Inter-tier Interference Suppression in Heterogeneous Cloud Radio Access Networks

0.38 MB·

by  Mugen Peng

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Inter-tier Interference Suppression in Heterogeneous
Cloud Radio Access Networks
Mugen Peng, Hongyu Xiang, Yuanyuan Cheng, Shi Yan, and H. Vincent Poor
Abstract—Incorporating cloud computing into heterogeneous radio heads (RRHs), the C-RAN facilitates the implementa-
networks, the heterogeneous cloud radio access network (H- tion of centralized coordinated multi point (CoMP) transmis-
CRAN) has been proposed as a promising paradigm to enhance
sion[4].Withsuchanarchitecture,mobileoperatorscaneasily
6 both spectral and energy efficiencies. Developing interference
expand and upgrade their networks by deploying additional
1 suppression strategies is critical for suppressing the inter-tier
0 interference between remote radio heads (RRHs) and a macro RRHs, and thus the corresponding operational costs can be
2 base station (MBS) in H-CRANs. In this paper, inter-tier in- greatlyreduced.Unfortunately,oneofthemainrestrictionson
terference suppression techniquesare considered in the contexts theimplementationofC-RANsisthenon-idealfronthaulwith
n of collaborative processing and cooperative radio resource al-
limitedcapacityandlongtimedelay.Overcomingthenegative
a location (CRRA). In particular, interference collaboration (IC)
J impactoftheconstrainedfronthaulonspectralefficiency(SE)
and beamforming (BF) are proposed to suppress the inter-tier

6 interference, and their corresponding performance is evaluated. and energy efficiency (EE) is not straightforward [5].
Closed-form expressions for the overall outage probabilities,
The heterogeneous cloud radio access network (H-CRAN)
] system capacities, and average bit error rates under these two
T schemes are derived. Furthermore, IC and BF based CRRA has recently been proposed to decouple the control plane
I optimizationmodelsarepresentedtomaximizetheRRH-accessed and user plane to enhance the existing C-RAN concept, in
.
s users’sumratesviapowerallocation,whichissolvedwithconvex which the functions of control plane are only implemented
c optimization. Simulation results demonstrate that the derived
in traditional macro base stations (MBSs) [6]. In H-CRANs,
[
eaxcpcurersastieo;nsanfdortthheesreelpaetirvfeormpearnfocermmaentcreicsbeftowreIeCn aICndaBnFd aBrFe RRHs are used to provide high bit rates for users with
1
schemes depends on system parameters, such as the number diverse QoS requirements in hot spots, while the MBS is
v
of antennas at the MBS, the number of RRHs, and the target deployed to guarantee seamless coverage and deliver the
7
8 signal-to-interference-plus-noiseratio threshold. Furthermore, it control signalling of the whole network. User equipments
isseenthat thesumratesofIC andBFschemesincreasealmost
0 (UEs) can access RRHs transparently in H-CRANs, which
linearly with the transmit power threshold under the proposed
1 allows UEs to operate over a single carrier frequency and
CRRA optimization solution.
0
at low cost. In comparison with C-RANs and heterogenous
1. Index Terms—Heterogeneous cloud radio access network, networks (HetNets) [7], H-CRANs have been demonstrated
0 interference suppression, interference coordination, cooperative to achieve significant performance gains through advanced
6 radio resource allocation.
collaborative signal processing. However, because MBSs and
1
RRHs are underlaid with the same carrier frequency in the
:
v
I. INTRODUCTION same coverage area, severe inter-tier interference is incurred,
i
X which degrades the performance of H-CRANs significantly.
To meet the rapidly growing mobile data volume driven
r
a by applicationson platformssuch as smartphonesand tablets, Unlike the traditional HetNets, the intra-tier interference
the nextgenerationof wireless networksface significantchal- among dense RRHs in H-CRANs can be fully eliminated by
lenges in improving system capacity and guaranteeing users’ large-scalecooperativeprocessingthroughthefronthaul,while
quality of service (QoS) [1]. Cloud radio access networks(C- the inter-cell interference between adjacent BSs in HetNets
RANs) have been proposed to provide high bit rates, while should be mitigated by the distributed CoMP techniques
reducing both capital and operating expenditures [2] [3]. By through backhaul. Furthermore, the inter-tier interference to
migratingthebasebandfunctionalitiesofbasestations(BSs)to the RRH user equipments (RUEs) in H-CRANs can be co-
acentralizedbasebandunit(BBU)poolanddistributedremote ordinated through spatial multiple-input and multiple-output
(MIMO) processing in the MBS with multiple antennas [8],
The work of Mugen Peng was supported in part by the National Natural and the inter-tier interference at the MBS user equipments
Science Foundation of China (Grant No.61361166005), the National Basic (MUEs) can be endured because the MUE provides seamless
ResearchProgramofChina(973Program)(GrantNo.2013CB336600), and
coverage at only low bit rates. As a result, the inter-tier
theBeijingNaturalScienceFoundation(GrantNo.4131003).TheworkofH.
VincentPoorwassupportedinpartbytheU.S.NationalScienceFoundation interferencetoRUEsmakesitchallengingtoimproveSEinH-
underGrantECCS-1343210. CRANs, and thus advanced inter-tier interferencesuppression
Mugen Peng, Hongyu Xiang, Yuanyuan Cheng, and Shi Yan are with
techniquesareofinterest.Advancedinter-tierinterferencesup-
the Key Laboratory of Universal Wireless Communications for Min-
istry of Education, Beijing University of Posts and Telecommunications, pression techniques can be categorized as either collaborative
Beijing, China (e-mail: [email protected]; [email protected]; chi- processing in the physical layer or cooperative radio resource
[email protected]; [email protected]).
allocation (CRRA) in the upper layers [9]. This issue is the
H. Vincent Poor is with the School of Engineering and Applied Science,
Princeton University, Princeton, NJ,USA(e-mail: [email protected]). subject of this paper.
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A. Related Work on reception reliability.
Besides the IC and BF schemes in the physical layer,
Much recent attention has been paid to interference collab-
inter-tierinterferencecan besuppressedby cross-layerCRRA
orationandCRRA forC-RANs.Oneofthekeyadvantagesof
techniques in the upper layers. The significant cloud comput-
the C-RAN architecture is that it provides the BBU pool for
ing capability in the BBU pool enables the use of advanced
joint baseband signal processing across the multiple RRHs in
cross-layer CRRA. Traditional radio resource allocation for
both uplink and downlink, and thus it achieves significantly
cellular networks is largely based on heuristics and there is a
higher data rates than conventionalcellular networks. Thanks
lack of theoreticalunderstandingof how to design cross-layer
to the large-scale collaborative processing in the BBU, the
CRRA in an H-CRAN, which is usually more challenging
intra-tier interference across RRHs can be fully eliminated.
than that in traditional cellular and C-RANs due to practical
Such large-scale collaborative processing is often referred to
issuessuchasfronthaulcapacitylimitations,non-idealchannel
as network precoding or CoMP in HetNets.
state information (CSI), and the parallel implementation of
Numerous studies of network precoding for MIMO sys- algorithms.
tems, HetNets and C-RANs have been described in previous Someoptimizationobjectiveslikeweightedsumrate(WSR)
works [10]- [15]. For example, performance analysis under for CRRA involve multi-user interference, causing non-
various linear precoding schemes has been presented in [10], convexityandmakingtheproblemshardtosolve.Fortunately,
which can be directly applicable to H-CRANs. The authors the weightedminimummeansquareerror(WMMSE) method
in [11] have analyzed the throughputof multiuser MIMO for has proven to be effective in transforming such non-convex
distributed antenna systems based on zero-forcingbeamform- optimization problems into convex optimization problems.
ing (BF); however, the closed-form expressions for ergodic Specifically, for the WSR problem with beamforming vec-
capacity therein have been presented with approximations tors as variables, the objective function is non-convex with
instead of exact results. In addition, in [12], two coordinated regard to the vectors. However, it has been shown that WSR
BF designs have been taken into consideration in multicell maximization and WMMSE minimization are equivalent for
networks:theQoSBF,andthemax-minsignal-to-interference- the MIMO interference channel [18], in the sense that the
plus-noise ratio (SINR) BF. The goal of QoS BF is to two problems have the same optimal solution. Moreover,
minimizethetotalpowerconsumptionwhileguaranteeingthat the obtained WMMSE minimization after equivalent trans-
the received SINR of each user is above a pre-determined formation is convex with respect to each of the individual
threshold, while the max-min SINR BF aims to maximize optimization variables, and hence this non-convexproblem is
the minimum received SINR among all users under per-base- transformedintoamoretractableconvexproblem.Asaresult,
station powerconstraints. Furthermore,there are two kindsof the WMMSE method has been widely applied to handle non-
precodingschemesforMIMO,namelyinterferencecollabora- convex power consumption minimization [19], joint power
tion (IC) [13] and BF [14]. In [13], an adaptive transmission and antenna selection optimization [20], and weighted system
strategy to switch between IC and BF is proposed; however, throughput maximization [21]. Nevertheless, all of the above
the analytical results are restricted to the scenario with only studies focus only on downlink transmission. In [22], the
one low power node. Essentially, BF aims to maximize the uplink transmission is taken into consideration, and a joint
received signal strength for the desired users when the edge downlink and uplink user-RRH association and precoding
SINR is low, while IC is preferred when the edge SINR is designschemeisproposedtominimizethesystempowercon-
relativelyhighandtheinterferenceshouldbesuppressed[15]. sumption,inwhichthejointdownlinkanduplinkoptimization
Inspired by [11]- [15], in this paper both IC and BF schemes problem is transformed into an equivalent downlink problem,
are extended to H-CRANs as advancedcollaborative process- andtheWMMSEmethodisusedtotransformthenon-convex
ing approaches to suppress the inter-tier interference, and the downlink problem into a convex problem with respect to the
overall outage probability, system capacity, and average bit entries of the precoding matrix.
error rate (BER) under IC and BF are used to evaluate their Moreover, the l -norm is often applied to express RRH
0
performance under different configurations. selection, which leads to integer programming problems. To
In addition, to exploit the performance of C-RANs, the transform such non-convex problems into convex problems,
ergodic capacity performance of the single nearest and N- l -norm approximation can be used. In [21], the authors
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nearest association strategies with varying transmit power of investigatere-weightedl -normapproximationinthefronthaul
1
RRHsinC-RANsiscomparedin[16].ThebestRRHselection capacity constraint. In the l -norm approximation method,
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scheme needs only a single RRH and hence reduces the each coefficient in the precoding matrix is assumed to be
system overhead by avoiding coordination of the distributed independent; however, such independence does not always
RRHs, while resultingin a certain performanceloss. With the hold in C-RANs. For example, one user is always served by
employment of precoding schemes, large-scale collaborative a selected cluster of RRHs, which means that the elements
processing gains can be achieved in C-RANs with dense not belonging to these RRHs in the precoding matrix are set
RRHs. It is indicated that no more than four RRHs should to zero [22]. Besides, one RRH can be switched off when
be associated for each UE to balance performance gains and all of its coefficients in the precoding matrix are set to zero
implementation cost. In [17], different performance metrics, [23]. In these cases, the coefficients of precoding matrices
such as outage probability, are used to compare downlink should be optimized jointly rather than individually, and thus
beamforming and antenna selection, as well as their impacts the l -norm approximation cannot be used directly because
1
3
TABLEI
the zero entries of the precoding matrices may not align in
SUMMARYOFABBREVIATIONS
the same RRH. To cope with this problem, the mixed l /l -
1 p CRRA cooperative radio resource allocation
norm approximation method can be adopted to induce group
CSI channel state information
sparsity. In [22] and [23], mixed l /l -norm approximation
1 p EE energy efficiency
methods are adopted to handle a group sparse based RRH
HetNet heterogenous network
selection problem. In [22], a traditional mixed l /l -norm
1 p H-CRAN heterogeneous cloud radio access network
method is used to transform group sparse based l -norm
0 IC interference collaboration
constraints. In [23], a three stage group sparse precoding
KKT Karush-Kuhn-Tucker
design algorithm is proposedto minimize the network energy
MBS macro base station
consumptionofC-RANs.Thenon-convexl -normconstraints
0 MIMO multiple-input and multiple-output
aretransformedintoconvexformsbyaweightedmixedl /l -
1 p MUE MBS user equipment
norm method. However, CRRA in H-CRANs for suppressing
QoS quality of service
inter-tierinterferencewhentheprecodingtechniqueswithlow
RRH remote radio head
complexity such as IC and BF are used in the physical layer
RUE RRH user equipment
has not been addressed.
RV random variable
MT mobile terminal
B. Contributions SE spectral efficiency
SINR signal-to-interference-plus-noiseratio
With the developmentof H-CRANs, the designof effective
UE user equipment
large-scale collaborative processing and cross-layer CRRA
WMMSE weighted minimum mean square error
schemes for suppressing both intra-tier and inter-tier inter-
WSR weighted sum rate
ference to improve SE is a key need. Considering the large-
scalecentralizedcollaborativeprocessingintheBBUpool,the
intra-tier interference among RRHs can, in principle, be fully
eliminatedwhenthenumberofRRHsisnottoolarge.Through high SINRs of the MBS, while the IC based CRRA
the IC or BF based CRRA, the inter-tier interference in H- outperforms the BF based CRRA in the regime of the
CRANscanbefurthersuppressed.Themajorcontributionsof low SINRs of the MBS.
this paper can be summarized as follows. Theremainderofthispaperisorganizedasfollows.Section
To mitigate the inter-tier interference between the MBS II describes the H-CRAN system model and formulates the
•
and RRHs in H-CRANs, IC and BF precoding schemes problem of interest. Section III analyzes the distribution of
are employedatthe multiple-antennaMBS. Performance SINR for MUEs and RUEs under IC and BF precoding
metrics, including outage probability, system capacity, schemes. The outage probability, average BER, and system
and average BER are analyzed for both IC and BF sumcapacityunderICandBFschemesarederivedinSection
schemes. In particular, closed-form expressions for dif- IV. Section V presents the BF and IC based CRRA optimiza-
ferentperformancemetricsunderIC andBF are derived. tionproblemsandthecorrespondingsolutions.Thesimulation
Based on the derived closed-form expressions under results for both collaborative processing in the physical layer
•
IC and BF, the key factors, such as the number of and the CRRA in the upper layer are introduced in Section
antennas on the MBS, the number of RRHs, and the VI. Section VII summarizes this paper. For convenience, the
SINRthreshold,impactingtheoveralloutageprobability, abbreviations are listed in Table I.
system capacity, and average BER are evaluated and
compared.
II. H-CRAN SYSTEMMODEL
Under the proposed IC and BF precoding schemes,
•
CRRA to optimize RUEs’ sum rates while guarantee- Unlike in C-RANs, the MBS in H-CRANs delivers the
ing the rates of MUEs is examined. The corresponding control signaling for the whole network, which decouplesthe
optimization problems based on both IC and BF are user plane and control plane. Furthermore, to alleviate the
formulatedasnon-convexproblems,whicharesolvedby heavyburdensonthe fronthaul,some UEswith highmobility
transforming them into convex problems and applying or with real-time traffic are given high priority to access the
the Karush-Kuhn-Tucker (KKT) conditions. Based on MBS. As a result, we can limit our attention to one MBS
the transformed Lagrangian function, the optimal power in the H-CRAN, under which multiple distributed RRHs are
allocation algorithms for both RRHs and the MBS are underlaid within the same coverage of the MBS. Thus, as
developed. illustrated in Fig. 1, the H-CRAN of interest consists of one
The analytical and simulation results suggest that the IC MBS and M RRHs. For any typical radio resource block,
•
and BF schemes should be adaptively switched between K single-antenna MUEs are served by the MBS, while only
based on the system configuration and the adopted per- one single-antenna RUE is associated with each RRH. To
formancemetrics. Meanwhile,the proposedCRRA solu- serve multiple MUEs simultaneously and suppress the inter-
tions can achieve the optimal throughput by optimizing tierinterferenceatRUEsinthedownlink,theMBSisequipped
the transmit power. We see that the BF based CRRA with N antennas (N M + K), while each RRH is
B B
≥
outperforms the IC based CRRA in the regime of the equipped with a single antenna.
4
respectively. Since the interference is much larger than the
noise in an interference-limited H-CRAN, the noise could be
ignored herein. Thus (2) can be approximated as
Fronthaul
Fronthaul Backhaul P h w 2
MUhEM1M1 NBangtMenRnias γMMk ≈ j=1PK,j6=kPM|hMMM|kMwjM|2k+ikPM=|1PR|hRiMk|2. (4)
gMR1 gMR2 hMMk gRRi The intra-tier interference among K MUEs and inter-tier
gRR1 RUEi interference between MUEs and RUEs can be suppressed by
RRH1 gRR2 RRHi precoding schemes in the MBS with multiple antennas.
RUE1 RRH2 MBS hRiMk
RUE2 MUEk III. INTER-TIERCOLLABORATIVE PRECODING SCHEMES
In this section, we describe two collaborative precoding
Fig.1. SystemmodelofanH-CRANwithoneMBSandM RRHs
schemes employed at the MBS with multiple antennas: IC
and BF. The IC scheme enhances the performance gain by
suppressing the interference to the RUEs and other MUEs,
while BF based processing aims at maximizing the signal
The transmit power per antenna in the MBS and RRHs is
gainattheintendeduseranddoesnotcoordinateinterference.
assumed to be P and P , respectively. The transmission
M R
We investigate the distribution of the SINR at the RUE and
symbols for the j-th MUE and the RUE associated with the
MUE, respectively,underthese two precodingschemes in the
i-th RRH are s and s , respectively, which are normalized
as E[ s 2]=MEj[ s 2i]=1.The receivedsignalatthe k-th following subsections.
Mj k ik
MUE(cid:13)and(cid:13)a typicalRUE associated with the i-th RRH can be
(cid:13) (cid:13) A. Interference Collaboration (IC)
written as
When the IC scheme is used at the MBS, the precoding
K M
vector w is chosen by nulling the interference to the RUEs
y = P h w s + P h s+n , k
MMk M MMk j Mj R RiMk i MMk and other MUEs, which means w Null(G˜ ), where G˜ =
Xj p Xi p k ∈ k k
[g ; ;g ;h ; ;h ;h ; ;h ]
K MR1 ··· MRM MM1 ··· MMk−1 MMk+1 ··· MMK
yRRi=pPRgRRisi+Xj pPMgMRiwjsMj +nRRi, ∈andC(M()+HK−d1e)×noNtBes, Nthuell(Gc˜okn)ju=gat{evt∈ranCspNoBs×e.1 :FGu˜rkthver=mo0r}e,,
·
(1) g w = 0, and h w = 0 ( j K,j = k). Thus
respectively, where hMMk ∈C1×NB represents the radio link γMRRRiiink(3) and γMMMkMinj(4k) under IC∀ ca∈n be sim6 plified as
between the MBS and the k-th MUE, and h represents
RiMk γIC =P g 2,
the interference link from the i-th RRH to the k-th MUE. RRi R| RRi|
gMRi ∈ C1×NB represents the interference link between γIC = PM|hMMkwk|2 . (5)
the MBS and the RUE associated with the i-th RRH, and MMk M P h 2
g represents the radio link between the i-th RRH and its i=1 R| RiMk|
seRrRveid RUE. Note that the inter-RRH interference amongst Hence from (5), γRICRiP∼ PRχ2RRi(2), where χ2RRi(2)
RRHs in H-CRANs can be ignored due to the centralized denotes a chi-squared random variable with two degrees of
signalprocessingintheBBUpoolthroughtheidealfronthaul. freedom. If the dimension of Null(G˜k) is greater than 1, i.e.,
We assume the radio links experience independent Rayleigh dim Null(G˜ ) >1,thetransmitprecodingvectorw could
k k
fading, so the components of hMMk and gMRi are indepen- be fu(cid:16)rther optim(cid:17)ized in the sense of maximizing the term
dent CN(0,1), hRiMk ∼ CN(0,1), and gRRi ∼ CN(0,1). |hMMkwk|2. This optimization problem can be formulated as
n and n are independent normalized additive zero-
MMk RRi wopt =argmax h w 2
mean Gaussian noises experienced at the k-th MUE and the k | MMk k|
typical i-th RUE, respectively, i.e., n (0,1), and s.t. w 2 =1, (6)
nRRi ∼ CN(0,1). wj ∈ CNB×1 reMprMesken∼tsCthNe precoding kwkkk Null(G˜k).
vector applied at the MBS for the j-th MUE. ∈
Denoting C = Null(G˜ ), the original optimization prob-
Accordingto (1), the received SINR for the k-th MUE and k k
lem is equivalent to
the typical RUE can be expressed as
γMMk = K PM|hMMkMwk|2 , (2) xs.otp.t =xar2gm=a1x,|hMMkCkx|2 (7)
P h w 2+ P h 2+1 k k
M| MMk j| R| RiMk| where x satisfies w = C x. This problem is convex with
j=1P,jγ6=k = PR|gRRiP=i|12 , (3) xopt = (khhMMMMkkCCkk)Hk,ki.e., k
RRi PMPKj (cid:12)(cid:12)gMRiwj(cid:12)(cid:12)2+1 wokpt =Ck(khhMMMMkkCCkk)kH. (8)
5
Following [15], h wopt 2 χ2 , The expression (15) can be approximately obtained as
|uhnRdieMrkIC|2i∼s sχta2RtiisMtikc(a2l(cid:12)(cid:12)l)y.MAeqMsukaivarkelesnu(cid:12)(cid:12)tlt,toth∼e rece2iv(NedB−S(IKN+RMin−1()4)) F (z) 1 e−bNz L−1(az)k k Ci bN i
Z ≈ − (M 1)! k! k(cid:18) a (cid:19) (17)
P χ2 − Xk=0 Xi=0
γMICMk ∼ M 2(PNRB−χ(22KM+M−1)). (9) (az+1)−(k+M−i)Γ(k+M −i).
Proof: See Appendix B.
Before starting the performance analysis, we present the
Here, by comparing the SINR distribution in (13) with
following lemmas.
the RVs defined in Lemma 2, the CDF of γBF can be
Lemma 1: Consider independent random variables (RVs) MMk
approximately expressed as
X χ2 andY χ2 .Thecumulativedistributionfunction
(CD∼F)2oLf Z = aY∼X+b2iMs PBF (x) 1 e−(K−1)x NB−1(ax)k k Ci K−1 i
FZ(z)=1− (Me−bz1)!L−1(akz!)k k Cki(cid:18)ab(cid:19)i (10) γMMk ≈(ax−+(1M)−−(k+1M)!−iXk)=Γ0(k+kM! Xi=i0), k(cid:18) a (cid:19)
− Xk=0 Xi=0 − (18)
(az+1)−(k+M−i)Γ(k+M i). where a= PR. Meanwhile, according to Lemma 1, the CDF
− PM
Proof: See Appendix A. of γRBRFi can be directly obtained as
derAivcecdoradsing to Lemma 1, the CDF of γMICMk can be directly PγBRFRi(x)=1−e−bx(cid:16)xa +1(cid:17)−K, (19)
1 NB−K−M (az)k where b= 1 .
PγIMCMk(x)=1−(M−1)! Xk=0 k! (az+1)−(k+M)Γ(k+M), ComparePdRwith IC, the above analytical results suggest
(11) that the received signal power at an MUE under BF changes
wchhie-srqeuaare=disPPtMRrib.uMtioena,nwi.eh.i,le, the CDF of γRICRi follows the fdreogmreeasχo22f(fNreBe−d(oMm+(KD−o1F))s).RMVetaonwahχil22eN,BtheRVRUwEitihntienrcferereansecde
power is increased from 0 to a χ2 RV. Thus the effects
PγIRCRi(x)=1−e−PxR. (12) of the precoding schemes on the sys2tKem performance are not
immediatelyclear.Inthefollowingsections,threeperformance
metrics, i.e., outage probability, average BER, and system
B. Beamforming (BF)
capacity, are characterized when the MBS employs these
Inthesingle-cellscenario,eigen-beamformingisoptimalfor precoding schemes.
themultiple-inputsingle-outputsystem[24].Forthek-thuser,
hH
the precoding matrix wk can be expressed as wk = MMk . IV. PERFORMANCE ANALYSIS OFPRECODING SCHEMES
Therefore, we can have h w 2 χ2 . AccouknhtiMnMgkfkor Inthissection,we analyzesystem performancegainsunder
| MMk k| ∼ 2NB
the term h w 2, since the design of the precoder w is thetwoprecodingschemes.FromthedistributionoftheSINR
independe|ntMoMfkhj| and w is a normalized vector wjith for the MUE and RUE, we see that the interference experi-
MMk j
unit-norm,we caneasily get h w 2 χ2. The γ in enced by the RUE is eliminated at the expense of sacrificing
(4) is statistically equivalent|toMMk j| ∼ 2 MMk the spatial degrees of freedom of the MBS. Therefore, the
effects of the precoding schemes on system performance is
P χ2
γBF M 2NB . (13) the focus of the following paragraphs, i.e., we characterize
MMk ∼ PMχ22(K 1)+PRχ22M the outageprobability,system sum capacity andaverageBER
−
when the MBS uses the different precoding schemes.
Since g and w are independent and w 2 = 1, we
MRi j k jk
also have g w 2 χ2 (2). Accordingly, we have
MRi j ∼ MRi A. Overall Outage Probability
(cid:12) (cid:12)
(cid:12) (cid:12) P χ2
γBF R· 2 . (14) A system outage occurs when any received SINR of any
RRi ∼ PM ·χ22K +1 potential link for the MBS-association and RRH-association
Lemma2:ConsiderindependentRVsX χ2 ,Y χ2 , falls below a threshold SINR. We use the overall outage
and Y χ2 . The CDF of Z = X ∼is 2L 1 ∼ 2M probabilitytoevaluatetheperformanceofthesetwoprecoding
2 ∼ 2N aY1+bY2 schemes [13]–[15], which can be formulated as
z aMbNxL 1
F (z)= − I(M,N,L,a,b,x)dx, (15) P =Pr min(γ , ,γ ,γ , ,γ )<γ
Z Z Γ(L)Γ(M +N) out { MM1 ··· MMK RR1 ··· RRM th}
0
=1 Pr γ >γ , ,γ >γ ,
where − { MM1 th ··· MMK th
γ >γ ,...,γ >γ ,
I(M,N,L,a,b,x)= ∞xM+N+L−1e−(y+1b)y RR1 th RRM th} (20)
Z where γ is the SINR threshold.
0 (16) th
1 1 Consideringthatallelementsofthechannelsforthevarious
F M;N +M; ( )y dy.
1 1(cid:18) − a − b (cid:19) pairs of transmitters and receivers are independent, (20) can
6
be rewritten as Proof: Given two independent RVs X χ2 , Y χ2 ,
K M and a>0,b>0, by defining Z = aYX+b∼, its2LCDF∼can2Mbe
P =1 Pr γ >γ Pr γ >γ expressed as [25]
out − { MMk th} { RRi th} (21)
kY=1 Yi=1
=1 [1 P (γ )]K[1 P (γ )]M. F (z)= ∞F (ayz+bz)f (y)dy
− − γMMk th − γRRi th Z Z X Y
0
tioDneudePto the saunbdstaPntial ,dicflfoesreendc-feosrmbetewxpeerensstihoensaffoorremPen- =1 e−bz L−1 k Ci(az)k(b)i (26)
γMMk γRRi out − (M 1)! k k! a
with the two precoding schemes are presented independently − Xk=0 Xi=0
as follows. (az+1) (k+M i)Γ(k+M i).
− −
−
IC: Substituting (11) and (12) into (21), the overall outage
With this CDF expression, we have
probability of the IC scheme in H-CRANs can be derived as
PIC=1 1 NB−K−M (aγth)k(aγ +1) (k+M) E[log (1+z)] = 1 ∞ 1−FZ(z)dz
out −(cid:20)(M 1)! k! th − 2 ln2Z 1+z
− Xk=0 0
Γ(k+M) Ke−MPγRth, (22) = ln2(M1 1)!L−1(a)ki−!M k Cki(ab)i
(cid:21) − kX=0 Xi=0
whBeFre:aSu=bsPtPiMRtu.ting (18) and (19) into (21), the overalloutage Γ(k+M −i)Z0∞ (z+1)(zzke+−b1z)k+M−idz.
a
probability of the BF scheme in H-CRANs can be derived as (27)
By applying the decomposition
PBF =1 e−(K−1)γth NB−1(aγth)k k Ci(K−1)i
out −(cid:20) (M 1)! k! k a 1
− Xk=0 Xi=0
(aγth+1)−(k+M−i)Γ(k+M−i)(cid:21)K(cid:20)e−PxR(γath+1)(cid:21)−KM. ((z1+11))(iz−+M−a1k)k+Mk−−ii+M (1 1)i+j−M−k−1 (28)
(23) = a − a − ,
z+1 − Xj=1 (z+ a1)j
Both (22) and (23) show that the overalloutage probability
the ergodic capacity in (27) can be rewritten as
strictly depends on N , K, M, γ , and the ratio of P to
B th R
P . It is hard to directly determine which precoder is better,
M
andthuswewillshowperformancecomparisonsforthesetwo E[log (1+z)]
2
mTheethpordescowdhinegnstcahkeimnge disifafedraepnttivceolynfisegluercatteidontsoimntionimaciczoeutnhte. = 1 L−1ai−M k Ci(b)iΓ(k+M i)
In2(M 1)! k! k a −
overall outage probability. − Xk=0 Xi=0
∞ (a1 −1)i−M−kzke−bzdz k−i+M k Cm
B. Sum Capacity Z z+1 − k
(cid:2) 0 Xj=1 mX=0
The sum capacity of the entire system can be expressed as (1 1)i+j−M−k−1( 1)m ∞(z+ 1)k−m−je bzdz
−
R= K E log (1+γ ) + M E log (1+γ ) . a − −a Z0 a (2(cid:3)9)
kX=1 (cid:2) 2 MMk (cid:3) Xi=1 (cid:2) 2 RRi ((cid:3)24) = In2(M1 1)!L−1aik−!M k Cki(ab)iΓ(k+M −i)
Before analyzing the sum capacity under IC and BF − Xk=0 Xi=0
k i+M k
schemes, we present the following lemmas. 1 − 1
( 1)i M kebΓ(k+1)Γ( k,b) Cm( )m
Lemma 3: Consider independent RVs X χ2 and Y a − − − − − k −a
χ2 , and define Z = X . We have ∼ 2L ∼ (cid:2) Xj=1 mX=0
2M aY+b b 1
a−k+m+j−1eabΓ(k i j+1, )( 1)i+j−M−k−1 ,
− − a a −
R (a,b,L,M)=∆ E[log (1+Z)] (30(cid:3))
1 2
where (29) is obtained by performing binomial expansion on
L 1 i M k
= ln2(M1 1)! − (a)k−! Cki(ab)iΓ(k+M −i) t3h.3e8t3er.1m0(azn+d Ea1q−. 3a1.)3k8.2T.4heinn([3206)].is obtainedaccordingto Eq.
− Xk=0 Xi=0
Lemma 4: For an RV X χ2, and Y = δX,δ > 0, we
(1 1)i M kebΓ(k+1)Γ( k,b) k−i+M k Cm( 1)m have ∼ 2
a− − − − − k −a
(cid:2) a−k+m+j−1eabΓ(k i j+1, b)(X1j=1 1mX)i=+0j−M−k−1 . R2(δ)=∆ E[log2(1+Y)]= ln12e1δE1(cid:18)1δ(cid:19), (31)
− − a a − (2(cid:3)5) where E1(z)= z∞ e−ttdt is the exponentialintegral function
R
7
of the first order. where β and β are coefficients that depend on the mod-
1 2
Proof: According to the chi-squared distribution, we have ulation mode, and Q(x) = 1 ∞exp( u2)du is the tail
√2π x − 2
the CDF of Y is probability of the standard normaRl distribution.
y For simplicity, we consider Binary Phase Shift Keying
FY(y)=1 e−δ, (32)
− (BPSK) modulation in this paper, which correspondsto β =
1
and thus β = 1. For other modulation formats, similar results could
2
E[log2(1+Y)]= ln12Z0∞ 1−1F+Yy(y)dy = (33) awlshoenbexo≥bt0a.inTehdu.sN,othteetahvaetrQag(ex)BEisRmcoannotboeniacpapllryoxdiemcareteadsinags
ln12Z ∞ 1e−+yδydy = ln12e1δE1(cid:18)1δ(cid:19). Be ≈ 2(K+1M)√π Z +∞ e√−zzPγe(z)dz, (39)
0 0
Due to the differences between the aforementioned γ where
MMk
andγ , usingLemma3andLemma4,closed-formexpres-
sionsRfoRrisum capacity R under these two precoding schemes γe =min{γMM1,...,γMMK,γRR1,...,γRRM}. (40)
are presented as follows. The CDF of γ can be expressed as
e
IC: Substituting the distribution of γIC and γIC into
• (24),thesumcapacityundertheICscMhMemkeinH-RCRRiANs Pγe(z)=Pr{min(γMM1,...,γMMK,γRR1,...,γRRM)<z}
K M
can be derived as =1− 1−PγMMk(z) 1−PγRRi(z) .
P (cid:2) (cid:3) (cid:2) (cid:3) (41)
RIC =R R,0,N M,M +R P , (34)
1 B 2 R
(cid:16)PM − (cid:17) (cid:16) (cid:17) Due to aforementioned differences in γ and γ ,
MMk RRi
where R1() and R2() follow (25) and (31). the expressions for Be under the two schemes are presented
· ·
BF:SubstitutingthedistributionofγBF andγBF into separately as follows.
• MMk RRi
(24),thesumcapacityundertheBFschemeinH-CRANs
IC: Substituting (11) and (12) into (41), and further
can be derived as •
into (39), the average BER under the IC scheme can be
P P 1
RBF =R R,K 1,N ,M +R M, ,1,K , obtained as
1 B 1
(cid:16)PM − (cid:17) (cid:16)PR PR (35)(cid:17) BIC 1 +∞ e−zPIC(z)dz, (42)
e ≈ 2(K+M)√π Z √z γe
where R () follows (25). 0
1
· where
Similar to the overall outage probability results in (22) and
(23), the derived sum capacity strictly depends on NB, K, PIC(z)=1 1 N−K−M (az)k(az+1) (k+M)
wMh,icahnpdrethceodreartiiosboefttPerR,atsothPisMd.epItenisdshoanrdthteosdpierceicfitclysyjustdegme γe −(cid:20)(M−1)! Xk=0 k! −
K
configurations. Mz
Γ(k+M) e−PR (43)
(cid:21)
with a= PR.
C. Average Bit Error Rate PM
BF: Substituting (18) and (19) into (41), and further
•
TheaverageBERisdefinedastheaverageBERofallradio into (39), the average BER under the BF scheme can
links, which can be expressed as be obtained as
Be =∆ K+1M(cid:18) K BMk + M BRi (cid:19), (36) BeBF ≈ 2(K+1M)√π Z0+∞ e√−zzPγBeF(z)dz, (44)
Xk=1 Xi=1
where
where Bk is the BER of the link between the MBS and the
k-th MUME, and BRi is the BER of the RRH-RUE link in the PBF(z)=1 e−(K−1)z NB−1(az)k k Ci(K−1)i
i-th cell. γe −(cid:20)(M 1)! k! k a
− Xk=0 Xi=0
Note that the average BER of two end nodes is dominated K KM
by the worst one [25]; therefore, we can rewrite the average (az+1)−(k+M−i)Γ(k+M i) e−PxR(z+1) − .
− (cid:21) (cid:20) a (cid:21)
BER approximately as
(45)
1
Be ≈ K+M max{BM1 ,··· ,BMK,BR1,··· ,BRM}. (37) TheaforementionedexpressionsforICandBF suggestthat
theaverageBERdependsonthesystemconfiguration,suchas
For commonly used modulation schemes, the BER of each
the numberof RRHs M, the numberof MUEs K, the transmit
link B can be written in the form
b power per antenna in the MBS P , and the transmit power
M
+ per antenna in the RRH P . It is hard to directly compare
B =E[β Q( 2β γ)]= ∞β Q( 2β z)p (z)dz, R
b 1 2 1 2 γ which is better between (42) and (44), and such comparisons
Z
p 0 p
(38) will be based on the numerical results shown in Section VI.
8
V. INTER-TIERCOOPERATIVE RADIO RESOURCE in (46) can be reformulated as
ALLOCATION
M
max IC = log (1+P g 2)
{PM,PRi} RR Xi=1 2 Ri| RRi|
s.t. P P ,
Under the inter-tier collaborative precoding schemes IC M MS
≤
and BF, CRRA can be used to further suppress the inter-tier P P , i=1,2,...,M,
Ri ≤ RSi
interference to optimize the throughput of H-CRANs. Since M
the MUE prefers to access the MBS for seamless coverage, P P ,
Ri ≤ RS
while the RUE often associates with RRHs to achieve high Xi=1
bit rate, we can maximize the RUEs’ aggregated rates while log (1+γ ) , k =1,2,...,K,
2 MMk ≥RMS
guaranteeing the MUEs’ summarized bit rates to model the P h wopt 2
throughput maximization problem. Furthermore, we can as- γIC = M MMk k , k =1,2,...,K.
sume that the power of each RRH is different to make the MMk Mi=(cid:12)(cid:12)1PRi|hRiMk(cid:12)(cid:12)|2
powerallocationforeachRRHflexible.Hence,thethroughput P (49)
maximization problem for H-CRANs can be formulated as
Noting that the RUEs’ sum rates IC are only determined
RR
M by the RRH’s power P , we have the following proposition.
Ri
msa.tx. PRMR =XPi=M1Slo,g2(1+γRRi) proPbrloepmos(i4ti9o)n. D1e:fiLneetA{kPM=opt,PPMRoSpi2|tRh}MMMSdkewn1okoptte|2.thTehesonluPtiMoopnt =to
≤ P , and −
MS
P P , i=1,2,...,M, (46)
Ri ≤ RSi 1 1
M Popt = , (50)
PRi ≤PRS, Ri λi+µ+ Kk=1νk|hRiMk|2 − |gRRi|2
Xi=1 where λ ,µ,ν are choPsen elaborately such that (49)-(54).
i k
log2(1+γMMk)≥RMS, k =1,2,...,K, Proof: Since the MBS power PM occurs only in the
wPRheSriearReMreSspiescttihveelyQothSetphorwesehrollidmoitfseoafcthheMMUBES, PanMdSRaRnHd cIConssctrhaeimntes,aannddoopetismnaoltPafMfecctatnhebReUacEhsi’esvuemd irnatethseRfIRoClloiwnitnhge
i, and PRS is the total power threshold of the RRHs. Note limitation under a fixed PRi:
hthoaltdsprfoobrltehme k(4-t6h)MisUfeEa:sible only if the following condition (2RMS −1) Mi=1PRi|hRiMk|2,P . (51)
h h P wopt 2 MSi
2RMS 1 PMSγMMk. (47) (cid:12) MMk k (cid:12)
− ≤ PM However,consider(cid:12)ingthemaxi(cid:12)mizationoftheMBS’scover-
age, we denote the optimal P as Popt =P . Substituting
This condition indicates that the QoS thresholds for the Popt into the original problemM(49),M(49) canMbSe simplified to
MUEs should not be too high. This can be intuitively under- M
the following problem:
stoodsincetheQoSconstraintsmustatleastbesatisfiedwhen
the maximum allowable power of the MBS P is applied. M
MS max log (1+P g 2)
T(4h7e)reaflowrea,ysthhroouldgshofuotrtahneyreMstUoEf,thwehipcahpegru,awraentaesessumtheatthaant {PRi} Xi=1 2 Ri| RRi|
s.t. P P , i=1,2,...,M,
optimal power allocation exists. Ri ≤ RSi
M (52)
P P ,
Ri ≤ RS
Xi=1
M
P h 2 A , k =1,2,...,K.
Ri| RiMk| ≤ k
A. Interference Collaboration Xi=1
It is observed that (52) is a typical convex optimization
problem,which can be solvedby employingKKT conditions.
When the IC scheme is used at the MBS, the precoding
Therefore, the Lagrangian function of (52) is defined as
vectorischosentoeliminatetheinter-tierinterferencetoother
MUEs and RUEs, i.e., M
L(P ,λ ,µ,ν )=ln2 log (1+P g 2)
(h C )H Ri i k 2 Ri| RRi|
wopt =C MMk k . (48) Xi=1
k k h C
k MMk kk M M
+ λ (P P )+µ(P P )
Hence, γ in (5) can be substituted into (46), and the i RSi − Ri RS − Ri
RRi Xi=1 Xi=1
transmit bit rate threshold for the MUE can be further
RMS K M
dtheeritvherdouifgh(p4u8)tmisasxuimbsitziatutitoendpinrotoblγemMMfokritnhe(5IC).bAacsceodrCdiRngRlAy, +kX=1νk(Ak−Xi=1PRi|hRiMk|2),
9
where λ 0, µ 0, and ν 0 are the non-negative La- corresponding SINRs for RUE i and MUE k, as follows:
i k
≥ ≥ ≥
grangemultipliersassociatedwith the constraintsin (52). The
P g 2
KKT conditionscan be appliedon the Lagrangianfunctionto γBF = Ri| RRi| , i=1,2,...,M,
RRi K
obtain 2
P g w +1
M MRi j
∂L(PR∂iP,λRii,µ,νk) =1+P|gRoRpiRt|ig|R2Ri|2 −λoipt γMBFMk = jP=1K(cid:12)(cid:12) PM|(cid:12)(cid:12)hMMkwkM|2 ,
K P h w 2+ P h 2
−µopt− νkopt|hRiMk|2 Mj=1P,j6=k| MMk j| iP=1 Ri| RiMk|
kX=1 k =1,2,...,K.
= 0, (53)
Hence the sum rates optimization problem for the BF
λopt(P Popt)=0, i=1,2,...,M, (54) scheme can be formulated as
i RSi − Ri
Popt P , i=1,2,...,M, (55) M
Ri ≤ RSi max BF = log (1+γBF )
µopt(P M Popt)=0, (56) {PM,PRi}RR Xi=1 2 RRi
RS −Xi=1 Ri s.t. PM ≤PMS,
M PRi ≤PRSi, i=1,2,...,M, (61)
PRopit ≤PRS, (57) M
Xi=1 PRi ≤PRS,
M Xi=1
νkopt(Ak−Xi=1PRopit|hRiMk|2)=0, k =1,2,...,K, (58) log2(1+γMMk)≥RMS, k =1,2,...,K.
M Finding the optimal power allocation for such a nonconvex
PRopit|hRiMk|2 ≤Ak, k =1,2,...,K, (59) problem is a very challenging task, since (61) is not jointly
Xi=1 convexin P ,P .However,despitethisdifficulty,wecan
{ M Ri}
where λopt, µopt, and νopt are optimal solutions to the provideastationarysolutionfor(61)sinceitisconvexineach
i k
Lagrangian function. variable and can be transformed into a convex problem:
Based on (53), an optimalsolutionto (52) can be obtained,
Optimal P under fixed P : For fixed P , BF is
i.e., • Ri M M RR
concave in P since
Ri
∂2 BF C2
Popt = 1 1 . (60) ∂{RP2R } =−(1+CiP )2 <0,
Ri λopt+µopt+ K νopt h 2 − g 2 Ri i Ri
i k=1 k | RiMk| | RRi| and (61) can be simplified into
P
Note that an optimal solution needs to satisfy (49)-(54).
M
However, optimal λopt, µopt, and νopt are not easy to
find. Fortunately, PRopiit is monotonicallky decreasing in each {mPRaix} Xi=1log2(1+CiPRi)
multiplier, which makes it possible to compute the optimal
s.t. P P , i=1,2,...,M,
λopt, µopt, and νopt. The following lemma providesintervals Ri ≤ RSi
i k M
containing the optimal multipliers.
P P ,
Lemma5:Theoptimalλoipt,µopt,andνkopt satisfying(44)- Xi=1 Ri ≤ RS
(49) are respectively within [0,λmax], [0,µmax], and [0,νmax], M
i k
mwhineirenλ|h|migRRaixRMi=k|2|2|ogR. Ri|2, µmax = mini{|gRRi|2}, and νkmax = Xi=1PRi|hRiMk|2 ≤Bk, k =1,2,...,K(,62)
Proof: The results follow from the fact that Popt 0. where
Ri ≥
g 2
C = | RRi| , i=1,2,...,M,
i
K
2
P g w +1
M MRi j
jP=1(cid:12) (cid:12)
(cid:12) (cid:12)
B. Beamforming P h w 2 K
B = M| MMk k| P h w 2,
k 2RMS −1 − Mj=X1,j=k| MMk j|
6
When the BF scheme is used at the MBS, the precoding
k =1,2,...,K.
vector of MUE k is determined by the h , i.e., w =
hH MMk k It is not difficult to see that (62) has a similar form to
MMk . With precodingvectorswk fixed, we can obtain the (52), and according to the solution to (52), we give the
khMMkk
10
optimal solution to (62) as follows: is (MK) mainly due to the computation of ν . With these
k
O
three multipliers obtained, the rate computation procedure in
1 1
Popt = , Step 4 requires a computational complexity in the order of
Ri λoipt+µopt+PKk=1νkopt|hRiMk|2 − Ci(63) O(K2NB), which mainly depends on the optimal MBS’s
transmitpowerdesign(70).InStep5,theadditionalcomputa-
with optimal Lagrange multipliers λopt 0, µopt 0, tionalcomplexityforupdatingalltheoptimalpoweris (M).
and νopt 0. Similarly, the optimail so≥lution need≥s to The last Step 6 of computing the achievable RUEs’ suOm rate
satisfykthe≥following constraints: RBRF needs a computational complexity with O(MKNB).
Considering a typical network scenario with N > M > K,
λopt(P Popt)=0, (64) B
i RSi − Ri the computational complexity of Algorithm 1 per iteration is
PRopit ≤PRSi, (65) O(MKNB), which mainly comes from the calculation of
the optimal MBS’s transmit power (70). Actually, under a
M
µopt(PRS −Xi=1PRopit)=0, (66) psirzoepeorfimniutilatilpizliaetrios,nthoef n{uPmRbi,ePrMof}itaenradtiothnes disetneormt lianregdesatnepd
M theproposedalgorithmcanquicklyconverges,whichhasbeen
Popt P , (67) demonstrated in the following simulation results.
Ri ≤ RS
Xi=1
M VI. NUMERICAL RESULTS
νkopt(Bk− PRopit|hRiMk|2)=0, (68) In this section, the performance of collaborative precoding
Xi=1 IC and BF algorithms in the physical layer is first evaluated.
M Then,theICandBFbasedCRRAsolutionsaresimulatedand
Popt h 2 B . (69)
Ri | RiMk| ≤ k discussed.Inparticular,severalperformancemetricsincluding
Xi=1 the system outage probability, sum capacity, and average
In this case, we also provide a lemma concerning the BER are presented for the collaborative precoding IC and
intervals containing the optimal multiplier. BF algorithms. The RUEs’ aggregated rates under IC and
Lemma 6: The optimal λoipt, µopt, and νkopt satisfying BF are considered to evaluate the proposed CRRA solution’s
(53)-(58) are respectively within [0,λmiax], [0,µmax], and performance.Tomatchwellwiththeconcernedsystemmodel,
[0,νkmax], where λmiax = Ci, µmax = mini{Ci}, and itisassumedthatanH-CRANscenarioconsistingofoneMBS
νOkmpatxim=amlPininu|nhdReCiMrikfi|x2eod.P :WiththeP fixed, BF wThitehMonBeSMiUsElo,caanteddMinRthReHscewntiethr oMf tRheUEcsellisacroeansiwdietrheda.
• M Ri Ri RR radiusof500meters,whiletheRRHsandMUEareuniformly
is monotonically decreasing in P . The optimal P is
M M distributed in the coverage area of the MBS. The RUE is
achieved at
uniformly distributed in the coverage area of each accessed
PMopt =max{Pkcand}, RRH with a radius of 50 meters.
M Fig. 2 shows the system outage probability under different
Pkcand = (2RMS −1)iP=1PRi|hKRiMk|2 , panredcotdhiengsysscthememeosutaasgefupnrcotbioanbsiliotyf tghreowSsINoRf tchoruerssheoladsγtthhe,
|hMMkwk|2−(2RMS −1) |hMMkwj|2 threshold of SINR increases. The number of antennas on the
j=1P,j6=k MBS is set to six, and one MUE is considered. The Monte
k =1,2,...,K. Carlosimulationresultsmatchwellwiththoseindicatedbythe
(70) presented closed-form overall outage probability expressions.
The algorithm can be summarized as follows. When M is set to 3, BF outperforms IC due to its capability
to increase the received signal power strength. However,
when M is 5, IC is preferred because it can alleviate the
Algorithm 1 The RUEs’ sum rate optimization for BF.
dominating interference. The outage probability gap for IC
1: Initialize All primal variables PRi, and PM. between M = 3 and M = 5 is larger than for BF, which
2: repeat
suggests that IC is more sensitive to the number of RRHs.
3: Step 3: Compute the multipliers λi, µ, and νk; Next, the impact of the number of antennason the MBS is
4: Step 4: Compute the PRi and PM according to (63) shown in Fig. 3, where we set M = 2, γ = 0 dB and one
and (70); th
MUE is considered. The overall outage probability decreases
5: Step 5: Update the optimal Popt,Popt;
6: Step 6:ComputetheachievabMleRUERsi’sumrate BF; withanincreasingnumberofantennasontheMBS.WhenNB
RR is relatively large, IC becomesbetter with the optimization in
7: until Convergence.
(6). When N is relatively small, BF outperforms IC. This
B
resultdemonstratesthatalargenumberofantennasattheMBS
In Algorithm 1, each step can be done with a closed- is preferredto increase system reliability when the numberof
form manner and the value of each variable can be easily antennas at the RRHs is fixed.
calculated, which makes the proposed algorithm efficiently Fig. 4 shows the system sum capacity under the two
work. In Step 3, the complexity of computing the multipliers precodingschemesversusSINR atthe MBS with M =2 and