A novel alternative to Cloud RAN for throughput densification: Coded pilots and fast user-packet scheduling at remote radio heads

0.62 MB·

by  Ozgun Y. Bursalioglu

A novel alternative to Cloud RAN for throughput
densification: Coded pilots and fast user-packet
scheduling at remote radio heads
1 1 1
Ozgun Y. Bursalioglu , Chenwei Wang , Haralabos Papadopoulos ,
2
Giuseppe Caire
1Docomo InnovationsInc, Palo Alto, CA
2Technische Universita¨t Berlin, Germany
7
{obursalioglu, cwang, hpapadopoulos}@docomoinnovations.com, [email protected]
1
0
2

n Abstract—We consider wireless networks of remote radio ofadditionalresources,whichincludenewlyavailablelicensed
a heads (RRH) with large antenna-arrays, operated in TDD, with and unlicensed bands, network densification, large antenna
J uplink (UL) training and channel-reciprocity based downlink
arrays and new PHY/network layer technologies. Also, to
4 (DL) transmission. To achieve large area spectral efficiencies,
meet the increased traffic demands per unit area induced by
2 we advocate the use of methods that rely on rudimentary
scheduling,decentralizedoperationateachRRHanduser-centric the multitude of new services and their requirements, 5G

] DL transmission. systems would need to provide much higher area spectral
T
A slotted system is assumed, whereby users are randomly efficienciesandareamultiplexinggains(e.g.,numberofusers
.I scheduled (e.g., via shuffled round robin) in slots and across streams served simultaneously per unit area) than their 4G
s the limited pilot dimensions per slot. As a result, multiple users
counterparts.
c in the vicinity of an RRH can simultaneously transmit pilots
[ on the same pilot dimension (and thus interfering with one Antenna densification through massive MIMO is expected

another). Each RRH performs rudimentary processing of the to play a key role in achievingthe large gainsin area spectral
1
v pilot observations in “sectors”. In a sector, the RRH is able to efficiency envisioned for 5G and beyond wireless networks.
8 resolve a scheduleduser’s channelwhen that user isdetermined Through the use of a large number of antennas at the base
to be the only one among the scheduled users (on the same
9 stations (BSs), massive MIMO can yield both large spectral
pilot dimension) with significant received power in the sector.
0 efficiencies and spatial multiplexing gains [9], [10]. Large
Subsequently,onlythesubsetofscheduleduserswhosechannels
7
are resolved in at least one sector can be served by the system. antenna arrays and massive MIMO are considered as key
0
Weconsideraspatiallyconsistentevaluationoftheareamulti- technologies for 5G and beyond, in particular because new
.
1 plexinggainsbymeansofaPoissonPointProcess(PPP)problem generation deployments would have to utilize the centimeter
0 formulationwhereRRHs,blockers,scatterersandscheduleduser
and millimeter Wave (mmWave) bandswhere wide chunksof
7 terminalsareallPPPswithindividualintensities.Also,westudy
1 directionaltrainingattheuserterminals.Oursimulationssuggest spectrum are readily available. Indeed, at mmWave with half-
: that, by controlling the intensity of the scheduled user PPP wavelength(critical) spacing, very large arrayscan be packed
v
and the user-pilot beam-width, many fold improvements can be onsmall footprints.Realizing the beamforminggainsthatcan
i
X expected in area multiplexinggains with respect to conventional be provided by such large-size arrays will be essential in
spatial pilot reuse systems.
r combattingtheharsherpropagationcharacteristicsexperienced
a
I. INTRODUCTION at mmWave.
A broad range of activities are currently underway towards To achieve large spectral efficiencies in the downlink (DL)
realizingthe ever-evolvingvision of 5G. Theirscope includes via multiuser (MU) MIMO, channel state information at the
the development and standardization of new technologies in transmitter(CSIT)isneeded[11].Following[10],CSITcanbe
3GPP [1], new channel models [2], experimental trials and obtainedfromtheusers’uplink(UL)pilotsviaTime-Division
demos, and the study of new services and their requirements Duplexing (TDD) and UL/DL radio-channelreciprocity. This
[3]. 5G technologies are expected to bring great performance approach allows training large arrays by allocating as few
gains with respect to their predecessorsin a multitude of per- UL pilot dimensions as the number of single-antenna users
formancemetrics,including,amongotherthings,userandcell simultaneously served.
throughput, end-to-end latency, massive device connectivity At higher carrier frequencies, UL-pilot based CSI acqui-
and localization. They are also viewed as essential elements sition becomes even more attractive than schemes relying on
for enabling the much broader gamut of services envisioned, DLtrainingandULCSIfeedback.First,athigherfrequencies
suchasimmersiveapplications(e.g.,virtual/augmented/mixed larger BS arrays can be packed within a fixed footprint, and,
reality) [4], [5], haptics [6], V2X [7] and the Internet of since a single UL pilot from a user terminal trains all the
Things[8].Tomeetsuchanambitiousandbroadgamutof5G BS antennas (no matter how many), UL-pilot based schemes
requirements, operators would have to rely on a combination are able to harvest the additionalBF gains available at higher
frequencieswithoutadditionaloverheads[9].Second,UL-pilot lotonitsassignedpilotdimension.Similartype ofdirectional
based schemes also induce lower latencies in CSI acquisition trainingwasexploitedinthecontextofcellulartransmissionin
than feedback based schemes [9]. This is a key advantage [14].BytakingadvantageofthesparsityofmmWavechannels
at higher frequencies where the latency requirements in CSI intheangulardomain,significantgainswerereportedinterms
acquisition are more stringent, as CSI is only accurate within of both area multiplexing gains and area spectral efficiencies.
the coherence time of the channel, and coherence time is We consider a PPP-based problem formulation where
inversely proportionalto carrier frequency. RRHs,blockers,scatterersanduserterminalsareallPPPswith
In this paper, we focus on operating a wireless network individualintensities. We also assume that the scheduled user
of remote radio heads (RRHs) with large antenna-arrays. We terminals form a PPP with an intensity that can be adjusted
consider TDD operation and DL data transmission, enabled to optimize the area multiplexing gains. Indeed, random user
by UL training and UL/DL radio channel reciprocity [12]. schedulingin this contextcorrespondsto appropriatethinning
To achieve large area multiplexing gains and area spectral of the original user terminal PPP.
efficiencies, we investigate the combined use of rudimentary We conduct extensive simulations by varying the type and
scheduling, decentralized operation at each RRH and user- extent of RRH sectorization, the user pilot beam-width and
centric DL transmission. Specifically, we consider a slotted the user schedulingintensity.By adjusting the intensity ofthe
systemwherethenetworkschedulesafractionofusersoneach scheduled-userPPP andthe user-pilotbeam-width,significant
of the UL pilot dimensions in each slot. As a result, multiple improvements in area multiplexing gains are reported with
users in the vicinity of an RRH can transmitUL pilots on the respecttoconventionalspatialpilotreusesystems.Thesegains
samepilotdimensionandcancausepilotcontamination.With greatly improve with RRH sectorization and are present if
pilot-contaminated CSI, a beam directed to an intended user one employs physical sectorization, virtual sectorization or a
terminal also inherently inherently beamforms at other user combination.
terminalsusingthesamepilotdimension,causinginterference The PPP-based ON-OFF connectivity model we employ
and substantially limiting massive MIMO performance. in this work can be viewed as a realistic extension of the
To address the issue of pilot contamination, we consider model in [13]. The model relies on a simple connectivity
rudimentaryprocessingofthepilotobservationsateachRRH, model involving LOS and NLOS paths. A link is “ON” if
which allows each RRH to resolve user channelsin “sectors.” that link strength exceeds a predetermined threshold. Thus,
AnRRHisabletoresolveanactive(scheduled)user’schannel the LOS link between a user and an RRH is “ON” if the line
in a sector when that user is determined as the only one ofsightpathisnotblockedandtheLOSreceivedpathstrength
among the active users (on the same pilot dimension with exceedsapredeterminedthreshold.Similarly,NLOSpathsare
significant received power) within that sector. Subsequently, “single-bounce” through a single scatterer with sufficiently
onlythe subsetof activeuserswhosechannelsareresolvedin high received path strength. We remark that, although our
atleastonesectorcanbeserved.Regardingthetypeofsector- model is very simple, it captures the main aspects of the
ization, we study physical sectorization, virtual sectorization problem and provides spatial consistency of the type not
andtheir combineduse. While physicalsectorizationrefersto immediately present in stochastic channel models such as
the conventional sectorization where each sector is operated 3GPP’s SCM [15]. In addition, by controlling the intensities
bya distinctantennaarray,virtualsectorizationarisesthrough oftheunderlyingPPPs,importantstatisticsofourmodel(such
sector-specific spatial filtering from a single antenna-array. as, e.g., number of paths between a connected user-BS link)
In order for each RRH to resolve user channels, special can be tunedto agreewith those in the stochastic 3GPP SCM
pilotcodingisneededforactiveuserswhosendpilotsoverthe model.
commonpilotdimension,i.e.,acrossthesetofsharedresource
elements (REs) for UL pilots. Recently, Bursalioglu et al. II. CHANNELMODEL
proposed ON-OFF type of non-orthogonalpilot codes, which In this section, we provide a spatially consistent ON-OFF
use a small fraction of additional REs per pilot dimension RRH connectivitymodelcapturingsignalattenuationforboth
to detect pilot collisions and to identify the user IDs whose LOS and NLOS paths. In particular, we consider a distance-
channelscanberesolvedonthefly[13].Otherclassesofnon- based1signalattenuationmodelforadirectLOSpathbetween
orthogonalpilotcodesweredescribedbyLietal.[14],which a user u and an RRH r. Let d ě 0 denote the distance
ur
assume wide-band scheduling transmission and are able to between user u and RRH r, and let
resolveuserchannelsusingcodeswithoutincurringadditional
overheads. 0 if the LOS path between u and r is blocked,
b “
ur
In thiswork,we conducta spatiallyconsistentsystem-level #1 otherwise.
evaluation of the area multiplexing gains by these systems.
Then the path attenuation on the direct path between user u
Besides sectorization at RRHs, we also consider the use of
and RRH r is modeled via gpd qb ,. We choose a smooth
directional training at the user terminals and its effect on ur ur
the provided area multiplexing gains. Given an appropriately
1ThedistancemetricweconsiderinthispaperisdefinedastheEuclidean
chosen beam-width (common across all user terminals), each
distance in the two-dimensional (X,Y)-plane. The vertical dimension is not
activeuserpicksarandombeam-orientationtotransmititspi- takenintoaccount.
transition path loss function gp¨q [16] given by d ăd fromRRH r is incoverageofthe RRH. Incontrast,
ur o
if user u is at distance d ąd from RRH r, the user is not
gpdq“p1`d{ǫq´α, for dě0, (1) ur o
in coverage of the RRH. Hence, the disk centered at user u
whereddenotesthedistancebetweentransmitterandreceiver, with radius do defines the support of all RRHs with respect
and ǫ and α denote the breakpoint distance and the pathloss to which user u could be in coverage. Similarly, from the
exponent, respectively2. RRH side, all the user terminals that could potentially be in
Simpleinspectionon(1)revealsthatgpdqpossessesthefol- the coverage of RRH r have to reside in the radius-do disk
lowingdesirableproperties:(i)itisamonotonicallydecreasing centered at RRH r.
function of the distance d, implying longer propagationpaths
III. SYSTEMOPERATION
are more attenuated; (ii) it satisfies 0 ď gpdq ď gp0q “ 1
showing that propagation always attenuates signal strength. We consider a slotted system where a subset of users are
Regarding NLOS paths, we restrict our attention to single- scheduled in each slot for UL pilot training and subsequent
bounce paths through a single scatterer. We consider a com- DLdatatransmission.Weletτ denotethenumberofavailable
monly used method for modeling reflected path attenuation orthogonalpilotdimensionsperfadingblock,andassumeeach
[17, Chapter 2], according to which the total attenuation of active user is scheduled on one of the τ pilot dimensions.
a reflected path is given as the product of the attenuation We will consider the use of both omni and directional UL
levels experienced by the individual paths. In particular, the pilots by active users. In the omni-case, we assume that a
path attenuation in a NLOS path between user u and RRH r user’s UL pilot coverage coincides with the user coverage in
enabled through a single-bounce reflection off a scatterer z is Sec. II. Directionalpilottransmissionsare parameterizedby a
given by positive integer B ě1, which remains common and fixed for
fpd ,d q“agpd qgpd q, (2) alluserterminals.Givena B ě1, theuser terminalcreatesB
uz zr uz zr
non-overlapping pilot beams that span the azimuth spectrum
where a ď 1 is the reflector-attenuation factor, and duz and (360degrees).Inthesimplest“geometric”case,eachbeamhas
dzr denotethe user-scatterer and the scatterer-RRH distances, beam-width360{B degrees.Duringeach schedulinginstance,
respectively. It can be readily verified that the single-bounce each active user transmits an UL pilot on randomly selected
path attenuation model (2) with gp¨q defined in (1) has the one of the B beams on the assigned pilot dimension.
following desirable properties: To ensure that coverage is identical for both omni and
(i) For any single-bounce path, 0 ď fpd ,d q ď 1. In directionalpilottraining,theULpilotofeachdirectionalbeam
uz zr
addition, fpd ,d q Ñ 1, if and only if d , d Ñ 0 is adjusted, so that the union of all B-beam coverage areas
uz zr uz zr
and aÑ1. coincides with the omni-pilot coverage, i.e., a disc radius of
(ii) The attenuationscaling of a single-bouncepath is a non- d . This approach ensures a fair comparison, and thus any
o
increasing function of the user-scatterer distance and of performance gains arising from the use of directional pilot
the scatterer-RRH distance: fpd ,d q ě fpd1 ,d1 q, training cannot be attributed to coverage extension.
uz zr uz zr
for any set of distances {d , d1 , d , d1 } satisfying Upon transmission of UL pilots, per-sector processing at
uz uz zr zr
0ďd ďd1 and 0ďd ďd1 . each RRH allows the RRH to resolve user channels on each
uz uz zr zr
(iii) Considering the triangle formed by the LOS paths con- ofitssectorsandsubsequentlyservetheresolveduserstreams.
necting the points u, z, and r, we have d `d ěd A user channel is considered resolved on a sector, if the user
uz zr ur
and fpd ,d q ď gpd q as well. Hence, when not channel is present on this sector (i.e. the user has a path with
uz zr ur
blocked, the received signal strength of the direct LOS sufficiently large strength on that sector) and if it is the only
path is at least as large as any reflected path, even when user present on the sector among the active ones on the same
a“1, i.e., even when there is no reflector-attenuation. pilot dimension. In the following subsections, we describe
Coverageis defined by means of a simple ON-OFF model: sectorization and the notion of presence of user channels on
user u is within the coverage of RRH r, if and only if there sectors, user scheduling and resolving user channels. We also
exists a path, either a LOS path or a NLOS path, received provideexpressionsfortheachievableareamultiplexinggains
with sufficiently large strength. Specifically, user u is within per pilot dimension by using these schemes.
the coverage of RRH r, if gpd qb ěδ or if there exists a
ur ur A. Sectorization
scattererz forwhichfpd ,d qěδ,forsomepredetermined
uz zr
threshold δ. In contrast, a user is in outage if it is not in the Sectorization has been traditionally employed for increas-
coverage of any RRH in the system. ing the spectral efficiency per site in cellular networks by
It is worth denoting by d the nominal distance at which partitioning each cell radially into sectors and reusing the
o
gpd q“δ, which implies that if b “1 a user u at distance spectral resources in each sector [18]. We let S denote the
o ur
number of radial sectors per site. Fig. 1 shows an example
2We remark that gpdurq refers to the “directional” propagation loss, i.e., of uniformly spaced radial sectorization with S “ 6 sectors.
attenuation that is specific to the path between user u and RRH r. This In this case, the circular coverage area centered at an RRH
is different from the commonly used distance-based pathloss models such
is divided into equal angle wedges, one per sector. We note
as, e.g., 3GPP’s SCM [15], which are modeling the omni pathloss, i.e., the
aggregate propagation lossacrossallpaths. that, in general, the S sectors can be constructed by means
!"#"$" canbeviewedasspanninga contiguoussetoftime-frequency
!"#"$" !"#"(" ’"../" elementsin the OFDM plane within the coherencebandwidth
!!("#"!!"!$(""$!! and time of the user channels [14].
!"#"(" ../"(" !)*++,-,-" !!(""#!$ We assume L “ τλUA users are randomly scheduled for
!"#"’" !!(""#!1$2&)3,-" %&" uplink pilot transmission over an area of size A, where λU is
0!,-"(" an appropriately chosen density of scheduled users so that L
is an integer. For comparison,in the contextof the traditional
!"#"$"
!"#"$" !!’"#"!!!""#!"($’""$"!! ’"../" oscrhtheodguolendalintrathineinegntisrcehaermeae,, ii.ne.,eaacshinsglloetsLche“dulτeduusesresr pareer
!"#"(" ../"(" !)*++,-,-" pilot dimension resulting in λU “ 1{A. Thus, τ users send
%&" orthogonal pilots on each fading block, i.e., K “ 1 user per
!"#"’"
!!’"#"!! pilotdimension.On the other hand,in the contextof the non-
0!,-"’" orthogonalULtrainingschemes,asin[13],[14],K ą1users
Fig.1. TwoRRHsareshownwithindodistancefromthetwoUTs.Thefirst are scheduled to send pilots per pilot dimension in the slots.
andthesecondRRHsare,respectively, represented bythetriangles 1and2.
Asaresult,thenumberofscheduledusersperslotisL“Kτ.
EachRRHemploys6sectors.Alsoshownareasinglescattererandasingle
blocker. Based on UL training, each sector of each RRH resolves
the channels of a subset of the L users and serves them
of traditionalphysical sectorization, virtual sectorization, or a simultaneously.Among scheduled users, only the ones whose
combination of both techniques. The impact of these options uplink pilots are received without any “collisions” from other
on the sectorization pattern and consequently on the system user pilots can be served. Also, these are the users whose
performance is considered in Sec. VI. channelscanbe “resolved”to be usedin designingprecoders.
Asin[14],weletXk “1denotethatauserkispresenton Thus, we consider a user k to be resolved on sector s of
j,s
tsreacntosmrsissoifonR,RXHjk,jsa“nd1s,eitfXthjke,sre“ex0isottshearwpaisthe.fFroomr oumsneri-pkiltoot RshRaHrinjgtihfeansadmoendlyimifenXsijko,sn“as1usaenrdkthanerdefiosrnwohiocthheXrjku,1sse“r k11.
RRHj withattenuationscalingexceedingδ “gpdoqandwith Letting σk denote the pilot dimension used by user k, Kσ
angle of arrival (AoA) falling within the support of sector s. denote the indices of users assigned to pilot dimension σ for
For directional training to have Xjk,s “1, we require, besides 1ď σ ďτ, and Djk,s denote whether or not user k’s channel
the above two conditions, that the path from user k to RRH can be resolved on sector s of RRH j, we have [14]:
j have angle of departure(AoD) falling within the supportof
user’sULpilotbeam.Evidently,directionalpilottransmissions Dk “Xk 1´Xk1 . (3)
have lower incidence of user-channel presence than omni j,s j,s» j,s fi
pilot transmissions, effectively sparsifying the observed user k1PKźσkztku´ ¯
– fl
channels at each RRH. The subset of present users whose channels are resolvable in
sector s of RRH j is thus given by
Fig. 1 provides an illustrative example involving two users
located close to each other, two nearby RRHs each with D “ k; Dk “1 . (4)
j,s j,s
geometricS “6radialsectorization,a single nearbyscatterer
and a single nearby blocker.3 Both users are assumed to use Assuming the two users in Fig. 1 are sc(heduled on the same
omni-directional pilots and to be within do distance of the pilot dimension, it is evident that D21,3 “ 1 and D12,3 “ 1.
two RRHs. In addition, all four reflected paths through the This toy example demonstrates the effect of sectorization in
scatterer, corresponding to all (user, RRH) permutations, are increasingareamultiplexinggainsbybeingabletosimultane-
also within coverage. The upper and lower figures separately ously serve two nearby users even if they are using the same
show the presence of user-1 and user-2 on RRH sectors. As pilot dimension.
the top figure reveals, user 1 is present on sector 4 of RRH In general, not all present users are resolvable. Letting
1 (reflected path), and sectors 2 and 3 of RRH 2 (through
X “ k; Xk “1 (5)
reflected and direct paths, respectively). Note that user 1 is j,s j,s
not present in sector 3 of RRH 1, as the the blocker blocks denote the set of all users t hat are presen(t in sector s of RRH
the LOS path. Similarly, user 2 is present on sectors 3 and 4 j, we have D ĎX . Indeed, inspection of (3) reveals that
j,s j,s
of RRH 1 and on sector 2 of RRH 2. if the two users k and k1 are present in sector s and use the
same pilot dimension, i.e., Xjk,s “ Xjk,1s “ 1 and σk “ σk1,
B. Scheduling & Resolving Users we have Dk “ Dk1 “ 0. This is consistent with the fact
j,s j,s
Next, we describe scheduling and resolving user channels. thatneither channelcan be resolveddue to the pilotcollision.
Since we assume wide-band scheduling, a scheduling slot Hence, the number of sectors that can resolve and thus serve
comprisesasetofconcurrentfadingblocks.Eachfadingblock user k is given by N “ S Dk , while the number of
k j s“1 j,s
users that are actually served in the slot is given by
3We assume ideal sectorization, i.e., there is no leakage between sectors. ř ř
Furthermore, allscatterers areassumedtobereflecting isotropically. L1 “|tk;Nk ą0u| (6)
and in general L1 ďL. NotethatMGpλUqcanbeoptimizedbyvaryingthescheduled
Wedefinetheslot-averagedareamultiplexinggainperpilot user intensity:
dimension (which is a function of scheduled user density λ
U MG˚ “ max MGpλUq, (9)
and area size A) as follows: 0ďλUďλaUll
1 T L1ptq where λ˚U denote the corresponding optimal value.
MGpA,λUq“ lim , (7) Itisworthre-iteratingthatthetraditionalorthogonalscheme
TÑ8T τA
t“1 haszeroareamultiplexinggain.Moreover,theareamultiplex-
ÿ
ing gains per pilot dimension of locally orthogonal schemes
where L1ptq represents the instantaneous multiplexing gain
thatrelyonconventionalreusewithoutanychannelresolution
over slot t in the area A and is given by (6).
capabilityarenominallyupperboundedby1 (sinceπd2 “1).
With a traditional orthogonal scheme, since L1ptq “ τ o
we have MGpA,1{Aq “ 1{A, which becomes vanishingly A. Simulation Parameters
small as A Ñ 8. This is well recognized in traditional
Allthesimulationsofthispaperare basedonthefollowing
networks and is dealt with conventional spatial pilot reuse.
parameter values: λ “ 5 (RRH intensity), λ “ 3 (blocker
R B
Such spatial reuse scheme would be inherentlylimited by the
intensity), A “20 (inverse of blocker area), α“4 (pathloss
nominal user-pilot coverage area πd2. Hence, the orthogonal b
o exponent),ǫ“d {4 (cutoffparameter for attenuation model),
scheme with coverage area πd2o provides an upper bound on a“1 (scatterer aottenuation) and λall “100 (user intensity).
the area multiplexing gains per pilot dimension provided by U
We first investigate the probability of outage. Specifically,
any such conventional cellular deployment with conventional
a user k is in outage if (with omni pilots) for all s,j, Xk “
spatial reuse, and which is equal to 1{pπd2q user streams per j,s
o 0.4 The outage probability depends on λ ,λ ,λ and A :
R S B b
unit area and per pilot dimension.
Largerλ or largerλ valuesdecreasethe outageprobability
R S
whileincreasingλ orA increasestheoutageprobability.We
B b
IV. PPP-BASED ANALYSIS investigate the outage probability for two different scattering
In this section, we analyze the proposed schemes in the environments:λS “50(lowscattererintensity)andλS “200
(high scatterer intensity). For the low scatterer intensity case
limit where the network size A goes to infinity. We exploit a
the outage probability is 1.9%, while for the higher scatterer-
PPP-based formulationto analyze the area multiplexinggains
per pilot dimension provided by the proposed schemes. intensity case it is 1.3%.
Theleft-hand-sidefigurein Fig. 2 showsthe distributionof
In a PPP-based layout, points are assumed to be dropped
thenumberofpathsintheuser-RRHchannelsincoveragefor
overaninfiniteareaaccordingtoaPPPwithacertainintensity
per unit area. We choose the unit area as πd2, which is equal thetwodifferentvaluesofλS.Asthefigurereveals,increasing
o
λ resultsin increasednumberof paths.The numberof paths
tothenominalcoverageareathatcanbeobtainedbyanomni- S
in our simulation environment plays a similar role to the
directional pilot from a user. Users, scheduled users, RRHs,
“numberofclusters”parameterin3GPP’sSCM specifications
scatterers and blockers are dropped according to PPPs with
intensities λall,λ ,λ ,λ ,λ , respectively. The scheduled [15]. In the SCM, this parameter is chosen between 12´20
U U R S B
depending on the scenario considered in the sub-6 GHz
user PPP with intensity λ , arises as thinned version of the
U
band. In this work, our parameter selection provides a lower
PPP corresponding to all of the users in the network, with
intensityλall.WhileRRHs,usersandscatterersareconsidered numberof paths, which might be more appropriatefor higher
U
frequency bands. The right-hand-side figure in Fig. 2 shows
as points on the layout, the blockers are considered as circles
the distribution of probability of blocking for LOS paths. In
with an area size of 1{A . In the extreme case λ “λ “0,
b S B
oursetup,NLOSpathsarenotaffectedbyblockersandhence
i.e., when there are no scatterers or blockers, the PPP setup
the blocking distribution is not a function of λ .
reduces to the one used in [13], [19] where area multiplexing S
gainexpressionswerederivedviaastochasticgeometrybased V. PERFORMANCE EVALUATIONS
analysis.Unlike[19] whereexactclosed-formexpressionsare
In this section, we investigate the effect of sectors and
derived for a 1-dimensional line network, in this paper we
directional training on area multiplexing gains and average
consider the 2-dimensional case. For the setting we consider,
uplinkpilottransmitpowerspentforeach packet.We provide
closed-form analysis based on stochastic geometry is much
various performance results of the proposed non-orthogonal
morecomplicatedduetopresenceofsectorization,directional
pilot codes. For evaluating performance, our simulations are
training, scatterers and blockers. As a result, we rely on
based ongeometricsectorization,i.e. radialsectorizationwith
simulation based investigations. In our simulations, we run
equalsize wedgescorrespondingtoanangleof2π{S radiants
many frames, where, in each frame, users, scatterers, RHHs
per sector.
and blockers are dropped according to their PPPs.
In the PPP evaluation, we are interested in the area multi- 4Withdirectionaltraining,ineveryschedulingslot.auserselectsabeamat
plexing gains per unit area and per pilot dimension: randomfromasetofbeamswhoseunioncoversthewhole360degreeazimuth
domain.Ifauserisnotinoutagewithomni-training,withdirectionaltraining
itwillbepresentatonesectorwithatleastoneofitsdirectionalbeams.Thus,
MGpλUq“ lim MGpA,λUq. (8) itwillnotbeinoutagewithdirectional training aswell.
AÑ8
1 λ = 200 1 4 S = 8
S
0.8 λS = 50 0.8 B = 12 SS == 41
G,
M
0.6 0.6 0
0 2 4 6 8 10 12
F F λ
D D U
C C
0.4 0.4 B = 110 S = 1
x, S = 4
0.2 0.2 pilot t 5 S = 8
#
p.
0 0 Ex 00 2 4 6 8 10 12
0 5 10 15 0 0.5 1 λ
Number of paths Prob. of blocking U
Fig. 2. Left figure: CDF of the number of paths in user-RRH channels in Fig.3. Topfigure:Areamultiplexinggainsperpilotdimensionvs.scheduling
coverage. Right figure: CDF of blocking probability in user-RRH pairs in userintensity(omniULpilots).Bottomfigure:ExpectednumberofULpilot
coverage. transmissions per delivered packet vs. scheduling user intensity (omni UL
pilots).
A. Omni-directional Training
at the BS, thereby leaving more sectors available to resolve
In omni-directional training, users are assumed to emit
other users’ channels. In [14], for a single cell scenario, a
uplink pilots isotropically. The upper figure in Fig. 3 shows
properchoiceoftheuserbeamwidthpositivelyimpactedboth
MGpλUq versus λU for B “ 1 for the cases where the multiplexing gains and long-term user rates.
number of sectors/RRH are S “ 1, 4, and 8. Inspection of
Directional beams with different width are obtained by
the figure reveals that, while the optimal scheduling intensity
processing at the user side similar to the sectorization at the
is λ˚ “ 3 for S “ 4, it is almost 6 for S “ 8. The user-
U RRHsite.Eachsectorcreatedattheusercanbethoughtofasa
scheduling intensity optimized area multiplexing gains per
beam candidatewhich the user randomlyselects. The number
pilot dimension are less than one with S “ 1, but they are
of sectors created at the user antenna array, B determines
almostdoubledwithS “4andmorethantripledwith S “8.
the width of the user beam. For radial sectorization, beam
Theincreasedmultiplexinggainswithnon-orthogonaltrain-
widthis equalto 2π{B. Forthe same outageprobability,with
ing come at the cost of more uplink pilot transmissions per
directionaltraining(B ą1),thetransmissionpowerspentper
delivered user streams. Indeed, not all scheduled users (that
B pilottransmissions is equal to the uplink power spent for a
transmit pilots) are resolved and thus served in any given
single pilot transmission with omni-training B “1.
scheduling instance, because of pilot collisions. It is thus
Fig. 4 compares omni-directional training with directional
of interest to compare the relative average power spent for
trainingof30˝ beams, i.e., B “12. Thisallowsservingmore
each packet transmission when comparing different schemes
than 8 users per pilot dimension per unit area while using a
and parameter values. For orthogonal training, a user pilot
quarteroftheexpectedpilottransmissionpowerperuserwith
transmission always results in a user being served provided
respecttotheorthogonalcase.Hence,usingdirectionalbeams
the user is not in outage. Thus, excludingusers in outage, for
and non-orthogonal training is able to serve instantaneously
orthogonaltraining,theexpectednumberofpilottransmission
many more users per unit area and at much less power cost
perservedpacketisequalto1.Withtheschemesweconsider,
to user devices.
assuming a user UL pilot (in a single slot) that results in
Fig. 5 reports MG˚ from (9), i.e., the user-scheduling in-
a user channel being resolved also enables serving a single
tensity optimizedarea multiplexinggainsper pilotdimension,
packet, we can capture the pilot of efficiency of a scheme via
for variousvalues of S and B and for two differentscatterer-
the expected number of pilot transmissions per each served
intensityscenarios.Asthefigurereveals,uniformlyhigherarea
packet.Thelower figurein Fig. 3 showsthe expectednumber
multiplexinggainsarepossibleinthe lowerscatterer-intensity
ofpilottransmissionsperpacketvs.λ fordifferentS values.
U environment.
As the figure reveals, while the overall multiplexing gain is
tripled with S “ 8 (at λ « 6q, the transmit uplink power
U VI. AREA MULTIPLEXINGGAINS WITH PRACTICAL
required per delivered packet is almost doubled compared
SECTORIZATION
to the orthogonal case. That is, on average two UL pilot
transmission are required per user to deliver a packet. In this section, we consider a PPP-based evaluation of the
area multiplexing gains that can be expected over wireless
B. Directional training
networks of RRHs using practical antenna configurationsand
In this section we study how varying the user beam-width practical sectorization. Traditionally, sectors at a macro cell
canaffecttheharvestedareamultiplexinggains.Indeed,using are obtained by mounting a separate antenna array at the BS
a directional beam at a user terminal makes its user-channel site for each sector. By using different array orientations in
sparser in terms of the number of sectors that are excited differentsectorsandbyphysicallyseparatingthemviapanels,
10
8
G, S = 5 λλSS == 220000,,B B = = 1 12
M λ = 50,B = 1
S
λ = 50, B = 12
S
0
0 20 40 60 80 100 120
λ
U a) P = 6, V = 1:

8
S = 2
pilot tx, 1 λλSS == 220000,,B B = = 1 12 b) P = 3, V = 2:
Exp. # λλSS == 5500,,B B = = 1 12
0
0 20 40 6λ0 80 100 120 c) P = 2, V = 3:
U
Fig.4. Topfigure:Areamultiplexinggainsperpilotdimensionvs.scheduling
user intensity. Bottom figure: Expected required UL transmit power per
delivered packet vs.scheduling userintensity. InbothfiguresS“8. d) P = 1, V = 6: !
10
λ = 200, B = 1
S
λ = 200, B = 4
S
λ = 200, B = 8
8 λS = 200, B = 12
S
λ = 50, B = 1
S
λ = 50, B = 4
S
6 λS = 50, B = 8
λ = 50, B = 12
MG* S Fig. 6. Practical sectorization designs (left) and associated sectorization
patterns (right).
4
shapeandelementspacing.Ingeneral,althoughequalnumber
2
of beams are assigned to each of the V virtual sectors, the
virtual-sector azimuth spread varies from sector to sector, in
01 2 3 4 5 6 7 8 contrast to physical sectors.
S In this section, we consider various combinationsof physi-
cal and virtual sectorization options, which result in the same
Fig.5. Schedulinguserintensityoptimizedareamultiplexinggainsperpilot
dimensionasafunctionoftheULpilotbeam-widthandthenumberofRRH number of sectors S. In particular, we consider combinations
sectors (geometric RRHsectorization). ofP physicalsectorsitesperRRH,eachwithaULAperform-
ing virtual sectorization in V virtual sectors, yielding a total
of S “ VP sectors. The ULA-induced virtual sectorization
sectorarrayscanbemadeto“cover”different“pie-type”slices scheme results in non-uniform sector sizes, which are the
of the cell. For example, by using P ULAs at a macro BS result of the transformation between the normalized virtual
site, a macro cell (centered at the BS) can be divided into P angle,θ andthephysicalangleφ.ForacriticallyspacedULA
360{P-degree sectors. In the commonly used case of P “3, this transformation is given by θ “πsinpφq`π [20], [23].
three 120-degree sectors are formed in the macro cell. Such Fig. 6 depicts several RRH designs exploiting various
physicalsectorswereleveragedin[13] tosubstantiallyreduce combinationsofvirtualandphysicalsectorization,allyielding
the number of RRH sites needed to achieve a given target S “ P ˆ V “ 6 sectors. All virtual sectors are created
multiplexing gain in a finite-area RRH deployment. by critically spaced ULAs. For each (P, V) combination
Besides traditional physical sectorization, virtual sectoriza- shown on the left-hand side of the figure, the corresponding
tionbasedonspatialprocessingattheBSantennaarrayisalso azimuth support of each of the 6 sectors is shown on the
possible [20], [14], [21], [22]. Ref. [14] considers a single- right-hand side. As the figure reveals, the pP “ 6, V “ 1q
cell scenario with a BS using a uniform linear array (ULA). and the pP “3, V “2q designs yield the geometric 6-sector
DFT based processing is considered for virtual sectorization sectorizationpatterns.ThepP “3, V “2qdesignforinstance
within the cell, according to which each sector is formed by relies on panels in the back of each ULA to restrict the paths
spatially filtering the ULA signal through a contiguous set hitting each ULA to come for a 120-degree azimuth spread.
of sector-specific DFT beams. Indeed, with large ULAs, DFT Fig. 7 showsthe area multiplexinggainsof allthese practi-
based processing is the appropriate choice for sectorization, cal designsagainstthose providedby geometricsectorization.
since, in the limit of large ULAs, the user-channelcovariance With each practical design, a ULA is exploited at each user
matrixbecomesapproximatelycirculant[21],[22].Inpractice, terminalforcreatingthe B directionalbeams.Also shownfor
poweremissionfromanantennaarrayisnotisotropic,andthe comparison is the performance with geometric sectorization
power radiation patterns highly depend on the antenna array at RRH and ULA at the user device. As it can be seen
trainingbeams,whileinthegeometricRRHsectorizationcase
users employ the B equal-width pilot beams considered in
Sec. V. Fig. 8 shows the area multiplexing gains per pilot di-
mensionofthetwoschemesforvariouspS, Bqcombinations.
As the figure shows, the geometric scheme, which results in
* /
uniform radial sectorization, achieves higher gains than the
$’(
single-ULA based scheme. However, it can also be seen that
$
theperformancelossduetousingvirtualsectorizationisrather
(’( small for all pS, Bq combinations considered.
(
,-.#’( -01’/223/!/-01’/4506/7/8/$ REFERENCES
# -01’/223/!/49:/4506/7/8/$ [1] 3GPP,http://www.3gpp.org.
49:!49:/;/8/$</=/8/& [2] TR38.900(V14.0.0),“Channel modelfor frequency spectrum above 6
)’( 49:!49:/;/8/)</=/8/" GHz”. 3GPP,Jul.2016.
) 49:!49:/;/8/"</=/8/) [3] “NGMN 5G White Paper,” NGMN, Tech. Rep., Feb. 2015,
49:!49:/;/8/&</=/8/$ https://www.ngmn.org/uploads/media/NGMN 5G White Paper V1 0.pdf.
"’(!/ " # $ % &! &" [4] Y. Qi, M. Hunukumbure, M. Nekovee, J. Lorca, and V. Sgardoni,
+ “Quantifying data rate and bandwidth requirements for immersive 5G
experience,” arXiv:1605.03331 [cs.IT],May2016.
[5] E. Bas¸tug˘, M. Bennis, M. Me´dard, and M. Debbah, “Towards in-
terconnected virtual reality: Opportunities, challenges and enablers,”
arXiv:1611.05356[cs.NI],Nov.2016.
[6] A. Aijaz, M. Dohler, A. H. Aghvami, V. Friderikos, and M. Frodigh,
“Realizing the Tactile Internet: Haptic communications over next gen-
eration5Gcellularnetworks,”IEEEWirelessCommunications,pp.2–9,
Fig.7. Schedulinguserintensityoptimizedareamultiplexinggainsperpilot Oct.2016.
dimension as a function of (nominal) UL pilot beam-width (360/B degrees) [7] P. Luoto, M. Bennis, P. Pirinen, S. Samarakoon, K. Horneman, and
forthepractical sectorization designsinFig.6. M. Latva-aho, “System level performance evaluation of LTE-V2X
network,” arXiv:1604.08734[cs.NI],Apr.2016.
9 [8] C.X.Mavromoustakis,G.Mastorakis,andJ.M.Batalla,Eds.,Internet
Geo., B = 1 of Things (IoT) in 5G Mobile Technologies. Springer International
Geo., B = 4
8 Geo., B = 8 Publishing, 2016.
Geo., B = 12
7 ULA, B = 1 [9] T.L.Marzetta, “Howmuchtraining isrequiredformultiuserMIMO?”
ULA, B = 4 inProceedingsoftheFortiethAsilomarConferenceonSignals,Systems
ULA, B = 8
6 ULA, B = 12 andComputers, Nov.2006.
[10] ——,“Noncooperativecellularwirelesswithunlimitednumbersofbase
5 stationantennas,”IEEETrans.onWirelessCommun.,vol.9,no.11,pp.
MG* 3590–3600, Nov.2010.
4
[11] G.Caire,N.Jindal,M.Kobayashi,andN.Ravindran,“MultiuserMIMO
achievable rates with downlink training and channel state feedback,”
3
IEEETrans.Inf.Theory,vol.56,no.6,pp.2845–2866, 2010.
2 [12] R.Rogalin,O.Y.Bursalioglu,H.Papadopoulos,G.Caire,A.F.Molisch,
A.Michaloliakos, V.Balan, andK.Psounis,“Scalable synchronization
1 and reciprocity calibration for distributed multiuser MIMO,” IEEE
Trans.onWirelessCommun.,vol.13,no.4,pp.1815–1831,Apr.2014.
01 2 3 4 5 6 7 8 [13] O. Y. Bursalioglu, C. Wang, H. Papadopoulos, and C. Caire, “RRH
S basedmassiveMIMOwith”onthefly”pilotcontamination control,”in
Proceedings oftheIEEEInternational Conf.onCommun.,May2016.
Fig.8. Schedulinguserintensityoptimizedareamultiplexinggainsperpilot [14] Z.Li,N.Rupasinghe,O.Y.Bursalioglu,C.Wang,H.Papadopoulos,and
dimension as a function of number of RRH sectors and UL pilot training C.Caire,“Directionaltrainingandfastsector-basedprocessingschemes
beamwidth:geometric (solid)andULAbased(dashed)sectorization. formmwavechannels,” arXivpreprintarXiv:1611.00453, Nov.2016.
[15] TR 36.873 (V12.2.0),“Study on 3D channel model for LTE”. 3GPP,
Jun.2015.
from the figure, designs in a) and b) are identical in terms [16] C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. John
of sectorization to the geometric case (with ULA at the WileyandSonsPress,1997.
[17] D. Tse and P. Viswanath, Fundamentals of Wireless Communication.
user device) and provide the same area multiplexing gain
NewYork,NY:Cambridge University Press,2005.
performance. The pP “ 2, V “ 3q and the pP “ 1, V “ 6q [18] H.Huang,O.Alrabadi,J.Daly,D.Samardzija,C.Tran,R.Valenzuela,
designs yield a small loss in performance, revealing that the andS.Walker,“Increasingthroughputincellularnetworkswithhigher-
ordersectorization,” inProceedings oftheForty-FourthAsilomarCon-
cost of virtual sectorization is inherently small.
ferenceonSignals,Systems andComputers,Nov.2010.
Finally, we compare the area multiplexing gains per pilot [19] M.HaenggiandA.Sarkar,“UniquecoverageinBooleanmodels,”arXiv
dimensionthatareprovidedbyasinglecriticallyspacedULA preprintarXiv:1608.02032v1, Aug.2016.
[20] A. M. Sayeed, “Deconstructing multiantenna fading channels,” IEEE
with random orientation at each RRH, i.e., by employing
TransactionsonSignalProcessing,vol.50,no.10,pp.2563–2579,Oct.
design option d) in Fig. 6 with pP “1, V “Sq, against the 2002.
ones provided by the geometric S-sector RRH sectorization. [21] J. Nam, A. Adhikary, J. Y. Ahn, and G. Caire, “Joint spatial division
and multiplexing: Opportunistic beamforming, user grouping and sim-
In the case of ULA-based RRH sectorization, users transmit
plifieddownlinkscheduling,”IEEEJournalofSelectedTopicsinSignal
directional pilots from a ULA able to create B virtual-sector Processing,vol.8,no.5,pp.876–890,Oct.2014.
[22] A. Adhikary, E. Al Safadi, M. K. Samimi, R. Wang, G. Caire, T. S. channel sensing: Anew approach toestimating sparsemultipath chan-
Rappaport, and A. F.Molisch, “Joint spatial division and multiplexing nels,” Proceedings of the IEEE, vol. 98, no. 6, pp. 1058–1076, Jun.
for mm-wave channels,” IEEE J. Sel. Areas Commun., vol. 32, no. 6, 2010.
pp.1239–1255, Jun.2014.
[23] W. U. Bajwa, J. Haupt, A. M. Sayeed, and R. Nowak, “Compressed