1
Dynamic Cell Expansion with Self-Organizing
Cooperation
Weisi Guo, Timothy O’Farrell
Department of Electronic and Electrical Engineering
University of Sheffield, United Kingdom
Email: {w.guo, t.ofarrell}@sheffield.ac.uk
Abstract—This paper addresses the challenge of how to reduce
the energy consumption of a multi-cell network under a dynamic
traffic load. The body of investigation first shows that the energy
reduction upper-bound for transmission improving techniques is
hardware-limited, and the bound for infrastructure reduction is
capacity-limited.
The paper proposes a novel cell expansion technique, where
the coverage area of cells can expand and contract based on the
traffic load. This is accomplished by switching off low load cellsites and compensating for the coverage loss by expanding the
neighboring cells through antenna beam tilting. The multi-cell
coordination is resolved by using either a centralized controller
or a distributed self-organizing-network (SON) algorithm. The
analysis demonstrates that the proposed distributed algorithm is
able to exploit flexibility and performance uncertainty through
reinforced learning and improves on the centralized solution. The
combined energy saving benefit of the proposed techniques is up
to 50% compared to a reference deployment and 44% compared
with alternative state-of-the-art dynamic base-station techniques.
I. I NTRODUCTION
A. Background and Review
In the past decade, the growth in mobile data traffic has
also seen a corresponding increase in the energy consumed
by cellular networks. Traditionally, operators have met any
increase in data traffic by deploying more cells or purchasing increased bandwidth. However, such solutions result in
increased energy consumption and operating costs. In order
to limit the ecological impact of the wireless communication
industry and be financially competitive, there needs to be a
change in strategy. Energy efficiency of wireless networks has
attracted significant research attention. The characterization of
energy- and spectral-efficiency relationships in noise-limited
channels was theoretically analyzed in [1].
In terms of transmission techniques: the transmission energy
efficiency of single cell MIMO and multi-cell CoMP [2] has
been investigated. However, a shared caveat in higher-order
MIMO is that the overhead energy consumption scales faster
than the capacity improvement [3]. This generally leads to an
increase in transmission energy efficiency, but a reduction in
overall energy efficiency. Whilst schedulers showed promising
transmission energy savings, the overall energy saving when
overhead is accounted for, is very low (∼ 5%).
In terms of architecture research, fixed wireless relays [4]
demonstrate increased energy- and cost-efficiency [5] compared to increasing cell density. For dynamic architectures
that varies with the offered traffic rate, passive sleep mode
and off-loading to access-points has been considered [6].
Techniques that reduce the number of active cell sectors and
antennas were considered in [6], [7], [8]. In order to maintain
coverage and reduce the number of active cells, changing the
coverage pattern of cells based on traffic load was proposed
in [9], [10]. To the best of our knowledge, how cells in this
dynamic configuration can compensate for potential coverage
holes, whilst minimizing energy consumption, haven’t been
investigated.
B. Proposed Solution
The rationale for sleep mode is that reducing the transmit
power of a cell can only save a certain amount of transmission
energy, whereas putting an entire cell-site in sleep mode can
save most of its total energy expenditure. An illustration of
a classical cell-site layout is shown in Fig. 1a, and the cell
expansion scheme is shown in Fig. 1b and c. The technique
dynamically reduces the amount of active wireless infrastructure as a function of the traffic load, and can dramatically
reduce the energy consumption of the network. The challenge
of multi-cell coordination (centralized and distributed) has
been considered in [9], [10], but to the best of our knowledge,
existing research has not tackled the fundamental challenges
of:
• How to resolve contention between cells that can both
enter sleep mode?
• When a cell enters sleep mode, its original coverage
area suffers both strong interference and an increased
pathloss degradation to compensating cells. How can this
be resolved?
Furthermore, existing solutions have lacked an integrated
approach to research. In order to achieve a realistic implementation of sleep-mode and cell-expansion on sectorized basestations, a combination of techniques need to be considered.
The novel contribution of our research is that it resolves
the aforementioned challenges by employing an integrated
combination of the following: dynamic antenna-beam tilting,
frequency reuse, distributed inter-cell coordination and cooperative transmission. The benefit of this approach is that it is
able to expand the cell coverage with greater spectral efficiency
and achieve this with a low-complexity distributed algorithm.
Furthermore, the paper compares this solution with centralized
coordination and alternative low energy research techniques.
2
Active BS
Active BS
θref
Sleeping BS
Compensating BS
θinner
θouter
θouter
θinner
Outer Cell (800 MHz)
Compensation Zone
Normal or Inner Cell (2.6 GHz)
(a)Reference Deployment: 3-Sector Cell-Sites with
2x2 SFBC MIMO
Fig. 1.
Illustration of Deployments: a) Reference Deployment, b) Proposed Deployment, and c) Proposed Deployment in Cell Expansion Mode.
II. S YSTEM M ODEL
A. Cell-Site Model
The paper considers an OFDMA based Long-TermEvolution (LTE) multiple-access system. The paper defines
a cell-site or base-station (BS) as an entity with many cell
sectors, where each sector is effectively an independent cell
from the user’s perspective. A single homogeneous layer of
NBS BSs are deployed, each with Nv vertical sets of Nh
horizontal sectors, and each sector has Na antennas. This
yields a total of Ns = Nv Nh Na antennas per BS, and a total of
NBS Ns antennas in the multi-BS radio-access-network (RAN).
In this paper, we consider the following types of network
architectures with the same number of antennas:
•
•
(c) Central Cell-Site Switched Off,
Neighbouring Cells Expand
(b) Proposed Deployment: 6-Sector Cell-Sites with
1x2 MIMO
Reference: 3-Sector BS with 2x2 Space-FrequencyBlock-Coding (SFBC) MIMO, as recommended by 3GPP
standards [11] and used to benchmark performance [12].
There are Ns = 6 antennas per BS and an illustration of
the deployment is shown in Fig. 1a.
Proposed: 6-Sector BS with 1x2 SIMO with MaximumRatio-Combining (MRC), which has the same peak power
consumption as the reference deployment. There are
Ns = 6 antennas per BS and an illustration of the
deployment is shown in Fig. 1b. The benefit of this
deployment is that it has the flexibility of expanding and
contracting the cell coverage by adaptively tilting the
antenna beam of the outer and inner sectors, as shown
in Fig. 1c.
B. Downlink Throughput Model
For a certain user i that is of a distance di,k from the
serving-cell k, the downlink received SINR (γi,k ) is calculated
as a function of the BS transmit power (P ), BS antenna gain
(A), and AWGN power (n), and fading gain (H):
γi,k =
−αi
Hi Kdi,k
Ai P
,
PNBS Ns
−α
n + j=1,j6=k Hj Kdi,j j Aj P
(1)
where the user experiences interference from up to NBS Ns
other co-frequency cells. The parameters and their values are
defined in Table. I. The generic sectorized BS antenna pattern
employed in the cells is given as [11]:
(Ab −min[12(
Ai (ϑi,k ) = 10
|ϑi,k −θk | 2
) ,Am ])/10
θ3dB
,
(2)
where ϑi,k is the angle between the user i and the horizontal
plane of the BS k, and θk is the antenna down-tilt angle of BS
k. The other antenna parameters are: θ3dB = 75◦ for azimuth
and θ3dB = 20◦ for elevation, Am = 25dBi, and the antenna
bore-sight gain is Ab = 17.6dBi.
The paper defines each BS as being able to employ a certain
operational strategy (sk,t ∈ S). This strategy can refer to sleep
mode, antenna tilt, or any host of transmission techniques. The
precise details in the context of this paper is defined later in
Section VI.
C. Traffic and Load
The traffic demanded by each user is assumed to be full
buffer and a round-robin scheduler is employed. The downlink throughput is obtained by using the SINR (1) and the
appropriate LTE adaptive modulation and coding scheme. The
aggregate throughput achieved in a cell k is the sum of the
throughput achieved by all its users at time t:
RBS,k,t,s =
NUE
X
i=1
RUE,i,k,t,s ,
(3)
3
TABLE I
S YSTEM PARAMETERS
Parameter
Operating Frequency
BS Coverage Radius
Interference Model
Pathloss Exponent
Pathloss Constant
AWGN power
Multipath Fading
Shadow Fading Var.
UE antenna Height
BS antenna Height
BS antenna pattern
BS transmission
Propagation Model
Scheduler
BS Transmit Power
BS Radio-head Eff.
BS Overhead Power
Backhaul Power
Symbol
rcell
α
K
n
H
σs2
A
λ
P
µ
POH
PBH
the load, the more efficient the power amplifier. Existing
literature has largely assumed that radio-head efficiency is
constant with the load, which means the radio-head power
consumption scales linearly with load. However, research in
[13] has shown that µ can vary between 50% to 10% for a
micro-BS. By fitting an expression to the data in [13], the
p value
of µ is approximately given by µ(Lk,t,s ) ≈ µpeak Lk,t,s ,
where µpeak is the efficiency achieved at maximum load
(Lk,t,s = 1).
Value
2600 MHz
500 m
19 BS Wrap Around
3.67
4.6 × 10−4
6 × 10−17 W
Rayleigh
9 dB
1.5 m
20m
(2)
2x2, 1x2 MIMO
3GPP WINNER [11]
Round Robin
20W
10-50% [13]
60W
50W
where the value of each user’s throughput (RUE,i,k,t,s ) is a
function of the achieved SINR (γ) and the scheduler function
(round robin in this case). This is obtained from the previously mentioned simulation. The paper defines the traffic rate
(Rtraffic,k,t , bits/s) offered to each cell as the aggregate traffic
intensity demanded by users (circuit- and packet-switched
packets). This varies with the cell concerned k, and the
time t, which is taken in 15 minute samples for simulation
results presented later in the paper. Therefore, at any particular
instance, a traffic rate is offered to the BS, and the load (L)
experienced by the BS with strategy s can be defined as:
Lk,t,s =
Rtraffic,k,t
+ max[(Lk,t−1,s ) − 1, 0],
RBS,k,t,s
(4)
where in order to not incur outage, Lk,t,s ≤ 1. If an outage
occurs, the remaining unsatisfied load (max[(Lk,t−1 )−1, 0]) is
added to the load of the next transmission time interval (TTI).
D. Power Consumption Model
A general power consumption model for a BS with Ns
antennas is comprised of a load-dependent and a loadindependent function [3]:
P
Lk,t,s + POH ) + PBH
µ
P p
≈ Ns (
Lk,t,s + POH ) + PBH .
µpeak
PBS,k,t,s = Ns (
(5)
In the load dependent part, P is the transmit power and µ is
the radio-head efficiency. In the load-independent part, POH is
the over-head power (base-band and cooling) and PBH is the
backhaul power. Data on the power consumption values can be
found in Table. I. As the load Lk,t,s in the BS varies, the radiohead efficiency µ also varies. Generally speaking, the greater
III. E NERGY S AVING B OUNDS
In this section, the paper considers the energy saving
bounds, which serves as motivation for sleep mode control.
The paper considers upper-bounds achieved if the capacity of
the RAN’s BSs have been improved (or equivalently if the
offered traffic rate has been decreased). There are 2 separate
paths to energy reduction:
• Reduce transmission power and save transmit energy.
• Switch-off BSs and compensate for coverage loss through
cell-expansion.
The energy saved by the test system, in comparison with the
reference is defined as the energy-reduction-gain (ERG):
PT PNBS
k=1 PBS,test,k,t,s (Ltest,k,t,s )
.
(6)
ERG =1 − Pt=1
PNBS
T
t=1
k=1 PBS,ref.,k,t,s (Lref.,k,t,s )
Assuming the throughput in the test system has been improved by a factor of ρs (due to strategy s), compared to the
reference system. The resulting energy saved compared to the
reference system is given in Lemma 1 of the Appendix as:
ERGhardware →
1
,
1+Ω
Ω = µpeak
POH +
P
PBH
Ns
(7)
for: ρs → inf .
It can be seen that the parameter Ω is strictly positive and is
a ratio of hardware power consumption parameters. Typically
the value of Ω = 1.7, with figures taken from Table. I. The
resulting ERG’s upper-bound is 30-40% and the saving can
be described as being hardware-limited.
The paper now considers an ideal case, whereby the amount
of active infrastructure can flexibly vary with the traffic load.
This concept can be achieved through sleep-mode operation
and the performance is improved with the proposed cellexpansion technique. The resulting ERG given in Lemma 1
of the Appendix is:
ERGcapacity → 1,
for: ρs → inf .
(8)
It can be seen that the ERG is entirely a function of the
parameter ρs , and can theoretically achieve 100%. In reality,
the energy-consumption of BSs in off- or sleep-mode is nonzero, and 100% energy reduction can not be achieved. As the
parameter ρs is an improvement in BS capacity, the energy
saving can be described as being capacity-limited.
IV. C ELL E XPANSION : C ELL L AYOUT
A. Cell-Site Structure and Frequency Bands
The rationale of cell-expansion as a low energy solution
is that it switches off a percentage of the BSs, as well as
4
to Fig. 1, our simulation results found that for a homogeneous
set of BSs, a shallow tilt of θnormal,k = 0 − 1◦ yielded a
small improvement in the cell-edge throughput, whilst the
greatest mean throughput was achieved with a down-tilt of
θnormal,k = 8◦ . By applying adaptive antenna beam-tilting to
the proposed inner-outer BS setup, it was found that the inner
cell should have a tilt of θinner,k = 12◦ and the outer cell a
tilt of θouter,k = 3◦ . When the coverage of cell expands, this
was found to change to θinner,k = 9◦ and θouter,k = 0◦ . This
yielded a significantly improved throughput profile compared
to alternatives.
60
Ref. Cell, 2.6GHz (8◦)
Ref. Cell, 2.6GHz (0◦)
Inner Cell (2.6GHz, 12◦) &
Outer Cell (2.6GHz, 3◦)
Mean Cell Throughput, Mbit/s
50
Inner Cell (2.6GHz, 12◦) &
Outer Cell (0.8GHz, 3◦)
40
Normal Coverage
Region
Compensation
Region
Normal Coverage
Region
30
20
BS in Sleep
Mode
10
0
BS in
Compensation
Mode
BS in
Compensation
Mode
0
500
1000
1500
Distance, m
Fig. 2. BS Configuration and Optimal Antenna Down-Tilt Angles for Cell
Expansion. All antenna down-tilt angles are optimized for maximum cell
throughput.
reducing the interference of the network in that process. This
way, a capacity-limited ERG can be achieved. The BS can
operate in the following modes:
1) Normal: in normal mode, the BS adjusts its antenna
down-tilt as to maximize the throughput of users within
its traditional coverage area.
2) Sleep: in sleep mode, the BS is switched off and its users
are passed to neighboring BSs, which must expand to
compensate for the coverage loss.
3) Expand: in expansion mode, the BS expands by tilting
its outer cell’s antenna towards the contracted cell area.
The inner cell’s down-tilt is also adjusted to maximize
the throughput of users within its traditional coverage
area.
As shown in Fig. 1b, the mechanism requires inner and
outer cells to be implemented. This is achieved by deploying
an additional vertical set of sectors and adopting different
antenna down-tilt angles. The outer sectors transmit with in the
800MHz band and the inner sectors transmit in the 2.6GHz
band. The 800Mhz channel allows the pathloss attenuation
to be reduced by approximately 10dB, which leads to an
improved signal strength under expanded cell coverage. This
is preferred to increasing the transmit power, which increases
energy consumption. The results in Fig. 2 show that by employing an inner and outer sector with 2.6GHz and 800MHz,
the achievable throughput is improved for both the normal cell
coverage region and the compensation region.
B. Dynamic Antenna Beam-Tilting
Existing work [14] has shown that dynamically tilting the
antenna can improve the throughput of the cell. The optimal
down-tilt for the reference deployment was found to be
between 6-8◦ , depending on the antenna pattern employed.
For antenna arrays, the vertical pattern is typically very nonuniform, and therefore optimization is performed via bruteforce search within a reasonable range of (2-20◦ ). Referring
V. C ENTRALIZED C OORDINATION
A. BS Groupings
As mentioned previously, the actions of one BS, directly
affects the performance of all other BSs, i.e., if a BS enters
sleep mode, the interference it causes to other BSs is reduced,
increasing their throughput. By allowing a fixed set of BSs
to take known actions, the network performance changes in a
way that is predictable. In centralized coordination, the aim is
to achieve an approximately deterministic performance, by
restricting which BSs can go into sleep mode to a limited set
of patterns. How this pattern is determined at any particular
instance, is determined by a central Sleep Mode Management
(SMM) controller.
This sub-section explains how the BSs in a RAN are
grouped together to form the previously mentioned patterns.
Each BS is associated to a set of other BSs via a logical
grouping identity. As shown in Fig. 3a and b, each BS has
two identities: Ifull = {A, B, C} and Ipart = {D, E}. The
identities are pre-determined at the network-planning phase.
Two centralized sleep-mode strategies (Sc ) are proposed:
• Full Compensation Strategy (1/3), Sfull : each sleeping
BS’s previous coverage region is compensated by 3
neighboring BSs’s expanded outer sectors (Fig. 3a). Up
to 1/3 of BSs in a network can be in sleep mode (upperbound energy saving of 33% compared to reference).
Therefore, within the Full Strategy Sfull , there are 3
different sub-strategies to choose from, each related to
a group of BSs.
• Partial Compensation Strategy (1/2), Spartial : each
sleeping BS’s previous coverage region is compensated
by 2 neighboring BSs’s outer sectors (Fig. 3b). Up to 1/2
of BSs can be in sleep mode (upper-bound energy saving
of 50% compared to reference). Therefore, within the
Partial Strategy Spartial , there are 2 different sub-strategies
to choose from, each related to a group of BSs.
As previously defined, each strategy refers to a category or
grouping of BSs. Each BS within that category is seen as
independent as the inter-BS distance is large. Therefore, each
BS inside a category can decide on its own, whether it can
enter sleep mode based on the predicted traffic load. That
prediction process is explained in the sections below.
B. Contention Between Groupings
A dilemma arises when multiple strategies can be implemented, and contention occurs between compensating BS
5
Compensation
Zone
Compensation
Zone
Compensation
Zone
D
B
B
1/3
Rexpand
Rexpand
D
E
1/2
2
Rsleep
Rsleep
1/2
C
1/3
1
D
E
Rnormal
B
2
1
E
Rsleep
1
2-BS Partnership
Rexpand
A
C
1
D
C
2
D
D
(a)Centralized Structure: Full Compensation Pattern (1/3)
BS Type A in sleep, Type B in compensation, and
Type C in normal mode
(b) Centralized Structure: Partial Compensation Pattern (1/2)
BS Type E in sleep, and Type D in compensation mode
(c) Distributed Structure: 2-BS Coordination (1/2)
BS Pair-Up: Type 2 in sleep, and Type 1 in
compensation mode
Fig. 3. Cell Expansion Strategies for: a) Centralized Full Compensation Strategy (regular,1/3); b) Centralized Partial Compensation Strategy (regular,1/2);
c) De-centralized Partner Selection Strategy (irregular).
TABLE II
C ENTRALIZED C OORDINATION DATA FOR SMM: BS T HROUGHPUT FOR
VARIOUS OPERATION MODES .
Operational Mode
Normal Mode (Rnormal )
Full Expansion (Rexp,1/3 )
Full Sleep (Rsleep,1/3 )
Partial Expansion (Rexp,1/2 )
Partial Sleep (Rsleep,1/2 )
Theory
33.3 Mbit/s
16.6 Mbit/s
10.0 Mbit/s
22.2 Mbit/s
8.1 Mbit/s
Simulation
30.2 Mbit/s
15.1 Mbit/s
12.3 Mbit/s
20.0 Mbit/s
7.3 Mbit/s
groups that wish to enter sleep mode. In order to account
for this potential conflict, a network-wide co-ordination must
be performed so that the SMM employs: the strategy (Sc ) that
allows the highest energy saving, whilst the offered traffic load
is still met. This is determined by the Minimum Energy Traffic
Constrained (METC) algorithm presented in (9) below and in
Fig. 4a.
The METC criteria is given as follows:
min[
Sc
NBS
X
PBS,k (Lk,t,s )t],
subject to: Lk,t,s ≤ 1,
∀k, (9)
k=1
which means the algorithm selects the strategy Sc that minimizes the instantaneously energy expenditure, subject to the
traffic condition is satisfied for all BSs at any time t. The
expected or predicted performance for each strategy is obtained using Table II. The cell-edge throughput per BS (R)
are averaged over all cells and time samples. The simulation
results are from the Monte Carlo simulator, and the theoretical
results are from a stochastic geometry framework given in
the Appendix, whereby the interference-limited capacity at a
distance r0 for a cell density of Λ is:
Z +∞
(10)
R̄s =
exp − Λπr02 Q(ζ, α) dζ.
0
As explained in Fig. 4a, the centralized coordination process
is as follows:
1) Each BS uploads its current load condition to the SMM;
2) Each BS is grouped with corresponding BSs according
to its logical identity;
3) For each strategy (Sc ), predict the resulting energy and
load performance based on Table II;
4) Find lowest energy strategy using the METC criteria in
(9);
5) Feedback operational mode commands to BSs.
The energy saving results for the centralized coordination in
comparison with other energy saving solutions is presented in
Section VII.
In terms of algorithm complexity and mutual information
exchanged, each BS has to upload its load information to the
SMM every time step t. Typically traffic is measured on 15
minute basis, and this seems a reasonable time step for sleep
mode as well. The complexity is in the order of NBS , with a
multiplication factor of the number of strategies. For an urban
environment RAN, this can be up to 100 BSs with 5 fixed BS
grouping combinations (strategies), and this is clearly a highcomplexity scheme. The remaining coordination challenge is:
can a lower-energy and lower-complexity solution be devised,
based on distributed coordination and machine-learning?
VI. D ISTRIBUTED C OORDINATION
A. Partner Selection
In this section, the paper proposes a distributed cell expansion algorithm that allows the BSs to select partners and coordinate cell expansion between themselves, without knowledge
of the modeling environment. This is illustrated in Fig. 3c.
However, there is an added challenge: without knowledge of
what action other BSs outside the partnership might take,
the expected throughput is undetermined. Depending on how
many neighbor BSs are in sleep mode, the distributed decision
process can cause unexpected performances. Similar to the
centralized coordination, BSs need to be grouped to create
6
Load information given
to BS
Upload Load
information to SMM
Is Load value
lower than sleep mode
threshold?**
*BS identities are predefined and 2 types
exist (full and partial).
Find resulting load and energy
saving for each group of BSs in
sleep mode (strategy) **
**Use look-up table that
predicts the resulting
traffic load, for both fulland partial-expansion
strategies.
NO
All BSs are in
active mode
YES
NO
Is Load value
lower than expansion
mode threshold?**
Request Sleep
Mode
YES
Is there
collision between
the BS requests?
Request Expansion
Mode
NO
METC
Algorithm: Do any
of the request combinations
meet the traffic load
requirements?
Select highest energy
saving strategy and
group of BSs to sleep.
YES
Select highest energy
saving BSs to sleep.
a) Centralized SMM Controller
•
BSs achieve their
requests
NO
All BSs in partnership
are in active mode
**Can also use machinelearning to decide on
action.
b) Distributed SMM Controller
Decision Model for Sleep Mode via: a) Centralized Cell Expansion; b) Distributed Cell Expansion.
a sleep-mode and expansion-mode association between BSs.
The paper considers a smaller group of 2-3 BSs, and proposes
two different forms of partner selection:
•
Not Available
Mode
YES
YES
Fig. 4.
NO
Exchange information with partner BS*
Closed Loop: Load
Threshold Feedback
Group BSs based
on identity*
METC
Algorithm: Do any of
the grouping s meet the traffic
requirements?
*BS partners are selected from nearest
neighbour BS list. See section on
Partner Selection for more details.
Load information given
to BS
Random Neighbor (RN): each BS establishes a temporary
partnership with a neighboring BS. Each BS picks its
neighbor in an ad-hoc manner based on whether it will
enter sleep mode or compensation mode, and which
neighbors are available. There is no guarantee that a
successful partnership can be negotiated.
Fixed Neighbors (FN): each BS establishes a fixed relationship with 2 neighboring BSs, to form a triangular 3BS relationship. Coordination is achieved between the 3BSs to decide which one of them enters sleep, expansion
and normal mode. Due to the fixed nature, there is
guarantee that a partnership can be found.
B. Distributed Decision Process
3) Partners check if their mutual requests are compatible, i.e., sleep-mode and expansion-mode is compatible,
whereas sleep-mode and not-available is not compatible.
If compatibility is met, the BSs have their requested
actions mutually accepted;
4) If the compatibility is not met and more than one
strategy is possible, for each strategy (Sc ), predict the
resulting energy and load performance based on previous
experiences.
The paper now formally defines the various parameters used
in the machine-learning process and analyze the benefits of
having open- and closed-loop threshold feedback.
The paper formally defines the following:
•
•
•
Once a partnership has been formed, the transition rules
between operational modes can be defined (as shown in
Fig. 4b:
1) Each BS makes an action decision based on the current
traffic load and a decision threshold. The resulting
action can be to request entering sleep-mode, make itself
available for expansion-mode or to signal being notavailable for expansion;
2) Each BS then communicates this information to its
partner BSs;
•
•
•
Environment: the network containing all BSs and subject
to a certain offered traffic rate that has a uniform temporal
and spatial distribution.
Agents: the BSs, where the observed BS is k ∈ NBS .
State: the current load L experienced by the agent concerned.
Action: each agent can take an action a ∈ A to enter
an operational mode (normal, expansion or sleep). As a
consequence of this action, the BS will reach a new state
(load, L).
Strategy: the strategy to take υ ∈ Sd that affects the
probability of taking the request action a ∈ A to reach a
sleep mode state.
Feedback: by taking an action that leads to a state, the
BS has an interference impact on the network containing
7
100
70
Aggressive
60
50
40
Sleep Mode
Saving
30
Conservative
10
90
ERG - Open Loop, =0.6
ERG - Closed Loop
Outage Pb. - Closed Loop
Exploration
(Δ = 15)
80
Exploitation
(Δ = 2)
ERG - Open Loop, =0.6
70
Performance, %
80
70
Performance, %
Performance, %
ERG - Closed Loop
Outage Pb. - Closed Loop
90
80
20
100
100
ERG - Open Loop
Outage Pb. - Open Loop
90
60
50
ERG
40
Outage Prob.
ERG
60
Outage Prob.
50
40
30
30
20
20
10
10
Radiohead Saving
0
0
0.2
0.4
0.6
0.8
1
Strategy, 
1.2
1.4
1.6
0
0
500
1000
1500
0
500
1000
1500
Iterations(t)
Iterations(t)
(b) Closed-Loop with Random Greedy Algorithm
with Exploration factor Δ = 2 and 15.
(a) Open-Loop Distributed Coordination
with Fixed Strategy, υ
Fig. 5. a) Open-Loop Distributed Coordination with Fixed Strategy; b) Closed-Loop Distributed Coordination with Random Greedy Algorithm with Exploration
factor ∆ = 2 and 15; simulation results only.
•
other BSs.
Reward: the power saved (compared to peak) in the
observed BS, at time t with state s:
<k,t,s = 1 −
•
PBS,k,t,s (Lk,t,s )
.
PBS,k,t,s (Lk,t,s = 1)
(11)
As shown in (5), the potential power saving when not in
sleep mode is in the radio-head, and when in sleep mode
is the total power.
Punishment: the outage probability, at time t with state
s:
Rtraffic,k,t − RBS,k,t,s
℘k,t,s =
.
(12)
Rtraffic,k,t
Observation: the BS observes the reward and punishment
of the previous action, as well as the resulting load on
the observed BS at time t.
Therefore, the observed BS trades-off the reward (energy
saved) of entering sleep mode and the punishment (outage)
of over-estimating the ability to meet the offered traffic rate.
Furthermore, there is also a tradeoff between exploiting what
the BS thinks is the best strategy based on existing knowledge
and exploring the alternative strategies.
•
C. Open Loop Performance
In open loop performance, the strategy is fixed for all BSs
(υ), which means the probability that triggers a sleep mode
request is fixed at any particular time instance (quasi-static
traffic model). The results presented in Fig. 5a show that:
• An over-aggressive BS (high υ) can enter sleep mode
only to discover that it can not meet the offered traffic
rate and cause an outage ot > 1.
• An over-conservative BS (low υ) never enters sleep mode
and saves only the radio-head energy (10%), but can
generally guarantee an arbitrarily low outage rate.
For a target outage rate of 5%, a maximum of 16% energy can
be saved with a strategy of υ = 0.6. The advantage with open
loop strategy is that only a single network-wide parameter (υ)
needs to be tuned to optimize performance during a single time
period. The disadvantage is that the network can not exploit
local spatial effects and create local threshold parameters.
D. Closed Loop Performance with Reinforced Learning
In closed loop performance, individual BSs keep track of
previous strategies’ performance results and picks a threshold
based on this memory information. The previous reward
(<k,t,s ) and punishment (℘) performances for a given strategy
s over a period of T is:
E[<k,s ] =
T
1X
<k,t,s ,
T t
E[℘k,s ] =
T
1X
℘k,t,s .
T t
(13)
For small-finite-state problems, Markov Decision Processes
(MDP) techniques such as Q-learning can be applied. Even
when the state transition probabilities are unknown (as is the
case here), they can be discovered using exploration. However,
the challenge addressed in this paper concerns an infinite-state
problem, where the BS can be in any state (any load) and an
action can potentially lead to any other state.
The Q-learning algorithm would take too long to discover
the MDP. Instead, the agent can weigh the discovery process
using Q-values (rewards) based on a soft-max distribution.
This paper considers a Random Greedy Strategy with Boltzmann Exploration, similar to automata learning:
• the agent (BS) always selects the estimated best strategy
based on the expected reward and punishment from previous iterations. However, there is a probability (prandom )
that it will instead select a random alternative strategy
that is not the estimated best strategy.
• under the Boltzmann Exploration strategy, the strategy
selection is based on a weighted probability biased in
favor of likelihood to yield high rewards:
prandom,k,t = P
e
E[<k,s ]
∆
k,s0
∆
E[<
s0 ∈Sd
e
]
(14)
for: E[℘k,s ] ≤ outage threshold,
subject to meeting the outage threshold and s0 represents
all other strategies (s0 6= s) in the available set of
8
Antenna Reduction: number of active antennas reduce
with traffic load [6], [7].
The results in Fig. 6 show that for an offered urban traffic
rate of 10-120 Mbit/s/km2 , the reference power reduction technique can only save up to 27% energy. By employing antenna
reduction, the energy saving is up to 33% compared to the
peak consumption. By employing cell expansion (centralized
with SMM), the energy saving is up to 64% compared to
peak value. By assuming a uniform variation in the offered
traffic rate intensity, the antenna reduction technique improves
on the existing reference by up to 17% (mean 9%). The cell
expansion technique improves on the reference by up to 50%
(mean 19%), and up to 44% (mean 11%) over the antenna
reduction technique. By assuming a realistic variation in the
offered traffic rate intensity, the antenna reduction technique
improves on the existing reference by up to 18% (mean 6%).
The cell expansion technique improves on the reference by
up to 50% (mean 10%), and up to 44% (mean 5%) over the
antenna reduction technique.
•
2800
2600
Power Reduction
RAN Power Consumption, W/km 2
2400
2200
2000
MIMO Reduction
1800
1600
Sector Reduction
Full Expansion, 1/3
1400
Reference (Sim.)
Antenna Reduction (Sim.)
Cell Expansion (Sim.)
Reference (Theory)
Antenna Reduction (Theory)
Cell Expansion (Theory)
1200
1000
800
600
10
Partial Expansion, 1/2
20
30
40
50
60
70
80
90
100
110
120
RAN Offered Load, Mbit/s/km2
Fig. 6. Power-Capacity-Tradeoff for different deployment schemes under a
varying traffic load. Simulation Results as symbols and Theory as lines.
strategies s0 ∈ Sd . The parameter ∆ adjusts the level
of exploration: small ∆ favors exploitation and large ∆
favors exploration. Generally, a large ∆ can guarantee
asymptotic optimality.
The results in Fig. 5b and c show that there is a tradeoff
between exploiting what is already known (rapid convergence)
and exploration (better asymptotic behavior). For a target
outage rate of 5%, an asymptotic average of 12% energy can
be saved with exploitive behavior (D = 2), with a convergence
time of ∼200 iterations. This performance is worse than
the optimal open-loop performance, where 16% ERG can be
achieved with a 5% outage rate and a strategy of υ = 0.6. With
greater exploration behavior (D = 15), an asymptotic average
of 24% energy can be saved, with a convergence time of
∼600 iterations. However, the level of convergence (variance)
is much greater than the exploitation case. The optimization
of convergence speed and optimality is beyond the scope
of this paper. The results have demonstrated that distributed
coordination can in fact use the uncertainty in performance to
its advantage, provided that a reinforced learning algorithm is
employed and the tradeoff between learning and exploitation is
adjusted to benefit asymptotic performance without leading to
an unbearable convergence rate. This can be further analyzed
in future work.
In Section VII, the paper presents the energy saving results
for the distributed solutions with different partner selection
schemes and compares its performance with the centralized
solution and other energy saving solutions.
VII. C ELL E XPANSION R ESULTS
A. Baseline Comparison
The paper begins by examining how the RAN energy
consumption scale down at low loads, given that an initial
deployment is made to satisfy a high offered load (L = 1). The
investigation considers the following methods for comparison:
• Reference: transmit power reduces with traffic load (5);
B. Centralized vs. Distributed Results
Generally speaking, compared to the centralized algorithm,
the lower-complexity distributed algorithm can achieve a comparable low-load saving (48%) and a higher high-load saving
(20%). However, the distributed coordination requires tuning
the learning rate. As mentioned previously in Section VI,
the paper proposed two different forms of distributed cellexpansion: Random Neighbor (RN) and Fixed Neighbors (FN)
partner selection. From the results in Fig. 7, it can be seen that
the energy saving at low loads for distributed-RN is lower than
the centralized solution. The energy saving compared to the
reference is up to 39% (mean 21%). From the results, it can be
seen that whilst the energy saving is between the centralized
and distributed-RN solutions at high loads, the distributed-FN
solution has a similar performance to the centralized solution
at low loads.
C. Cooperative Transmission
A key challenge is how to improve the received SINR in
the compensation region, which is limited by interference and
increased propagation. For a user with an SINR of γi,k , it
can either receive a single direct transmission or repeated
transmissions from the NCoop,i,k compensating BSs. The loss
1
. The resulting SINR gain (G+
in bandwidth is NCoop,i,k
i,k ) must
be:
G+
i,k >
(1 + γi,k )NCoop,i,k − 1
.
γi,k
(15)
If expression (15) is expressed in the context of the user
positions:
• Exponent Relationship: For users close to a serving cell
and experiencing a high SINR, the cooperation gain
NCoop,i,k −1
required would be: G+
.
i,k > γi,k
• Linear Relationship: For users in the compensation zone
and far from a serving cell, the SINR is typically low.
Using the binomial expansion approximation, the cooperation gain required would be: G+
i,k > NCoop,i,k .
9
load (Ltest,k,t,s =
2800
2600
ERG = 1 −
RAN Power Consumption, W/km 2
2400
2200
1600
Distributed
Advantage
Irregular
Coverage
1200
Reference
Cell Expansion (Centralized)
Cell Expansion (Centralized, CoMP)
Cell Expansion (Distributed - RN)
Cell Expansion (Distributed - FN)
1000
800
600
10
20
30
40
50
60
70
80
90
100
Ns ( µPpeak
POH +
CoMP Gain
1400
Ns ( µPpeak
is:
q
Lref.,k,t,s
ρs
+ POH ) + PBH
p
Lref.,k,t,s + POH ) + PBH
(16)
1
→
1+Ω
2000
1800
Lref.,k,t,s
)
ρs
110
120
RAN Offered Load, Mbit/s/km2
Fig. 7. Power-Capacity-Tradeoff for different schemes: reference, centralized
cell-expansion, cell-expansion with CoMP, distributed cell-expansion. Simulation Results only.
The results found show that up to 0.5 bit/s/Hz and 50%
spectral efficiency gain can be achieved in certain regions of
the switched off cell. However, cooperation in regions of high
SINR can lead to 60% less in spectral efficiency. Therefore,
a repetition cooperation scheme based on user positioning
can be employed, similar to those devised in [2]. The results
are presented in Fig. 7 and up to 28% spectral efficiency
improvement can be achieved for full expansion strategy.
VIII. C ONCLUSIONS
This paper has considered the challenge of how to scale
energy consumption with spatial and temporal variations in
the traffic. The paper first demonstrated that the energy saving
upper-bound of transmission based techniques is hardwarelimited, whereas sleep mode and deployment techniques is
capacity-limited. The proposed cell expansion technique allows a higher number of base-stations to be in sleep mode.
This is achieved by expanding the coverage of neighbouring
base-stations. The results show that the centralized coordination algorithm can achieve a deterministic coverage pattern
and a strong low-load energy saving (50%) and no highload saving (0%). Compared to the centralized algorithm, the
lower-complexity distributed algorithm can achieve a comparable low-load saving (48%) and a higher high-load saving
(20%). However, the distributed coordination requires tuning
the learning rate. Furthermore, integration with cooperative
transmission can further improve the baseline expansion performance by 28%.
A PPENDIX
A. Lemma 1: Energy Saving Bounds
The hardware-limited energy reduction gain (ERG) of a
reference system with load (Lref.,k,t,s ) and a test system with
PBH
Ns
where Ω = µpeak
. The conditions are for an initial
P
L
=
load of Lref.,k,t,s = 1 and an ideal load reduction to ref.,k,t,s
ρs
0.
The capacity-limited energy reduction gain (ERG) of a
s
reference system with (Ns ) and a test system with ( N
ρs )
antennas is:
p
Ns
P
Lref.,k,t,s + POH ) + PBH
ρs ( µpeak
p
ERG = 1 −
P
Ns ( µpeak Lref.,k,t,s + POH ) + PBH
(17)
1
→1− ,
ρs
for both systems being fully loaded (Lref.,k,t,s = 1), and
assuming that sleeping basestations consume close to no
energy.
B. Lemma 2: Theoretical Capacity for Different BS Modes
The paper employs recent developments in stochastic geometry to provide an approximate theoretical capacity performance for different cell expansion operational modes under centralized coordination. Stochastic geometry allows the
interference-limited capacity to be found for a multi-cell
network [15]. The major short-fall with the analysis is that
no antennas are considered. Another key difference is that a
random cell deployment topology is considered, as opposed
to hexagonal deployment.
The cell-edge capacity is defined as the capacity achieved
by a single user location that is at a distance r0 from the
2
serving cell. For a cell density of Λ = 1/πrcell
, the average
interference-limited (n = 0) cell-edge capacity is [16]:
Z +∞
R̄s =
P(Rs > ζ)dζ
Z0 +∞
=
exp(−βr0α n(2ζ − 1) − Λπr02 Q(ζ, α))dζ (18)
Z0 +∞
=
exp(−Λπr02 Q(ζ, α))dζ for: n → 0,
0
where the Q-function is defined as follows: The Q(ζ, α)
function is given by:
Z +∞
(2ζ − 1)−2/α
Q(ζ, α) =
du
1 + uα/2
(2ζ −1)−2/α
p
π
1
− arctan( √
)
for: α = 4,
= 2ζ − 1
2
2ζ − 1
(19)
where α is the pathloss distance exponent. The integrals can
be solved numerically using the Gauss-Korond technique.
In the normal cell operational mode, the worst cell-edge
user is at a distance r0 = rcell from the serving cell. The
10
achievable aggregate cell-edge capacity of a cell-site with Ns
sectors each with Bcell bandwidth is:
Z +∞
Rnormal = Ns Bcell
exp(−Q(ζ, α))dζ = 33.3Mbits/s
0
(20)
where we consider 10MHz band per sector with Ns = 3 outer
sectors, the edge-throughput per BS is 33.3 Mbits/s.
In the full compensation (1/3) cell operational mode, the
worst cell-edge user is at a distance r0 = 2rcell from the
serving cell (Fig. 3b). That is to say, a serving cell has to
serve as far as the location of a sleeping neighbouring cellsite. The achievable aggregate cell-edge capacity of a cell-site
with Ns sectors each with Bcell bandwidth is:
Z +∞
Rsleep,1/3 = Ns Bcell
exp(−4Q(ζ, α))dζ = 10.0Mbits/s.
0
(21)
The compensating or expanding cell-sites have in turn, lost 3
sectors and therefore suffer a capacity loss of 12 . Given the
the result in (20), the expanding cell’s capacity is therefore
Rexp,1/3 = 16.6 Mbits/s.
In the partial compensation (1/2) cell operational
mode,
√
the worst cell-edge user is at a distance r0 = 5rcell from
the serving cell (Fig. 3c). The achievable aggregate celledge capacity of a cell-site with Ns sectors each with Bcell
bandwidth is:
Z +∞
Rsleep,1/2 = Ns Bcell
exp(−5Q(ζ, α))dζ = 8.1Mbits/s.
0
(22)
The compensating or expanding cell-sites have in turn, lost
1 sector and therefore suffer a capacity loss of 13 . Given the
the result in (20), the expanding cell’s capacity is therefore
Rexp,1/2 = 22.2 Mbits/s.
Acknowledgement
The work reported in this paper has formed part of the Green
Radio Research Programme of the Mobile VCE. Fully detailed
technical reports on this research are available to industrial
members of the Mobile VCE. www.mobilevce.com
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Weisi Guo received his M.Eng., M.A.
and Ph.D. degrees from the University
of Cambridge. He is currently an
Assistant Professor at the University
of Warwick and is the author of the
VCEsim LTE System Simulator. His
research interests are in the areas of
self-organization, energy-efficiency, and
multi-user cooperative wireless networks.
Tim O’Farrell holds a Chair in Wireless Communication at the University
of Sheffield, UK. He is the Academic
Coordinator of the MVCE Green Radio Project. His research encompass resource management and physical layer
techniques for wireless communication
systems. He has led over 18 research
projects and published over 200 technical papers including
8 granted patents.