdl = (Nc − ξc ) · 2Nc · ρ · q
(12)
In addition, each of the sites involved in a cooperation must be
provided with the data bits of all jointly served UEs. However,
for similar reasons as the uplink case, the communication with
the core network is not considered here.
with a base line processing power per sector of Psp = 58W.
III. E NERGY C ONSUMPTION OF C ELLULAR BASE
S TATIONS
A simple model of the long term base station energy
consumption is given in [9]. In this work the impact of energy
needed for signal processing and transmit power on the total
energy dissipation is assumed to be linear. In order to also
capture backhauling energy needs we propose to extend this
model to the general form
PBS = a · Ptx + b · Psp + c · Pbh ,
(13)
where PBS , Ptx , Psp and Pbh denote the average consumed
energy per base station, the radiated power per base station,
the signal processing power per base station, and the power
due to backhauling, respectively. The coefficients a, b, and
c model effects that scale with the corresponding power type
such as amplifier and feeder losses, cooling, or battery backup
[9]. In the following, we briefly review the three power types.
Generally, the investigation presented in this study assume full
load conditions, i.e., the dependency of energy consumption on
load conditions through such as sleep modes is not considered.
A. Transmission
Transmit power effects the overall base station power consumption through the efficiency of the power amplifier, the
cooling equipment as well as battery backup required for
operation. The average transmit power per base station scales
with the inter site distance D according to the path loss model
as
10 log(Ptx ) = 10 log Pmin + 10 log K + 10 · λ log D/2. (14)
where Pmin is the required minimum receive power at the
mobile and the term 10 log K +10 log D
2 is the path loss at the
cell edge in dB for a given inter site distance D. For power
computation we require coverage of 95 % and assume the
base stations are centered at their cell areas. We apply average
values of K with respect to shadowing and LOS probabilities
as given in Tab.1 in the appendix.
B. Signal Processing
Base band digital signal processing is performed in all
cellular base stations. The complexity of the operations and the
energy consumption depends amongst others on the employed
air interface as well as the amount of cooperation between
base stations. In the LTE-Advanced testbed implementation
[10] about 10% of the overall analog and digital processing
power are due to uplink channel estimation and roughly
3% are due to uplink and downlink MIMO processing. The
former scales linearly with Nc due to the increasing number
of estimated links. Assuming an MMSE filter operation, the
latter requires Nc3 operations, however, the computation is
performed only once per cooperation cluster such that average
MIMO processing per base station only scales quadratically
with Nc . With a base value of psp the signal processing power
per sector as a function of different cooperation sizes scales
as
Psp = psp · 0.87 + 0.1Nc + 0.03Nc2 ,
(15)
C. Backhauling
Reflecting the state-of-the-art in most cellular networks, we
model backhaul as a collection of wireless micro wave links
of 100 Mbit per second capacity and a power dissipation of
50 W each. Thus for a given average backhaul requirement
per base station cbh , the additional backhaul power computes
as
cbh
Pbh =
· 50W.
(16)
100Mbit/s
IV. S YSTEM E VALUATION
In this section we evaluate cellular network model of
varying density employing different cooperation sizes. We
discuss results obtained by Monte Carlo simulations.
a) Simulation Setup: The simulations are performed as
follows. For each Monte Carlo sample a single user is randomly placed into each of the 57 observed cells and the
channel matrix stated in (3) and (5) is obtained via a standard
path loss model and independent rayleigh fading samples with
key parameters summarized in Tab.1, Tab.2, and Tab.3 in the
Appendix.
We assume power control in the uplink, where a target
receive power density at the BS side is chosen for each value
of inter site distance D, so that at most 5% of all UEs are
operating above their power limit of 20 dBm. In the downlink,
the total transmit power per BS is a function of D as stated
in (14), which is then invested equally into alls sub-carriers.
We generally apply cooperation in a flexible way, where the
cooperation size is chosen for each fading realization such that
the sum rate of uplink and downlink is maximized. Since we
assume full buffer users, all BS are under full load.
b) Net Site Throughputs: Fig.2 displays the total net
throughput, i.e., after subtraction of pilot, control and feedback
overhead as given in (9) and (10), obtained as the sum of
uplink and downlink throughput. The overall throughput is
decreasing for larger site distances due to the uplink where UE
powers are limited. About 25 % gain from a cooperation size
of 7 can be observed for site distances below 500 m and above
1000 m. Note that a significant performance improvement is
visible if the cooperation size is increased from 2 to 3, as for
Nc = 2 there is typically still one dominant interferer outside
the cluster [6], [7].
c) Site Powers: Fig.3 and Fig.4 display the corresponding total power dissipation per site and power fractions due
to transmission, processing, and backhauling according to the
power model given in Section III. We observe from Fig.4 two
regimes of energy consumption: For small site distances, it
is governed by signal processing and backhauling, whereas
for large inter site distances the transmission power becomes
equally significant due to the over linear increase of the path
loss in (14). If large cooperation clusters are used the impact
of CoMP energy need in addition to other processing per
site amounts to over 30 % and slightly below 20 % of total
power account for CoMP processing and backhauling for site
distances below 500m and above 1000 m, respectively (Fig.3).
3
10
N =1
Other processing
c
120
N =2
CoMP processing N =2...7
c
110
c
N =3
c
100
Nc = 4
90
Nc = 5
80
N =6
70
c
N =7
c
≈ 25 % gain
60
Mean power in W
Mean throughput per site in Mbit/s
130
2
10
Backhaul Nc=4...7
1
10
50
Transmission
40
0
30
0
500
1000
1500
Inter site distance in m
10
2000
Fig. 2: Throughput per site for different inter site distances
0
500
1000
1500
Inter site distance in m
2000
Fig. 4: Fractions of power dissipation per site due transmission, processing, and backhauling for different cooperation
sizes
1800
N =1
c
200
N =2
c
180
N =3
1400
Mean energy efficiency in kbit/J
Mean site power in W
1600
c
Nc = 4
1200
Nc = 5
1000
N =7
≈ 19 % increase
N =6
c
c
800
600
400
0
≈ 34 %
increase
500
1000
1500
Inter site distance in m
≈ 10 % gain and loss
(relative to Nc=1)
N =1
c
N =2
c
160
N =3
140
Nc = 4
c
Nc = 5
120
N =6
c
100
N =7
c
80
≈ 20 % gain
(relative to Nc=1)
60
40
2000
Fig. 3: Total power dissipation per site as function of inter site
distances
In this regard, note that the base line processing power of
psp = 58W per sector assumed here can be considered low for
a system with 10 MHz of bandwidth. [9].
d) Bit per Joule Efficiencies: Fig.5 depicts the overall
bit per Joule efficiency of the system. With increasing site
distances the bit per Joule efficiency decreases due to increasing transmit powers and decreasing sum throughputs. For site
distances below 500 m the bit per Joule efficiency increased
for cooperation sizes up to four BS and decreased with higher
cooperation sizes compared to no cooperation. For large site
distances over 1000 m the bit per Joule efficiency is always
increased through cooperation. For cooperation sizes larger
than three, the additional spectral efficiency gains are rather
small (compare Fig.2, however, the additional energy needs
are larger due to additional backhaul power (Fig.3. For this
reason, highest gains in bit per Joule efficiency are observed
for a setup where only co-located base stations cooperate and
no backhauling is required.
20
0
500
1000
1500
Inter site distance in m
2000
Fig. 5: Bit per Joule efficiency of CoMP schemes for different
inter site distances
V. S UMMARY
AND
D ISCUSSION
In this work, models were introduced to observe both
achievable rates and base station power dissipation in cellular
systems, under varying inter-site-distances and CoMP cooperation sizes. Results show that both degrees of freedom, densification and CoMP, lead to substantial capacity improvements.
but while network densification can improve energy efficiency,
it seems that CoMP may in fact lead to a decreased energy
The bit per Joule efficiency of the system is only moderately
affected by the use of CoMP schemes, with potential gains of
10 % and 20 % for small and large site distances, respectively.
From a bit per Joule perspective and for the power model
used in this research, cooperation between non co-located base
stations does not appear beneficial due to the diminishing
additional spectral efficiency gains for cluster sizes above three
on the one hand and the additionally required backhauling
power for those clusters on the other. Highest energy efficiency
gains were observed when all cooperating BS are co-located
throughout all site distances.
For the power model used in this research, where base
station transmit powers are adjusted to the network density, the
contributions of processing and backhauling power dominate
power related to transmission for small site distances. This fact
should be kept in mind, considering recent research activities
focusing strongly on optimization of power amplifiers for relatively high transmit powers of 20 W and above, in particular
in the light of decreasing site distances for future generations
of mobile technology.
A PPENDIX
The effective values for the parameters in equation (1)
obtained from the propagation models presented in [8] are
summarized in Tab.1. The values are computed for antenna
heights of 25 m and r0 = 1 m. Outdoor-indoor penetration
loss is assumed to be 20 dB [8].
Tab. 1: Effective propagation parameters based on [8]
Urban macro cell
LOS (r <384 m)
LOS (r ≥384 m)
NLOS
LOS probability
λ
−10 log10 (U)
σ10log10 Ψ
2.20
35.60
4
4.00
−10.90
4
3.91
17.40 6
r
r
PLOS = min 18
, 1 1 − e− 63 + e− 63
r
Tab. 2: LTE-based system model parameters
Link related parameters
Carrier frequency
Bandwidth
FFT size
# Subcarriers occupied
Pilot density per channel use ρ
Control overhead per channel use
Quantization bits per complex pilot q
Quantization bits per complex symbol z
Subcarrier spacing Bsc
Mobile terminal sensitivity
Thermal noise
Inter-cell interference margin
SNR required
Noise per subcarrier
Receiver sensitivity per subcarrier
2.4 GHz
10 MHz
1024
600
8/168
3/14
8
16
15 kHz
-174 dBm/Hz
3 dB
0 dB
-132 dBm
-120 dBm
Tab. 3: LTE-based link budget (2)
Parameter
# Antennas
Antenna gain (main lobe)
Max tx power
Noise figure
BS
2
15 dBi
46 dBm
4 dB
UE
1
-1 dBi
20 dBm
7 dB
ACKNOWLEDGEMENT
This work was supported in part by European Community’s
Seventh Framework Programme (FP7/2007- 2013) under grant
agreement n◦ 247733.
Tab. 4: Power model parameters (see also [9])
Parameter
a
b
c
psp
Value
7.35
2.9
1
58 W
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