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TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIESTrans.
Emerging Tel. Tech. (2014)
Published online in Wiley Online Library
(wileyonlinelibrary.com). DOI: 10.1002/ett.2850
RESEARCH ARTICLE
Energy-efficiency maximisation for cooperative
andnon-cooperative OFDMA cellular networksa surveylvaro Ricieri
Castro e Souza1*, Jos Roberto de Almeida Amazonas1 and Taufik
Abro2
1 Department of Telecommunication and Control Engineering,
Escola Politcnica of the University of So Paulo, So Paulo, Brazil2
Electrical Engineering Department, State University of Londrina,
Londrina, Paran, Brazil
ABSTRACT
In this survey, techniques to enhance energy efficiency (EE) in
orthogonal frequency division multiple access (OFDMA)and orthogonal
frequency division multiplexing (OFDM) systems, with or without the
utilisation of the cooperativenetwork paradigm, considering also
the features provided in the standards of modern cellular wireless
networks, suchas LTE-Advanced and WiMAX, are discussed. For the
non-cooperative EE maximisation case, we summarise
resourceallocation problems and also describe some techniques that
can be combined with the basic power/subcarrier allocationproblems.
When considering the cooperative OFDM(A) case, we first discuss
four basic variables that arise with the relaystation implantation,
and after that, other features are also listed, which can be
combined with the previously discussedissues. Finally, we review
some of the standardisation documents available for
fourth-generation systems in order to obtainsystem parameters and
simulation scenarios, discuss some methods to analyse and solve the
optimisation problems thatcan be proposed with the aforementioned
techniques and then point out important open trends and research
challenges inthe EE maximisation problem considering OFDM(A)
scenario. Copyright 2014 John Wiley & Sons, Ltd.
*Correspondence
. R. Castro e Souza, Department of Telecommunication and Control
Engineering, Escola Politcnica of the University of So Paulo,So
Paulo, Brazil.E-mail: [email protected]
Received 12 February 2014; Revised 30 May 2014; Accepted 11 June
2014
1. INTRODUCTION
With the increasing number of subscribers and mobilemultitask
devices, such as smartphones and tablets, andthe offering of data
communication for notebooks anddesktops, the main concern in modern
cellular systems isto efficiently provide a high data rate for the
served users,which can be translated into increasing the spectral
effi-ciency (SE). This can be seen, for example, by comparingthe SE
for two cellular systems downlink scenarios, whichevolved from 0.05
bps/Hz in the GSM (2G) systems [1]to a peak SE of 30 bps/Hz for the
LTE-Advanced (LTE-A) 11 (4G) systems [2]. Several techniques are
utilisedto provide this remarkable gain as, for example,
multiple-input multiple-output (MIMO) and adaptive modulationand
coding, but this capacity enhancement also comeswith increased
power consumption. As pointed out byseveral works, the power
consumption for information andcommunications technology is
becoming a significant per-centage of the worldwide power
consumption [3], and asignificant part of this consumption in
mobile communica-tions comes from the radio access network [4, 5],
which
has negative impacts for both users and operators: at theuser
side, as the battery technologies evolve in a muchslower rate than
the offered services [6], the lifetime ofthe battery-powered
devices is limited. For operators, theincreased power consumption
results in higher operationalcosts [7] while, in [8], is pointed
that 50% of the overallexpenses of the service providers is due to
base station (BS)powering. Another perspective is the environmental
issue,because electricity production results in pollution, as
theVodafone case reported in [7]. Indeed, a recent study
[8]indicates that information and communications technologyis
responsible for 2% of the global CO2 emissions.
In order to balance the increasing data rate and the
cor-respondent power consumption, the energy-efficiency (EE)metric
has been recently proposed as an important figureof merit for
efficient wireless communication networks.Defined as the ratio
between the achieved data rate and thepower consumed to provide it,
this metric indicates howefficiently the system transforms power
into transmitteddata, allowing one to determine the operation point
wherethe system transmits more information bits per energy unitor
where each information bit has the lowest energetic
Copyright 2014 John Wiley & Sons, Ltd.
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
cost, providing an extended lifetime for users and
resourcesavings for operators. The EE can be evaluated from
theusers perspective or from the whole network, and forboth cases,
it is possible to include the power spent withequipments and signal
processing, in order to analysethe impact of all components in the
system. Consideringonly the EE perspective in the resource
allocation problemcan result in significant impact on other
important systemperformance metrics [1] as, for example, the
spectral effi-ciency (SE). In this way, it is fundamental to the
systemperformance to include performance metrics as constraintsin
the optimisation problem if they are strictly necessary.
As it is well known, the orthogonal frequency divisionmultiple
access (OFDMA) technique is the most populartransmission topology
for high data rate communicationsystems, such as WiMAX and LTE-A,
which are twopromising candidates for 4G systems [5]. This is due
toseveral advantages of OFDMA, such as the robustnessto the
inter-symbol interference (ISI), caused by multi-path propagation
and specially impactful when symbolrate is high, and the higher
diversity dimensions, as wecan consider frequency, multi-user and
time dimensionsin the resource allocation strategies [9, 10]. In
OFDMA,the total bandwidth is split in narrowband subchannels,which
allows to reduce the symbol rate in each subcarrierwhile
maintaining the overall data rate. Hence, it is possi-ble to obtain
a symbol period higher than the channel delayspread, reducing the
negative impact of multipath propa-gation while increasing
communication reliability. In thecontext of EE optimisation, the
transmission power andsubcarrier allocation are the main
optimisation parametersin the literature, but there are other
features that can beintroduced, as sleep/active mode switching and
modulationorder optimisation.
Despite all advantages of OFDMA systems, oneproblem that any
wireless communication system faces isthe channel conditions,
mainly represented by fast fadingand intensive path loss, which are
inherent to the propaga-tion environment and network topology [10,
11]. The prob-lem of path loss becomes even worse in
high-frequencycommunications, as the 5-GHz carrier frequency
presentedin both LTE-A and WiMAX and in densely constructedareas,
such as metropolitan areas. For the fading case, whenthe channel
experiences deep fading, it is impossible orimpractical to maintain
communication. In order to reducethese problems, one of the most
promising techniquesis the cooperative communications. Under this
paradigm,relay stations (RSs) are placed at the cell to improve
cov-erage and/or capacity, mainly for users in coverage holesor
cell-edge area, retransmitting the received signal frommobile
stations (MSs) or BSs to destination. In this way, itis possible to
reduce the effects of path loss and form a vir-tual antenna array
(such as virtual MIMO) [10] to providespatial diversity, providing
robustness to deep fading whilereducing power consumption, which
can be translated intoEE improvement. When considering EE
optimisation forcooperative OFDMA, various aspects can be
optimised,
such as time/frequency sharing, relay placement
andretransmission protocol.
Under the perspective of multiple possible approachesfor EE
maximisation, this survey reviews basic concepts inOFDMA systems,
cooperative communications and energyefficiency, in order to
effectively discuss representativeEE maximisation techniques and to
provide an interestingtool to evaluate/analyse EE in 4G cellular
systems. Thesurvey is organised as follows: In Section 2, we
presentthe OFDMA system model, cooperative networks tech-niques and
the EE optimisation approach, as well as theterminology deployed in
this survey. In Section 3, wedescribe methods for EE maximisation
in non-cooperativeOFDMA networks, while in Section 4, we do the
samefor cooperative OFDMA systems. In Section 5, we dis-cuss
methodologies for simulation and evaluation methodsfor EE
optimisation problems, also, a brief guideline forsystem parameters
and scenarios choices based on a listof documents from different
standardisation workgroups isprovided. Finally, Section 6 concludes
this survey and putinto perspective the principal research
challenges and opentopics of interest.
2. SYSTEM DESCRIPTION
This section gives an overview of the main techniques usedin 4G
systems and discussed in this survey. Although theEE paradigm is
proposed for several multiple access (MA)techniques and network
topologies, only the OFDMAmodel is presented because the focus of
this survey is4G-based systems. In this way, we provide an
overviewOFDM/OFDMA systems, cooperative networks and theEE
definition.
2.1. OFDM/OFDMA
The orthogonal frequency division multiplexing (OFDM)technique
consists in splitting a user-data stream intoseveral substreams,
which are sent in parallel on severalsubcarriers, obtained by
splitting the total bandwidth innarrower channels. Considering that
X is the set of symbolsto be transmitted, each symbol Xi modulates
the ith sub-carrier, with jXj 6 N, where N is the number of
availablesubcarriers. The rationale of this approach is to
increasethe individual symbol time (Ts,i) in each subcarrier
withoutincreasing the total time to transmit X (Ts), in such a
waythat Ts,i is higher than the channel delay spread Td , which
isfundamental to reduce the effects of ISI, without affectingthe
data rate that remains the same [9]. The symbol time ineach
subcarrier is given by Ts,i D NTs, resulting that N isdefined in
order to achieve Ts,i ! Td , that is, N ! Td=Ts.
Figure 1 shows an OFDM block diagram and illustratesthe overall
process. The symbols are modulated in thefrequency domain by taking
the N-point inverse discreteFourier transform (IDFT) of X. As the
data stream X isserial, it first passes through the
serial-to-parallel converter,then the IDFT is applied, obtaining
the time samples x,
Trans. Emerging Tel. Tech. (2014) 2014 John Wiley & Sons,
Ltd.DOI: 10.1002/ett
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
Figure 1. OFDM system block diagram, where X is the set of
symbols to be transmitted, h is the multipath channel coefficients
andbX is the set of estimated symbols.
which are serialised again by the parallel-to-serial con-verter.
After that, the data stream is transmitted over awireless channel
with impulse response given by h Dh0, h1, " " " , hj, " " " , hv!,
where v is the length, in samples,of the channel delay spread.
At the detector side, the received time signal y passesthrough a
serial-to-parallel converter, then the DFT isapplied, and the
frequency samples Y are serialised anddetected, generating the
estimated symbols vector bX. Notethat in the OFDM transmission
technique, the various sub-carrier signals are generated digitally
and jointly by aninverse fast Fourier transform algorithm in the
transmitter,and their spectra strongly overlap on the frequency
axis.This being so, generating the transmit signal is simpli-fied,
and the bandwidth efficiency of the OFDM/OFDMAsystems is
significantly improved.
As the DFT/IDFT is used, it is necessary that the signaland
channel convolution be circular, which implies that xor h has to be
periodic. On the other hand, despite Ts,i !Td , it is possible that
some symbols are still affected bymultipath propagation [9]. In
order to overcome the effectsof these two situations, a cyclic
prefix (CP) is inserted,which consists of copying the Ng > v
last (first) samples ofx to the beginning (ending) of the OFDM
symbol, whichequates the linear and circular convolutions results.
Also,the CP insertion makes the received signal ISI-free.
Con-sidering that the signal at the source has N C Ng samples,the
convolution with the fading channel results in a signalwith N C Ng
C v samples. By discarding the first Ng sam-ples, which are
corrupted by the delayed samples of the
previous signal, and the v last samples of the received sig-nal,
which interfere with the next OFDM symbol, there areN samples that
are ISI-free at the cost of a data rate penaltyimposed by the
redundancy. In summary, the CP is insertedafter the IDFT at
source-side and removed before the DFTat receiver-side.
The main parameters associated to the OFDM systemare (i) number
of subcarriers (N), which must satisfy thechannel delay spread
constraint; and (ii) CP size, whichmust be at least equal to the
number of channel multipathcopies.
Despite all the aforementioned advantages, there aretwo main
drawbacks in OFDM systems [9, 12]: the highlyprecise frequency
synchronisation needed and the peak-to-average power ratio (PAPR).
The first one is causedby the sinc functions in frequency domain at
the detec-tion, because the inter-carrier interference (ICI) is
zeroonly when the frequency is perfectly synchronised;
thissynchronism can be lost because of the imperfect oscil-lators
and the Doppler effect, generated by user mobility.The second one
is intrinsically caused by the multicarrierstrategy. In time
domain, the OFDM symbol is composedby many narrowband signals,
which could result in peaksof power much larger than the average
power, makingthe power amplifier to operate in the nonlinear
region,incurring in distortion and loss of efficiency. As
describedin the following, the OFDMA technique results to bethe
solution for the second problem, at least under theusers
perspective.
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
Figure 2. Basic cooperative strategies.
As OFDM is a multiplexing strategy, it can be com-bined with
different MA dimensions, as time division MA,code division MA
(CDMA) or frequency division MA(FDMA). Because the 4G standards
consider the MA infrequency, we will focus on the OFDMA system
model. InOFDMA, for each user is allocated a number of subcarri-ers
in a given time slot, which are updated in the followingslot [9].
In this way, it is possible to recognise at least twodiversity
dimensions: time and multi-user. The time dimen-sion comes from the
fact that if the channel quality is poorfor a user in all
subcarriers in a given time slot, it is possibleto make this user
wait for another time slot. The multi-user dimension can be
explored from the perspective ofthe choice of which users allocate
which subcarriers, givena specific metric, such as, for example,
the instantaneouschannel state information (CSI).
Because in the OFDMA system the users compete to usethe
subcarriers, it is necessary to define for each allocationperiod
the user-subcarrier mapping and the transmissionpower for each user
in the mapped subcarriers. On thedownlink, BS defines the mapping
and then transmits thisinformation to the active users via control
messages, sothat each user only decodes the information on the
allo-cated subcarriers. On the uplink, there are two
possibilities:for distributed solutions, the users decide the
subcarrierallocation, and each one of them must inform the BS
theallocated subcarriers; while for centralised solutions, theBS
proceeds as in the downlink case.
Depending on the metric(s) to be optimised, that is,data rate
maximisation, power consumption minimisationor fairness provision,
different subcarrier, time and powerallocation algorithms can be
deployed. The algorithms arenot specified along the OFDMA model or
standards [9],and each implementation must decide how to deal
withthe associated problem. If we consider K users, N sub-carriers,
time slot equal to the symbol time Ts and powerp 2 0, Pmax!, where
Pmax is the maximum allowed trans-mission power, the allocation
problem becomes extremelycomplex to be optimally solved in real
time. That beingso, commercial systems such as LTE-A and WiMAX
usetime slots with multiple symbols and group subcarriers toform
subchannels, reducing the number of possible combi-nations and, in
consequence, the computational complexityof the optimisation
problem [9].
It is well known that the power amplifier of mobiledevices, due
to cost reasons, cannot be as efficient as thosedeployed in the
BSs, making the uplink PAPR quite sig-nificant. The OFDMA system
reduces the impact of thePAPR problem in the uplink of the OFDM
system [9].In OFDMA systems, each user uses only a portion of
theavailable subcarriers, and because the PAPR is proportionalto
the number of used subcarriers, each user experiments alower PAPR
and is able to use less power than when eachuser uses all
subcarriers in only one time slot.
2.2. Cooperative cellular networks
In order to overcome the destructive nature of wirelesschannels,
one of the most promising techniques is thecooperative
communications paradigm. In this scenario,one or more equipments,
called relays, retransmit thesignal received from the source to the
destination, pro-viding spatial diversity if the source-destination
link isavailab1le or improving coverage otherwise. As the pathloss
is nonlinear and inversely proportional to the source-destination
distance [11, 13], if the user deploys relay(s)in a multi-hop
communication, the power spent with prop-agation losses can be
reduced substantially, increasing themobile terminal, as well the
overall system, efficiency interms of power consumption. The
spacial diversity canbe seen as virtual MIMO [11], where the
relays, plusthe direct transmission, act as virtual antennas. This
is aninteresting method to provide spatial diversity in
cellularcommunications, allowing the increase of the cell
coverage(macro-diversity); moreover, because the required
antennaseparation to provide uncorrelated signals for MIMOsystems
is at least half wavelength (micro-diversity) [9],in cases where
carrier frequency is in the hundreds ofmegahertz range or less, it
becomes unrealistic to obtainuncorrelated signal replicas in mobile
cellular devices,such as cell phones.
A simple example of a cooperative communication canbe seen in
Figure 2, where the source node S communicates
Considering that the path loss is commonly defined as Lod!npl ,
whereLo is a constant depending on system parameters, d is the
communica-tion distance and npl is the path-loss exponent, which
depends on thepropagation scenario, and in general 2 6 npl 6 6.
Trans. Emerging Tel. Tech. (2014) 2014 John Wiley & Sons,
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
with the destination node D using a single-relay node RS.There
are several ways to do it [10]:
(1) S transmits to D in the first time slot, and RS over-hears
and then retransmits in the second time slot(Figure 2(a)).
(2) S transmits to RS in the first time slot, and then
RStransmits to D in the second time slot (Figure 2(b)).
(3) S transmits to D in the first time slot, RS transmitsthe
overheard message in second time slot and S alsotransmits a new (or
copied) message in the secondtime slot (Figure 2(c)).
(4) S transmits to RS in the first time slot, and bothRS and S
transmit to D in the second time slot(Figure 2(d)).
Another classification of RSs concerns the type of equip-ment
[14]. If the equipment is dedicated to retransmissionand installed
as part of the cell infrastructure, it is calledfixed RS. On the
other hand, if the user equipments areable to retransmit
information of other users, they arecalled mobile RSs. Although
both implementations arepossible, the fixed approach is the choice
for the 4G stan-dards, given that there are dedicated power supply
anddedicated equipment for relay operation, while the mobiledevices
would have to share limited power and time toact as relay node,
despite the higher diversity that couldbe achieved in this
configuration. Another advantage offixed relays is that they can be
installed in a plannedway, aiming to provide better coverage to
otherwiseuncovered holes or to provide higher data rates where itis
necessary.
Based on Figure 2, it is possible to infer that the relaycan
either be recognised as a network equipment by BSsand MSs or not
[15, 16]. The first condition, presentedin Figure 2(b) and (d), is
called non-transparent relaying.In this way, the RSs are considered
as a BS, communi-cating directly with the mobile users. This mode
is usedto extend coverage, because the link MS-BS is unavail-able
[17]. The second mode, presented in Figure 2(a)and (c), is called
transparent relaying and correspondsto the case where MSs and BS
communicate directly,and the RSs just overhear the transmission and
thencollaborate by retransmitting. This model is used toincrease
throughput/reliability or to reduce power con-sumption, because the
MSs are already covered by theBS [17].
To retransmit the information, there are also two types
ofprotocols [10, 18]. The first one refers to the case in whichthe
RSs decode the received signal before retransmit-ting it, called
regenerative protocols, while in the secondcase, the signal is
analogically processed before retrans-mission, being called
non-regenerative protocols. The bestknown implementations are the
decode-and-forward (DF)and amplify-and-forward (AF) protocols,
respectively. Themain advantages of regenerative protocols are the
pos-sibility of more sophisticated processing, including
re-modulation and coding changes, aiming to not propagate
noise and interference from the received signal to the nextnode,
while the drawbacks are the processing cost, extralatency and
possibility of wrong detection. As pointedout by Laneman [19], the
AF protocol presents a higherdiversity order than the DF
protocol.
Finally, there is the method to separate the backhauland access
links in some dimension, because these linkscannot operate in the
same time/frequency/space with-out interfering with each other. As
shown in Figure 3,there are three different links in cooperative
communi-cations: the direct link, where MS and BS
communicatedirectly; the backhaul link, where RS and BS
communicateand the access links, where MS and RS communicate toeach
other. Furthermore, because the backhaul and accesslinks cannot
operate in the same time/frequency/spacebecause of
self-interference [20], as depicted in Figure 4,it is necessary
either to separate these links in onedimension or to deal with the
self-interference. The pos-sible solutions to avoid the
self-interference are [21]as follows:
(1) Inband relaying: backhaul and access links are sep-arated by
sharing the resources in time domain, orby sufficient antenna
separation at RSs, to avoidself-interference.
Figure 3. Link scheme for cooperative communications.
Figure 4. Self-interference (or loop-interference) when
accessand backhaul links are not well isolated: (a) downlink
and
(b) uplink.
Trans. Emerging Tel. Tech. (2014) 2014 John Wiley & Sons,
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
(2) Outband relaying: one RF channel is dedicated toeach link,
or the original RF channel is split in twofixed portions of the
total bandwidth.
Regarding the commercial scenario, both LTE-A andWiMAX mainly
consider fixed relays and regenerativeprotocols [18, 21, 22],
because the adaptive modulation andcoding (AMC) feature is only
possible with the deploy-ment of regenerative protocols. Besides,
for LTE-A, bothtransparent and non-transparent modes are allowed,
andalso inband and outband relaying, the last with a second
RFchannel. Just to clarify the common LTE-A nomenclature,in this
case, there are two types of RSs: the type-I RSs arenon-transparent
equipments, deploying regenerative proto-cols and operating at the
MAC layer, just like a regularBS from the MSs point of view, while
the type-II RSs aretransparent equipments that can operate with
regenerativeor non-regenerative protocols [23].
When the self-interference is accepted, techniques asfull-duplex
inband relaying and two-way relaying can beadopted. The use of
full-duplex inband RSs has beencogitated in two agenda items of
3GPP [24, 25], wherethe self-interference is handled by antenna
isolation andinterference cancellation. When using full-duplex
inband,access and backhaul links operate at the same time in
thesame direction: for downlink, we have BS-RS and RS-MSlinks
operating at the same time, while in the uplink, wehave MS-RS and
RS-BS transmissions at the same time.This method has obvious
advantages over the half-duplexinband and full-duplex outband
methods. For the formercase, the system uses two time slots to
transmit the samedata; as a result, the capacity is halved, while
for the lattercase, the extra required carrier halves SE. In the
full-duplexinband method, there is only one carrier to use, and it
isnecessary to use only one extra time slot, which may beconsidered
irrelevant overhead, given a sufficiently largenumber of
transmissions.
In [24], it is stated that a full-duplex inband relayingcan be
specially applicable when the RS-BS antenna hasa natural isolation
to the MS-RS antenna as, for example,in subway stations and densely
populated buildings as, forexample, shopping centres, where the
MS-RS antenna canbe installed inside the building and the RS-BS
antenna out-side. The main drawback listed in [24] is that if the
RSis installed far from the BS as, for example, near the celledge,
the BS-RS signal can be several orders of magni-tude lower than the
signal transmitted by the RS to theMSs, resulting that even if most
of the self-interference iscancelled, the residual interference
level can be compara-ble with the BS-RS power level. As described
in [24], theinterference cancellation at the RS can achieve an
excellentresult once:
Recently, mobile relaying scenario, such as train relaying
communi-cations, has been considered in LTE-A and WiMAX
standards.
# the RS perfectly knows the interfering signal, as it
istransmitting it;
# the control symbols and fed-back signals can be usedfor
channel estimation;
# the channel between the antennas is static.
The previous considerations suppose that the RS has twoantennas
and use one to transmit and another to receive.However, in [26],
the two antennas are used both to receiveand to transmit as
well.
The two-way relaying is a method originally used fordirectly
connecting two MSs via an RS. In the first timeslot, both MSs
transmit to the RS, which processes thereceived signal and then
retransmits a combined ver-sion of the signal to both MSs in the
second time slot.Because the MSs know the data they transmitted in
thefirst slot, it is possible to use it for interference
cancel-lation and then obtain the data transmitted by the otherMS.
Because the MS-BS link can be seen as a two-waylink, this concept
can be extended to the cellular scenarioin order to reduce the
number of necessary time slots[27] and, consequently, improve
system performance interms of both energy and SE. The two-way
relaying canbe also carried out in three time slots, if the
interferencein the first slot is prohibitive or may result in
signifi-cant loss in performance. Two-way relaying analysis inOFDM
systems can be found in [28] and [29], and Figure 5illustrates the
half-duplex inband, full-duplex inband andtwo-way relaying modes
and the respective number oftime slot necessary to complete a
downlink and uplinkcooperative transmission.
2.3. Energy efficiency
The EE metric is used to evaluate the efficiency with whichthe
communication system converts consumed energy intoeffective
transmitted data. This evaluation changes theparadigm from the data
rate efficiency, mainly measuredby SE, to the cost of the data rate
in terms of power con-sumption. The basic EE metric units are bits
per joule,that is, the number of transmitted effective bits per
jouleconsumed, and joules per bit, that is, the amount ofenergy
consumed to transmit one effective bit. In this con-text, an
effective bit refers to a bit that carries effectiveinformation
from the source to the destination, discard-ing protocol headers,
signalling data and redundant bitsinserted by error detection
codes. The EE metric can beevaluated as
" D GP
!bits
joule
"(1)
where G is defined as the effective throughput, or goodput,and P
is the total power consumption.
Considering the bit-per-joule definition, there are twomain
approaches to model the energy-efficiency problem.
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
Figure 5. Inband relaying modes and the necessary slots to
complete a downlink and an uplink transmission.
The first one considers that the system provides a fixed
datarate, and then an efficiency function f ."/ accounts for
pos-sible bit/symbol errors. In general, this efficiency
function
depends on the instantaneous signal-to-interference plusnoise
ratio (SINR) # between source and destination,resulting that " can
be modelled as
Trans. Emerging Tel. Tech. (2014) 2014 John Wiley & Sons,
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
" D
KPkD1
NPnD1
`.k,n/f .#.k,n//r.k,n/
KPkD1
NPnD1
%p.#.k,n// CKP
kD1pc.k/
!bits
joule
"(2)
where in the context of OFDM(A), `.k,n/ is the proportionof the
number of information bits L to the total numberof bits M, which
discards bits used for CP and coding oneach subcarrier, because the
coding can be different in eachsubcarrier; #.k,n/ is the
instantaneous SINR for the kth useron the nth subcarrier; r.k,n/ is
the fixed rate that can beprovided to the kth user on the nth
subcarrier in bits persecond; p.#/ is the necessary transmission
power in orderthe link on the nth subcarrier to achieve a given
SINR # , inWatts; % is the power amplifier inefficiency and pc.k/
refersto the circuit consumption in Watts.
The SINR for the kth user on the nth subcarrier can becalculated
as
#.k,n/ Dp.k,n/jh.k,n/j2Now C I.n/
(3)
where jh.k,n/j2 is the channel gain for the kth user on thenth
subcarrier, which includes the fast fading and path-loss effects; w
is the subcarrier bandwidth, in Hertz; No isthe power spectral
density of the additive Gaussian whitenoise, in Watts per Hertz and
I.n/ is the interference fromother users on the nth subcarrier,
which can be origi-nated by imperfect frequency synchronism in the
detector,subcarrier sharing or multicell interference.
The efficiency function is used to discard receptionerrors,
because the EE numerator refers to goodput. Ingeneral, this
function approximates the package successrate [30], because using
the exact formulation implies thetrivial solution p.#/ D 0 [31]
when the circuit power isnot taken into account. As f .#/ is a
cumulative densityfunction (CDF), the two main constraints are
f .#/ D#
0, # < 01, # ! 1 (4)
To avoid the trivial solution p.#/ D 0, it is definedthat f .0/
D 0. The parameters of f .#/ must reflectthe system model in order
to obtain suitable results. Forinstance, when considering low-order
phase-modulation(binary phase shift keying, quadrature phase shift
keying)and additive white Gaussian noise, the approximationf .#/ D
.1 $ e!! /M is a well-known choice [31, 32].
The second approach is to consider the data rate as afunction of
the achieved SINR, including or not the effi-ciency function in the
formulation. In this case, the EEfunction " is generally given
by
" D
KPkD1
NPnD1
`.k,n/r$#.k,n/
%
KPkD1
NPnD1
%p.#.k,n// CKP
kD1pc.k/
!bits
joule
"(5)
where f .#.k,n// D 1 is omitted and r$#.k,n/
%is defined in
terms of the Shannon capacity equation [33]:
r.#.k,n// D w log2.1 C #.k,n// bits/s! (6)
As the Shannon capacity is an upper bound of the
achievedcapacity, in general, an SINR gap {.k/ is considered
toaccount for this limitation [34], resulting that the data ratecan
be rewritten as
r.#.k,n// D w log2.1 C #.k,n/{.k// bits/s! (7)
with
{.k/ D$1.5
ln .5BERk/, 0 < {.k/ 6 1 (8)
where BERk is the maximum tolerable bit error rate for thekth
user.
The circuit power pc can be modelled by a static compo-nent,
which accounts for the power consumed even whenthe equipment is not
transmitting, and a dynamic part,which depends on the current data
rate, as discussed in [35]and [36]. In general, only the fixed
amount of power spentindependently of any transmission has been
consideredin simple power consumption models. Indeed, consider-ing
the circuit power consumption in the EE maximisationcontext tends
to make the system to transmit at higherdata rates, in order to
dilute this fixed power consumptioneffect. Parameters as % and pc
are system dependent andcan be obtained in standards or
approximated given certainspecifications, such as cell size,
deployment scenario andfunctionalities, as discussed in [36].
It is worth noting the difference between the powerminimisation
and EE maximisation problems. The powerminimisation metric focuses
on minimising the allocatedpower in order to achieve a given
minimum data rate,while the EE problem focuses on determining the
allocatedpower that results in the highest ratio between
transmitteddata and consumed energy. When the problem has no
min-imum rate constraints, it is possible that certain users
orsubcarriers have been put in outage because the instanta-neous
channel conditions are not good enough in a specifictime slot. Even
for the rate constrained problem, if a userhas a good channel
quality, it is possible that its data rateis much higher than the
minimum rate criterion, resultingthat the optimum power allocation
for the EE criterion isnot necessarily the minimum consumption
obtained fromthe power minimisation problem. Another example
comesfrom the increased circuit power situation: from the
per-spective of the power minimisation problem, the circuitpower
does not affect the allocated transmission power,while under the EE
maximisation, perspective increasingcircuit power increases the
allocated data rate and, con-sequently, the allocated transmission
power in order todissipate the constant term.
The earlier works in EE focused in maximising theEE without
taking into account quality of service (QoS)constraints [3032],
such as data rate and delay. As
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QoS is fundamental in modern cellular standards, recentworks
include such metrics as constraints, investigatingthe impact of
them and proposing techniques to opti-mise EE, considering QoS
aggregation and QoS overtime, that is, maintaining QoS over time
slots and notnecessarily instantaneous QoS. The impact of using
EEmetrics is also analysed in terms of trade-offs
betweenwell-established metrics, such as spectral and EE
(EE-SE)trade-off [3739], operational/deployment cost,
allocatedbandwidth [1] and delay constraint [40].
2.4. Notation
Tables I and II present the terminology used in this surveyfor
the acronyms and symbols, respectively.
3. EE IN OFDM/OFDMA
As OFDMA is the main MA technique for 4G cellularsystems and EE
is becoming an important system evalu-ation criterion, there are
several works in literature con-sidering EE maximisation in OFDMA.
The works mainlyfocus on allocating subcarriers and transmission
power toobtain higher EE, using frequency, multi-user and/or
timediversities in the algorithms, which is in general named
scheduling algorithm. As the power/subcarrier (or
evensubchannel) allocation problem is non-polynomial-hard[41, 42],
in general, suboptimal strategies have been usu-ally proposed. Some
insights about resource allocation inOFDMA networks can be found in
[43], where a survey onuplink resource allocation for OFDMA systems
is carriedout. Despite the fact that EE is not taken into account,
someof the conclusions can be used to plan the EE resource
allo-cation framework. Examples of that include the impact ofbuffer
model, instantaneous or ergodic QoS metrics, howto define system
data rate (if continuous or given by theAMC), as well as individual
subcarrier allocation or con-sidering a group of subcarriers or
even the resource blocks(RBs), which are portions of subcarriers
and time.
As an example of suboptimal approaches, the authorsin [42]
describe the optimal RB/power allocation problemfor the uplink of a
single-cell OFDMA system and findthat the complexity is about O
$KNKRB
%, where NRB is the
number of resource blocks per allocation interval. As
thiscomplexity is prohibitive for commercial implementations,the
idea behind the paper is to develop iterative subopti-mal
algorithms, which allocate one RB per time, repeatingthe process
until there are no RBs and available users toallocate to them. Two
algorithms are developed to iter-ate over the available RBs, one
considering a determinateRB order and the other evaluating what is
the best RB
Table I. Table of acronyms.
Acronym Description Acronym Description
AF Amplify and forward MAC Media access controlAMC Adaptive
modulation and coding MAI Multiple access interferenceARQ Automatic
repeat request MCS Modulation and coding schemeBER Bit error rate
MIMO Multiple-input multiple-outputBS Base station M-QAM M-symbol
quadrature amplitude modulationBPSK Binary phase shift keying MRC
Maximal-ratio combiningCAPEX Capital expenditure MS Mobile
stationCDF Cumulative density function NP Non-polynomialCDMA Code
division MA OFDM Orthogonal frequency division multiplexingCF
Compress and forward OFDMA Orthogonal frequency division MACoMP
Coordinated multipoint OPEX Operational expenditureCP Cyclic prefix
PAPR Peak-to-average power ratioCSI Channel state information PSR
Package success rateDF Decode and forward QoS Quality of serviceDFT
Discrete fourier transform QPSK Quadrature phase shift
keyingDS-CDMA Direct-sequence CDMA RB Resource blockEE Energy
Efficiency RF Radio frequencyFDMA Frequency division MA RO Relay
orderingGSM Global system for mobile communications RS Relay
stationHARQ Hybrid ARQ SE Spectral efficiencyICI Inter-carrier
interference SER Symbol error rateICT Information and
communications technology SISO Single-input single-outputIDFT
Inverse DFT SF Shorten and forwardIRI Inter-relay interference SG
Stochastic geometryISD Inter-site distance SINR
Signal-to-interference plus noise ratioISI Inter-symbol
interference SNR Signal-to-noise ratioLTE(-A) Long term evolution
(-advanced) TDMA Time division MAMA Multiple access WiMAX Worldwide
interoperability for microwave access
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Table II. Table of symbols.
Symbol Description Symbol Description
Factor of relay placement adjust O../ Asymptotic complexity
order! SINR or SNR, depending on definition P Total power
consumption!TH Minimum ! to cooperate p Allocated transmission
power" Energy-efficiency utility function p.!/ Power consumption to
achieve !% Power amplifier inefficiency pc Circuit powerd Distance
between two nodes Pmax Maximum power allowed for a given userf.!/
Efficiency function R Cell radiusG Effective throughput (goodput) r
Data rateh Channel impulse response vector Ts,i Time of each symbol
Xihi ith channel impulse response Ts Time to transmit XK Number of
users Td Channel delay spreadL Number of information bits per
packet v Length, in samples, of the channel delay spreadLo
Path-loss constant W Available bandwidthM Number of bits per packet
X Set of symbols to be transmittedN Number of subcarriers x Signal
to be transmitted in time domainnpl Path-loss exponent Xi ith
individual symbol to be transmittedNg Size of the cyclic prefix Y
Signal received in frequency domainNRB Number of resource blocks y
Signal received in time domainNs Number of subchannels
to be allocated in the current iteration. Numerical resultsshow
that the proposed algorithms can provide a subopti-mal EE with
lower complexity, but a gap higher than 10%is obtained between the
EE optimal solution and the pro-posed algorithms when the number of
users and subcarriersare increased, mainly for the second
parameter.
In [5], the authors formulated the EE maximisationproblem for
single-cell OFDMA systems in both uplinkand downlink, considering
as QoS metrics a minimumindividual or total rate criterion,
respectively. In the down-link description, weights are used in
data rate to providefairness/priority, while a max min optimisation
criterion inthe uplink case has been considered in order to
optimisethe lowest individual EE. The EE maximisation in down-link
is modified to an equivalent max min problem, whichis similar to
the uplink model, and suboptimal algorithmsare presented. For both
modes, the algorithms have twophases: first, they virtually
allocate the worst subcarrier toeach user, that is, this process is
considered as virtual allo-cation because the worst subcarrier is
not really allocatedto the corresponding user, but only used for
the urgencymeasurement. In fact, more than one user can be
virtuallyallocated to the same subcarrier, also, this subcarrier
canbe allocated for a user that has not been considered at
thebeginning of the algorithm and then iteratively choose theuser
with the lowest EE and allocate the best subcarrier forthis user,
updating the achieved EE. The results obtainedwith the suboptimal
approach are close to that obtainedwith the optimal solution, which
has been achieved by test-ing all possible configurations of
subcarriers and using awater-filling algorithm to allocate power
for each config-uration, where the optimal water level for EE is
obtainedwith a bisection method.
Maintaining the single-cell scenario and considering
thedownlink, the authors in [44] describe an alternative way
to increase EE. Including the circuit power term from MSsin
receiving mode on the EE formulation, Equation (1),the problem now
consists in minimising the time that theMSs are in active mode, so
that the transmissions for eachuser is concentrated in few time
slots and the power spentin receiving mode is saved. After
time-slot allocation, apower control algorithm allocates the
necessary power toeach user, which can be changed to consider other
metricswithout affecting the first algorithm, as pointed out by
theauthors. So, it is possible to adapt an algorithm such as theone
in [5] to further improve EE.
In [41], it is considered a multicell downlink OFDMAscenario
with AMC, where the allocated subcarriers areswapped in an
intermediate step in order to guarantee QoSto more users, and then
the power allocation is rerun,verifying if it is useful to change
the modulation andcoding scheme between two subcarriers allocated
to thesame user, in order to reduce the consumed power
and,consequently, the generated interference. Reducing
theinterference, other users can reduce transmission powerover
those subcarriers, which can lead to an overallpower reduction,
called as virtuous loop. The algorithmpresents significant gains in
terms of spectral and energyefficiencies regarding conventional
approaches, such asround-robin scheduling.
Maintaining the multicell scenario, the authors in [45]also
consider the problem of subcarrier and power alloca-tion for
maximising EE but with the N subcarriers groupedinto Ns subchannels
and deploying pricing strategies. Aspointed out in [46], pricing
mechanisms are an effectiveway to reduce transmission power and
therefore multicellinterference, resulting in higher EE. The
subchannel/powerallocation is split in two steps: in the first one,
equalpower is considered, and each subchannel is allocated tothe
user with highest SINR. To avoid underserved users
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and improve fairness, at the final of this step, an adjust-ment
is made to distribute subchannels from users with twoor more
subchannels to users with any assigned subchan-nel. The second step
consists in allocation of power to theassigned subchannels,
considering the bits per joule metricwith pricing coefficient.
The joule-per-bit metric is used in [4], where a single-cell
downlink OFDMA system case is investigated. As theauthors discuss,
referencing [47], the bit-per-joule metricpresents lack of
linearity between the consumed energyand the transmitted power,
which can lead to incorrectconclusions; in spite of this, the
bit-per-joule metric iswidely adopted. The problem consists in
allocating sub-carriers and bits (consequently power) to each
subcarrierin order to provide a minimal SE to the system and
mini-mal data rate for each user, considered as the QoS metrics.The
problem is formulated using a set of modulations, thatis, discrete
data rate, and the fractional problem devel-oped is solved using
Dinkelbachs parametric approach, inan iterative way. The
interesting result presented is thatjoule-per-bit decreases when
system loading increases, thatis, the system becomes more efficient
when system load-ing increases. This can be explained as follows:
(i) withmore users, higher data rate is necessary, which reduces
thenegative impact of circuit power consumption at the BS;(ii) a
higher multi-user diversity can be achieved with moreusers; and
(iii) the low number of users considered initially.The EE-SE
trade-off is investigated by increasing the min-imum data rate per
user and, as a consequence, the overallSE; numerical results show
that increasing the minimumdata rate/SE requirements, the EE is
reduced.
All the aforementioned works consider an OFDM/OFDMA system where
the users do not share the samesubcarrier/subchannel at the same
cell and time. In order toinvestigate if that is the optimum
scenario for EE maximi-sation, in [48], it is considered the
downlink of a single-cellsingle-input single-output (SISO) OFDM
system wherethe users are able to share the subcarriers,
introducingMA interference. Analysing the proposed problem,
theauthors conclude that even with the possibility of subcar-rier
sharing, the optimum solution is that only one useruses each
subcarrier at a given time, which corresponds tothe OFDMA approach.
With this information, the problemis simplified to the OFDMA case,
and numerical resultsare obtained by simulation, without any QoS
guarantee.It is also presented a simplification to obtain the
optimalpower/subcarrier allocation, using bisection method overthe
transmission power to solve the optimisation problem.
There are also other techniques that could be deployedwith OFDMA
to further improve EE. One of them is thecoordinated multipoint
(CoMP), which allows the BSs inneighbour cells to jointly define
which users each one willcover and also which subcarriers will be
allocated, aimingto improve coverage and reduce interference, while
pro-viding ways to reduce transmission power and improveEE. Another
common technique is MIMO, where the sta-tions are equipped with
multiple antennas, for transmission
and/or reception, in order to provide spatial diversity
and/ormultiplexing gains.
In the CoMP technique, BSs from neighbour cells areconnected to
a central unit, generally by high-capacitylinks, which processes
the information sent by these BSsin order to determine which
station, or stations, will beallocated to a given user and also the
subcarrier(s) wherethis transmission will occur. According to [8,
49], CoMPtechniques can be classified in two types:
(1) Joint processing: in this scheme, one user isselected to
receive/transmit in a given time/frequencyresource, and then a
group of BSs (joint transmis-sion) or only one (dynamic cell
selection) is selectedto operate with this user. When a group of
BSs isselected, it is possible to exploit diversity, whichcan
result in significant reliability gain or cover-age improvement to
cell-edge users, while selectingone BS at each transmission also
exploits macro-diversity, because it is possible to choose the
BSwith the best channel conditions; this is similar to
theopportunistic relaying technique described in [50].
(2) Coordinated scheduling/beamforming: the transmis-sions are
coordinated between the BSs in order toreduce the inter-cell
interference, with only one BStransmitting to each user. In this
way, there is no user-data exchange between the BSs, only the
channelinformation is transmitted to the central unit in orderto
decide the resource allocation. The cell-edge userscan receive less
interference and, as a consequence,improve performance.
These techniques are compared in terms of EE for anLTE-based
downlink scenario in [8], considering threewell-known schedulers:
maximum carrier-to-interferenceratio, round robin and proportional
fairness. In thedeployed scenario, it is demonstrated that the
dynamic cellsolution presents the highest EE for all the
consideredschedulers, followed by joint transmission and
coordi-nated scheduling/beamforming. In terms of the schedulers,the
maximum carrier-to-interference ratio scheduler resultsin the
highest EE for all the techniques, which can beexplained by the
better exploitation of multi-user diversity.
As discussed in [51], system capacity in CoMP sys-tems is
directly proportional to the backhaul link capacity,which implies
that the best performance is obtained withinfinite capacity
backhaul link to exchange the necessaryinformation about users,
including CSI and data to betransmitted. Obviously, the deployment
and energy costof such backhaul links, even if they are dedicated
to thisfunction, is prohibitive, so it is necessary to determine
theimpact of limited backhaul capacity. Thus, in [51], eachBS has a
limited backhaul link and needs to decide withwhich BSs are the
best to cooperate with in order to reduceinter-cell interference
and maximise capacity. By consid-ering power/subcarrier allocation,
zero-forcing precodercoefficients, fairness and backhaul
allocation, a heuristicalgorithm is developed, which first
allocates the backhaul
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link and then iterates over the user scheduling
consideringpower/precoder fixed and power/precoder optimisation
forfixed scheduling.
From the EE perspective, limited backhaul resourceallocation is
investigated in [52], considering multicelldownlink OFDMA and a
central unit that processes theinformation received from all BSs
and then communicatesto each one, exchanging the necessary data
through lim-ited backhaul channels. With this limitation, the
trade-offbetween EE, backhaul capacity and network capacity
areanalysed considering that, for each user, must be assured
aminimum data rate, and the backhaul link presents a max-imum data
rate constraint, while power, subcarriers (userselection) and
zero-force beamforming have been consid-ered as optimisation
parameters. The optimisation problemis solved in three steps, one
for each variable, performedin an iterative way. It is analysed the
EE behaviour underdifferent maximum transmission power, backhaul
capaci-ties and number of active users. Interestingly, it has
beenshown that EE is not directly proportional to backhaulcapacity,
because of the power consumption cost nec-essary to increase
backhaul capacity that overcomes thecapacity gain.
For MIMO systems, there are several considerationson
energy-efficient system design. For example, in [53],the authors
analyse the SNR gains obtained with multi-ple antennas in both
receiver and transmitter equipments,considering different cell
radius scenarios and number ofantennas. Numerical results show that
for an increasingnumber of antennas and same cell radius, the SNR
gainis substantially increased. However, because the
energy-efficient design must consider operational costs as,
forexample, circuit power and computational complexity,these
results require a more accurate analysis. One caseis analysed in
[54], considering MIMO deployment in apico-cell scenario. In this
case, the results demonstratedthat the power consumption is
increased for the same SNR,which results in lower EE. As multiple
antennas in mobiledevices can be hard or even impossible to
implement,considering multiple antennas only for the BS equipmentis
also an interesting scenario, as the case described in[55]. Indeed,
numerical results show that when the num-ber of antennas is
increased, the average EE for the MSsis improved, and a significant
gain is achieved when thenumber of MSs grows. Also, the jointly
power/subcarrieroptimisation procedure promotes an improvement in
theEE when compared with only the adoption of powerallocation
procedure.
An important consideration in MIMO systems is theimpact of
circuit power consumption, as discussed in [56].It is well known
that MIMO systems reduce the necessarypower to achieve a given bit
error rate (BER) requirementbecause of the diversity/array gain,
but the extra circuitcomponents necessary to operate a MIMO system
canreduce or even nullify the transmission power reductionbenefit.
Hence, for a fixed rate/modulation system, there isa breakpoint
distance for which a MIMO system outper-forms a SISO system. To
reduce the negative impact of the
circuit power consumption, the authors propose to optimisethe
modulation order based on the EE metric, enabling thesystem to
sleep and turn off the circuitry. This optimisationprocedure,
combined with MIMO availability, outperformsSISO systems in almost
any transmission distance, at thecost of increased instantaneous
transmission power.
Still considering MIMO systems, there is the possi-bility of
using a significantly large number of antennasat the BS, which has
been named large, dense or mas-sive MIMO. In this topology,
hundreds of antennas aredeployed only at the BS, while the MSs are
equipped withone or few antennas. As described in [57], deploying
amassive number of antennas at the BS makes the MS-BSchannels to
become pairwise orthogonal; as a result, MAconfigurations using all
the time-frequency resources at thesame time can be implemented
with low degradation whenan adequate receiver (uplink) or precoding
(downlink) isaggregated; besides, under massive antenna condition,
thesmall-scale fading can be averaged out. Based on
theseconsiderations and comparing linear receiving filters,
theauthors in [57] show that it is possible to achieve a highgain
in terms of energy and spectral efficiencies for themulti-user
case, mainly when an improved linear receiveris deployed as, for
example, the zero-forcing detector.The impact of the detector
choice on the EE-SE perfor-mance results maintain some similarity
with those obtainedfor interference-limited systems, such as CDMA
[30, 35,58]. When considering the low power regime (or low
SEregime), it is demonstrated that both EE and SE can bemaximised,
despite that this scenario is generally not ofgreat interest.
The EE formulation used in [57] only considers thetransmission
power consumption, discarding the effects ofthe power dissipated by
the RF/antenna circuits. Even ifthis fixed power is small, when
considering hundreds ofantennas, it is likely that the impact of
this term becomessignificant. In [59], the circuitry power is
considered in theEE formulation of a massive MIMO system. The
problemconsists of optimising the transmission power,
subcarrierallocation, number of active antennas and data rate
poli-cies for the downlink of a single-cell OFDMA system
withsubcarrier reuse. It is considered as constraint an
outageprobability limit in each subcarrier, which is incorporatedin
the data rate equation to simplify the solution. Byusing fractional
programming, Dinkelbachs method andLagrangian decomposition, it is
demonstrated that allocat-ing the maximum number of antennas does
not necessarilymaximise the EE, given the circuitry power
consumptioncost of adding an extra antenna.
Table III summarises representative works and resultsanalysed in
this section.
4. EE IN COOPERATIVE OFDMA
As already mentioned, cooperative communications haveseveral
benefits that can result in higher EE, not onlyin terms of power
consumption but also in deploymentcosts, because RSs have less
functionalities and processing
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Table III. Representative papers for EE in OFDM/OFDMA
non-cooperative systems.
Year Paper Contribution
2011 [5] Power/subcarrier allocation for single-cell
downlink/uplink case, considering EE fairness with minimum
rateconstraint. Suboptimal iterative solutions are presented for
both cases;
2011 [47] Framework for energy-efficiency communication systems,
with a realistic BS power model and also a trafficmodel that allows
to analyse the energy-efficiency algorithms in large-scale areas,
such as a country, which hasdifferent user densities and data
necessities;
2012 [41] Smart allocation algorithm, which makes a subcarrier
rearrangement between users to admit more users, andalso a
power/bit reallocation to reduce power consumption;
2012 [42] Suboptimal iterative algorithm that allocates the
subcarriers/power in a fixed or optimised order to the userthat
provides the higher EE gain in each iteration;
2012 [43] Survey on uplink resource allocation for OFDMA
networks, considering centralised/distributed scheduling,multicell
scenario and describing open trends;
2012 [44] The scheduler concentrates the MSs RBs in few time
slots, in order to make MSs sleep in some slots to savethe power
spent in receiving mode;
2012 [4] EE maximisation by allocating subchannels and bits to
each user with overall SE and individual data rateconstraints. The
EE-SE trade-off is investigated by increasing the rate/SE
constraints;
2012 [59] Analysis of very-large MIMO systems for EE
maximisation in downlink OFDMA, considering circuit
powerconsumption and optimising the number of active antennas;
2013 [48] Show that OFDMA has higher EE than OFDM systems for
downlink case, that is, sharing the subcarriers doesnot increase
EE, and a bisection method to solve subcarrier/power
allocation;
2013 [57] Analysis of very-large MIMO systems for EE and SE in
single-carrier systems with linear filter optimisation;
2013 [8] Analysis of CoMP techniques in terms of energy
efficiency, with downlink LTE-based scenario and
differentschedulers.
power. When considering the deployment of cooperativenetworks in
cellular scenarios, there are several aspects toconsider, for
example,
(1) RS placement, which includes the placement loca-tion and the
number of stations installed;
(2) cooperation protocol: regenerative or non-regenerative;
(3) inband or outband channel operation;(4) which relays
cooperate and how to assign them;
Besides these four basic aspects, there are others thatcan be
included, as frequency reuse patterns and CoMP,and the associated
optimisation variables, such as transmis-sion power, subcarrier
(from the OFDMA case) and timeallocation, now including the RS
nodes in the optimisa-tion problem. In this way, there are several
opportunitiesin the EE maximisation design for cellular
cooperativeOFDMA networks. In this section, we discuss the
fouraspects mentioned and then present salient techniques thatcan
be combined with cooperative networks to providehigher
energy-efficient systems.
4.1. Retransmission protocols andoperation modes
Analysing first the retransmission protocols, we point outtwo
possibilities: non-regenerative and regenerative pro-tocols. If we
consider only the commercial aspect, the
LTE-A standards only consider the regenerative protocolsfor
implementation, as some features such as the AMCis only possible at
the relays when they are able to fullydecode the received signal
and then adapt the modula-tion and coding scheme to the conditions
of the nexthop. Because the proposal of this survey is the
literatureoverview, we also consider the non-regenerative
protocolsas a possible choice.
The two most common protocols are the AF and DF,respectively, a
non-regenerative and a regenerative proto-col. The basic approach
for both protocols is to process thereceived signal and then
retransmitting the information tothe destination node. As pointed
out in several papers, thisapproach can result in poor
retransmitted information ifthe received signal is highly
corrupted, which is in generalcaused by poor SINR. If we consider
AF, under low SINR,the amplified signal consists mainly of
interference andnoise, while for DF, BER becomes significantly
high, andthe retransmitted data do not correspond to the
informationsent by source. One possible way to overcome this
problemis to adopt a threshold to decide if the RS is able to
coop-erate. In this case, the QoS metric that the RS must obey
ismapped into SINR threshold #TH, and if the achieved SINRis
greater than #TH, the associate RS is able to cooperate;as a
result, relaying mode becomes advantageous.
When choosing the relaying protocol, we also define ifthe relay
operation is made in time or frequency domain[60]. For the
non-regenerative protocols, the operationcan be made in both
domains, amplifying the received
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signal in the time domain or taking the DFT to access
thereceived signal in each subcarrier/subchannel and adap-tively
amplifying each one, retransmitting the signal afterthe IDFT
computation. From the EE perspective, it isnecessary to investigate
if the obtained gain can compen-sate the complexity/energy cost
associated to both DFToperations. When considering the regenerative
protocols,the only possibility is the frequency domain
operation,because the information is modulated in frequency
domain.
There are few papers comparing regenerative and non-regenerative
protocols for OFDMA from the EE perspec-tive. Looking at the
simplest possible case, as described inFigure 2, there are some
results. For example, consideringthe existence or absence of return
channel, in [61], the EEof AF and selective DF, which is a protocol
that only relayswhen the MS-RS link succeeds, is compared. In the
pro-posed scenario, there is not a best protocol for all cases,and
this choice depends on certain factors, as equipmentdistances and
network topology.
The authors in [62] consider a similar case but usingonly AF and
selective DF and a circuit power consumptionmodel that reproduces
the extra cost of the DF operation.It is proposed the optimisation
of the modulation in orderto minimise the energy-per-bit metric in
a three-nodesystem, for different node distances. Under this
model,the selective DF outperforms AF protocol, which is
theopposite result obtained of the first case. This fact showsthat
both protocols and their variants must be further inves-tigated in
the OFDMA cellular case in order to provideaccurate results,
because the topology is not restricted tothe three-node case.
In addition to classical AF and DF, there are other relay-ing
protocols that can be used. For example, an extension tothe AF
protocol called shorten-and-forward (SF) protocolhas been proposed
in [63]. The main concern in SF pro-tocol is that when the signal
is transmitted over two hopsand no detection is performed by the
RS, the CP can notbe enough to overcome the delay spread inserted
by bothhops. In this way, finite response filters are used at the
RSto reduce the increased signal length. The SF approach canresult
in EE gains because it is possible to use a shorten CP,which
reduces the throughput penalty in OFDMA, and canalso be a
determinant for multi-hop AF systems, to avoidISI for relayed
users.
When considering the separation of backhaul and accesslinks,
there are also two modes: inband or outband. In theinband method,
the time/frequency resources are dividedby these two links in the
time domain, resulting that theexisting infrastructure can be
maintained. The main draw-backs are synchronisation issues and
possible interferenceif this task was not well solved. On the other
hand, the out-band mode deploys a complete separation of the links
as,
The return channel is used to indicate or not the necessity of
RScooperationIn general, the failure or success of a given link is
observed in termsof the received SINR, for a given threshold, which
results in the modeldescribed in the second paragraph of Section
4.1
for example, the use of a second carrier frequency for oneof the
links. In this case, the synchronisation problem isnot an issue,
because both links are separated, at the costof new equipments and,
in the case of an extra carrier fre-quency, the cost of this extra
frequency band. These twoschemes are depicted in Figure 6,
including a third modelthat is proposed in [64] and described in
the following.
In [64], the authors investigate the backhaul/accesslinks
separation considering capacity enhancement for adual-carrier OFDMA
system with DF relays. There arefour proposed carrier allocation
modes, two inband andtwo outband, and an interesting result is that
both schemesachieve almost the same statistical throughput (in
terms ofcumulative density function) and relative gain. This
resultcomes from the fact that the allocated resources in each
Figure 6. Schemes for access/backhaul links separation:(a)
inband, (b) outband and (c) mixed inband/outband proposed
in [64].
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case are almost the same: regarding the inband case, allcarriers
are allocated half of the total time, while in the out-band case,
only one carrier is available but is allocated allthe time. Despite
this equality, it is also pointed out thatsome factors can result
in capacity loss for the inband case,given by synchronisation,
backhaul/access switching andthe necessity of transmitting control
data from BS to RSusing resources that are reserved for user data.
A capacityloss of about 8 % 12% is expected. In order to enhanceEE,
it is also investigated the resource sharing optimisa-tion, given
by dynamically sharing the resources for thebackhaul link.
Numerical results show the effectiveness ofthese optimisations,
mainly for the worst users.
In [65], the authors consider the downlink of a multicellOFDMA
system, in which each cell is aided by some RSs.The proposed relay
protocol separates the backhaul andaccess links in time, splitting
equally the access time, andthe two-hop and one-hop communication
in frequency, byallocating orthogonal subchannels to each mode. The
opti-misation problem considers the transmission mode (oneor two
hops), subchannel allocation and relay processingdesign, while the
BSs transmission power is consideredfixed. The proposed solution
consists in trying all the possi-ble modes and subchannel
allocations and then evaluatingthe relay processing design, which
has been shown noloose in optimality when compared to the optimal
solu-tion, which consists of trying all the combinations of
thesethree variables. Despite this simplification, the complexityis
still prohibitive; hence, these problems can be sequen-tially
solved in a single-cell way by a heuristic strategy. Itis shown
that the DF protocol results in higher power effi-ciency, measured
in bits per Watts, than the two protocolsbased on AF protocol with
multiple-relay or single-relayselection strategies.
Besides the pure inband/outband strategies, in [18]and [64], a
mixed inband/outband separation model isproposed. As the backhaul
link can become the system bot-tleneck, mainly when the number of
relays/relayed usersincrease, it is defined that the second carrier
is used onlyfor backhaul and direct links, while the first carrier
is usedby these two links and the access link, using time divi-sion
between backhaul and access links. This alternativeis proposed to
increase the efficiency of link usage, as inpure outband systems,
if one link is underloaded, the spec-tral resource is wasted, and
to prevent backhaul bottleneck,providing extra bandwidth. As
pointed out in [64], thismethod outperforms both inband and outband
cases.
Another possibility is the deployment of the full-duplexinband
relaying, as pointed out in Section 2.2. The full-duplex inband
relaying with interference cancellation isconsidered in [66], where
full-duplex and half-duplex AFand DF relaying can be dynamically
selected in orderto provide a higher average-weighted system
throughput.When the self-interference residual term is low to
mod-erate, the full-duplex relaying becomes the most
selectedstrategy, because it can reduce the number of time
slotsnecessary for cooperation: considering that one packetneeds
one time slot to be transmitted, transmitting Np pack-ets requires
2Np slots in half-duplex and only Np C 1 slots
in full duplex. When the residual interference becomesmore
significant, the numerical results in [66] show thatthe DF
half-duplex protocol is more selected that the AFfull-duplex, due
to the fact that AF also amplifies the resid-ual interference and
noise. In [67], this the same schemeis proposed for MIMO-OFDMA
systems, and it is shownthat the full-duplex mode is preferred when
the numberof antennas is higher and the residual interference is
lowor medium, given its higher SE, while higher interferencereduces
the gain obtained with full-duplex, and then thehalf-duplex method
is the most likely to be selected. Inboth cases, the AF protocol is
marginally adopted, giventhe noise/interference amplification.
The full-duplex inband relaying is also investigated in[68],
considering the AF protocol. In the proposed sys-tem model, it is
considered that the destination is indoorand the RS has an outdoor
antenna to communicate withthe source and an indoor antenna to
communicate with thedestination. A direct link between source and
destinationis also available, but it is not considered in the
numericalevaluation. In addition to the antenna isolation and
interfer-ence cancellation, the authors also discuss the impact of
AFgain optimisation to reduce the residual interference andimprove
SINR, showing through numerical results that itis possible to
determine an amplifying gain that maximisesthe received SINR mainly
when the residual interferencechannel gain becomes higher. In [69],
the authors analysefull-duplex and half-duplex relaying for AF and
DF proto-cols and, based on the SINR of the links and the
residualinterference, determine the boundaries where each
relayingmethod or the direct transmission is more efficient in
termsof system capacity. The analysed system topology is ableto
switch between direct transmission, half-duplex relayingand
full-duplex relaying modes, but the switching betweenAF and DF
protocols is not available.
Energy efficiency for direct, half-duplex inband relay-ing and
two-way relaying transmissions in single-carriersystems has been
compared in [70]. The objective in theproposed analysis is to
determine the minimum power toachieve a given data rate between two
nodes in both direc-tions, considering asymmetric traffic in each
direction andAF protocol. Considering the cost of the interference
can-cellation deployed at the receivers for two-way mode, aswell as
the cost of detection, it is shown that none of thetransmission
modes have higher EE in all scenarios, andthe best mode depends on
the path-loss exponents, dis-tance between the nodes and the RS,
necessary data rateand the fixed power costs. An interesting
conclusion is thatwith higher path-loss exponent and minimum data
rate, thetwo-way relaying tends to result in higher EE than
directtransmission, which is a result that cannot be achieved
withhalf-duplex inband relaying, because the extra
time-slotrequirement imposes a double data rate [35]. In
metropoli-tan 4G scenarios, the combination of high data rates
andsevere attenuation can result in an interesting scenario
fordeploying two-way relaying.
Under multicarrier scenario, Sun et al. [29] discussesan
energy-efficient approach for OFDM systems, where a
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
hybrid method combining half-duplex inband and two-wayrelaying
modes has been proposed. Considering delay-sensitive users, it is
specified the amount of bits that mustbe transmitted at the two
time slots, and then the prob-lem is modified to a power
minimisation problem. In thishybrid model, the two-way and
half-duplex relaying modesdeploy disjoint subsets of subcarriers,
because one of theequipments does not need to transmit in that
subcarriers,that is, the number of used time slots in this hybrid
mode isalways equal to two. The optimisation problem considersthat
each equipment has a circuit power and a subcarrierprocessing
power, where the last one depends on the num-ber of active
subcarriers. Hence, there exists a trade-offbetween transmission
power minimisation and total powerminimisation, which leads to a
reduction in the numberof allocated subcarriers. The numerical
results show that aconsiderable gain can be achieved in terms of EE
with thishybrid relaying method, and, again, that the EE for
two-way relaying is higher than the half-duplex inband relayingin
the high SE region.
Basically, the only decision to make in outband mode iswhich
link to allocate in each available carrier. The com-mon approach is
to define that one carrier supports thedirect/access links, and the
second is used only for thebackhaul link, as they can limit system
performance. Onthe other hand, the inband mode has some parameters
tochoose as, for example, the backhaul/access links propor-tion, as
discussed in [71] and [72]. In [72], it is analysed thedynamic time
allocation for backhaul and access links andresource reuse for the
downlink of a single-cell OFDMAmacro-cell aided by RSs aiming to
maximise capacityunder fairness constraint. In the proposed method,
MSsfrom different RSs are able to share the subchannels, thatis,
spatial reuse of resources is permitted only in the accesslink.
Numerical results show the achievable gains with thecombination of
these techniques, which can be maximisedif relay placement
optimisation is also considered. In [73],the time sharing is also
mentioned, but no numerical resultsare provided. When considering
the outband mode with anexclusive carrier to the backhaul link, one
possible problemarises when a few number of users deploys RSs,
resultingin resource wasting. In order to avoid this situation,
somedirect users can be allocated to the backhaul link if it
isunderloaded [64].
In [71], relaying techniques based in bandwidth sharingand time
sharing are discussed, initially assuming caseswith only one relay,
and then a problem with multiplerelays is described, but only the
single-relay case is con-sidered. A salient result is that the
time-sharing system canbe equivalent to the bandwidth sharing if
average powermetrics are considered, while if peak power
constraintsare considered, the performance can be worse in terms
ofpower minimisation. All the proposed problems includeequipment
prioritisation, which turns possible to increasethe power cost of
specific equipments as, for example, theMSs, which have limited
batteries. The case of multiplerelays is simulated, and a flexible
bandwidth sharing model
is proposed to allocate resources for BS-RS links, which isshown
to reduce power consumption over fixed strategies.
The EE achieved with the cooperation schemes ofFigure 2(b) and
(c), named, two-hop half-duplex andmulticast cooperative scheme,
respectively, has been inves-tigated in [74]. Considering the
downlink of an OFDMAsystem and optimised resource sharing between
theaccess/backhaul links, the numerical results show that
thetwo-hop protocol results in higher EE, while the
multicaststrategy maximises the average data rate. Another
resultcomes from [75], in which the strategies from Figure 2(a)and
(b) are compared in terms of EE maximisation; numer-ical results
corroborate the superiority of the later schemein terms of EE.
Table IV summarises representative works and resultsanalysed in
this section.
4.2. RS deployment
The distance from the RSs to the BS, the number of RSsand even
the distribution of the RSs in the cell couldresult in different EE
gains. When the RSs are close tothe BS, more users are assisted by
relays, but the back-haul link could be saturated, and when the RSs
are nextto cell edge, few users can exploit the benefit of
relaying.With few RSs, the MS-RS distance can be higher,
whichresults in higher power consumption to compensate pathloss.
Increasing this number results in higher probability offinding a
better RS, but again, the backhaul link may limitthe EE gain.
Finally, if the distribution of RSs is consideredfor practical
scenarios, taking into account, for instance,identifiable
geographical coverage holes and zones withincreased number of
users, tends to obtain increased EEthan considering stochastic
placement approach. The prin-cipal models for the RS deployment
problem are depictedin Figure 7.
The relay deployment problem can also consider theeconomical
cost of the installation, as described in [76].Therein, the cost
factor depends on the deployment den-sity of RSs and BS stations,
considering system capacitynormalised by cell area and deployment
of type-I and type-II relays. In order to solve the cost
minimisation problem,all the combinations of type-I and type-II RS
and BSdensities that result in the same normalised capacity
arefound, and then the point of tangency to linear cost line,which
represents equal cost for BS-RS density, is takenas minimum
deployment cost point. The RS deploymentis compared with micro-BS
deployment, and it is shownthat more RSs are necessary to obtain
the same perfor-mance as the micro-BS case, but the costs are lower
forRS deployment, implying that RSs are the best choice.Extending
this work and only considering type-II relays,the authors in [77]
introduce user experience satisfactionmetrics to the problem,
indicating that not necessarily thebest-cost deployment results in
best experience satisfac-tion for the mobile users. In [78], the
authors compare thedeployment of RSs with femtocells deployment,
and it isshown that topology with RSs can achieve lower power
Trans. Emerging Tel. Tech. (2014) 2014 John Wiley & Sons,
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
Table IV. Representative papers for retransmission protocols and
operation modes.
Year Paper Contribution
2009 [68] Analysis of full-duplex relaying for AF-based systems,
considering indoor-outdoor communication;
2010 [62] Energy-per-bit minimisation by optimising the
modulation order for AF and selective DF deploying ornot MRC for
both protocols;
2011 [64] Analysis of inband and outband modes with different
combinations of carrier usage, resource sharingoptimisation and
proposition of a mixed inband/outband mode;
2011 [74] Demonstrate that the two-hop model (Figure 2(b))
results in higher EE than the multicast two-hopmodel (Figure 2(c)),
while for capacity, the opposite occurs;
2011 [66] Analysis of half-duplex and full-duplex relaying for
AF and DF protocols, with an algorithm that switchesbetween the
duplexing modes and retransmission protocols;
2011 [69] Analysis of half-duplex and full-duplex relaying for
AF and DF protocols, determining boundaries toswitch between
direct, half-duplex and full-duplex for each relaying protocol;
2011 [70] Comparison of the achievable EE for non-cooperative,
half-duplex inband relaying and two-way relayingtransmission modes,
with or without detection/interference cancellation energetic
costs;
2012 [61] EE for AF and selective DF with network coding and
with/without return channel and fairness, and theEE contours, which
are the data rates that results in the same EE;
2012 [63] Application of shorten-and-forward to reduce ISI due
to the extra delay spread caused by the two-hopcommunication;
2012 [65] Optimisation of subchannel allocation, transmission
mode and relay processing to increase powerefficiency, comparing AF
and DF protocols for single-relay or multirelay selection;
2012 [71] Bandwidth/time-sharing scheme for type-I relays in
LTE-A systems for power minimisation, consider-ing equipment
prioritisation and data rate requirements;
2012 [72] Dynamic time allocation for backhaul and access links
and resource reuse in the access link fordownlink aiming to
maximise capacity under fairness constraint;
2013 [29] Analysis of hybrid half-duplex inband and two-way
relaying for OFDM systems.
consumption than femtocell-based deployment whilereducing
operational and capital expenditure when com-pared with macro-BS
only scenarios.
The simplest approach to a relay-based network is toconsider
that the RS is between the BS and all mobile users,so that all
users are relayed [79]. For the cellular networkcase, this is not a
suitable model, because we can haveusers closer to the BS, which
can communicate directlywith it. A more sophisticated approach to
the relay place-ment problem is to define that the RSs are placed
in acircumference of radius R centred at the BS, where R isthe cell
radius and 0 < < 1, where the number of RSsand the parameter
are modified aiming to optimise EE.This method is well established
in the literature and haseven been used for second-generation
systems, as CDMA[80]. In [35], the relay placement optimisation is
inves-tigated in the uplink of direct-sequence CDMA systems,with
non-regenerative outband RSs and outage probabil-ity constraint. It
is shown that even for the most inefficientdetector, the RSs bring
significant gains for EE and outageprobability reduction, which
combined to filter optimisa-tion at least double the EE normalised
by bandwidth, giventhe extra carrier for outband relaying.
Furthermore, consid-ering the OFDM/OFDMA case, this BS-centred
approachwithout placement optimisation can be seen in [65] and
[81], while in [71] and [72]||, the placement distance
and/ornumber of relays are analysed aiming to obtain powersaving
and capacity gain, respectively.
The benefits of a well-planed RSs deployment can beconfirmed
analysing the results from [82], at least interms of system
capacity. The authors consider a multi-cell scenario, where only in
the central cell, the relayscan be placed in candidate locations in
a ring area cen-tred at the BS, while in the other cells, the RSs
arelocated using uniform distribution over a circumferencealso
centred at the BS. For comparison purpose, simula-tion results
include a second approach, where all cells usethe BS-centred
uniform distribution. In this context, twooptimisation problems are
proposed: maximise overall sys-tem capacity or maximise the
capacity for cell-edge users,which are defined as the users that
cannot achieve a targetSINR. Solved using nonlinear programming, it
is shown bynumerical results that the optimised deployment of
relaysreduce the probability of low data rates over the
uniformplacement and non-cooperative scenario.
In [83], an iterative RS placement algorithm for multicellWiMAX
systems is proposed, in which the RS that pro-vides the higher
capacity gain at each iteration is selected.
||In this work, the relay placement is carried out in a ring
area and notin an circumference, but the method is almost the
same.
Trans. Emerging Tel. Tech. (2014) 2014 John Wiley & Sons,
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
Figure 7. Relay deployment strategies: (a) RSs uniformly
dis-tributed over a circumference of radius R centred at BS,(b) RSs
placed inside a ring area delimited by R and R and(c) stochastic
placement. NRs D 6 in (a) and (b) and NRs D 8
in (c).
Instead of choosing a placement radius, the RSs can beplaced in
any candidate position associated to an annularsection of each
cell, which begins at the limit of BS cov-erage area, which
corresponds to the area where the BS isable to provide sufficient
quality for the MSs. Numericalresults confirm the throughput gain
when deploying thisiterative RS placement algorithm in the
multicell system.
When considering coverage extension, the authors in[84] develop
a method to determine the non-transparentRS placement radius in
order to achieve a higher cover-age radius. Defining coverage as
the area where a specificSINR detection threshold is maintained,
the coverage ismaximised in such a way that both the BS-RS and
RS-MS links are able to achieve the SINR threshold, and the
number of RSs is determined in order to obtain non-overlapping
coverage between two RSs, without optimis-ing this variable, and
they are placed in a circumferencecentred at the BS. This approach
is evaluated numericallyfor both single-cell and multicell cases,
where the first oneis optimally solved and the second one is solved
by aniterative suboptimal algorithm.
Instead of deploying RSs for each cell, in [85], theauthors
discuss a two-cell case and propose to place justonly one RS in
between the two cells. The whole idea con-sists in reducing the ICI
and the inter-relay interference,which results from the standard
cooperative approach byusing this unique relay for both cells. In
the first time slot,each BS transmits to the users, and the relay
overhears thistransmission from both cells. In the second time
slot, theRS chooses one of the received signals in each
subcarrierand then retransmits to all covered users. In this way,
eachrelayed user receives its own information or the informa-tion
of the other cell user. If it receives its own information,the user
can use combination techniques to obtain diversitygain; in the
other case, the relayed information can be usedto cancel the ICI,
also resulting in SINR gain.
Unlike the hypothetical models considered earlier, themodel
described in [73] considers the coverage map of onearea in London
and discusses RS deployment in order toprovide better coverage and
higher capacity and also com-pares the obtained results with the
deployment of micro-BSs. RS and micro-BS equipments can be
installed in anylocation of the studied region, and this decision
is madeby employing a metric defined by the authors that consid-ers
the outage probability, backhaul link quality, coverageand system
capacity, which can be weighted to providedifferent objectives. As
the micro-BSs have a dedicatedlink with the BS, the backhaul link
bottleneck does notaffect the result, and no access/backhaul
resource sharingis necessary, which results in higher coverage and
capac-ity gain when compared with RS deployment. Hence, onecan
identify a possible trade-off between cost efficiencyand
coverage/capacity enhancement when comparing [76]and [73].
A different metric from all the aforementioned citedworks is
known as stochastic geometry (SG). Used inseveral resource
allocation problems and networks per-formance analysis, the SG
approach is employed, forinstance, in the RS placement problem
[86]. As the place-ment problem is considered under a stochastic
perspective,the placement distance and geometry are also
stochastic,allowing us to analyse the effects of RS and BS
densi-ties on the systems EE. The stochastic approach does notseem
to reflect commercial deployment situations, but theauthors
remember that the existent deployments found inpractical scenarios
are highly non-regular, which resultsthat SG approach is an
adequate framework for cellularnetwork efficiency evaluation.
Another advantage of thesolution in [86] is that the EE is
determined by the expec-tation of the stochastic definition of the
problem, resultingin an analytical solution, at the cost of
considering fixedpower allocation.
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. R. Castro e Souza, J. R. D. A. Amazonas and T. Abro
Relevant works and results for relay deployment opti-misation
problem compiled in this section are listed inTable V.
4.3. Relay assignment