Table Of Content1
Energy Efficiency of Downlink Transmission
Strategies for Cloud Radio Access Networks
Binbin Dai, Student Member, IEEE and Wei Yu, Fellow, IEEE
Abstract—Thispaperstudiestheenergyefficiencyofthecloud in the fifth-generation (5G) wireless network needs to be
radio access network (C-RAN), specifically focusing on two fun- accompanied by a call for improvement of energy efficiency
damentalanddifferentdownlinktransmissionstrategies,namely
to the same extent.
the data-sharing strategy and the compression strategy. In the
Cloud radio access network (C-RAN) is an emerging net-
data-sharing strategy, the backhaul links connecting the central
6
processor(CP)andthebase-stations(BSs)areusedtocarryuser work architecture that shows significant promises in improv-
1
messages–eachuser’smessagesaresenttomultipleBSs;theBSs ing both the spectrum efficiency and the energy efficiency
0
2 locallyformthebeamformingvectorsthencooperativelytransmit of current wireless networks [2]. In C-RAN, the BSs are
the messages to the user. In the compression strategy, the user
connectedto a centralprocessor (CP) throughbackhaullinks.
n messages are precoded centrally at the CP, which forwards a
The benefits of the C-RAN architecture in energy saving are
a compressedversionoftheanalogbeamformedsignalstotheBSs
J for cooperative transmission. This paper compares the energy several-fold.First, underthe C-RAN architecture,most of the
7 efficiencies of the two strategies by formulating an optimization basebandsignalprocessingintraditionalBSs canbe migrated
problem of minimizing the total network power consumption to the cloud computing center so that the conventional high-
] subject to user target rate constraints, where the total network cost high-power BSs can be replaced by low-cost low-power
T power includesthe BS transmission power, BS activation power,
radio remote heads (RRHs). Second, the existence of CP
I and load-dependent backhaul power. To tackle the discrete
s. and nonconvex nature of the optimization problems, we utilize also allows for the joint precoding of user messages for
c the techniques of reweighted ℓ1 minimization and successive interference mitigation. With less interference generated, the
[ convex approximation to deviseprovably convergent algorithms. transmit power at the BSs can thereforebe reduced. Third, as
Our main finding is that both the optimized data-sharing and
2 onaverage(andespeciallyduringnon-peaktime)asignificant
compression strategies in C-RAN achieve much higher energy
v portion of network resources can be idle [3], the CP can
efficiency as compared to the non-optimized coordinated multi-
0 pointtransmission,buttheircomparative effectivenessinenergy perform joint resource allocation among the BSs to allocate
7
saving depends on the user target rate. At low user target resources on demand and put idle BSs into sleep mode for
0
rate, data-sharing consumes less total power than compression, energy saving [4].
1
however, as the user target rate increases, the backhaul power
0 The above-mentioned benefits of C-RAN in energy saving
consumption for data-sharing increases significantly leading to
. are concerned with the BS side. However, the additional
1 better energy efficiency of compression at the high user rate
0 regime. energy consumption due to the increased backhaul between
6 the CP and the BSs also needs to be taken into account
Index Terms—Cloud radio access network (C-RAN), data-
1 [5]. In this paper, we investigate the potential of C-RAN in
sharing strategy, compression strategy, energy efficiency, power
v: minimization, base-station activation, base-station clustering, improving energy efficiency of the communication aspect of
i beamforming, backhaul power. the network by considering the energy consumption due to
X
BS activation, transmission, and backhaul provisioning. The
r
backhaul energy consumption depends on the backhaul rate,
a I. INTRODUCTION
which further depends on the interface between the CP and
ULTRA-DENSE deployment of small cells and cooper-
the BSs. In this paper, we investigate two fundamental and
ative communications are recognized as two promising
different transmission strategies for the downlink C-RAN. In
technologiestomeettheeverincreasingdemandofdatatraffic
the data-sharing strategy, the CP uses the backhaul links to
for future wireless networks [1]. However, both technologies
share user messages to a cluster of cooperating BSs. The
comeatthecostofincreaseinenergyconsumptionbecauseof
backhaul cost of the data-sharing strategy depends on the
theadditionalenergyneededtosupporttheincreasingnumber
number of BSs that the user messages need to be delivered
ofbase-station(BS)sitesandthesubstantiallyincreasedback-
to: larger cluster size leads to larger cooperative gain, but
haul between the BSs for cooperation. The excessive energy
also higher backhaul rate. In an alternative strategy called
consumption of wireless networks not only has an ecological
the compression strategy, the CP performs joint precoding
impactintermsofcarbonfootprintbutalsohasaneconomical
of the user messages centrally then forwards a compressed
impact on the operational cost to the mobile operators. Thus,
version of the precoded signals to the BSs. The backhaul
the compelling call for improvement of spectrum efficiency
cost of the compression strategy depends on the resolution
of the compressed signals: higher-resolution leads to better
Manuscript submitted onApril 15,2015; revised onSeptember 15, 2015;
accepted on December 11, 2015. This work was supported by Huawei beamformers, but also larger backhaul rate.
Technologies,Canada,andNaturalSciencesandEngineeringResearchCoun- This paper aims to quantify the energy saving of C-
cil (NSERC) of Canada. The authors are with The Edward S. Rogers Sr.
RAN while accounting for both the BS and the backhaul
Department of Electrical and Computer Engineering, University of Toronto,
Toronto,ONM5S3G4,Canada(e-mails:{bdai,weiyu}@comm.utoronto.ca). energy consumptions, and specifically to answer the question
2
of between the data-sharing strategy and the compression [17]–[19]. Specifically,[17] proposesa jointBS selection and
strategy, which one is more energy efficient? The answer beamforming design algorithm to minimize the total power
to this question is nontrivial as there are three factors that consumptioninthedownlink,while[18]generalizestoajoint
can lead to energy reduction: decrease in BS transmit power, downlink and uplink total power minimization problem. Both
turning-off of the BSs, and reduction in backhaul rate. These [17] and [18] take advantage of the fact that if a BS is not
threefactorsareinterrelated.Forexample,itmaybebeneficial selected to serve any user at the current time slot, it can be
to keep more BSs active and to allocate higher backhaul rate put into low-power sleep mode for energy saving purpose. In
in order to allow for better cooperation among the BSs so contrast, [19] assumes fixed BS association but exploits the
that more interference can be mitigated. This leads to less delay tolerance of the users to improve the energy efficiency
transmit power consumption, but it can also lead to higher inCoMPtransmission.Indelay-tolerantapplications,BSscan
BS and backhaul power consumption. This paper intends aggregatethe user messages and transmit them with high rate
to capture such interplay using an optimization framework. during a short time frame while remain idle for the rest of
Specifically, we propose a joint design of the BS transmit the time slots under power-saving sleep mode. Fast deacti-
power, BS activation and backhaul by minimizing network- vation/activation of hardware power-consuming components
wide power under given user rate constraints for both the achieve significant energy reductions [4], [20].
data-sharingstrategyandthecompressionstrategy.Theresult- In this paper, we adopt a similar energy saving perspective
ing optimization problems are nonconvex in nature and are as in [17] but consider in addition the compression strategy.
highly nontrivial to solve globally. This paper approximates Compressionstrategy differsfromdata-sharingstrategyin the
the problems using reweighted ℓ minimization technique [6] waythatthebackhaulisutilized.Weadoptthemodelproposed
1
and successive convex approximation technique, and devises in [21] to model the power consumption of backhaul links as
efficient algorithms with convergence guarantee. We identify a linear functionof backhaulrates. This is in contrastto [17],
operating regimes where one strategy is superior to the other, where the backhaulpower is modeled as a step function with
and show that overall optimized C-RAN transmission can only two levels of power consumption depending on whether
lead to more energy efficient network operation than the non- the backhaul link is active or not.
optimized coordinated multi-point (CoMP) transmission. In addition to the backhaul power, we also consider the
BS power consumption by adopting the model proposed in
[22], which approximates the power consumption of a BS
A. Related Work
as a piecewise linear function of transmit power. In such
The potential of C-RAN in improving the performance for model, BS sleep mode corresponds to a constant but lower
future wireless networks has attracted considerable attentions powerconsumptionwithzerotransmitpower.BSactivemode
recently.Intheuplink,[7]and[8]showthatwiththecapability correspondstoahigherconstantpowerplusanonzerotransmit
of jointly decoding user messages in the CP, the throughput power.Theoverallframeworkofthispaperisajointoptimiza-
of traditionalcellular networks can be significantly improved. tionofBStransmitpower,BSactivationandbackhaulratefor
A similar conclusion also has been drawn in the downlink. both the compression and the data-sharing strategies.
In particular, [9] proposes a joint design of beamformingand From the optimization perspective, the total power con-
multivariate compression to maximize the weighted sum rate sumption for the data-sharing strategy involves a sum of
for the compression strategy, while [10] and [11] consider weighted nonconvex ℓ -norms, which is highly nontrivial
0
joint beamforming and BS clustering design to maximize the to optimize globally. Instead, we adopt the reweighted ℓ
1
weighted sum rate for data-sharing. technique [6] to approximate the nonconvex total power into
This paper focuses on the energy efficiency of C-RAN a convex weighted sum of transmit power, where the weights
in the downlink. Several metrics have been proposed in the areiterativelyupdatedinawaytoreducenotonlythenumber
literature to measure the energy efficiency of a network. For of active BSs but also the backhaul rate. Such technique
example,theareapowerconsumptionmetric(watts/unitarea) has also been applied to minimize the total backhaul rate in
is proposed in [12] to evaluate the energy efficiency of net- [23], and to optimize the tradeoff between the total transmit
works of different cell site densities. Another widely adopted power and total backhaul rate in [24]. On a related note,
measurement in energy efficiency is bits per joule metric, the discrete ℓ -norm can also be approximated using other
0
which hasbeenstudied in [13] undera simplified single-user- tractable continuous functions such as Gaussian-like function
two-BSs model from an information-theoreticalpointof view in [25] and exponential function in [26]. It has been reported
andalsostudiedin[14]–[16]fororthogonalfrequencydivision recently in [27] that those approximation methods show sim-
multiple access (OFDMA) based cooperative networks from ilar effectiveness in inducing sparsity.
the practical system design point of view. Further, the mathematical expression of the total power
In this paper, we formulate the problem of minimizing consumption for the compression strategy involves a differ-
the total required power for downlink C-RAN in order to ence of two logarithmic functions, which is also nonconvex.
provide a given set of quality-of-service(QoS) targets for the We propose to approximate the first logarithmic function
scheduled users. Such an optimization problem can also be using the successive convex approximation technique, which
thought of as minimizing watts per bit (or maximizing the transforms the objective function into a convex form. The
bits per watt) at givenuser service rates. In this domain,most adoptedreweightedℓ minimizationtechnique and successive
1
ofthepreviousworksarerestrictedtothedata-sharingstrategy convex approximation technique in this paper are related to
3
the majorization-minimization (MM) algorithm [28], which rates. The energy efficiency of the data-sharing strategy is
deals with an optimization problem with nonconvexobjective superior to that of the compression strategy in the low-rate
function by successively solving a sequence of optimization regime. However, the backhaul power consumption of the
problems with approximate objective functions. This paper data-sharingstrategyincreasessignificantlywith theuserrate.
utilizestheknownsufficientconditionsofconvergenceforthe Thus, in high user rate regime, the compression strategy may
MM algorithm in the literature [29] to show the convergence be preferred from an energy saving perspective.
of the proposed algorithms for both the data-sharing and the
compression strategies.
C. Paper Organization and Notations
Finally, we mention that the data-sharing and compression
The remainder of this paper is organized as follows. Sec-
strategiesconsideredinthispaperarenottheonlypossibilities
tion II introduces the system model and power consumption
for the downlink of C-RAN. There is a potential to combine
model considered throughoutthis paper. Section III considers
these two strategies by sending directly the messages of only
the total power minimization under the data-sharing trans-
the strong users to the BSs and compressing the rest [30].
mission strategy, while Section IV considers the compression
Also, reverse compute-and-forwardstrategy that accounts for
strategy. Simulation results are presented in Section V and
the lattice nature of the transmitted message is also possible
conclusions are drawn in Section VI.
[31].However,suchstrategyisdifficulttooptimizebecauseof
Throughoutthispaper,lower-caseletters(e.g.x)andlower-
the need in choosing the right integer zero-forcing precoding
case bold letters (e.g. x) denote scalars and column vectors
coefficients at the CP so that the effective noise, caused by
respectively. We use C to represent complex domain. The
the non-integerpenaltydue to practicalchannels,at each user
transpose, conjugate transpose and ℓ -norm of a vector are
is minimized. p
denoted as (·)T, (·)H and k·k respectively. The expectation
p
ofarandomvariableisdenotedasE[·].Calligraphylettersare
B. Main Contributions usedtodenotesets, while|·| standsforeitherthesizeofaset
This paper considers energy-efficient design of the data- or the absolute value of a scalar, depending on the context.
sharing strategy and the compression strategy for downlink
C-RAN by formulating a problem of minimizing the total II. SYSTEMAND POWERCONSUMPTION MODEL
network power consumption subject to user rate constraints.
In this section, we describe the overall system model and
The first contribution of this paper is the modeling of both
power consumption model for the downlink C-RAN consid-
the BS power and the backhaul power consumption in the
ered throughoutthis paper.
network. The BS power consumption model includes a low-
power sleep mode, while the backhaul power consumption is
modeled as a linear function of backhaul traffic rate. A. System Model
Forthedata-sharingstrategy,weproposeanovelapplication Consider a downlink C-RAN with L BSs serving K users.
of reweighted ℓ minimization technique to approximate the All the BSs are connected to a CP via backhaul1 links and
1
nonconvex BS activation power and backhaul power. Such each user receives a single independent data stream from the
approximation technique reduces the nonconvex optimization BSs. All the user messages are assumed to be available at the
problem to a conventional convex transmit power minimiza- CP and are jointly processed before being forwarded to the
tion problem, which can be solved efficiently using the BSs through the backhaul links. We assume that the CP has
uplink-downlink duality approach or through transformation access to globalchannelstate information(CSI) but point out
as second-order cone programming (SOCP). Moreover, we thatsuchassumptioncanberelaxedsothatonlytheCSI from
adopt a reweighting function that enables us to connect the the neighboring BSs of each user is needed in the CP.
reweightedℓ minimizationtechniquewiththeMMalgorithm. Tosimplifynotationsandease analysis,we assumethatthe
1
This connection allows us to prove the convergence behavior BSs and the users are equipped with a single antenna each,
of the proposed algorithm for the data-sharing strategy. although the proposed algorithms in this paper can be easily
For the compression strategy, in addition to the reweighted generalizedtothecaseofmulti-antennaBSsasdiscussedlater
ℓ approximation to the BS activation power as in the data- in the paper. Let x ∈ C denote the transmit signal at BS l,
1 l
sharing strategy, we propose a successive convex approxima- we can write the received signal y ∈C at user k as
k
tion to the backhaul power, which is in a nonconvex form
y =hHx+n , k ∈K={1,2,··· ,K} (1)
as a difference of two logarithmic functions. The proposed k k k
successiveconvexapproximationtechniqueandthereweighted where x=[x ,x ,··· ,x ]T is the vector of transmit signals
1 2 L
ℓ1 approximation technique can be combined together. The across all the L BSs and h ∈CL×1 is the vector of channel
k
combinedalgorithmfalls into the class of the MM algorithms
gains from all the L BSs to user k. The received noise n
k
and has convergenceguarantee.
is modeled as a complex Gaussian random variable with zero
Through simulations, we show that optimized data-sharing
and compression strategies in C-RAN can bring much im- 1This paper refers the link between CP and BSs as backhaul, which
proved energy efficiency as compared to the non-optimized is appropriate if the data-sharing strategy is used. However, in a C-RAN
architectureimplementingthecompressionstrategywheretheBSsaresimply
CoMP transmission. However, the comparative energy saving
RRHs, the connection between RRH and CP can be referred to more
ofdata-sharingversuscompressiondependsontheuser target appropriately asfronthaul.
4
mean and variance σ2. Each user decodes its own message begeneralizedtootherbackhaultechnologies,suchaspassive
s ∈C from the received signal y . optical network, fiber-based Ethernet, etc., as mentioned in
k k
In this paper, we investigate two fundamental but different [32]. Note that [17] also considers the sleep mode capability
transmissionstrategies,thedata-sharingstrategyandthe com- for backhaul links. We point out that such consideration
pression strategy, for the downlink C-RAN for delivering the can be unified with P and P in the BS power
l,active l,sleep
messages touserkviathetransmitsignalxfromtheBSs.In consumption model (3).
k
particular,we compare the potentialof these two strategies in 3) Total Power Consumption: Based on the above BS
improvingthe energy efficiency. Before discussing the details power consumption model (3) and backhaul power consump-
ofthe two strategies,we firstdescribethe powerconsumption tion model (4), we can write the total power consumption
model adopted in this paper. P for C-RAN as
total
P = PBS +PBH
B. Power Consumption Model total l l
l∈L
Traditional cellular network transmission strategy design X(cid:0) (cid:1)
typically only considers transmit power at each BS, which = ηP + (P −P )
l l,tx 1{Pl,tx} l,active l,sleep
is written as l∈L(cid:18)
X
Pl,tx =E |xl|2 ≤Pl, l∈L={1,2,··· ,L}, (2) +Pl,sleep+ρlRlBH
(cid:19)
where Pl is the(cid:2) tran(cid:3)smit power budget available at BS l.
However,afullcharacterizationofpowerconsumptionataBS = ηlPl,tx+1{Pl,tx}Pl,∆+ρlRlBH
shouldalso consider the efficiencyof the poweramplifier and l∈L(cid:18) (cid:19)
X
other power-consuming components such as baseband unit, + P (5)
l,sleep
cooling system, etc. In addition, the power consumption of
l∈L
X
backhaul links connecting the BSs to the CP also needs to
constant
be taken into account for the specific C-RAN architecture
considered in this paper. In the following, we describe the where {·} is the indicator function defin|ed a{sz }
1
power consumption model adopted in this paper for the BSs
1, if x>0
and the backhaul links respectively. = , (6)
1{x} 0, otherwise
1) Base-Station Power Consumption: The characteristic of (cid:26)
power-consuming components in a BS depends on the BS and P = P −P is the difference between the
l,∆ l,active l,sleep
design. We adopt the following unified power consumption minimum active BS power consumption and the sleep mode
modelproposedin[22],whichisapplicablefordifferenttypes BS power consumption.
of BSs. This model approximates the BS power consumption
As we can see from (5), there are three possibilities in
as a piecewise linear function of the transmit power Pl,tx: improving the energy efficiency of C-RAN: reducing the
ηP +P , if 0<P ≤P transmit power, putting BSs into sleep mode, and decreasing
PBS = l l,tx l,active l,tx l, l∈L
l P , if P =0 the backhaul traffic. However, these three aspects cannot be
l,sleep l,tx
(cid:26) (3) realizedsimultaneously:deactivatingmoreBSsmeansreduced
where η > 0 is a constant reflecting the power amplifier capability for interference mitigation among the active BSs,
l
efficiency, feeder loss and other loss factors due to power which leads to higher transmit power in order to maintain
supply and cooling for BS l, P is the transmit power the QoS for the users; higher backhaul rate can allow for
l,tx
defined in (2) and P is the minimum power required more user information being shared among the BSs so that
l,active
to support BS l with non-zero transmit power. If BS l has theBSscanbettercooperatetomitigateinterference,thusless
nothing to transmit, it can be put into sleep mode with low transmitpower may be needed.A joint design is necessary in
power consumption P . Typically, P <P so order to balance the roles of transmit power, BS activation
l,sleep l,sleep l,active
that it is beneficial to turn BSs into sleep mode, whenever and backhaul traffic rate in achieving energy efficiency. In
possible, for energy-saving purpose. the following, we describe the general problem formulation
2) Backhaul Power Consumption: In C-RAN, the BSs are consideredin thispaperforsuch jointdesignusedin boththe
connected to the CP with the backhaullinks. The power con- data-sharing and the compression strategies.
sumptiondue to backhaullinks varies with differentbackhaul
technologies. In this paper, we model the backhaul as a set
C. Energy Efficiency Maximization
of communicationchannels,each with capacity C and power
l
dissipationPBH ,andwritethebackhaulpowerconsumption This paper aims to understand the energy efficiency for
l,max
as downlink C-RAN, which can be defined as the ratio of the
RBH
PBH = l PBH =ρ RBH, l∈L (4) achievable sum rate and the sum power consumption, i.e.
whereρ =Pl BH /CClisal,cmoanxstantslcallingfactorandRBH is bPPytkottRahlke swpheceirfiecRtrkanissmtihsseiodnatsatrartaetgeyfaonrduPser k idsettehremtionteadl
l l,max l l total
the backhaultraffic between BS l and the CP. This modelhas consumed power defined in (5). Towards this end, this paper
been used in [21] for microwave backhaul links and can also takesthe similarapproachasin[19] tofix theserviceratesof
5
scheduled users and consider the minimization of total power
consumption:
Central Processor
minimize P (7)
total s ,s
1 2
subject to R ≥r , ∀k ∈K
k k
E |x |2 ≤P , ∀l ∈L
l l s1 R1BH=R1 s1 R2BH= s2 R3BH=R2
where rk is the fixed targe(cid:2)t rate(cid:3)for user k. The solution to s2 R1+R2
theaboveproblemgivesustheenergyefficiency PkRk ofthe
Ptotal
system at the operating point (r ,r ,··· ,r ). To maximize
1 2 K
energyefficiency,we need to furthersearchoverall operating x1=w11s1 x2=w21s1 x3=w32s2
points. For the rest of the paper, we study and compare +w22s2
BS 1 BS 2 BS 3
the minimum required total power for different transmission
strategies under the same operating point (r ,r ,··· ,r ) in
1 2 K
the downlink of C-RAN. Note that problem (7) implicitly
User 1 User 2
assumes fixed user scheduling. There also exists a possibility
ofdoingjointuserschedulingandpowerminimizationbycon-
Fig. 1. Downlink C-RAN with data-sharing transmission strategy. In this
sideringaproblemofminimizingthetotalpowerconsumption
illustrativeexample,theCPtransmitsuser1’smessages1toBSs1and2,and
across multiple time slots subject to a minimum target for user2’smessages2toBSs2and3.TheBScluster(1,2)thencooperatively
each user’s average rate. Such problem is considerably more serves user 1 and the BS cluster (2,3) cooperatively serves user 2 through
jointbeamforming.
complicated.
D. Data-Sharing versus Compression
to the cloud computer center in the C-RAN architecture. We
Data-sharing and compression are two fundamentally dif- refer the readers to [34].
ferent transmission strategies for the downlink of C-RAN for
delivering data to the users. These two strategies correspond
III. DATA-SHARING STRATEGY
to alternative functional splits in C-RAN. In the data-sharing
transmission strategy, the CP routes each scheduled user’s in- In this section, we study the minimumtotal powerrequired
tendedmessagetoaclusterofBSsthroughthebackhaullinks; for the data-sharing strategy in order to support the given
the cluster of BSs then cooperatively serve that user through scheduled users at guaranteed service rates.
jointbeamforming.Incontrast,inthecompressionstrategy,the
precodingoperationisimplementedcentrallyattheCP,which
A. Problem Formulation
thenforwardsacompressedversionoftheanalogbeamformed
signal to the BSs through the backhaul/fronthaul links. The Consider the data-sharing transmission strategy for the
BSsthensimplytransmitthecompressedbeamformingsignals downlink of C-RAN as illustrated in Fig. 1, where the each
to the users [9], [30], [33]. user’s message is shared among a cluster of serving BSs. Let
The data-sharing strategy differs from the compression wlk ∈ C be the beamforming coefficient for BS l to serve
strategy in backhaul utilization. In data-sharing, the backhaul user k. If BS l is not part of user k’s serving cluster, wlk is
rate is a function of the user message rate and the BS cluster set to be zero. The transmit signal xl at BS l can be written
size, while in the compression strategy the backhaul cost is as xl = k∈Kwlksk. We model the user messages sk’s
determined by the compression resolution. Intuitively, as the as independent and identically distributed complex Gaussian
P
user target rate and BS cluster size increase, the backhaul random variables with zero mean and unit variance. The
rate for the data-sharing strategy would increase significantly, transmit power Pl,tx formulated in (2) can be written as
leadingtohighenergyconsumption.However,inthelowuser
P = |w |2, l ∈L. (8)
rateregimewheretheBSclustersizeissmall,data-sharingcan l,tx lk
be more efficient than compression as the latter suffers from kX∈K
quantization noise. Therefore, there exists a tradeoff between Substituting x = w s into (1), the received signal
l k∈K lk k
data-sharing and compression in terms of backhaul rate and y at user k is
k
energyefficiency at differentuser targetrate operatingpoints. P
In the followingtwo sections, we describe in details the data- yk =hHk wksk+ hHk wjsj +nk, k ∈K, (9)
sharing strategy and the compression strategy, and propose j6=k
X
corresponding algorithms to find the minimum required total
where w = [w ,w ,··· ,w ]T is the network beam-
power for each strategy. k 1k 2k Lk
former for user k. Based on (9), the received signal-to-
Throughoutthis paper,we primarilyaccountfor the energy
interference-plus-noiseratio(SINR)atuserkcanbeexpressed
consumptiondue to communicationsin either the backhaulor
as
the transmission front-end at the BSs, rather than the energy
hHw 2
consumptiondueto computing.Thereis significantadditional SINR = k k , k ∈K (10)
energysavingduetomigratingsignalprocessingfromtheBSs k j6=k(cid:12)(cid:12)hHk wj(cid:12)(cid:12)2+σ2
P (cid:12) (cid:12)
(cid:12) (cid:12)
6
and the achievable rate for user k is then user. The overall optimization problem (14) aims to choose
SINR the optimal cluster of serving BSs for each scheduled user
k
Rk =log2 1+ Γ , k∈K, (11) for minimizing the total power consumption while satisfying
(cid:18) m (cid:19) theuserQoSconstraints.Duetothe indicatorfunctionsinthe
where Γ stands for the signal-to-noise ratio (SNR) gap due
m objectivefunction(14a),problem(14)isnonconvex(discrete),
to practical modulation scheme.
so finding its global optimum solution is challenging. In the
For the data-sharing strategy, if user k is served by BS
following,weproposetoapproximatethenonconvexindicator
l, then the CP needs to send user k’s message s , along
k function using reweighted convex ℓ -norm and show that
1
with the beamforming coefficient w , to BS l through the
lk with a particular reweightingfunction the proposedalgorithm
backhaul link. In this paper, we assume that the channels are always converges2.
slowvaryingandignorethebackhaulrequiredforsharingCSI
and beamformers, and only consider the backhaul capacity
consumption due to data-sharing. Hence, the backhaul rate B. Proposed Algorithm
for BS l, RBH, is the accumulated data rates of those users
l We make an observationthat the indicator function defined
served by BS l, which can be formulated as
in (6) is equivalent to the ℓ -norm of a scalar. The ℓ -norm
0 0
RlBH = 1{|wlk|2}Rk, l∈L, (12) ovefcatovre,cstooirtirsedduecfiensetdoatshethiendniucamtobrerfuonfcntioonnzienrotheenstcriaelsarincatshee.
k∈K
X Incompressivesensingliterature[6],nonconvexℓ -normmin-
where is the indicator function defined in (6) and 0
1{|wlk|2} imizationproblemcan be approximatedas convexreweighted
indicates whether or not BS l serves user k.
ℓ minimizationproblem.Wetakeadvantageofthistechnique
1
Substituting (8) and (12) into (5), the total power mini-
and propose to approximate the indicator functions in the
mization problem (7) can be formulated for the data-sharing
objective function (14a) as
strategy as
mi{nwilmk}ize Xl∈L ηlkX∈K|wlk|2+1{Pk∈K|wlk|2}Pl,∆ 1{Pk∈K|wlk|2} =(cid:13)(cid:13)(cid:13)kX∈K|wlk|2(cid:13)(cid:13)(cid:13)0 ≈µlkX∈K|wlk|2 (15)
(cid:13) (cid:13)
+ρlk∈K1{|wlk|2}Rk! (13a) 1{|wlk|2}(cid:13)=(cid:13)|wlk|2(cid:13)(cid:13)0 ≈νlk|wlk|2 (16)
X with weights µ and ν it(cid:13)erativel(cid:13)y updated according to
SINR l lk (cid:13) (cid:13)
subject to R =log 1+ k ≥r , k ∈K (13b)
k 2(cid:18) Γm (cid:19) k µ =f |w |2,τ = c1 ,
|wlk|2 ≤Pl, l ∈L. (13c) l k∈K lk 1! k∈K|wlk|2+τ1
X
k∈K c
X ν =f |w |2,τ = P 2 (17)
Note that the l∈LPl,sleep term in (5) is a constant and has lk lk 2 |wlk|2+τ2
been droppedin the objective function (13a). It is easy to see (cid:16) (cid:17)
P where {w } is the beamformer from the previous iteration,
that the minimum rate constraint (13b) is met with equality lk
τ > 0 and τ > 0 are some constant regularization factors,
at the optimalpoint. Hence, problem (13) can be equivalently 1 2
and c ,c are constants.
formulated as 1 2
Note that in the above iterative updates of µ and ν , the
l lk
mi{nwilmk}ize Xl∈L ηlkX∈K|wlk|2+1{Pk∈K|wlk|2}Pl,∆ BmSitspwowitherstmoaulsletrrakn,s|mwlikt|p2o,watecr,urPrekn∈tKite|rwaltkio|2n,aorresgmivaelnl ltarargnes-r
weights µ or ν in the next iteration. This further decreases
l lk
+ρlkX∈K1{|wlk|2}rk! (14a) Pforkc∈eKs B|wSlkl|2toowrar|dwlskl|e2epinmtohdeen(ei.xet.,iterka∈tiKon|w, alkn|d2 =eve0n)tuoarltloy
subject to SINRk ≥γk, k ∈K (14b) beremovedfromuserk’sservingcluster(i.e.,|wlk|2 =0).The
P
|w |2 ≤P , l∈L (14c) weight µl has the effect of putting appropriate BSs to sleep
lk l
mode, while ν has the effect of determining the BS cluster
lk
k∈K
X size for user k, which in turn affects the backhaul capacity
where the variable R in (13a) is replaced by the target
k consumption of user k.
rate rk in (14a) and γk = Γm(2rk −1) in (14b). The The resulting optimization problem after the ℓ -norm ap-
new SINR constraint (14b) is also met with equality at the 1
proximation is formulated as follows:
optimality.However,wekeep(14b)asaninequalityconstraint,
so that it can be reformulated as a convex second-order cone minimize α |w |2 (18)
lk lk
(SOC) constraint [35]. Note that problem (14) is equivalent {wlk} l∈Lk∈K
XX
to problem (13) in the sense that they have the same optimal
subject to (14b), (14c)
solutions and the same feasibility region.
Note that the above optimization is over the beamforming
2Infact, it converges tothe stationary point solution ofan approximation
coefficients and also implicitly over the BS cluster for each toproblem(14).
7
Algorithm 1 Total Power Minimization for Data-Sharing D. Complexity Analysis
Strategy
Algorithm 1 is an iterative procedure between updatingthe
Initialization:Set the initial values for {µl,νlk} accordingto weights {µ ,ν } and solving the weighted transmit power
l lk
(17) with the {wlk} chosen as a feasible point of problem minimization problem (18). The problem (18) can be formu-
(14);
lated as an SOCP and solved using the interior-pointmethod,
Repeat:
e.g.usingthe convexoptimizationsolver[37].Thetotalnum-
1) Fix{µl,νlk},findtheoptimal{wlk}bysolvingproblem ber of variables in problem (18) is LK and the total number
(18) usingtheuplink-downlinkdualityapproach[36] or of SOC constraints is (L+K). The complexity order for
by transforming it into an SOCP problem [35]; solvingsuchaproblemthroughinterior-pointmethodisgiven
2) Update {µl,νlk} according to (17). as O (L+K)(LK)3 [38]. Assuming that Algorithm 1
Until convergence requir(cid:16)esatotalnumber(cid:17)ofT1 weightupdates,theoverallcom-
plexityorderforAlgorithm1isthenO T (L+K)(LK)3 .
1
where α = η + µ P + ρ ν r . Problem (18) is a Notethatintheabovecomplexityord(cid:16)er,K isthenumber(cid:17)of
lk l l l,∆ l lk k scheduledusers, which is comparableto the numberof active
weighted sum transmit power minimization problem, which
BSs in the network.In addition,instead of consideringall the
can be solved efficiently through the uplink-downlink duality
L BSs in the entire network, we can set the nearest L < L
approach [36] or by transforming it into an SOCP problem c
BSs around each scheduled user as its candidate serving BS
[35]. We now summarize the proposed algorithm to solve the
cluster. This furtherreducesthe computationalcomplexityfor
total power minimization problem (14) for the data-sharing
Algorithm 1 with negligible performance loss.
strategy in Algorithm 1.
Note that a similar problem as to (14) is considered in our
E. Generalization to the Multi-Antenna System
previous work [24], where we formulate the problem as a
tradeoff between the BS transmit power and the backhaul Algorithm 1 can be readily generalized to the case with
capacity. This paper considers a more realistic BS power multiple transmit antennas at each BS. In such case, one
consumption model with sleep mode capability, and also only needs to replace the beamforming coefficient wlk with
accounts for backhaul power consumption. The considered the beamforming vector wlk ∈ CNl×1 from BS l to user k,
problem(14)inthispapercanalsobethoughtofasproviding where Nl is the number of antennas at BS l. The rest of the
a tradeoff between the per-BS power consumption and the optimization parameters are straightforward extensions based
per-BS backhaul capacity consumption, where the tradeoff on wlk [24].
constant ρ is specifically chosen according to the backhaul Algorithm 1 can also be applied to the case with multiple
l
power consumption model (4). receive antennas at each user but with fixed receive beam-
former. In this case, the only change is to replace the channel
C. Convergence Analysis gain vector hk with the effective channel gain h˜k = Hkuk,
Algorithm 1 relies on the reweighting heuristic (17) to whereHk ∈CL×Mk anduk ∈CMk×1 arethechannelmatrix
seen by user k and the receive beamformer at user k, M
deactivateBSsandreducetheBSclustersizeforenergysaving k
is the number receive antennas at user k. However, the joint
purpose. To establish the convergence proof for Algorithm 1
design of transmit beamformer and receive beamformer for
under arbitrary reweighting function is challenging, however,
the multiple receive antennas case is more complicated. One
we show in the following that if the reweighting function is
possible way is to iteratively design the transmit beamformer
chosen as
assumingfixedreceivebeamformerandupdatethereceiveras
1
f(x,τ)= , (19) theoptimalminimummeansquareerror(MMSE)beamformer.
(x+τ)ln(1+τ−1)
i.e. the constants in (17) are chosen as c = 1 ,c = IV. COMPRESSION STRATEGY
1 , Algorithm 1 can be seen as a1spelcni(a1l+cτa1−s1e)of2the In this section, we aim to minimize the total power con-
ln(1+τ2−1) sumption for downlink C-RAN under the compression strat-
MM algorithms [28] and is guaranteed to converge.
egy.
Theorem 3.1: Starting with any initial point, the sequence
∞
w(n) generated by Algorithm 1 with the reweighting
lk A. Problem Formulation
n=1
fnunctioon chosen as (19) is guaranteed to converge. Consider the compression transmission strategy for down-
Proof: See Appendix A.
link C-RAN as illustrated in Fig. 2. Let xˆ = w s
Finally, we point out that the choice of the reweighting l k∈K lk k
denote the beamformed signal formed in the CP for BS l.
function (19) is not unique. There exist other reweighting P
The CP compresses xˆ into x and sends x to BS l. In this
l l l
functions that may work well in different problem setups
paper, we assume that each xˆ is compressed independently3
l
[6].Recently,[27]hasexperimentedwithotherapproximation
andmodelthecompressionprocedureasthefollowingforward
functions to the ℓ -norm, e.g. exponential function and arc-
0 test channel:
tangent function, in addition to the logarithmic function (32)
x =xˆ +e , l∈L, (20)
l l l
used in this paper,and observedsimilar effectivenessof these
functions in inducing sparsity. 3Correlated compressionisalsopossibleandhasbeenconsidered in[9].
8
theoretically ideal quantizer. Similar to [33], we introduce a
Central Processor notion of gap to rate-distortion limit, denote as Γq > 1, to
account for the loss due to practical quantizer and formulate
xˆ =w s +w s
l l1 1 l2 2
the backhaul capacity consumption for BS l as
l=1,2,3
Γ |w |2
RBH =log 1+ q k∈K lk , l∈L. (24)
x1 R1BH x2 R2BH x3 R3BH l 2 P ql2 !
Substituting (21) and (24) into (5), the total power mini-
mization problem for the compression strategy is formulated
as follows
x1=xˆ1+e1 x2=xˆ2+e2 x3=xˆ3+e3
BS1 BS2 BS3 {wmlki,nql} l∈L ηl k∈K|wlk|2+ql2!+1{Pk∈K|wlk|2+ql2}Pl,∆
X X
Γ |w |2
+ρ log 1+ q k∈K lk (25a)
l 2 q2
P l !!
s.t. SINR ≥γ , k ∈K (25b)
k k
User1 User2 |w |2+q2 ≤P , l ∈L (25c)
lk l l
k∈K
Fig. 2. Downlink C-RAN with compression transmission strategy. In this X
illustrative example, the CP centrally precodes both users’messages s1 and wheretheSINRin(25b)isdefinedin(23).Duetotheindicator
s2 toxˆl,l=1,2,3, andforwards the compressed precoded signals xl,l= function as well as the backhaul rate expression in (25a), the
1,2,3, to each of the BSs. Each BS transmits the compressed beamformed
optimizationproblem (25) is nonconvex.In the following,we
signalreceived fromtheCPtobothusers.
describethetechniquestoapproximate(25a)inaconvexform.
where el ∈C is the quantization noise independentof xˆl and B. Proposed Algorithm
is assumed to be Gaussian distributed with zero mean and
The difficulties in solving problem (25) lie in both the
varianceq2. Substituting(20) to (2), thetransmitpowerat BS
l indicatorfunctionandthenonconvexbackhaulrateexpression
l under the compression strategy can be written as
in the objective function (25a). For the indicator function, we
P = |w |2+q2, l∈L. (21) can utilize the similar technique used in the previous section
l,tx lk l
to approximate it using reweighted ℓ -norm:
k∈K 1
X
Comparing (21) with (8), we can see that different from the
data-sharing strategy, the BS transmit power in the compres- 1{Pk∈K|wlk|2+ql2} =(cid:13) |wlk|2+ql2(cid:13)
sion strategy involves a quantization noise power in addition (cid:13)kX∈K (cid:13)0
(cid:13) (cid:13)
to the beamforming power. (cid:13) (cid:13)
≈(cid:13)β |w |2+(cid:13)q2 (26)
Substituting (20) into (1), the received signal y at user k l lk l
k !
under the compression strategy can be written as kX∈K
where β is iteratively updated according to the following
l
yk =hHk wksk+ hHk wjsj +hHk e+nk, k ∈K, (22) reweighting function
j6=k
X
c
wtrahnesrmeiette=d [fero1,me2a,l·l·t·h,eeLL]TBSiss.thAesqwuaentciaznatisoene,nboeisseidvesectthoer βl =f k∈K|wlk|2+ql2,τ3!= k∈K|wlk|32+ql2+τ3
X (27)
inter-user interference and background noise, each user now P
also receives an additional quantization noise term hHe from where {wlk,ql} come from the previous iteration, τ3 > 0 is
k some constant regularization factor, and c is a constant.
the BSs. The user received SINR is expressed as 3
Forthebackhaulrate(24),wecanexpressitasadifference
SINR = hHk wk 2 , k ∈K. of two logarithmic functions: log2 ql2+Γq k∈K|wlk|2 −
k j6=k hHk wj (cid:12)(cid:12)2+ l(cid:12)(cid:12)∈L|hlkql|2+σ2 (23) i2nρlqlol,g2thqel. fiArlstthotuegrmh thise ssteicllonndontec(cid:16)romnv−ex2.ρTllPoogd2eqalliswictohn(cid:17)vthexe
The backPhaul c(cid:12)(cid:12)apacity(cid:12)(cid:12) conPsumption for the compression nonconvexityofthebackhaulrate,weproposetosuccessively
strategy is related to the level of quantization noise q2: lower approximatethe first logarithmicfunctionusing the following
l
quantization noise requires higher backhaul rate. Under the inequality
forward test channel (20), the achievable compression rate is
the mutual information between x and xˆ, according to rate- log q2+Γ |w |2
distortiontheory[39],givenaslog 1+ Pk∈K|wlk|2 ,where 2 l qk∈K lk !
2 q2 X
i.e.k∈xˆKl.|wHlko|w2evisert,heprapcotwicearl oqfuathnetizs(cid:16)eirgnmalaytobbelefacromf(cid:17)rpormesstehde, ≤ log2λl+ ql2+ΓqλPllnk∈2K|wlk|2 − ln12 (28)
P
9
Algorithm 2 Total Power Minimization for Compression TABLEI
SIMULATIONPARAMETERS.
Strategy
Initialization:Setthe initialvaluesfor{β }and{λ }accord- Cellular Hexagonal
l l
Layout 7-cellwrapped-around
ing to (27) and (29) respectively with {w ,q} chosen as a
lk l Channelbandwidth 10MHz
feasible point of problem (25); Distance betweencells 0.8km
Repeat: NumberofRRHs/cell 4
Numberofantennas/(RRH, user) (1,1)
1) Fix {β ,λ }, find the optimal {w ,q } by solving the
l l lk l MaximumtransmitpowerforRRHPl 20Watts
convex optimization problem (30); Active modepowerforRRHPl,active 84Watts
2) Update {βl} and {λl} according to (27) and (29) re- SleepmodepowerforRRHPl,sleep 56Watts
spectively. Slopeoftransmitpowerηl 2.8
Backhaul linkcapacity Cl 100Mbps
Until convergence Maximumbackhaul powerPBH 50Watts
l,max
Antennagain 15dBi
Background noise −169dBm/Hz
duetotheconcavityoflog (x).Theaboveinequalityachieves PathlossfromRRHtouser 128.1+37.6log10(d)
2 Log-normalshadowing 8dB
equality if and only if Rayleigh smallscalefading 0dB
SNRgapΓm 0dB
λl =ql2+Γq |wlk|2. (29) Gaptorate-distortion limitΓq 4.3dB
k∈K Reweighting parameters (τ1,τ2,τ3) (10−5,10−8,10−5)
X
The right-hand side of (28) is a convex quadratic function in
{w ,q } for fixed λ . This fact motivates us to successively
lk l l
1.5
solve the problem (25) with log q2+Γ |w |2 re-
2 l q k∈K lk
placed by the right-hand side of(cid:16)(28) forPfixed λl, the(cid:17)n to 1
iteratively update λ according to (29).
l
Combining the above described ℓ -norm reweighting and
1
0.5
successive convex approximation techniques, we get the re-
sulting optimization problem under fixed β and λ as
l l
m 0
minimize φ |w |2+ ψ q2−2ρ log q k
l lk l l l 2 l
{wlk,ql} Xl∈LkX∈K Xl∈L(cid:0) (cid:1) −0.5
1
+ ρ log λ − (30)
l 2 l ln2
l∈L (cid:18) (cid:19) −1
X
constant
subject to (25b), (25c) −1.5
| {z } −1.5 −1 −0.5 0 0.5 1 1.5
km
whereφ =η +βP + ρlΓq andψ =η +β P + ρl .
l l l l,∆ λlln2 l l l l,∆ λlln2
Similar to the SINR constraint in (14b), the constraint (25b)
Fig.3. Acellular topologywith7cells and4RRHseachcell,whereeach
can also be equivalently reformulated as an SOC constraint. dotrepresents aRRH.
Thus, problem (30) is a convex optimization problem and
can be solved efficiently using standard convex optimization
solver, e.g. [37], with polynomial complexity. that the CP performs independent compression for each an-
We summarize the proposedalgorithm for solving problem tenna.Jointcompressionamongtheantennasmayimprovethe
(25) in Algorithm 2, which admits guaranteed convergence performance but results in a different optimization problem.
property as stated in the following theorem. Similarto Algorithm1, generalizationof Algorithm2to mul-
Theorem 4.1: Starting with any initial point, the sequence tiplereceiveantennasattheusersideisalsostraightforwardif
w(n),q(n) ∞ generatedbyAlgorithm2withthereweight- the receivebeamformerisassumed to befixed,however,joint
lk l n=1 design of transmit and receive beamformer is by no means
inng functionoin (27) chosen as (19) is guaranteedto converge.
trivial and requires additional efforts.
Proof: See Appdendix B
Algorithm 2 shows a similar computational complexity as
V. NUMERICAL EVALUATION OFENERGY EFFICIENCY
Algorithm1butwithadditionalLquantizationnoisevariables
to be optimized in each iteration. Assuming that Algorithm 2 Inthissection,weevaluatetheenergyefficiencyofthedata-
converges in T iterations, its complexity order is then given sharingandcompressionstrategiesfordownlinkC-RANusing
2
as O T (L+K)(LK+L)3 . the proposed algorithms for a 7-cell network with wrapped-
2
around topology. Each cell here refers to a geographic area
(cid:16) (cid:17)
with 4 RRHs as shown in Fig. 3. Equivalently, the network
C. Generalization to the Multi-Antenna System
consists of 28 BSs. The out-of-cell interference combined
Algorithm 2 can be readily applied to the scenario where with background noise is set as −150 dBm/Hz. The gap
multiple transmit antennas are available at the BSs assuming to rate-distortion limit is set as Γ = 4.3 dB corresponding
q
10
35 Data-Sharing(Alg.1)w/1user/cell user as the strongest Lc = 14 BSs to reduce the amount of
Compression(Alg.2)w/1user/cell CSI acquisition for the CP. From Fig. 4 we can see that all
Data-Sharing(Alg.1)w/2users/cell
the BSs are active at the first iteration, however, the number
Compression(Alg.2)w/2users/cell
30
Data-Sharing(Alg.1)w/3users/cell of active BSs decreases as the iteration goes on. Intuitively,
Compression(Alg.2)w/3users/cell more users are served, more BSs need to remain active. This
s
BS 25 can be verified from Fig. 4. We also observe from Fig. 4 that
ve Algorithm1fordata-sharingexhibitsfasterconvergencespeed
Acti thanAlgorithm2forcompression,wheretheformerconverges
of 20 within 30 iterations while the later requires 50 iterations to
ber converge in the worst case.
m
u We then evaluatethe convergencebehaviorof the proposed
N 15
algorithms in Fig. 5. As in Fig. 4, different number of
scheduled users are tested and each user’s target rate is set to
10 be20Mbps.Aswecansee,theobjectivevaluesmonotonically
decreaseandconvergeforboththedata-sharing(Algorithm1)
andthecompression(Algorithm2)strategies.SimilartoFig.4,
5
10 20 30 40 50 60 70 wealsoobservefasterconvergencespeedfordata-sharingthan
Iteration forcompressionin Fig. 5. Thisis possiblydueto thefactthat
compressionstrategyinvolvesmorevariablestobeoptimized.
Fig. 4. Trajectories of number of active BSs under rk = 20 Mbps target We now compare the performance of the data-sharing
rateforeachuser.
strategyandthecompressionstrategyintermsofpowersaving
in Fig. 6. In addition, we consider two reference schemes. In
2000
the first scheme, each user is only served by its strongest BS
Data-Sharing(Alg.1)w/1user/cell
that is not already associated with another user. This scheme
Compression(Alg.2)w/1user/cell
Data-Sharing(Alg.1)w/2users/cell is termed as “Single BS Association”, for which the transmit
1600
5) Compression(Alg.2)w/2users/cell power for each user can be minimized using the strategy in
3
31)(/ CDoamta-pSrhesasriionng((AAllgg..21))ww//33uusseerrss//cceellll [41]. In the second scheme, each user’s message is shared
( amongthe 4RRHs in its owncellandis cooperativelyserved
m
ble 1200 bythe4RRHsusingthecoordinatedbeamformingstrategyof
o
Pr [36].Suchschemeistermedas“Per-CellCoMP”.The“Single
of
e BS Association” and “Per-Cell CoMP” are two extreme cases
u
Val 800 in terms of number of active BSs: the former only has K
e
v (number of scheduled users) active BSs while in the latter all
cti
bje the 28 BSs in the entire network remain active.Each point in
O
400 Fig. 6 is averaged over 100 channel realizations.
Aswe cansee fromFig.6, “Per-CellCoMP”consumesthe
mostpowersincealltheBSsareactiveinthisscheme.“Single
0 BSAssociation”consumestheleastpower,similartothedata-
10 20 30 40 50 60 70 80
sharing strategy, but only at low user rate regime because the
Iteration
minimumnumberofBSsareselectedtoservetheusersinthis
scheme.However,astheuserrate orthe numberofscheduled
Fig.5. Convergence behaviorofproposedalgorithmsunderrk =20Mbps
targetrateforeachuser. users increases, “Single BS Association” becomes infeasible
veryquickly.Forinstance,inFig.6(b)wherethereare2users
per cell, “Single BS Association” can only support each user
to the uncoded fixed rate uniform scalar quantizer [40]. For with 10 Mbps service rate, while in Fig. 6(c) the case of 3
simplicity, the SNR gap is set to be Γm = 0 dB. The users per cell, “Single BS Association” is notfeasible even at
parametersin the BS power consumptionmodel(3) are taken 10 Mbps per user.
from[22] while the parametersfor the backhaulpower model It is worth noting that “Single BS Association” consumes
(4)arefrom[21].Alltheparametersrelatedtothesimulations the same amount of power as data-sharing in the low user
are listed in Table I. target rate regime in Fig. 6, as the latter essentially reduces
We first evaluate the effectivenessof the proposedℓ -norm to single BS association at low user rates. However, there is
1
reweightingtechniquein turningoffBSs. We plotthe number stillsignificantadvantageinmigratingsignalprocessingtothe
of active BSs remainedin each iteration for both data-sharing cloud in a C-RAN as compared to the conventional cellular
(Algorithm 1) and compression (Algorithm 2) strategies in architecture in term of computation power saving, which is
Fig.4.Theusertargetrateissettobe20Mbpsforeveryuser notincludedin themodelinthispaper.Itisalsoworthnoting
anddifferentnumberofscheduledusersaresimulated.Instead that the optimized data-sharing and compression strategies
ofconsideringallthe28BSsintheentirenetworkaspotential outperform the non-optimizedper-Cell CoMP significantly in
servingBSsforeachuser,wesettheinitialBSclusterforeach Fig.6,highlightingtheimportanceofoptimizationapproaches
