Table Of ContentMatching Theory for Backhaul Management in Small Cell
Networks with mmWave Capabilities
Omid Semiari†, Walid Saad†, Zaher Dawy‡, Mehdi Bennis∗
†Wireless@VT, Bradley Department of Electrical and Computer Engineering, VirginiaTech, Blacksburg, VA, USA,
Email: {osemiari,walids}@vt.edu
‡ Department of Electrical and Computer Engineering, American University of Beirut, Beirut, Lebanon, Email: [email protected]
∗Centre for WirelessCommunications-CWC, University of Oulu, Finland, Email: [email protected].fi
5 Abstract—Designingcost-effective andscalable backhaulsolu- SCBSs to communicateover broadbandbackhaullinks, while
1 tions is one of the main challenges for emerging wireless small causing negligible interference to other, wireless backhaul
0 cell networks (SCNs). In this regard, millimeter wave (mmW) links in the SCN. However, mmW signals attenuate rapidly
2 communicationtechnologieshaverecentlyemerged asanattrac-
with distance and cannot easily penetrate obstructing objects.
tive solution to realize the vision of a high-speed and reliable
n wireless small cell backhaul network (SCBN). In this paper, a Consequently, mmW frequencies are usually used for line
a novel approach is proposed for managing the spectral resources of sight (LOS) point-to-point communication. Due to these
J
of a heterogeneous SCBNthat can exploit simultaneouslymmW limitations, mmW communication has to coexist with the
1 and conventional frequency bands via carrier aggregation. In
conventionalsub-6 GHz band which is attractive for non line
1 particular, a new SCBN model is proposed in which small cell
base stations (SCBSs) equipped with broadband fiber backhaul of sight (NLOS) transmissions [4]. Therefore, aggregating
] allocate their frequency resources to SCBSs with wireless back- mmW band with sub-6 GHz band at the backhaul network
T
haul, by using aggregated bands. One unique feature of the provides an appealing and robust solution for small cell
.I studiedmodelisthatitjointlyaccountsforbothwirelesschannel backhaulnetworks(SCBNs), especially, in dense urbanareas.
s characteristics and economic factors during resource allocation.
The concurrent transmissions at different frequency bands
c
Theproblemisthenformulatedasaone-to-manymatchinggame
[ is achievable by using carrier aggregation (CA) technique,
andadistributedalgorithmisproposedtofindastableoutcome
1 of the game. The convergence of the algorithm is proven and introduced in LTE-Advanced standard [7]. Another practical
v the properties of the resulting matching are studied. Simulation challenge for supporting an SCBN with mmW is the need
0 results show that under the constraints of wireless backhauling, for multi-MNO support [4]. In fact, an SCBS with NLOS
1 the proposed approach achieves substantial performance gains, backhaul links may need the relaying support of neighboring
4 reaching up to 30% compared to a conventional best-effort SCBSs that belong to a second MNO. Therefore,multi-MNO
2 approach.
operation will significantly increase the flexibility for mmW
0
I. INTRODUCTION utilization.
.
1
The rapid proliferation of smartphones, tablets, and In this regard, different wireless backhaul solutions have
0
bandwidth-intensive wireless services has drastically strained been proposed so far for SCNs. The authors in [8] propose
5
1 the resources of existing cellular networks [1]. To cope with a fair resource allocation for the out-band relay backhaul
: this increasing traffic demand, small cell networks (SCNs) links,enabledwithCA. Theproposedapproachin[8] aimsto
v
have been introduced as a promising approach to boost the maximizethe throughputfairness amongbackhauland access
i
X coverage and capacity of current cellular networks [2]. These links in LTE-Advanced relay system. In [9], a backhaul re-
r anticipated performance gains will be due to a cell size source allocation approachis proposedfor LTE-Advancedin-
a
reduction and a dense deployment of small cell base stations band relaying. This approach optimizes resource partitioning
(SCBSs).Nonetheless,thisparadigmshiftincellularnetworks between relays and macro users, taking into account both
will lead to new challenges, specifically for the backhaul backhaulandaccesslinksquality.In[10],adynamicbackhaul
networkdesignandmanagement[2].Infact,duetounplanned resource allocation approach is proposed using evolutionary
and dense deployment of small cells, it may not be economi- game theoretic approach. Instead of static backhaul resource
cally viable for mobile network operators (MNOs) to deploy allocation, the authors take into account the dynamics of
broadbandfiber backhaulfor everySCBS [3]. Therefore,new users’ traffic demand and allocate sufficient resources to the
cost-effective backhaul solutions are required that provide base stations, accordingly. Although interesting, the body of
sufficient bandwidth to support the backhaul traffic of the workin[5], [8]–[10]doesnotconsidermmWcommunication
densely deployed SCNs. at the SCBN and is primarily focused on modeling rather
One promising solution for backhauling in SCNs is via the than resource allocation. In addition, it does not account for
use of millimeter wave (mmW) communications [3]–[6]. The the effect of backhaul cost in modeling backhaul networks
mmW spectral band ranging between 30-300 GHz will allow and solely focuses on physical layer metrics, such as links’
the deployment of highly directional antennas, as well as the capacity and fairness.
possibility of transmission over a large available bandwidth, Inwireless networks,the backhaulcostcoversa substantial
up to 1 GHz. Such characteristics of mmW would help portionofthetotalcostofownership(TCO)forMNOs[3].In
fact, it is economically inefficient for an individual MNO to
affordtheentireTCOofanindependentbackhaulnetwork[3].
Therefore, MNOs may need to share their backhaul network
resources with other MNOs that demand backhaul support
for their SCBSs. Hence, beyond the technical challenges of
backhaul management in SCNs, one must also account for
the cost of sharing backhaul resources between MNOs. The
work in [11] proposes an economic framework to lease the
frequencyresourcestodifferentMNOsbyusingnovelpricing
mechanisms. In [12], the authors propose a cost evaluation
model for SCBNs. This work highlights the fact that inte-
grating heterogenous backhaul technologies is mandatory to
achieve a satisfactory performance in an SCBN. Moreover,
they show that the TCO of an SCN is much higher than Fig.1.Asmallcellbackhaul network withcarrier aggregation.
conventional cellular networks. Therefore, it is more critical the core network. We assume that D-BSs belong to a second
to consider backhauling cost in SCBN design. The provided network operator q2 and have to pay the A-BSs for receiving
solutions in [11], [12] concentrate only on the economic backhaulservice.ThesystemmodelisshowninFig.1.Atthe
aspectsofthebackhaulnetwork,whileasuitableSCBNmodel backhaul,eachSCBSk ∈KisenabledwithCAtechniqueand
mustintegratethecostconstraintswiththephysicalconstraints can operate in two differentbands, simultaneously.The set of
of the wireless network, such as traffic demand. aggregatedbands,knownascomponentcarriers(CCs),include
The main contribution of this paper is to propose a novel millimeter wave (mmW) and sub-6 GHz bands, denoted by
resource management approach for CA-enabled small cell N1 and N2, respectively. The mmW band expands from 30
backhaul networks. In particular, we consider an SCBN in GHzto300GHz.Duetodifferentpropagationcharacteristics,
which MNOs seek to minimize their overall cost for using thefrequencybandsinN1 are suitableforline ofsight(LOS)
the backhaul, while maintaining the required data rates at the point-to-point(P2P)links,whilethesub-6GHzbandinN2are
backhaulnetwork.We proposeanovelapproachthatallocates more likely to be used for non-LOS (NLOS) communication.
the backhaulfrequency resource blocks to demanding SCBSs Inaddition,thebackhaulsignalsareOFDMmodulatedsoasto
with no fiber backhaul support. We formulate the problem cope with the channel frequency selective fading and achieve
as a matching game and study its properties. To solve this high data rates. Here, N1 and N2 are composed, respectively,
game, we propose an algorithm that convergesto a two-sided of N1 and N2 backhaulresource blocks (BRBs) and the total
stable solution and guaranteesthe promised quality of service aggregated BRBs is N =N1+N2.
(QoS) at the SCBN. In addition, we compare our results with
A. Propagation Model for mmW Band and Sub-6 GHz Band
two other schemes: heuristic best-effort and random resource
allocation. Our results show that by exploiting inexpensive The main components of the propagation loss within the
and available mmW band,the proposedapproachcan achieve mmW frequency band include pathloss, atmospheric gaseous
substantial gains compared to other resource management losses, and the rain attenuation loss. For mmW propagation,
schemes. To our best knowledge, this paper is the first to we use the model proposed in [6] for the cellular urban
develop a resource allocation solution that jointly accounts scenarios:
for the economicsand wireless properties of an SCBN that is L =β+α10log (d)+χ. (1)
mmW,LOS 10
endowedwithbothmmWandcarrieraggregationcapabilities.
The rest of this paper is organized as follows. Section II Infact,(1)isknowntobethebestlinearfittothepropagation
describes the system model and formulates the problem. measurement in mmW frequency band [6], where α is the
SectionIIIpresentsourdistributedapproachandtheproposed slope of the fit and β, the intercept parameter, is the pathloss
algorithm to solve the problem. Section IV provides the (in dB scale) for 1 meter of distance. In addition, χ models
simulation results and Section V concludes the paper. the deviation in fitting (in dB scale) which is a Gaussian
random variable with zero mean and variance ξ2. Extensive
II. SYSTEMMODEL field measurement have shown that large bandwidth mmW
Consider a small cell backhaul network composed of K networks in urban settings are tend to be noise limited [4],
SCBSsfromthesetK.Moreover,letK1 ⊂Kdenotethesetof [6]. This is due to the fact that mmW band allows the
SCBSs that are connected to the core network via fiber links, implementation of dense antenna based network architecture
which we refer to hereinafter as anchored BSs (A-BSs). The with high directional gains.
A-BSs are owned by a certain network operator q1. The rest However,thisisnottrueforsub-6GHzband,astheantenna
of the SCBSs, called demanding SCBSs (D-BSs) within the beamsare muchwider. Hence,the propagationin thisband is
set K2 ⊂K, are not equipped with broadbandfiber backhaul. interference limited. Assuming no power control, the signal-
Instead,toservetheiraccesslinkusersatdownlink,theD-BSs to-interference-plus-noiseratio (SINR) at the receiving SCBS
need the assistance of the A-BSs to receive the traffic from in the sub-6 GHz band is given by:
2
ψ |h |
γk1nk2 = Pj∈K1\kk11ψjk|1hnjkn2k2|2+σ2, (2) oHtehreer,wγiske1,nγk2k1ndke2terismtihneesSsINigRnalo-btota-ninoeidsefrroamtio,(2i)f. Mno∈reoNve1r,,
where hk1nk2 representsthe channelstate of the link between ωn denotes the bandwidth of BRB n which is different for
A-BSs k1 and D-BSs k2 over BRB n ∈ N2. In addition, ψk each CC. The SINR/SNR distribution is a function of cells’
andσ2 denote,respectively,thetransmitpowerofA-BSkand location,transmitpower,backhaulresourceallocationandthe
the variance of the receiver’s Gaussian noise. propagation model of the carrier.
Withthisinmind,wecantranslatetheoptimizationproblem
B. Problem Formulation
in (3a)-(3f) into the assignment of D-BSs k2 ∈ K2 to
We consider the SCBN during downlink transmissions at
the N BRBs of A-BSs k1 ∈ K1, in both carriers. During
the radio side. In the downlink, the A-BSs forward the traffic
this assignment, the network has to minimize the cost of
from the core network to the D-BSs by using the available
backhaulserviceforD-BSs,whiletakingintoaccounttherate
CCs. For example, in Fig. 1, D-BS (b) can have a backhaul
demandsandbudgetconstraints.Thisproblemisa0-1integer
link,eitherthroughLOSmmWwithA-BS(a)orNLOSsub-6
programming,which is a satisfiability problemas such one of
GHz link with A-BS (b). However, D-BS (c) may only have
Karp’s 21 NP-complete problems. Therefore, it is difficult to
NLOS backhaul link with A-BS (a). Since the A-BSs and D-
solve (3a)-(3f) via classical optimization approaches [13].
BSsbelongtotwodifferentMNOs,networkoperatorq2 hasto To addressthisproblem,we proposea distributedapproach
makeapaymenttonetworkoperatorq1 forallowingitsA-BSs thatcan providea suitable solutionfor the proposedbackhaul
to relay the backhaul traffic of q2’s network. For tractability, resourceallocationproblem.GiventheBRBpricesetbyMNO
we assume that q2 pays q1 for each BRB that A-BSs allocate q1, our goal is to develop a self-organizing, decentralized
to D-BSs for relaying the backhaul traffic.
approach, that can guarantee the QoS of the D-BSs, while
Compared to the sub-6 GHz band, mmW links are more
taking into account their limited budget.
vulnerable to the signal blockage and are less congested.
Therefore, MNO q1 must intuitively provide cheaper service III. MATCHING THEORY FORBACKHAUL MANAGEMENT
over mmW band than sub-6 GHz band. Let P be a set of To solve the proposed SCBN resource management prob-
pairs pk1 = (pk1,1,pk1,2),∀k1 ∈ K1 , where pk1,i,i ∈ {1,2} lem, we propose a novel approach based on matching theory.
denotes the price that q1 will charge q2 to allocate a BRB of Matchingtheoryisapromisingapproachtorealizedistributed
A-BS k1 in the Ni band to a D-BS. In this model, the goal resource management in wireless networks [14], [15]. The
ofMNO q2 is tominimizethe costof itsSCBN by exploiting merit of matching theory is that it allows to provide a decen-
CA capabilities, while ensuring the required backhaul QoS. tralized solution with tractable complexity for combinatorial
To simplify the notation, we use N =N1∪N2, to represent allocation problems, as such that of (3a)-(3f).
the set of all BRBs in both CCs. In essence, a matching game is a two-sided assignment
Given the BRB price set by MNO q1, we need to find the problem between two disjoint sets of players in which the
optimalbackhaulresourceallocation,suchthateveryD-BSk2 playersof each set are interestedto be matchedto the players
can meet its requireddata rate Rd . We assume that every D- of the other set, according to some preference relations. A
k2
BS k2 is associated with a maximum budget Bk2 that allows preference relation ≻ is defined as a complete, reflexive, and
k2 touseBRBs fromA-BSs. Therefore,MNOq2 hastosolve transitive binary relation between the elements of a given set.
the following optimization problem: Here, we denote ≻m as the preference relation of player m
and denote a≻ b, if player m prefers a more than b.
m
minηim∗ ize Ctotal = X X X X pk1,iηk1nk2(3a) In the proposed backhaul resource management problem,
i∈{0,1}n∈Nik1∈K1k2∈K2 thepreferencerelationswoulddependonboththerateandthe
s.t., Rk2(η,γk1nk2)≥Rkd2, ∀k2 ∈K2, (3b) cost of the backhaul link. Matching theory allows to specify
preference relations, by defining individual utility functions
X X X pk1,iηk1nk2 6Bk2, ∀k2 ∈K2, (3c) forA-BSsandD-BSs,whichsimplifiesaccountingforthecost
i∈{0,1}n∈Nik1∈K1 constraintswithintheresourceallocationproblemin(3a)-(3f).
X X ηk1nk2 ≤N,∀k1 ∈K1, (3d) A. Backhaul Management as a Matching Game
n∈Nk2∈K2
For the studied backhaul management problem, the match-
X ηk1nk2 ≤1,∀n∈N,∀k1 ∈K1, (3e) ing game will occur between the D-BSs in K2 and the BRBs
k2∈K2 in the set N. The BRBs are controlledby their corresponding
η ∈{0,1}, (3f)
k1nk2 A-BS throughout the matching process. We introduce a two-
where the backhaul resource allocation variable is such that sided one-to-many matching game in which each BRB will
ηk1nk2 = 1, if A-BS k1 allocates BRB n ∈ N to D-BS k2, be matched to maximum one D-BS, while a D-BS can be
and η =0, otherwise.The total achievablebackhaulrate assigned to one or more BRBs. Formally, we can define the
k1nk2
for SCBS k2 can be written as: matching game as follows:
Definition 1: Given the two disjoint finite sets of players
Rk2(η,γk1nk2)=X X ωnlog2(1+γk1nk2)ηk1nk2, (4)
K2 and N, a matching game µ is defined as a function from
k1∈K1n∈N
K2 →K1×N from which we have
TABLEI
1. ∀n∈N,µ(n)∈K2, PROPOSEDBACKHAULMANAGEMENTALGORITHM
2. ∀k2 ∈K2,µ(k2)⊆K1×N,
3. µ(n)=k2, if and only if n∈µ(k2). Inputs:K1,K2,N1,N2,P
Initialize: D-BSs in K2 find the BRB prices and determine the channel
In matching theory, the quota of a player is defined as a states, throughout receiving control signal from A-BSs in K1. Initialize the
maximumnumberofplayers,thataplayercanbematchedto. setSk2 tothetotal available BRBsoftheA-BSs.
Stage1:
Here, the quota of BRBs is set to one, while there is no pre-
(a)D-BSsrankalltheBRBsinK1×N,using(6).
determinedquotaforD-BSs.Inaddition,wehave(k2,n)∈µ, (b)EveryD-BSk2∈K2 applies foritsmostpreferred BRBn∗ from
if BRB n is assigned to D-BS k2 through matching µ and Sk2 andremovesn∗ fromSk2.
(k2,n)∈/ µ, otherwise. Stage2:
In this game,given the BRB prices, each D-BS in K2 aims (a)BRBsn∈K1×N calculate utility ofeachapplicant using(7).
(b) Amongall applicants and its current match µ(n), BRB n accepts
to reduce the cost of backhauling, while meeting its required
themostpreferred D-BSandrejects therest.
data rate demand. In other words, for each D-BS k2 ∈K2, (c)Ifk2isacceptedbyBRBnbelongingtoi-thCCofk1,setRk2 =
Rk2+wlog2(1+γk1nk2)andCk2 =Ck2+pk1,i.Inaddition,ifk2
miniηmize Cks2.t.=, Ri∈kX{20(,η1,}γnX)∈N≥iRk1Xkd∈2K,1pk1,iηk1nk2, ((55ba)) rSekp2ea=tiasSn∅trd,aegjoCeerckt1C2edka=2nbdyC>aSktBB2agRk−e2B.p2nku1∈n,it.iµl(fkor2)e,vseertyRkk22∈=KR2k,2ei−thwerloRgk22(1>+Rγkdk12nk,2o)r
Stage3:
C 6B . (5c)
k2 k2 The actual data traffic will be forwarded from A-BSs to the SCBSs
In fact, (5a)-(5c) is the distributed version of the main opti- k2∈K2 overBRBsn∈µ(k2).
Output:Stablematchingµ∗
mizationproblemin(3).Theone-to-manymatchinggamewill
automatically satisfy the allocation constraints in (3d)-(3f).
The problem in (5) implies that the preference relations of Underastablematchingµ∗,onecanensurethatA-BSswill
D-BS k2, ≻k2, depends on both the channel state of each not reallocate their BRBs to other D-BSs. Hence, it ensures
backhaul links and the price of BRBs. Therefore, we must the promised QoS to the D-BSs, or more specifically, to the
introduce suitable utility functions for each player set, using MNO q2.
which the players can define their preference relations. Let Theclassicalapproachusedtosolveamatchinggameisby
Vk2,n(.)andUn,k2(.)denote,respectively,theutilityfunctions adoptingtheso-calleddeferredacceptancealgorithmwhichis
of players in K2 and N. Hence, D-BS k2 prefers BRB n1 to knowntoconvergetoastablematching,givenfixedpreference
n2, n1 ≻k2 n2, if and only if Vk2,n(n1)>Vk2,n(n2). relationsandfixedquotas[14],[15].Inourproblem,however,
TheSCBSk2 ∈K2 willyieldautilityVk2,n toBRBn∈N wecannotfixthequotasforD-BSs,sinceitisneitherspectral
of A-BS k1 ∈K1 based on the following utility function: norcostefficientto allocatemoreBRBs thanaD-BS requires
V (γ ,p )=ω log(1+γ )−ζp , (6) to manage its backhaul traffic.
k2,n k2nk1 k1 n k2nk1 k1,i
Therefore, the approach of [14] and [15] are inapplicable
where i = 1, if n is a BRB of the mmW band, otherwise
and a new algorithm must be developed to find a stable
i = 2. In (6), ζ is a weighting parameter that controls the
matching. To this end, we propose the algorithm in Table I.
tradeoff between the cost and the link’s achievable rate. By
Priortothestartoftheassignmentalgorithm,theD-BSsobtain
using this utility, the D-BSs will seek to be matched to the
the channel state from the control signals sent by the A-BSs,
cheapestBRBs throughthelinkswithhigherachievablerates.
Furthermore, the A-BSs aim to assign each of their BRBs alongwiththepricevaluespk.Then,eachD-BSk2 initializes
to a particular D-BS in K2, from which the link’s achievable the set Sk2 = K1×N as the list of all BRBs that D-BS k2
may apply to them.
rateismaximized.Therefore,theutilitythatBRBnbelonging
to A-BS k1 assigns to SCBS k2, Un,k2, is given by In Stage 1, the D-BSs rank the BRBs, based on the
given prices and the achievable rate of the links, as per (6).
U (γ ,R )=ω log(1+γ ). (7)
n,k2 k2nk1 D,k2 n k2nk1 Furthermore, each D-BS k2 applies for its most preferred
Having formulated the backhaul management problem as BRB,n∗ =argmaxnVk2,n(γk2nk1,pk1),fromthesetSk,then
a matching game, our next step is to provide a solution that removesn∗ from Sk, in order to avoid applying for the same
allows the D-BSs to take advantage of CA capabilities and BRB multiple times.
satisfy their rate demands. In Stage 2, BRBs receive the applications and calculate
the correspondingutility values, using (7). Each BRB accepts
B. Proposed Backhaul Management Algorithm and Solution
the most preferred D-BS, k∗ =argmax U (γ ), and
2 k2 n,k2 k2nk1
Tosolvetheproposedmatchinggame,onesuitableconcept rejects previous µ(n) as well as the rest of the applicants.
is the so-calledtwo-sidedstable matchingbetweenthe D-BSs If accepted by BRB n, the SCBS k adds the achievable rate
and BRBs, defined as follows [14]: fromthat link to R . In addition,it subtractthe cost of BRB
k2
Definition 2: A pair (k2,n) ∈/ µ is said to be a blocking n from its total cost Ck2. In case D-BS k2 has been accepted
pair ofthematchingµ,if andonlyifn≻k2 µ(k2)andk2 ≻n byBRB nandnowisrejected,k2 willsubtracttheachievable
µ(n). Matching µ∗ is stable, if there is no blocking pair. rateofthislinkfromR andaddsthepriceofntoitsbudget.
k2
TABLEII
SIMULATIONPARAMETERS 120
Proposed Approach
Notation Parameter Value Random allocation
K Totalnumberofsmallcells 10 100 Best−effort
(N1K,1N2) TotNalunmubmerbeorfoBfRAB-BsSs (192,2100) bits/s) Required rate, Rkd2
(ω1,ω2) Bandwidth ofBRBs (4.86MHz,480KHz) S (M 80
ψ Transmitpower 1W B
−
αξ StandarddPeavthiatlioosnsoexfpmonmeWntpathloss 42.1[6[6]] per D 60
β Pathlossat1m 70dB ate
Rd Ratedemand 100Mbits/s e r 40
pkk1 PriceofBRBs (0.1,10) erag
σ2 Noisepower −90dBm Av
20
The players iterate based on Stage 1 and Stage 2, until we 00 20 40 60 80 100 120 140 160 180 200
reach a stage in which, for every D-BS, either Rk2 >Rkd2, or Number of mmW band BRBs (N1)
S = ∅, or C > B . Following Stage 2, in Stage 3, the
k2 k2 k2 Fig. 2. Average rate per D-BS vs the number of mmW BRBs (N1). The
actualdatatrafficwillbeforwardedfromA-BSstotheSCBSs pk1 =(0.1,10) forboth A-BSs, ζ =1Mbits/s/price unit, andN2 =100.
k2 ∈K2 over BRBs n∈µ(k2). The rate demand is RD = 100Mbits/s for each D-BS. The budget of each
D-BSislimitedto60.
Theorem 1: The proposed algorithm in Table I is guar-
anteed to converge to a two-sided stable matching between
D-BSs and BRBs.
Proof: The convergence of the proposed algorithm in
TableIisguaranteed,sincea D-BSneverappliesforacertain s)110
s/
BRBtwice.Hence,intheworstcase,allD-BSswillapplyfor bit
M100
ashllowBRthBastoonnccee,thwehailcghorriethsumltscoSnkv2er=ges∅,,t∀hek2re∈sulKti2n.gNbaecxkt,hawuel D−BS ( 90
resource allocation between D-BSs and BRBs is two-sided per 80
e
stable. Lets assume that there exists a pair (k2,n) ∈/ µ that e rat 70
blocks the outcome of the algorithm. Since the algorithm has at
converged,we can conclude that at least one of the following Aver15600
casesistrueaboutk2:Rk2 >Rkd2 ,orSk2 =∅,orCk2 >Bk2. 100 8 10
ThefirstcaseisRk2 >Rkd2.Thismeansk2doesnotneedto 50 4 6
add more BRBs to µ(k2). In addition, k2 would not replace Budget of each D−BS (Bk2) 0 0 Price 2of BRB in sub−6 GHz band (pk,2)
any of n′ ∈ µ(k2) with n, since n′ ≻k2 n. Otherwise, k2 1
would apply earlier for n. If k2 has applied for n and got Fig. 3. Average rate perD-BS vs different budgets Bk2 and BRB prices of
rejected, this means µ(n)≻n k2, which contradicts(k2,n) to sub-6GHzband,pk,2.Theweighting parameter ζ=0.1Mbits/s/price unit.
beablockingpair.Analogoustothefirstcase,Sk2 =∅implies Theconstant meshgridshowstherequiredrateRdk =100Mbits/s.
that k2 has got rejected by n, which means µ(n) ≻n k2 and random allocation, all of which are enabled with CA. The
(k2,n) cannot be a blocking pair. best-effort algorithm allocates BRBs to D-BSs based on the
Finally, Ck2 > Bk2 means k2 cannot afford more BRBs. maximum achievable rate, while the random BRB allocation
Moreover, k2 would not replace any of n′ ∈ µ(k2) with n, simply allocates BRBs to D-BSs, randomly.
dueto the same reasoningascase 1. Thisprovesthetheorem.
In Fig. 2, we show the average rate per D-BS resulting
from the proposed algorithm as the number of mmW band
IV. SIMULATION RESULTSAND DISCUSSION BRBs varies. The results are compared with two other al-
Foroursimulations,weconsideranSCBN withtwoA-BSs gorithms, the best-effort scheme and the random allocation
andeightD-BSs.AllSCBSsaredistributedrandomlywithina scheme. Here, constant solid line at 100 Mbits/s indicates the
2km×2kmsquarearea. Thecenter frequencyof mmWband rate requirement of each D-BS and the budget per D-BS is
and sub-6 GHz band is 73 GHz and 5.8 GHz, respectively. limited to 60. The achieved rates for all three approaches
The simulation parameters are summarized in Table II. The increase with the increase in mmW bandwidth, since more
wireless mmW links are noise limited, while the channels in BRBs will be available for each D-BS. Fig. 2 shows that
sub-6 GHz band experience Rayleigh fading with the path theproposedapproachachievessubstantialperformancegains,
loss exponent set to three. The simulations are averaged over reachingupto30%and190%,respectively,comparedtobest-
a large number of iterations for different channel fading and effort approach and random allocation for the network with
SCBSlocations.Wecomparetheperformanceoftheproposed N1 =180. Due to the limited budget, the proposed approach
approach with a heuristic best-effort algorithm as well as the will shift from using the sub 6-GHz band towards exploiting
backhaulcarrieraggregation.Wehaveformulatedtheproblem
400
Number of iterations, R =100Mbit/s as a one-to-many matching game which provides a mean
D
Number of iterations, R =50Mbit/s to solve the proposed backhaul management problem with
350 D
manageablecomplexity.Tosolvethegame,wehaveproposed
300 analgorithmtomatchD-BSstotheA-BScontrolledbackhaul
ons250 resource blocks and proved the two-sided stability of its
ati outcome. Simulation results have shown that the proposed
er
of it200 algorithm outperforms the heuristic best-effort and random
er allocationapproachesandachieveshigherrates,subjecttothe
b
Num150 budget constraints of the small cells.
Theresultsprovideinsightfulguidelinesondesigningwire-
100
less backhaul networks, in which the network operators may
50 need to combine the monetary aspects with the physical
constraints of the network. In addition, the results emphasize
0
4 6 8 10 12 14 16 18 20 on the potentialgains of utilizing available mmW band in the
Number of SCBSs (K)
backhaulnetwork,along with the congested sub-6 GHz band.
Fig. 4. Thenumber of iterations with 95% confidence vs K with K1 =2,
andfortwodifferentratedemands,Rd =100Mbits/sandRd =50Mbits/s. REFERENCES
k k
Thepk1 =(0.1,10)forbothA-BSs.ThebudgetofD-BSsislimitedto60. [1] Cisco, “Cisco visual networking index: Global mobile data traffic
inexpensive and available mmW links, as the number of forecastupdate, 2010-2015,” Whitepaper, February2011.
[2] T.Q.S.Quek,G.delaRoche,I.Guvenc,andM.Kountouris,SmallCell
mmW BRBs increases. In contrast, the greedy best-effort
Networks: Deployment, PHY Techniques, and Resource Management.
algorithmdisregardsthelimitedbudgetofD-BSsandallocates
CambridgeUniversity Press,2013.
BRBs only based on the quality of the links. Overall, Fig. 2 [3] S. Hur, T. Kim, D. J. Love, J. V. Krogmeier, T. A. Thomas, and
A. Ghosh, “Millimeter wave beamforming for wireless backhaul and
revealsthepotentialsofaggregatingmmWbandwithexisting
accessinsmallcellnetworks,”IEEETransactionsonCommunications,
backhaul technologies, specially when the wireless backhaul
vol.64,no.10,pp.4391–4403, October2013.
cost is a limiting constraint for MNOs. [4] S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter-wave cellular
wirelessnetworks:Potentialsandchallenges,”ProceedingsoftheIEEE,
Fig. 3 shows the average rate per D-BS resulting from the
vol.102,no.3,pp.366–385, March2014.
proposed algorithm, versus different budget values and BRB [5] F.Boccardi, R. W.H. Jr, A. Lozano, T.L. Marzetta, and P.Popovski,
prices. The constant mesh grid shows the required rate Rd = “Five disruptive technology directions for 5G,” IEEE Communications
k
Magazine, vol.52,no.2,pp.74–80,Feb.2014.
100 Mbits/s. In Fig. 3, we can clearly see that for low price
[6] A. Ghosh, R. Ratasuk, P. Moorut, T. S. Rappaport, and S. Sun,
values, the required rate is achieved, almost for all budget “Millimeter-Wave enhanced local area systems: A high-data-rate ap-
values. In addition, comparing Fig. 3 with Fig. 2, we can see proach for future wireless networks,” IEEEJournal on Selected Areas
inCommunications, vol.32,no.6,pp.1152–1163,June2014.
thatchoosingasmallervalueforζ inFig.3hasdecreasedthe
[7] P.Bhat,S.Nagata,L.Campoy,I.Berberana,T.Derham,G.Liu,X.Shen,
average rate. That is due to the fact that ζ controls the effect P.Zong,andJ.Yang,“LTE-Advanced:Anoperatorperspective,” IEEE
of BRB prices in the proposed backhaul resource allocation. Communications Magazine, vol.50,pp.104–114, February2012.
[8] G. Liebl, T. M. de Moraes, A. Soysal, and E. Seidel, “Fair resource
Therefore,formorelimitedbudgets,D-BSsshouldpicklarger
allocation for the relay backhaul link in LTE-advanced,” in Proc. of
values for ζ, to be able to meet the required rate. IEEE Wireless Communications and Networking Conference (WCNC),
Fig. 4 shows the convergence time of the proposed algo- (Shanghai, China), April2012.
[9] S.Yi and M. Lei, “Backhaul resource allocation in LTE-advanced
rithm, as the number of SCBSs grows. This figure compares
relaying systems,” in Proc. of IEEE Wireless Communications and
the number of iterations for two different values of rate de- Networking Conference (WCNC),(Shanghai, China),April2012.
mands Rd =100 Mbits/s, and Rd =50 Mbits/s. The number [10] I.V.Loumiotis,E.F.Adamopoulou,K.P.Demestichas,T.A.Stamatiadi,
k k
and M. E. Theologou, “Dynamic backhaul resource allocation: An
of iterationsof the proposedalgorithmis expectedto increase
evolutionary gametheoretic approach,” IEEETransactions onCommu-
with the networksize, as clearly seen in Fig. 4. However,this nications, vol.62,no.2,pp.691–698,February2014.
figure shows that the convergenceof the proposed distributed [11] S.Sengupta and M.Chatterjee, “Aneconomic framework fordynamic
spectrum access andservice pricing,” IEEE/ACMTransactions onNet-
algorithm does not exceed 400 iterations for a very dense
working, vol.17,pp.1200–1213, August2009.
SCBNwith20SCBSs.Indeed,theconvergencetimeincreases [12] M. Mahloo, P. Monti, J. Chen, and L. Wosinska, “Cost modeling
linearlyasthe networksizegrows,thus,yieldingareasonable of backhaul for mobile networks,” in Proc. of IEEE International
ConferenceonCommunications(ICC)workshops,(Sydney,NSW),June
scalability and complexity. In addition, the convergence time
2014.
for Rkd = 50 Mbits/s is almost half of the this value when [13] R.M.Karp,R.E.Miller,andJ.W.Thatcher,“Reducibilityamongcom-
Rd = 100 Mbits/s. Thus, Fig. 4 shows that the traffic at the binatorial problems,” Complexity of Computer Computations, pp. 85–
k
103,1972.
radioaccessnetworksubstantiallyaffectstheconvergencetime
[14] A. E. Roth and M. A. O. Sotomayor, Two-sided matching: A study
of the backhaul resource allocation. ingame-theoretic modeling andanalysis. Cambridge University Press,
1992.
V. CONCLUSION [15] E. Jorswieck, “Stable matchings for resource allocation in wireless
networks,” inProc.of17thInternational Conference onDigital Signal
Inthispaper,wehaveproposedanoveldistributedbackhaul Processing(DSP),(Corfu,Greece), July2011.
management approach for small cell networks enabled with
