Beam-searching and Transmission Scheduling in Millimeter Wave Communications

0.25 MB·English

by  Hossein Shokri-Ghadikolaei

Beam-searching and Transmission Scheduling in
Millimeter Wave Communications
Hossein Shokri-Ghadikolaei, Lazaros Gkatzikis, and Carlo Fischione
Automatic Control Department, Electrical Engineering and ACCESS
KTH Royal Institute of Technology, 10044, Stockholm, Sweden
emails: {hshokri, lazarosg, carlofi}@kth.se
Abstract—Millimeter wave (mmW) wireless networks are wireless local area networks (WLAN). In existing standards,
5
capable to support multi-gigabit data rates, by using directional one of the network devices is assigned the role of the coordi-
1
communications with narrow beams. However, existing mmW nator,whoschedulestransmissionsinacentralizedmanner.In
0
2 communications standards are hindered by two problems: deaf- particular, channel access is determined through a hybrid car-
ness and single link scheduling. The deafness problem, that is, a
riersensemultipleaccess/collisionavoidance(CSMA/CA)and
n misalignment between transmitter and receiver beams, demands
time division multiple access (TDMA) scheme. A superframe
a a time consuming beam-searching operation, which leads to
consists of three phases. A beaconperiod,a contentionaccess
J an alignment-throughput tradeoff. Moreover, the existing mmW
period, where devices compete to register their requests for
2 standards schedule a single link in each time slot and hence
1 do not fully exploit the potential of mmW communications, channelaccesstothecoordinator,andachanneltimeallocation
where directional communications allow multiple concurrent period, which is further divided into several time slots and
] transmissions. These two problems are addressed in this paper, each is assigned to a single transmitter-receiver pair. Existing
T whereajointbeamwidthselectionandpowerallocationproblem standards do not exploit the full potential of mmW communi-
I isformulated byan optimization problemfor short range mmW cations. In fact, high data rates are achieved due to the high
s. networks with the objective of maximizing effective network signal-to-noise ratio (SNR), which is a result of directional
c throughput. This optimization problem allows establishing the
communications,andextendedbandwidthavailabilityinmmW
[ fundamental alignment-throughput tradeoff, however it is com-
bands. Pencil beams, however, promises extensive frequency
putationally complex and requires exact knowledge of network
1 reuse while simplifies interference management [4], [5].
topology, which may not be available in practice. Therefore,
v
two standard-compliant approximation solution algorithms are
6 In this paper, we suggest that efficient transmission
developed, which rely on underestimation and overestimation of
1 scheduling mechanisms could significantly improve the net-
interference.Thefirstoneexploitsdirectionalitytomaximizethe
5 work throughput (spectral efficiency), by scheduling multiple
reuse of available spectrum and thereby increases the network
2 transmissions in the same time slot, as long as they do
throughput,whileimposingalmost nocomputationalcomplexity.
0 The second one is a more conservative approach that protects not cause harmful interference to each other. The amount
1. all active links from harmful interference, yet enhances the of interference caused depends also on the beamwidths that
0 networkthroughputby100%comparedtotheexistingstandards. devicesoperatewith.Thisintroducesanalignment-throughput
5 Extensive performance analysis provides useful insights on the tradeoff. That is, a narrower beamwidth introduces significant
1 directionality level and the number of concurrent transmissions searchingoverhead,sincemanydirectionshavetobesearched,
: that should be pursued. Interestingly, extremely narrow beams butprovidesahighertransmissionrateduetohigherdirectivity
v are in general not optimal.
gains, whereas larger beamwidths speed up search process
i
X Keywords—Directional communications, mmW networks, con- at the expense of loss in the transmission rate. In order to
r current transmissions, deafness, spectral efficiency. addressthose problems,we proposea jointformulationof the
a beamwidth selection and transmission scheduling problems in
mmW communications,andanalyze the impactof each of the
I. INTRODUCTION
system parameters on the network throughput.
Millimeter wave (mmW) communications appear as a
promising option to meet the ever growing demand for multi-
A. Related Work
gigabit data rates, at least over short distances. MmW com-
munications refer to the electromagnetic spectrum between Our work is focused on capturing the major tradeoffs
30 and 300 GHz, which corresponds to wavelengths from in mmW communications, which are mainly due to beam-
10 mm to 1 mm. Small wavelength enables integration of searching overhead and concurrent transmission scheduling.
numerous antenna elements in the current size of radio chips, In the following, we present an overviewof existing works in
whichinturnpromisesasignificantdirectivitygain.Themain the field.
characteristicsofmmWaredirectionality,largebandwidth,but
A mainissue in mmWcommunicationsisdeafness,which
also high attenuation [1].
is a direct consequence of directional transmission and recep-
MmW has been considered lately by several standardiza- tion. It occurs when the main beams of a transmitter and the
tion bodies as an ideal candidate for short range communica- intendedreceiverare notaligned.To addressthisissue, beam-
tions. Specifically, IEEE 802.15.3 task group 3c [2] works on searching has been proposed to establish a communication
the development of high rate wireless personal area networks link [6], [7]. In this case, an exhaustive search over all
(WPAN),whereasIEEE802.11adtaskgroup[3]isfocusedon possiblecombinationsoftransmissionandreceptiondirections
is performed through a sequence of pilot transmissions. In
fact, mmW devices adopt analog beamforming, also called Timeslotduration T
beam-searching, using simple phase shifters, rather than a t
i
complex digital beamforming based on instantaneous channel
state information, since the latter would impose formidable
complexity in mmW due to the large number of antennas [1]. Alignment Datatransmission
Although the beam-searching concept facilitates the beam-
forming phase, it introduces an alignment overhead, that is,
the time required for finding the best beams. This overhead Fig.1. Timeslotsegmentation ofeachlinki.Increasingalignment timeτi
reducestimeavailablefordatatransmission,butreducesthedeafnessproblem.
dependson the numberof directionsthathave to be searched,
which in turn depends on the selected transmission and
reception beamwidths. Current standardization activities [2], vides useful insights on the directionality level and
[3] suggest a two-stage beam-search technique, to reduce the number of concurrent transmissions that should
alignmentoverheadandpowerconsumption.Initially,acoarse be supported.
grained sector-level sweep is performed,followed by a beam-
level alignment phase. An exhaustive search over all possible
II. SYSTEMMODELAND PROBLEM FORMULATION
transmission and reception directions is applied in each level.
For a given beamwidth (fixed granularity of searching), [6] Consider an mmW network consisting of one coordinator
suggests a new search technique as a replacementof the two- and N transmitter-receiver pairs (links). As shown in Fig. 1,
stage exhaustive search to reduce the alignment overhead. a time slot consists of two phases: i) alignment and ii) data
Here,wesuggestthatthealignment-throughputtradeoffshould transmission.Withoutlossofgenerality,weassumethatsector-
be addressed by optimizing beamwidth per se, thus our work levelalignmenthas beenestablished priorto alignmentphase,
and [6] are complementary. i.e., as part of routing [10]. In the first phase, transmitter
and receiver of each link i have to decide on the optimal
The option of activating concurrent transmissions for op-
refined beams within their sectors, by searching over all
timally exploitingthe directionality of mmW communications
possible combinations. This exhaustive search is compliant
was proposed only recently. The authors of [8] consider the
with IEEE 802.15.3c where all possible combinations within
problem of maximizing the number of scheduled flows such
a sector are tested to find the alignmentthat maximizes SNR.
that their quality of service requirement is not violated. A
greedy scheduling scheme is proposed, where in each time
A. Modelling Alignment Overhead
slot an additional link is activated if its contribution to total
throughput is positive, that is, throughput gain from this Let T denote the time required for a pilot transmission,
p
additionallinkislargerthantheinterferencecaused.Asimilar which hasto beperformedfor everycombination,andψt, ϕt,
i i
greedy heuristic is proposed in [9], where a priority ordering ψr, and ϕr be sector-level and beam-level beamwidths at the
i i
oflinksisassumed.Additionallinksareactivatedaccordingto transmitterandreceiversidesoflinki,respectively.Therefore,
this priority order and as long as signal-to-interference-plus- under exhaustive search, the total duration of this searching
noise ratio (SINR) at all receivers exceeds a threshold. The (alignment) procedure is
main issue of all those approaches is that they are reactive ψt ψr
protocols, that is, a link has to be activated to deduce if τ ϕt,ϕr = i i T , (1)
i i i ϕt ϕr p
it is compatible with other transmissions. Instead, here we (cid:24) i(cid:25)(cid:24) i (cid:25)
demonstrate that directionality and high attenuation in mmW where ⌈·⌉ is the c(cid:0)eiling (cid:1)function, returning the smallest fol-
communicationscanbeexploitedtoderiveaccuratescheduling lowing integer. Notice that the number of pilots has to be
mechanisms. integer. Once the optimal directions for transmission and
reception have been determined, the communication link can
B. Our Contribution be established, and data transmission phase starts. We assume
thatafterthealignmentprocedure,thetransmitterandreceiver
The main contributions of this paper are summarized into always find a path to establish data communications, even
the following through a reflection if the direct link is not available [11].
By discarding noncontinuous ceiling function, we derive a
• We identify the tradeoffs and the corresponding con-
continuousapproximationofτ . Thelatter cannotexceedtotal
trols that differentiate mmW communications from i
time slot duration T, and hence a lower bound on feasible
other technologies.
beamwidths can be derived, namely
• We provide a unifying optimization-based framework T
ϕtϕr ≥ pψtψr .
that brings together beam-searching and transmission i i T i i
scheduling and explicitly addresses the major chal- Besides, since alignment takes place within the sector-level
lenges of mmW communications, namely deafness beamwidths, we have ϕt ≤ψt and ϕr ≤ψr.
i i i i
and interference management.
• We demonstrate how the proposed framework can be B. Modelling Effective Transmission Rate
translatedintoprotocolsthatextendthecapabilitiesof
Let gc denote channel gain between transmitter of link i
existing standards. i,j
and receiver of link j (in short, transmitter i and receiver j),
• We evaluate the performance gains arising from the capturingbothpathlossandblockfading,nthepowerofwhite
proposed protocols. Our performance analysis pro- gaussian noise, and p the transmission power of transmitter
i
j from transmitter i is p gt gc gr , which depends on p ,
i i,j i,j i,j i
ϕt, and ϕr. Signal to Interference and Noise Ratio (SINR) at
Receiveri i j
Transmitteri receiver of link i is
qr
qt j,i Receiverj SINRi = N pigit,jgic,jgir,j . (4)
i,j p gt gc gr +n
qr k k,i k,i k,i
i,j kkP=6=1i
We assume that interference can be treated as noise at each
qt receiveri,implyingthat,accordingtoShannonformula,linki
j,i
canachievearateoflog (1+SINR )fortheremainingT−τ
2 i i
seconds, which can be normalized by time slot duration T, to
Transmitterj derive the normalized throughputwithin a time slot.
Equation (4) indicates that narrower transmission and re-
Fig.2. Illustrationoftheanglesbetweentransmittersandreceiversθt and ceptionbeamwidthsleadtohigherdirectivitygainandhencea
i,j
θr .Solidarrowscorrespond totheboresightangle. higherdatarate.Asdictatedby(1),thisgainisobtainedatthe
i,j
expenseofhigheralignmenttimeτ andconsequentlylesstime
i
for data transmission. This arises a tradeoff between the time
TABLEI. SUMMARYOFMAINNOTATIONS
Symbol Definition devoted to alignment phase and the effective data rate. Notice
T Timeslotduration alsothatdecisionsofdifferentlinksarecoupledthroughSINR,
Tp Pilottransmissiontime and hence scheduling multiple parallel transmissions within a
N Numberoflinks time slot is non-trivial.
SINRi Signal-to-interference-plus-noiseratiooflinki
θt Anglebetweentransmitteriandreceiverj C. Maximizing Network Throughput
i,j relativetotransmitterboresightangle
θr Anglebetweenreceiverjandtransmitteri In this paper, we consider the problem of joint beamwidth
i,j relativetoreceiverboresightangle selection andtransmission schedulingthathasto be solvedby
ϕt Beam-leveltransmitterbeamwidthoflinki
i the coordinator in each time slot. In particular, we consider a
ϕr Beam-levelreceiverbeamwidthoflinki
i generalizedversionofthelatterwheretheoptimaltransmission
ψt Sector-leveltransmitterbeamwidthoflinki
ψir Sector-levelreceiverbeamwidthoflinki power of each transmitter has to be selected such that the
i
network throughput (or equivalently spectral efficiency) is
pi Transmissionpoweroftransmitteri
pmax Maximumtransmissionpower maximized. If we collect all control variables ϕti, ϕri, and
n Noisepower pi in vectors ϕt, ϕr, and p, respectively, the problem under
τi Channelestablishmentdelay consideration can be formally stated as
git Antennagainattransmitteri N
gjr Antennagainatreceiverj maximize R= 1− τi log (1+SINR ) (5a)
gic,j Channelgainbetweentransmitteriandreceiverj ϕt,ϕr,p T 2 i
Xi=1(cid:16) (cid:17)
subject to ϕt ≤ψt, 1≤i≤N , (5b)
i i
i. Table I summarizes the main notations used throughoutthe ϕr ≤ψr , 1≤i≤N , (5c)
paper. For analytical tractability, we approximate the actual i i
antenna patterns by a sectored antenna model, which is a ψtψrT /T ≤ϕtϕr , 1≤i,j ≤N , (5d)
i j P i j
common assumption [12], [13]. This simple model captures
0≤p ≤pmax, 1≤i≤N . (5e)
directivity gains, the front-to-back ratio, and the halfpower i
beamwidth, which are considered the most important features Notice that for notational simplicity, function arguments have
ofanantennapattern.Inidealsectorantennapattern,thegains beendiscarded.Antennabeamwidthsaffectbothτ andSINR ,
i i
are a constant for all angles in the main lobe, and equal to a whereas transmission powers only affect the latter. Optimiza-
smallerconstantinthesidelobe.Letθit,j andθir,j betheangles tion problem formulated in (5) is generally non-convex, and
betweentransmitteriandreceiverj relativetotheirrespective hence solving it is a challengingtask. In addition, SINR and
i
boresight angle (see Fig. 2). We denote by git,j and gir,j the consequently the objective function depend on the network
transmission and reception gains at transmitter i and receiver topology, as dictated by θt and θr in (2) and (3). Such
i,j i,j
j toward each other, that is information cannot be available at the coordinator in most
git,j θit,j,ϕti = 2π−(2ϕπti−ϕti)z , if |θit,j|≤ ϕ2ti , (2) oinfveWstiPgAatNe satrnudctuWraLlAprNopesyrtsiteesmosf.pIrnobtlheme n(5e)x,twsheiccthioenn,abwlee
( z, otherwise us to propose two standard-compliant and easy to implement
and (cid:0) (cid:1) algorithms of low complexity.
2π−(2π−ϕrj)z , if |θr |≤ ϕrj
gr θr ,ϕr = ϕr i,j 2 , (3)
i,j i,j i ( z, j otherwise III. JOINT BEAMWIDTH SELECTIONAND TRANSMISSION
where 0(cid:0)≤z <(cid:1)1 is the gain in the side lobe, with z ≪1 for SCHEDULING
narrow beams. The gain in the main lobe can be derived by The optimization problem formulated in (5) is generally
fixing the total radiated power of the antennas over parameter non-convex, making it difficult to be optimally solved. To
space of z, ϕt, and ϕr. Then, the received power at receiver derive some insight on the arising tradeoffs, we first focus
i i
on the single link case (N = 1), which is also the case for problem(5)providesthemaximumnetworkthroughput,under
existing mmW standards [2]. Next, we consider the general the assumption that the coordinator knows the exact topology
problem of concurrent transmissions and we demonstrate that ofthenetwork.Totacklethisissue,weproposetwotopology-
it can be reduced to multiple parallel single link instances. agnostic approaches. The first one is a conservative approach
that generally overestimates the interference experienced by
A. Single Link Scenario each link. In the second approach, we perform transmission
scheduling by assuming that resulting interference will be
Consider a network consisting of a single link i, where no
negligible,whichissupportedbythepseudo-wiredabstraction
interference is experienced by the receiver. For a given time
of mmW communications [5].
slotthis is also the case of existingstandards.Once alignment
procedure has been completed, both transmitter and receiver
operateintheirmainlobes,henceθt =θr =0.Thisimplies Overestimation of interference
i,i i,i
that SINR expression, formulated in (4), reduces to
The main idea behind this approach is to estimate in-
gc 2π−(2π−ϕt)z 2π−(2π−ϕr)z
SNR = i,ip i i . terference at sector level, which is generally higher than
i n i(cid:18) ϕti (cid:19)(cid:18) ϕri (cid:19) interference experienced at beam-level. An IEEE 802.15.3c
(6)
or 802.11ad compliant device has to be equipped with an or-
Proposition I: Consider problem (5) for a single link thogonalfrequencydivisionmultiplexing(OFDM)transceiver,
scenario, where N = 1 and SINR is replaced by SNR which enables differentlinks to operate in differentfrequency
according to equation (6). Optimal transmission power in this channels at the same time. Inspired by FlashLinQ protocol
case is pmax. proposed in [9], we can derive the following low-overhead
protocoltoestimateinterference.First,thecoordinatorassigns
Proof:Sinceincreasingtransmissionpowerdoesnotaffect
orthogonal channels to different links, one to each link. Each
the alignment overhead, yet monotonically enhances SNRi, transmitter i transmits with power pmax inside its sector and
transmitting at the maximumpower is optimal p∗ =pmax . (cid:4)
i in its dedicated channel, without introducing any interference
Result I: Consider optimization problem (5) for single to otherlinks. Here,we assumethatthe sector ofthe intended
link scenario. For parameters in the region of interest, the receiver/transmitter can be derived from a local table [10].
optimalantennabeamwidths(ϕti)∗and(ϕri)∗canbeaccurately Each receiver i measures SNR in link i, denoted by SNRi,
approximated by a hyperbola (ϕt)∗(ϕr)∗ = ϕ∗, where ϕ∗ is and also overhears the received power from every transmitter
i i i i
a constant that depends on system parameters ψt, ψr, T , T, j with sector-level beam. The latter provides an estimation of
i i p
pmax, z, gc and n. the amount of interference-to-noise-ratio from transmitter j,
i,i
denoted by INR . Then, each link checks if it can be acti-
Proof: The proof is provided in Appendix A. (cid:4) ji
vated with other links concurrently without receiving/making
Theaboveresultsimplythatthedimensionoftheoptimiza- harmful interference. From the analysis provided in [15], the
tion problem in the single link scenario can be reduced from sufficient condition for link i to be independent of link j
3 variables, namely p , ϕt and ϕr, into a single one, namely (treating interference as noise) is
i i i
ϕi , ϕtiϕri. Next, we derive an additional property of the SNRi ≥INRj,i, and SNRi ≥INRi,j . (7)
objective function, which validates the existence of a tradeoff
Eachreceiverievaluatestheinterferencelevelfromtransmitter
between alignment overhead and achievable throughput. p p
j and according to sufficient conditions (7) creates the set of
Proposition II: Consider optimization problem (5) for interferers,thatis,thesetoflinkswithwhichlinkishouldnot
single link scenario. For system parameters in the region of be activated simultaneously. Notice that interference has been
interest, the optimal antenna beamwidth ϕ∗ is the unique estimated at sector level, whereas actual transmissions take
i
solution of ∂R/∂ϕ =0 . place over fine-grainedbeams. Thus, this is an overestimation
i
of the actual interference during communications with pencil
Proof: The proof is provided in Appendix B. (cid:4)
beams, providing a conservative approach that overestimates
Proposition II implies that adopting extremely narrow interference,sotoensurethatnocollisionsoccur.Thereceivers
beams is not always optimal in terms of throughput due to feedback their interferer sets to the coordinator. The coordi-
the huge alignment overhead. Also, wide beams devastate the nator then derives a conflict graph that shows the links that
directivitygains,and hencetheydo notprovidethe maximum cannot be activated concurrently. Next, we provide a detailed
throughput. Given channel gain gc , the network coordinator description of the proposed scheme.
i,i
canfindtheoptimalbeamwidthsϕ∗ throughasimplegradient
i A conflict graph G =(V,E) is defined by a set of vertices
descent algorithm [14]. In the next subsection, we show how
V and edges E. A vertex i ∈ V represents communication
the coordinator can obtain an estimation of the channel gain
link i and an edge (i,j) ∈ E indicates that links i and
between the transmitter and receiver i. We now turn our
j cannot be activated simultaneously due to high mutual
attentiontothemultiplelinkscase,andshowthestepsrequired
interference. In fact, the interferer set of link i, which is
to converta multiple links scenario to single link scenario, so
reported to the coordinator by receiver i, represents the set
to efficiently address the general optimization problem (5).
of neighbors of vertex i in the conflict graph. Finally, an
independent set of graph G is a subset of V that contains no
B. Multiple Links Scenario
adjacent vertices, indicating that those vertices (links) can be
Although current standards schedule a single link within concurrently activated without any harmful interference. This
each time slot, narrow beams promise significant through- enables a transformation of power allocation subproblem of
put gain by exploiting concurrenttransmissions. Optimization (5) to transmission scheduling instance. That is, the coordina-
ProtocolI Interference-awareschedulinginmmWcommunications Protocol II Interference-agnostic scheduling inmmW communica-
1: Initially,thecoordinatorassignsorthogonalchannelstodifferent tions
links. A single channel is assigned to each. 1: Initially,thecoordinatorassignsorthogonal channelstodifferent
2: Each transmitter i transmits with power pmax with sector-level links. A single channel is assigned to each.
beam in its dedicated channel. 2: Each transmitter i transmits with power pmax with sector-level
3: Eachreceiverimeasuresreceivedpowerfromtransmitteriwith beam in itsdedicated channel.
sector-level beam and computes SNRi. 3: Each receiver i estimates channel gain of link i, that is, gic,i.
4: Each receiver i overhears the received power from each trans- 4: All receivers feedback their channel gains.
mitter j with sector-level beam and computes INR . 5: Thecoordinatoroptimizesbeamwidthofeverylinkindividually,
j,i
5: Eachreceiverievaluatessufficientconditions(7)andcreatesthe and each transceiver adjusts its beamwidth accordingly. All
set of interferers. transmissions take place at maximum power pmax.
6: All receivers feedback their interferer sets to the coordinator.
7: Thecoordinatorcreatesaconservativeconflictgraph,andsched-
90
tor, uoluetsolifnkasllbaisneddeponen(d8e).nt sets, should activate at maximum s]7800 17.784917.1921 16.5992 16.0064 15.4136 14.8208
e
powerthelinksoftheindependentsetthatachievesmaximum gre
dltiihninsrdkoceuupisgenshndepdidvueintid.ncuyFtahololeryfsaiuitnssgginillviegnenklaisn,isknitdmhseecppelceneonaodgrirerodan.ditnieasnetottrdacneasdncedonupte,tiamtsoizamelrueetaaudcahyl on beamwidth [de456000 17.784917.1921 16.5992 16.0064 151.461.030664
indeLpeetndIekntbseetsi.nTdehpeenn,dperonbtlesemt(k5,)caanndbeIcabsetatsheasscehtedouflianlgl Recepti30 17.1921 16.5992
pmraoxbilmemizetshathteacnteitvwatoersktthheroluingkhspuot.fTthheatiinsd,ependent set that 20 17.7849 17.1921
Imk⊆axIi,mϕti,zϕer iX∈Ik(cid:16)1− τTi(cid:17)log2(1+SNRi) (8a) 10151.614.610113.0576069.41919272.178240T9rans3m0issio4n0 beam50width6 [01d7e.7g8r4e79e0s] 80 90
subject to ϕt ≤ψt, 1≤i≤N , (8b)
i i Fig.3. Optimalregionoftransmissionandreception beamwidths.
ϕr ≤ψr, 1≤i≤N , (8c)
i i
ψtψrT /T ≤ϕtϕr , 1≤i,j ≤N , (8d) IV. NUMERICAL RESULTS
i j P i j
In order to derive some insight on the behaviour of the
where SNR is given by (6), since there is no interference
i identified tradeoffs, we consider scenario of several mmW
inside an independent set.
devices,randomlylocatedinan area of10×10m2, operating
Giventheindependentsets,problem(8)canbesolvedeffi- in60GHzwithmaximumpowerof2.5mW, whicharetypical
cientlybyusinggradientdescentalgorithms.However,finding valuesin bluetooth-basedWPAN. We assume 90◦ sector-level
allindependentsetsisanNP-hardproblemingeneral[16].For beamsbothattransmitterandreceiverside.UsingMonteCarlo
sparse conflict graphs, which is the case in mmW networks simulations, we evaluate the network throughput, in bits per
with pencil beams, efficient solutions exist [17]. Protocol I time slot per hertz, over 100 random topologies.
describestherequiredstepstoconvertthejointbeamwidthse-
Fig. 3 illustrates Result I by depicting contours of the
lectionandpowerallocationproblem(5) to a jointbeamwidth
throughput of a single link against transmission and recep-
selection and transmission scheduling problem (8).
tion beamwidths. The bold black curve shows the optimal
beamwidth region for which throughput is maximized. This
Underestimation of interference correspondstoϕtϕr =240,fortheexampleconsidered.Based
i i
on this result, for the rest of simulations, we assume that
According to the pseudo-wired abstraction of mmW com-
ϕt =ϕr for all i.
munications [5], that is, the condition that a relatively small i i
number of active links operating with narrow beams do not Fig. 4 demonstrates the alignment-throughput tradeoff
cause interference to each other, we may neglect interference. for a single link mmW network. For narrow beamwidths,
Thus, we may optimize each link individually, as if it was beam-searchingoverheadis dominating, whereas as operating
operating on its own. Then, the problem of joint optimization beamwidthsincrease,directivitygainbecomesmoreimportant.
ofantennabeamwidthandtransmissionpowerforN linkscan Generally, the optimal point is a balance between directivity
be decomposed to N parallel single link problems. Each can gainoverthebenefitofadditionaltransmissiontime.Moreover,
be solved in polynomial time as described in Section III-A. reduced pilot transmission overhead T /T, enables the trans-
p
Protocol IIdescribesthestepsoftheproposedunderestimation mitter and receiver to execute more beam-searching iterations
approach. For an ultra dense network, where interference using the same time budget. As a result, performance is
is non-negligible even under directional communications, an improved,and narrowerbeams are more beneficial. It is note-
adaptive algorithm could be investigated to modify channel worthythatPropositionIIholdsinallthreedepictedscenarios.
access action of every link upon every failure, but this is That is, they have positive derivative at the beginning of their
beyond the scope of this work. feasible set and negative one at the end.
25 V. CONCLUSION
T / T = 1e−2
p Millimeterwave(mmW)communicationspromiseasignif-
put [bits/slot/Hz]1250 TTpp // TT == 11ee−−34 iwstchpaiiersncetilpaeilsamsppephnrry,eostvwwiecoemarlkedcnseh,tmaiirfonancttsshepterreaisctmtetirdcaasnlytohefafcfithmcatimalelkneWincnyggefroseffuqalunrlieesnxianctdygvgabefnrantonaemdgraset.itohIonnef
h
ug this huge potential requires optimizing alignment-throughput
Thro10 tradeoffand novelsolutionsfor optimalschedulingof concur-
ork rent transmissions. The problem of joint beamwidth selection
w
Net 5 and power control was formulated. It was shown that such
a problem cannot be efficiently solved, since the network
0 topology needs to be known. To tackle this, two approaches
0 10 20 30 40 50 60 70 80 90
Transmission beamwidth [degrees] wereproposedbasedonoverestimationandunderestimationof
Fig.4. Alignment-throughput tradeoff inmmWnetworks. interference. Overestimation approach activates only a small
number of non-interfering links to ensure that no harmful
interference will be received by any active links. This over-
150 protection leads to reduced performancegain, yet doubles the
Oracle
network throughput compared to the existing standards. The
Underestimator
Hz]120 Overestimator underestimationapproachby neglectinginterference,which is
put [bits/slot/ 90 Single Link Activation aacovcmalolpisdleeaxstiostyu.tmheptoiopntifmoarlmpoedreforartmelaynlcaergweimthmlWighntectwomorpkust,aytiioenldasl
h
g
u
hro 60 In this work we proposed standard-compliant algorithms
T
ork for short range mmW scenarios. Most of the identified trade-
etw 30 offs arise also in cellular mmW networks, where a hy-
N
brid digital-analog beamforming has to be conducted due to
formidablecomplexityofpuredigitalbeamformingdesignfor
0
1 3 5 7 9 11 13 15
largenumberofantennas.Extendingtheproposedschemesand
Number of links in the network
addressing the additional challenges that arise in the context
Fig.5. Comparisonofdifferentconcurrenttransmissionschemesinmultiple
of cellular networks is an interesting topic for future study.
linksscenarios.
APPENDIX A
Fig. 5 comparesthe performanceof the proposedschemes To proveResult I, we show that beamwidthsappear in the
for multiple links scenarios. For comparison purposes, we optimization problem only in the form of ϕtϕr. Thus, instead
i i
depict Oracle which is the solution of optimization prob- of optimizing over individual ϕt and ϕr, we can optimize
i i
lem(5),whereasSingleLinkActivationrepresentsthenetwork the throughput over a new decision variable ϕ , ϕtϕr. The
i i i
throughputachievedifthelinkofhighestSNRisactivated.The above claim holds on alignment procedure, since it can be
followingpointscanbemadefromthisfigure.First,allocating fullydescribedbyϕ .Consideringoptimaltransmissionpower
i
onlyonechannelpertimeslot,whichisthecaseintheexisting pmax, we recast (6) to
standards, does not exploit fully the time slots in mmW net- gc 2π−2πz 2π−2πz
works.Thisinefficiencyincreaseswiththenumberoflinks.In SINR = i,ipmax +z +z
i n ϕt ϕr
particular,with10links,525%,401%,and177%performance (cid:18) i (cid:19)(cid:18) i (cid:19)
enhancement can be achieved by the Oracle, interference
under-estimator, and over-estimator, respectively. Given that (2π−2πz)2 (2π−2πz)z(ϕt+ϕr)
the number of links in local networks is limited, typically =c2 + i i +z2 ,
ϕ ϕ
less than 20 links, the underestimation approach can provide  i i 
low complexity solutions that are close to the optimal. Good  S1 S2 
performanceisexpectedforsmallscalenetworks,whereusers where c =gc pmax/n. Now, if S ≫ S , we can neglect
2 i|,i {z } | 1 {z2 }
operatewithnarrowbeams.Forultradensenetworks,however, the term S , so SINR and consequently achievable rate will
2
highamountofinterferenceinvalidatesthebasicpseudo-wired be completely described only by ϕ . After some algebraic
i
assumption, based on which the proposed underestimation manipulations, we can show that the condition holds if
approach has been developed. Instead the conservative ap- 1−z
ϕt+ϕr ≪2π .
proach guarantees that no harmful interference arises at the i i z
cost of a significant throughput reduction, yet it outperforms For narrow beams, z ≪ 1, which along with ϕt ≤ ψt and
i i
the current single link activation scheme. This gain increases ϕr ≤ ψr, confirms the above condition. For example, under
i i
also with the number of links, since a higher number of links realistic assumptions of ψt = ψr = π/2 and z = 0.1, the
i i
increases the probability of having more independent links. condition translates to
In general, deciding which is the most appropriate scheme π π
ϕt+ϕr ≤ + ≪18π,
depends heavily on the computation complexity that can be i i 2 2
handled, number of links, and quality of service requirements which is true. Therefore,we can conclude that for the param-
of individual links. eters in the region of interest, term S is negligible compared
2
to S , thus the throughputof link i can be well approximated 1, since T is the time slot duration which should be much
1
by higher than the transmission of a single pilot T . Neglecting
p
c (2π−2πz)2 the alignment overhead (1−c1/ϕi) from (9), the throughput
1− ϕ1 log2 1+c2z2+c2 ϕ , (9) willbeastrictlydecreasingfunctionofϕi,confirmingthatthe
(cid:18) i(cid:19) i ! derivative takes negative values at the end of the feasible set.
wherec =ψtψrT /T andc aretwoconstantswithinatime This completes the proof. (cid:4)
1 i i p 2
slot.
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