WiLiTV: A Low-Cost Wireless Framework for Live TV Services

0.72 MB·

by  Rajeev Kumar

WiLiTV: A Low-Cost Wireless Framework for Live
TV Services
Rajeev Kumar†,Robert S Margolies∗,Rittwik Jana∗,Yong Liu†and Shivendra Panwar†
† Department of Computer and Electrical Engineering, New York University, NY 11201, USA
∗ AT&T Labs Research, 1 AT&T Way, Bedminster, NJ 07921, USA
Abstract—With the evolution of HDTV and Ultra HDTV, Core Aggregation
Router Router DSL STB
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1 QualityofExperience.Serviceprovidersareconstantlytryingto Internet Service Provider Domain Ethernet
20 dcoiffneternenttmiaoteretheeffimcsieenlvtelys wbyithinlnoowveartincogstneawndwhaiygsheorfpdeisntertirbauttiionng. {Data acquisition{Core {Distribution {Access WL{ANHome
n In this work, we propose a cost-efficient wireless framework (a) Traditional IPTV architecture
a (WiLiTV) for delivering live TV services, consisting of a mix of 8S0at2e.l1li1ten ARonutetnerna
J wirelessaccesstechnologies(e.g.Satellite,WiFiandLTEoverlay Satellite Link
links). In the proposed architecture, live TV content is injected LTE Link
0 WiFi Link
into the network at a few residential locations using satellite
1
dishes. The content is then further distributed to other homes

using a house-to-house WiFi network or via an overlay LTE Satellite
]
M network.OurproblemistoconstructanoptimalTVdistribution
network with the minimum number of satellite injection points,
M while preserving the highest QoE, for different neighborhood
densities.Weevaluatetheframeworkusingrealistictime-varying
s. demand patterns and a diverse set of home location data. Our (b)OurproposedWiLiTVarchitecture:-contentisfirstdelivered
c studydemonstratesthatthearchitecturerequires75–90%fewer to a community through a few selected houses and LTE BSs
[ satellite injection points, compared to traditional architectures. with satellite antennas, and is then distributed to houses using

Furthermore, we show that most cost savings can be obtained WiFi and LTE relays.
1
using simple and practical relay routing solutions.
v Fig.1:ComparisonofIPTVandourproposedWiLiTVarchitectures.
9
6 1. Introduction infrastructure cost by broadcasting live TV content to every
6 Today, the vast majority of households receive TV content subscriber/household equipped with a satellite dish antenna.
2
0 via cable/fiber, IP network, or satellite. As illustrated in However, satellite providers still incur a high initial cost to
. Fig.1(a),InternetProtocolTV(IPTV)streamsliveTVcontent install a dish antenna for each new customer household. In
1
from a few regional hub offices to set-top boxes over either New York, for example, installing a single satellite dish costs
0
7 a dedicated private network or over-the-top via the core IP approximately $1,000 [7].
1 network[1].TosatisfyQualityofService(QoS)requirements, Service providers constantly strive to differentiate them-
v: IPTV must be provisioned with a sufficiently high bandwidth selves by innovating new ways of distributing content more
i in the distribution network [2]. efficientlywithlowercostandhigherpenetration.Therefore,in
X
However, with the evolution of HDTV, 4K content, and the thispaper,weproposealow-cost,WirelessLiveTV(WiLiTV)
r prevalence of thousands of channels, the need for bandwidth architecture that leverages a range of access technologies
a
is ever increasing [3]. Even with advanced video compression (Satellite, WiFi and LTE) to provide high quality live TV ser-
techniques, each Standard and High Definition TV (SDTV, vices.AsshowninFig.1(b),theWiLiTVarchitecturestrategi-
HDTV)channelrequires2and9Mbps,respectively.Thus,the callyequipsafewhouseholdsand/orLTEBaseStations(BSs)
currentinfrastructurewillsoonbestressedwiththisescalating with satellite dish antennas and relays TV content to other
demand. residential homes using WiFi and/or cellular networks. Our
One solution to the growing demand is to deploy more proposedarchitectureoffloadsTVcontentfromthetraditional
cables/fibers. However, deployment of wired infrastructure is core IP network or a dedicated wired IPTV infrastructure to
costly, especially in rural areas. The per-house fiber-laying long-haul satellite links and local high speed wireless links
cost can go up to $19,000 if the number of households per among households, leveraging the recent advances in wireless
mile is less than five [4]. Another possible solution is to technologies, such as Massive MIMO and Millimeter Wave.
scale up the capacity of the IP core to handle the increased With this novel architecture, our design goal is to satisfy the
traffic;however,thiswillrequireadditionalroutingequipment, live TV demands of all households at the lowest possible
thus resulting in greater infrastructure cost [5] and greater infrastructure cost. It consists of two sub-problems:
energyconsumption[6].SatelliteTVprovidersavoidthewired • Source Provisioning: which households are chosen to in-
stallsatelliteantennasanddownloadallliveTVchannels? 2. RelatedWork
• Relay Routing: how should live TV channels requested An IPTV architecture can be divided into five main parts,
by each household be relayed from the sources?
(i) a data acquisition network, (ii) core backbone network
These two sub-problems are tightly coupled: source provi- containingsuperhuboffices(SHO),(iii)aregionaldistribution
sioning determines the potential sources that a household can network containing video hub offices (VHO), (iv) access
download content from; and if some households cannot find networkcontainingDSLAMs,and(v)customerhomenetwork
a relay routing solution to get their desired channels, new containing residential gateways and set-top-boxes [9], [10].
sourceshavetobeaddedtothedistributionnetwork.Thereisa To decrease bandwidth requirements in the core backbone
fundamentaltrade-offbetweenthecomplexityofrelayrouting networkandforfastTVchannelswitching,multicastchannels
andthecostsavinginsourceprovisioning.Thecurrentsatellite andgroupsaretypicallyused.However,maintainingmulticast
TV providers, such as Dish Network [8], is at one end of the puts an extra burden on the network, especially for building
trade-off spectrum, where each household installs a satellite and pruning multicast groups. Furthermore, IP multicasting
antenna and no relay routing is needed at all. At the other is a good candidate for popularly viewed channels. On the
end, one can minimize the number of satellite antennas to be other hand, it is costly to maintain multicast groups for
installed by maximally utilizing any possible wireless relay distributing less popular TV channels [11]. Peer-to-peer is
routing among households to satisfy their live TV demands. another technology that has been investigated for distributing
Anypracticalsolutionhastofindthesweetpointandstrikethe live TV [10]. However, there are challenges associated with
rightbalancebetweencomplexityandcost-saving.Tosystem- P2P for accommodating fast TV channel switching and TV
aticallyevaluatetheimpactofvariousrelayroutingfactorson channel recovery, especially when streaming peers leave the
costsaving,weformulateaseriesofjointprovisioning-routing system abruptly. This can result in interruption while viewing
optimization problems to find the lowest costs under different live TV and eventually a poor QoE. We are thus motivated
routing constraints, including relay hop count limit, splittable to find a suitable architecture which pushes TV content to the
ornon-splittableflows,LTEavailability,anddynamicorstatic end users using a diverse set of access links simultaneously.
solutions. The optimization models developed are used to This diversity is useful to provide resiliency and bandwidth
numericallyinvestigatetheroutingcomplexityandcostsaving aggregation to satisfy the cumulative demand from the end
tradeoffthroughcasestudieswithrealhouseholdtopologyand users. Our proposed WiLiTV architecture is able to push TV
user demand data. The key contributions of this paper are as content to the households, facilitate fast channel switching
follows, while also providing a cost-effective solution for distribution
of less popular TV channels.
1) We present the WiLiTV architecture to provide high
Several studies present the challenges of and solutions for
quality live TV services to users via a mix of wireless
providingliveTVserviceswithQoSguaranteesusingwireless
access technologies (i.e., satellites, WiFi relayed com-
technologies (WiFi, WiMax, etc.) [12]–[17]. Note that in all
munication, and LTE overlay network).
these studies, TV content is delivered to the access network
2) We formulate a series of novel joint optimization prob-
lems to systematically evaluate the trade-off between through SHO and VHO, which results in a large bandwidth
requirement and energy consumption in the distribution net-
the cost saving in satellite antenna provisioning and
work. By contrast, our solution does not need the backbone
the complexity in relay routing, considering various
network and offloads TV traffic to local wireless networks.
practical provisioning and routing constraints.
3. SystemModelandAssumptions
3) Theformulatedoptimizationproblemscanbesolvedus-
ingbinaryprogramming,ormixed-integerprogramming AsillustratedinFig.1(b),ourwirelessdistributionnetwork
forsmallandmediumnetworks.Forlargenetworks,we for live TV consists of three types of nodes:
develop greedy heuristic algorithms to obtain close-to- 1) A small number of households equipped with satellite
optimal solutions. antennas act as the injection points for live TV content.
4) We evaluate the proposed WiLiTV architecture using They also have WiFi access points for relaying content
real household topology and user demand data from a to WiFi-only households.
major live TV service provider. Our results demonstrate 2) LTE BSs equipped with satellite antennas act as addi-
that WiLiTV requires 75% to 90% fewer satellite injec- tional live TV injection points, and can deliver content
tion points, compared to traditional architectures. Most to LTE-enabled households over unused LTE bands.
of the cost savings can be achieved with simple and 3) Regular households are equipped with WiFi access
practical relay routing solutions. points and LTE receivers. A regular household receives
This paper is organized as follows. In Section 2 we discuss TV content from WiFi or LTE. It can also relay the
therelatedwork.Thesystemmodelandassumptionsmadeare received TV content to other regular households.
described in Section 3. The formulation of joint optimization Asaresult,ahouseholdcanreceiveTVcontentbythefollow-
problems are presented in Section 4. Section 5 and Section 6 ing methods: (i) directly from satellite antenna, (ii) through
contain the associated solution techniques and the numerical WiFi relay, (iii) through LTE relay, and (iv) through both
results, respectively. Section 7 concludes the paper. LTE and WiFi relays. Fig. 1(b) illustrates the TV reception
and relay methods at each node. Moreover, content can be LTElinksinthetopologyareunidirectionalfromaLTEBSto
relayed using either all-or-nothing flows or fractional flows. households. A LTE BS uses a single channel for transmission
In all-or-nothing flows, a household receives all content from in its coverage area. Thus, resources must be shared between
asinglesource/relaynode;usingfractionalflows,ahousehold households receiving TV content from the same LTE BS. We
receives content simultaneously from multiple sources/relays. use TDMA for resource sharing. Let 0 ≤ λ ≤ 1 be the time
ij
TV traffic demand at household i is denoted by δ (in Mbps). share of the link from LTE BS i ∈ L to household j ∈ V,
i
(cid:80)
The demand can also be expressed as ψ ∗b, where ψ is the λ ≤ 1, ∀i ∈ L. To characterize LTE links, the pathloss
i i j ij
numbers of channels being demanded at household i and b is from LTE BS to households is calculated using [22],
the capacity required per channel in Mbps.
PLLOS =103.8+20.9log(d) (3.4)
ij
A. Relay using WiFi
where(??)representspathlossfromanLTEBStoahousehold
The WiFi relay network is modeled as an undirected graph
fortheline-of-sightlink.Usingthemaximumallowedtransmit
G = (V,E), where V is the set of households and E is
power of LTE BSs and the pathloss model, we evaluate the
the set of WiFi links between households. WiFi transmis-
LTE capacity as [23],
sions between neighboring households operate on orthogonal
channels, and are highly directional by making use of beam- CLTE =βWlog (1+γSNR), (3.5)
ij 2
forming techniques. Point-to-point connections among house-
whereβisthefractionofbandwidthusedfordatatransmission
holds avoid wasting airtime in collision avoidance. Further-
whiletherestisusedforcontrolsignaling.Typically,βranges
more,thehouseholdsareboundedbyadegreeofconnectivity
between0.5−0.8.Similarly,γisthefractionofreceivedsignal
representedbyρ,i.e.,ahouseholdhasamaximumofρpoint-
to noise ratio that contributes to broadband speed. Typically,
to-point links with neighboring households. We assume all
γ lies between 0.5 to 0.6.
WiFi transmitters have the same transmit power P, and path
For easy reference, all the notation is presented in Table I.
losses (PL) between two households are the same along both
directions (PL = PL , between household i and j) [18]. A
ij ji TABLE I: Notation
WiFi link exists from household i to j if j lies within the
communication range of i; specifically, if the received signal Parameter Description
strength on j is greater than the receiver sensitivity [19], V,L,V(cid:48) Setofhouseholds,LTEBSsandboth,respectively
E,E(cid:48) SetofWiFilinks,setofWiFiandLTElinks
P−PL ≥ξ;∀i, j∈V, (3.1)
ij S,R,T SetofSource,RelayandTerminalnodes,respectively
whereξistheWiFireceiversensitivity,anditisassumedtobe δi Demandathouseholdi
identicalforallWiFireceivers.Accordingto[20],thepathloss h Maximumallowedhopsinthetopology
on a WiFi link can be calculated as ρ Maximumdegreeofconnectivityatsourceandrelaynodes
PL(d)=LLFS((dd)+)S+F3;5liofgd(<dd)B+P,SF; if d ≥d , (3.2) Cuiijj CBfoairnpacarocynittvyeanrotifadbliilsnetkriinbfdruoitcimaotninnogdiefliintokfjromnodeito jisselected
FS BP dBP BP
Xi Binary variable indicating if household i has a satellite
where d is the distance between the transmitter and receiver,
antenna
L (d) is the free space pathloss in dB, d is the breakpoint
FS BP Yi Binary variable indicating if household i relays video to
distance and SF is shadow fading in dB. The free space neighboringhouseholds
pathloss is defined as lsi Binary variable indicating if node i downloads video di-
rectlyfromvirtualsource s(fractionalflow)
LFS =20log(d)+20log(f)−147.5, (3.3) fij Videotrafficonlinkfromito j(fractionalflow)inMbps
where f isthecarrierfrequency.Fromthetransmitpowerand λij Timeshareofnode jfromLTEBSi
pathloss computed with equations ??-??, the received signal ∆i(t) Binary variable indicating if household i requires TV ser-
vicesattimeinstancet
strength at j can be calculated. We use the tables in [20],
τi AvailableresourcesattheLTEBSi
[21] to map the received signal strength to the corresponding
modulation and coding scheme and the achievable capacity 4. JointOptimizationofSatelliteAntennaPlacementand
of WiFi links. Since all transmitters have the same transmit RelayRouting
power,andpathlossissymmetric,wehaveC =C fori(cid:44) j.
ij ji In this section, we develop optimization models to system-
B. Relay using WiFi and LTE aticallyevaluatethedesigntrade-offsinWiLiTV.Weconsider
LTE BSs can be additional injection points of live TV the following routing complexity factors.
content, subject to the availability of LTE bandwidth at the 1) Relay Hop Count: Ideally, each connected island of
BS. Let L indicate the set of LTE BSs having significant households only needs one source, and TV content can
spare LTE resources. The network topology is augmented as be relayed to all households using an arbitrary number
G(cid:48) =(V(cid:48),E(cid:48)),withV(cid:48) =(V∪L)andE(cid:48) consistingofallWiFi of hops. However, live TV services have stringent QoS
and LTE links. LTE BSs can only be a source node. Thus, all requirements on delay, bandwidth and reliability. It is
well known that multi-hop wireless relays can lead to we can formulate a binary programming problem as follows:
long delay, low end-to-end throughput and poor relia- (cid:88)
Minimize: X (4.1)
bility [24]. In this paper, we limit relay routing to be at i
most two hops. We will compare the cost saving with {Xi,uij} i∈V(cid:88)
one-hop and two-hop relay routing. Subject to: uij ≤ρXi, ∀i∈V; (4.2)
2) Splittable Flows: As discussed in Section 3, with frac- j:(cid:104)i,j(cid:105)∈E
(cid:88)
tional flows, one household can download content from u =(1−X ), ∀j∈V; (4.3)
ij j
multiple relay paths from multiple sources. This can i:(cid:104)i,j(cid:105)∈E
(cid:88)
potentially increase the wireless link utilization and
u C ≥δ (1−X ), ∀j∈V. (4.4)
ij ij j j
coverage of each source, leading to higher cost saving.
i:(cid:104)i,j(cid:105)∈E
As with any multi-path routing, splittable flows have
to deal with delay disparity on different paths, and The objective (??) is to minimize the number of satellite
antennas.Constraint(??)dictatesthatifnodeiisselectedasa
datatransmissionreliabilitydecreasesasmorelinksand
nodes are employed. We will compare the efficiency of sourcenode(Xi =1),thenumberofitsreceiversisboundedby
thedegreeofconnectivityρ;otherwise(X =0),nodeicannot
relay routing with and without splittable flows. i
have any out-going video traffic. Constraint (??) reflects the
3) LTE Availability: A LTE BS can cover a wider range
fact that a non-source node downloads video content from
than a WiFi transmitter. But LTE bandwidth resources
exactly one incoming link, and a source node does not have
areexpensive.Wewillevaluatethecoveragegainadded
anyincomingvideotraffic.Constraint(??)statesthat,atanon-
by LTE BS to justify its bandwidth cost.
source household, the aggregate bandwidth of all incoming
4) Dynamicvs.StaticSolution:UserTVdemandsnaturally
links must be greater than its total TV demand.
vary over time. To maximally reduce cost, one should
2) Two-hop and Non-splittable Relay Routing: Now we
design dynamic source provisioning and relay routing
relax the maximum relay hop count to two. Thus, some
solutions to match the changing user demand. However,
non-source households may relay video traffic for other non-
itisnotpracticaltochangesatelliteantennalocationson
source households. There are three types of households in
anhourlyordailybasis, andreconfiguringrelayrouting
the network: source nodes with satellite antennas, non-source
maycauseshort-termservicedisruption.Staticsolutions
nodes relaying video for other nodes (called relay nodes), and
are easier to implement. We will formally study the
non-source nodes without any relaying traffic (called terminal
performance gap between dynamic and static solutions.
nodes). Using X, introduced in the previous formulation, all
i
non-source nodes have X = 0. We further introduce another
i
To systematically evaluate the impact of various source pro-
binary variable Y ∈ {0,1}, i ∈ V to indicate whether a node
i
visioning and relay routing strategies on cost saving, we relays other nodes’ traffic. Then for a relay node we have
formulate a series of joint provisioning-routing optimization X =0andY =1,andforaterminalnode,wehaveX =0and
problems to find the lowest costs under different routing Yi= 0. Fig. i2 illustrates the three types of nodes inithe two-
i
constraints in this section.
hop relay, and how terminal nodes download video content
from the source through a common relay node. The joint
optimization problem with two-hop relay can be formulated
as a new binary programming problem:
(cid:88)
Minimize: X (4.5)
i
A. Fixed Demand with WiFi {Xi,Yi,uij} i∈V
Subject to:
(cid:88)
u ≤ρ(X +Y), ∀i∈V; (4.6)
We start with the simple scenario where user demands are ij i i
j:(cid:104)i,j(cid:105)∈E
fixed and only WiFi relays are available. We use the graph G (cid:88)
u =(1−X ), ∀j∈V; (4.7)
havingonlyWiFitransmittersandreceivers.Wefirstformulate ij j
the optimization problems for non-splittable flow routing with i:(cid:104)i,j(cid:105)∈E
one-hop and two-hop relays respectively. We then generalize 0≤ Xi+Yi ≤1, ∀i∈V; (4.8)
it to splittable flow routing with limited hop count. Y ≤2−Y −u , ∀i, j∈V; (4.9)
j i ij
(cid:88)
u C ≥δ u + δ u −Θ(1−X −Y), ∀(cid:104)i, j(cid:105)∈E.
1) One-hop and Non-splittable Relay Routing: For this ij ij j ij k jk i i
scenario,weassumethatahouseholdisatmostonehopapart k:k(cid:44)i,j
(4.10)
from its corresponding source node. Let X ∈ {0,1}, ∀i ∈ V
i
be the binary variable indicating whether a node is equipped Constraint (??) bounds the maximum degree of connectivity
with satellite antenna. Similarly, u ∈ {0,1}, ∀(cid:104)i, j(cid:105) ∈ E be at source and relay nodes (both have X + Y = 1), and
ij i i
the binary variable indicating if a link from node i to node terminalnodescannothaveoutgoingvideotraffic(X +Y =0).
i i
j carries node j’s TV demands. Using these binary variables, According to constraint (??), all non-source nodes download
Virtual Virtual
Source Links
Source Relay
u =1
ij Real Nodes & Links
Terminal
X =1 X =0 X =0
i j k
Y =0 Y =1 Y =0
i j k
Fig. 2: Two-hop Relay Routing: node i is a source node (Xi = 1), Fig. 3: Virtual Network Topology for Splittable Relay Routing.
node j is a relay (Y = 1), downloading traffic from i (u = 1),
j ij
relaying video to other terminal nodes (X =Y =0).
k k the following mixed-integer programming problem.
(cid:88)
Minimize: l (4.11)
si
{lsi},{fij} i∈V
Subject to:
(cid:88) (cid:88)
their video from exactly one incoming link. Constraint (??) f + f =δ + f , ∀i∈V; (4.12)
si ji i ik
states that a node in the distribution network can only assume j:(cid:104)j,i(cid:105)∈E k:(cid:104)i,k(cid:105)∈E
(cid:88) (cid:88)
one role out of source, relay or terminal node. Constraint (??) f = δ; (4.13)
enforcesthatarelaynodedoesnotreceivetrafficfromanother si i
i∈V i∈V
relay node. This is because if node j receives video from a
f ≤C , ∀(cid:104)i, j(cid:105)∈E; (4.14)
relay node i, then Y =1 and u =1. Then to make (??) hold, ij ij
we must have Y =i0, i.e, j cainjnot be a relay node anymore. fsi ≤lsiCsi, ∀i∈V; (4.15)
j (cid:88) (cid:88)
Ontheotherhand,ifiisasourcenode,Y =0,evenifu =1, f ≤h δ, ∀i∈V. (4.16)
i ij ij i
we can still have Yj = 1 (i.e., j can still relay video to other (cid:104)i,j(cid:105)∈E i∈V
nodes). The last constraint guarantees each outgoing wireless
Constraint (??) is the flow-conservation law at node i, i.e.,
link from a source or relay has enough bandwidth to carry
the total incoming traffic at node i (left-hand side) equals the
video traffic assigned to it. The first term on the righthand
sum of the demand of node i and the total outgoing traffic
sideisthevideotrafficfromthesource/relaynodetoitsdirect
(right-hand side). (??) implies that all the video downloading
receiver. The second term is non-zero only if i is a source
traffic in the virtual graph originates from the virtual source.
and j is a relay; it represents the traffic of all households
(??) guarantees traffic on each relay link is bounded by its
downloading video from i through relay j. The last term is
capacity, and (??) makes sure that a virtual link can carry
zero if i is a source or relay, and if i is a terminal node, Θ is
video traffic only if it is activated. Finally, the left-hand side
a large number so that the inequality automatically holds.
of (??) is the total video traffic on all relay links, i.e., the
sum of the traffic generated by all households on all links.
For each household, the total traffic it generates on all links
3) Splittable Relay Routing with Average Hop-count Limit:
equals its total video demand multiplied by its average relay
In the last two optimization formulations, we considered all- hop count. (??) effectively limits the average relay hop count
or-nothing flows and each household downloads all its video
of all households to a constant h.
demands from one source/relay through one wireless link. To
furtherimprovetheflexibilityandefficiencyofrelayrouting,a
B. Fixed Demand with WiFi and LTE
household can receive video from multiple sources and/or re-
lays simultaneously through multiple relay paths. We develop As discussed in Section 3-B, an LTE BS can be a potential
a variation of the well-known multi-commodity flow problem injectionpointofliveTVcontent.Wenowdiscusstheproblem
to cover this case. As illustrated in Fig. 3, we first augment formulation with LTE BSs by extending the formulations in
the distribution network with a virtual source node (indicated the previous section.
by s), that connects to all the nodes in the topology through 1) One-hop and Non-splittable Relay: As modeled in Sec-
virtual links with very high capacities. All video demands are tion 3-B, we extend the distribution network from G to
servedfromthevirtualsource.Ifahouseholdinstallsasatellite G(cid:48) = (V(cid:48),E(cid:48)) by including LTE BSs and LTE links from
antenna, it is equivalent to saying that we activated its virtual LTE BSs to their covered households. The WiFi optimization
link from the virtual source for direct video downloading. problem defined in (??) to (??) can be extended to cover the
The objective of minimizing the number of satellite dishes LTE case. Each LTE BS can be a potential injection point,
is equivalent to minimizing the number of activated virtual we extend X defined on G to G(cid:48), X = 1, ∀i ∈ L, if and
i i
links. We define a binary variable l indicating whether the only if we install satellite antenna on LTE BS i. Then the
si
virtuallinkfromthevirtualsource stonodeiisactivated.We optimization objective is to minimize the number of satellite
furtherdefine f asthevideotrafficvolumeonlink(cid:104)i, j(cid:105).The antennas among LTE BSs and households, i.e., min(cid:80) X.
ij i∈V(cid:48) i
optimizationwithsplittablerelayroutingcanbeformulatedas Constraints for households defined in (??), (??) and (??) still
hold. We introduce additional constraints for LTE BS: and economical, since WiFi/LTE links and relay routing can
(cid:88) be conveniently reconfigured using Software Defined Radio
λij ≤ Xiτi, ∀i∈L; (4.17) and/or Software Defined Networks.
j∈V
1) Dynamic Provisioning of Satellite Antennas and Dy-
λ C ≥δ u , ∀i∈L,∀j∈V. (4.18)
ij ij j ij namicRelayRouting: Inadynamicformulation,allthedesign
The constraint in (??) states that if BS i does not have a variables{Xi,Yi,uij, fij,lsi,λij}inthestaticformulationsshould
satellite antenna, households cannot download video from it; beconvertedto{Xi(t),Yi(t),uij(t), fij(t),lsi(t),λij(t)}.Otherthan
if it does, then the total time shares of all covered household the time-dependent demands {δi(t),i ∈ V}, we introduce
isboundedbyavailableresourcesattheLTEBS.(??)implies another binary variable ∆i(t) such that if household i has TV
that the allocated bandwidth from BS i to household j is traffic demand at time t, then ∆i(t)=1, otherwise 0. The one-
greater than the demand of j. hop and non-splittable relay routing problem defined in (??)
2) Two-hop and Non-splittable Relay: In two-hop relay, through (??) can be formulated for each time period t as:
(cid:88)
LTE BSs can only be potential sources, so we can extend the
Minimize: X(t) (4.19)
i
optimizationproblemdefined(cid:80)in(??)through(??)byupdating {Xi(t),uij(t)} i∈V
the objective function to min X, and adding constraints (cid:88)
i∈V(cid:48) i Subject to: u (t)≤ρX(t), ∀i∈V; (4.20)
(??) and a new LTE capacity constraint updated for two-hop ij i
j:(cid:104)i,j(cid:105)∈E
relay: (cid:88)
(cid:88) uij(t)=(1−Xj(t))∆j(t), ∀j∈V; (4.21)
λ C ≥δ u + δ u −Θ(1−X), ∀i∈L,∀j,k∈V.
ij ij j ij k jk i i:(cid:104)i,j(cid:105)∈E
k,k(cid:44)i,j (cid:88)
u (t)C ≥δ (t)(1−X (t)), ∀j∈V. (4.22)
ij ij j j
Similar to (??), this constraint ensures that the link from BS i
i:(cid:104)i,j(cid:105)∈E
to household j carries video demands of household j and all
Constraint (??) indicates that if a household has no demand
other households using j as a relay.
at time t, then it does not need incoming video traffic. For
3) SplittableRelayRouting: TheinclusionofanLTEBSto
the two-hop and non-splittable relay routing problem defined
thesplittablerelayroutingformulationdefinedin(??)through
in (??) through (??), we can change all design variables and
(??)isstraightforwardbyextendingtheobjectivefunctionand
allconstraintstoworkonnodesandlinksinG(cid:48) =(V(cid:48),E(cid:48)).The demands to be time-dependent, and update (??) as:
(cid:88)
onlychangeisthatforaLTElink,thelinkcapacityconstraint u (t)=Y (t)+∆ (t)(1−X (t)−Y (t)), ∀j∈V,
ij j j j j
(??) becomes:
i:(cid:104)i,j(cid:105)∈E
f ≤λ C , ∀i∈L, j∈V, which says that node j needs to download video through
ij ij ij
exactlyoneincominglinkifeither jisarelaynode(Y (t)=1),
j
reflecting that a LTE link is only active for a fraction of time. or it is a terminal node (X (t) = Y (t) = 0) and has
j j
C. Time Varying Demand demand (∆ (t) = 1). For the splittable relay routing prob-
j
Sofar,theformulationsassumeuserTVdemands{δ,i∈V} lem defined in (??) through (??), it is sufficient to directly
i
are fixed. In reality, user demands naturally vary over time. replace {fij,lsi,δi} with time-dependent variables/constants
Let t=1,··· ,T be the typical time periods, and {δi(t),i∈V} {fij(t),lsi(t),δi(t)}. Similar modifications can be made for for-
be the user demands at time period t. One approach is to mulations with LTE in Section 4-B.
designthedistributionnetworktohandleeachuser’smaximum 2) Static Provisioning of Satellite Antennas and Dy-
demandoveralltimeperiods,thatistoletδ0i (cid:44)maxt=1,···,Tδi(t) namic Relay Routing: In this case, variables reflect-
and plug in the time-independent demands {δ0,i ∈ V} to the ing the positions of satellite antennas {Xi,lsi} are time-
i
staticformulationsintheprevioussectionstoobtainstaticpro- independent,whiletheothervariablesaretime-dependent,i.e.,
visioning and relay routing solutions. This over-provisioning {Yi(t),uij(t), fij(t),λij(t)}. We can quickly convert the dynamic
might waste too much resources. In this section, we evalu- formulations in the previous section into the corresponding
ate different ways to cope with time-varying user demands. semi-dynamic formulation. For example, for the one-hop and
Specifically, we consider the following cases: 1) dynamic non-splittable relay routing problem defined in (??) through
provisioning of satellite antennas and dynamic relay routing; (??), we can have the semi-dynamic version as:
2) static provisioning of satellite antennas and dynamic relay (cid:88)
Minimize: X
i
routing, and 3) static provisioning of satellite antennas and {Xi,uij(t)} i∈V
static relay routing. Satellite antenna installation cannot be (cid:88)
Subject to: u (t)≤ρX, ∀i∈V,t=1,··· ,T;
easily adjusted on an hourly or daily basis. The first solution ij i
is not really practical. However, it gives us the lower bound j(cid:88):(cid:104)i,j(cid:105)∈E
on the required number of satellite antennas to meet time- uij(t)=(1−Xj)∆j(t), ∀j∈V,t=1,··· ,T;
varying user demands. The third solution may require more i:(cid:104)i,j(cid:105)∈E
(cid:88)
satelliteantennasthantheprevioustwo.However,itissimpler u (t)C ≥δ (t)(1−X ), ∀j∈V,t=1,··· ,T.
ij ij j j
to implement in practice. The second solution is practical
i:(cid:104)i,j(cid:105)∈E
Similar modifications can be made for all other formulations node set (line 10), and also remove its incoming video link
in the Section 4-A and 4-B. from the relay topology (line 11). After we update the source
3) StaticProvisioningofSatelliteAntennasandStaticRelay and terminal node sets, all links going to source and terminal
Routiing: In this scenario, all design variables are time- nodes no longer need to be considered, and thus are removed
independent, only the demand constants {δ(t),∆(t)} are time- fromtherelaymatrix.Aftertheiterations,nodesthosearenot
i i
dependent. All the formulations in the dynamic case can be marked as either source or terminal node are isolated nodes
modified accordingly. For example, the one-hop and non- that need satellite antennas. Finally, the relay topology and
splittable relay case become: source set are returned.
(cid:88)
Minimize: X
i Algorithm1:Greedyalgorithmforone-hopnon-splittable
{Xi,uij} i∈V(cid:88) relay
Subject to: u ≤ρX, ∀i∈V,t=1,··· ,T;
ij i Input: Relay matrix (A)
j:(cid:104)i,j(cid:105)∈E Output: Satellite antennas positioning and one-hop relay
(cid:88)
u =(1−X ), ∀j∈V,t=1,··· ,T; topology
ij j
i:(cid:104)(cid:88)i,j(cid:105)∈E 1: Initialization: S←φ, T ←φ, Atmp ←A, Aopt ←φ
uijCij ≥δj(t)(1−Xj), ∀j∈V,t=1,··· ,T. 2: while Atmp is not empty do
i:(cid:104)i,j(cid:105)∈E 3: Calculate the bin of each node based on Atmp, and
find node i with the largest bin.
5. ApproximationAlgorithms
4: S=S∪{i}
InSection4,differentscenariosaremodeledeitherasbinary 5: if |B(i)|≤ρ then
programmingormixed-integerprogrammingproblems,which 6: R(i)=B(i)
are both NP-hard problems. When the network size is small, 7: else
one can use various optimization tools, such as CVX in 8: randomly select ρ nodes in B(i) to R(i).
MATLAB [25], [26], to get the exact optimal provisioning 9: end if
and relay routing solutions. However, when the network size 10: T =T ∪R(i)−{i}
is large, the computation time might become prohibitive. In 11: Aopt =Aopt∪{(cid:104)i,k(cid:105),∀k∈R(i)}−{(cid:104)k,i(cid:105),∀k∈V}
thissection,wedevelopheuristicapproximationalgorithmsto 12: Atmp =A−{A(m,n):m∈V,n∈S∪T}
obtain close-to-optimal solutions for large networks. 13: end while
The problem formulations in Sections 4-A1 and 4-A2 are 14: return relay topology Aopt and source set
similar to the classic set cover problem. Our objective is to S =(V−S−T)∪S
opt
determine the minimum number of nodes that can cover all
other nodes in a given directed graph G with limited link
capacity. Let A denote the relay matrix, where A[i, j] = 1 Algorithm 1 can be extended to cover the two-hop non-
if and only if there is a wireless relay link from node i to j, splittable relay case. Similar to the one-hop case, we develop
and the capacity of link (cid:104)i, j(cid:105) is larger than δ , the total video a greedy iterative algorithm. At each iteration, we add node i
j
demand of j. Let B(i) (cid:44) {j ∈ V : A[i, j] = 1} be the set of with the largest number of one-hop children as a new source.
nodes that can potentially download their TV demands from The links from node i to their children R(i) are added to the
node i. Then call B(i) the bin of node i. relay topology. Different from the one-hop case, some nodes
The One-hop and Non-splittable Relay problem formulated in R(i) might further act as relays and forward video to two-
inSection4-A1canbeapproximatelysolvedusingthegreedy hopchildrenofi.LetD(i,R(i))bethesetofnodesconnecting
heuristic algorithm defined in Algorithm 1. Let S be the set to i through R(i), i.e.,
of chosen source nodes, and T the set of terminal nodes that D(i,R(i))(cid:44){k∈V:∃j∈R(i) such that C ≥δ }.
receive their TV channels from some source node in S. At jk k
each iteration, node i with the largest bin size is selected as a Note,anodek∈D(i,R(i))mightconnecttoithroughmultiple
new source node. All nodes in node i’s bin are added to the relay nodes in R(i)), and it can be added as a two-hop child
terminalnodesetT.Ifi’sbinhasmorethanρnodes,thenwe of i through any one of them in the relay topology. To build
randomly select ρ nodes to be covered by i. All the nodes in the two-hop relay tree rooted at i, we develop another greedy
i’s bin are added to the terminal node set. All links from i to iterative algorithm. Due to the space limit, we only give the
its receivers are added to the relay topology. Our problem is algorithm sketch as follows.
differentfromthetraditionalsetcoverproblemaseachelement 1) We first build the one-hop relay tree from i to R(i),
ofabinhasitsownbin.Thus,afterselectinganodeassource, and update the spare capacity on link (cid:104)i, j(cid:105), j ∈ R(i) as
thenodesinitsbinarenotremovedfromthenetwork,because C˜ =C −δ .
ij ij j
theycanstillactassourcesforothernodesinfutureiterations. 2) We select the node, say j , with the highest spare
0
As a result, when we select a new source, it might have been capacity from node i to grow the second hop relay.
covered by some source node and added to the terminal set 3) Amongallchildrenof j ,wefirstselectanodek thatis
0
in previous iterations. We need to remove it from the terminal connected to i only through j , if no such a node exists,
0
nd 65 bound on the required number of satellite antennas. In Fig. 5,
Total Dema[Mbps] 2455 wmeusptrebseenetquthipepneudmwbietrhosfanteoldlietes(ahnoteunsenhaosldfosrolrivLeTTEVBScso)ntthenatt
4 8 12 16 20 24 distribution in different scenarios for different communities.
Time (in a Day)
WithoneIEEE802.11nstreamandone-hoprelay,50%,30%,
Fig.4:Demandpatternincommunity(i):meantotaldemandperhour
38% and 29% nodes must be equipped with satellite antennas
(50 samples) with vertical bars denoting 95% confidence intervals.
in the four communities, respectively. Similarly, with four
we randomly select a child k of j . If C˜ ≥ δ , we
0 ij0 k parallel IEEE 802.11n streams and one-hop communication,
add k as a two-hop child of i through j in the relay
0 36%, 19%, 30% and 23% nodes must be equipped with
topology, and update the spare capacity C˜ =C˜ −δ .
ij0 ij0 k satellite antennas. When LTE BSs are available, the required
If no child of j can be added to the relay topology, we
0 numberofsatelliteantennasfurtherdecreases.Inthebestcase
set C˜ =0.
ij0 scenario,withaheterogeneousnetworkconsistingofbothLTE
4) GobacktoStep2,unlesseitherthesparecapacityofall
and WiFi links over a two-hop relay with fractional flow, the
first-hop links originated from node i become zero, or
required number of satellite antennas are 13% for community
all nodes in D(i,R(i)) are added to the relay topology.
(i) for four streams. Similarly for four streams using WiFi
After we build the two-hop relay tree rooted as node i, we links over two hops, the required number of satellite antennas
move on to find the next source with the highest degree until reducesto9%,23%and11%forcommunity(ii),(iii)and(iv)
all the nodes are covered. respectively.ThissuggeststhatadditionalWiFilinkcapacities
6. PerformanceEvaluation resultingfrommorestreamsdirectlytranslateintocostsavings
on satellite antennas, especially with two-hop relays Also
We evaluate the proposed WiLiTV architecture using real
noticethat,eventhoughfractionalflowsaremoreflexiblethan
household topology and user demand data from four com-
munities with different household sparsity served by a major all-or-nothing flows, in the evaluated scenarios, they bring no
or marginal performance gains over the corresponding all-or-
service provider in the USA. Community (i) consists of 22
nothing flows. This suggests that non-splittable relay routing
nodeswithhouseholdssparselylocated.Communities(ii),(iii)
may achieve most of the cost savings in practice, without
and (iv) consists of 21, 13 and 17 households, respectively.
incurring the complexity and reliability concerns of splittable
The average distance between households in the community
relay routing.
(i) is around 75m, while in the latter three communities it
is less than 55m. The case with the LTE Base Station is B. Dynamic Solution for Time-varying Demand
considered for community (i) only, and its location and the
Fig. 6 plots the required number of satellite antennas for
available LTE resources are taken from the database of BS
time-varyingdemandwithimpracticaldynamicantennaprovi-
for that community. Using the optimization formulations in
sioning and dynamic relay routing as studied in Section 4-C1.
Section 4, we find the optimal source provisioning and relay
topologiesunderdifferentrelayroutingcomplexityconstraints. We consider non-splittable relay routing to determine the
variation of the required satellite antennas. They serve as
We further explore the use of parallel streams supported in
the lower bounds for satisfying time-varying demands. The
IEEE 802.11n. Using beam-forming and Multiple Input, Mul-
verticalbarsinthefiguredenotethe95%confidenceintervals.
tiple Output (MIMO) antenna techniques, up to four parallel
We can observe that the result highly depends upon the TV
streams can be supported in IEEE 802.11n.
content demand. Similar to previous observation for fixed
Fig. 4 shows a typical demand pattern over a day. From
demand, the required numbers of satellite antennas decrease
this real demand data, obtained from a service provider, we
fromone-hoprelaytotwo-hoprelay.Onecanalsoobservethat
computetheprobabilitydistributionsfortherequestednumber
the confidence intervals with two-hop relays are significantly
of TV channels for each household at each hour of a day. In
higher than one-hop relay. This suggests that the additional
each simulation, we draw user demand samples from these
gain from two-hop relays are more time-dependent. For two-
probability distributions. The carrier frequencies for WiFi and
hop WiFi, we can observe that there is a larger gap between
LTEare5GHzand2GHzrespectively,thechannelbandwidth
one stream and two streams. This observation can simply be
forbothWiFiandLTEare20MHz.Thedegreeofconnectivity
explained from the fact that a higher number of streams is
of household is ρ=5. The data rate of each TV channel is 5
useful to support multi-hop communications. Similar results
Mbps, and the maximum relay hop count is h = 2. For these
are obtained for fractional flows with both WiFi and hetero-
simulation parameters, our heuristic algorithm obtains the
geneous networks.
identical result with a shorter computation time (particularly
in the two-hop scenario, where the exact algorithm takes tens C. Static Satellite Antenna Provisioning
ofsecondswhileourheuristicalgorithmtakesafewseconds).
Finally, an optimal distribution topology is obtained with
A. Fixed Demand
staticsatelliteantennashaving,(i)reconfigurableand,(ii)non-
First, we consider source provisioning and relay routing reconfigurable links, as discussed in Sections 4-C2 and 4-C3.
usingpeakdemandperhouseholdobservedoveralongperiod Fig. 7 compares the required numbers of satellite antennas to
of time. The fixed peak demand scenario gives us an upper satisfy time varying demands at all time instants to results
d Satellite Antennas 1680 987876 7 WWWWWWiiiiiiFFFFFFiiiiii aaawwwnnniiidddttthhh 5LLL OTFTTTrwnEEEaeoc www tHHioiiiotttonhhhppa lsFOT Frwnaleooc tw5HHiooonppals Flow 684 766655 433 WWWWWWiiiiiiFFFFFFiiiiii aaawww4nnniiidddttt4hhh LLL OTF3TTTrwnEEEaeoc www tHHioiiiotttonhhhppa lsFOT Frwnaleoo4c twHHiooonppals Flow 684 765654 43 WWWWWWiiiiiiFFFFFFiiiiii aawwwa4nnniiidddttt3hhh LLL3OTFTTTrwnEEEaeoc www tHHioiiiotttonhhhppa lsFOT Frwnale4ooc twHHiooonppals Flow 64 654543 4 WWWWWW4iiiiiiFFFFFF3iiiiii aawwwa3nnniiidddttthhh LLL OTFTTTrwnEEEaeoc www tHHioiiiotttonhhhppa lsOFT4 Frwnaleooc twHHiooonppals Flow
quire4 44 44 44 2 22 2 2 22 2 22 22
Re
(i) (ii) (iii) (iv) (i) (ii) (iii) (iv) (i) (ii) (iii) (iv) (i) (ii) (iii) (iv)
(a) Number of Streams = 1 (b) Number of Streams = 2 (c) Number of Streams = 3 (d) Number of Streams = 4
Fig. 5: Required number of satellite antennas in four considered communities to satisfy the maximum (fixed) user TV demands.
5 4 2.0
d Satellite Antennas45 SSSSttttrrrreeeeaaaammmm ==== 1234 34 SSSSttttrrrreeeeaaaammmm ==== 1234 32 SSSSttttrrrreeeeaaaammmm ==== 1234 1.5 SSSSttttrrrreeeeaaaammmm ==== 1234
quire3 1.0
Re
5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25
Time (in a Day) Time (in a Day) Time (in a Day) Time (in a Day)
(a) WiFi over one hop (b) WiFi over two hops (c) WiFi and LTE over one hop (d)WLANandLTEovertwohops
Fig. 6: Community (i): variation of required satellite antennas with non-splittable relay to satisfy demand at each time instant.
10
Required Satellite Antennas68795 999 777 76FTNTRiiieoxmmgne6cee-dor VVeDngfiaaecrrgmoyyunii6arnnfiangggbd ulDD6er eeaLmmb6ilneaak nnLsddi nwwkiistthh 687495 8 5 5 6 5 5 6FTNTRiii5eoxmmgneceerdo5e VVgDncfiaaeorrgmyynuiifiarnnagn5ggbud lDDrea 5eebLmmlienaa 5Lknnsddin wwksiitthh 6873495 8 6 6 65 5 6FTRTN5iiieoxmmgneceerd5oe VVgDncfiaaeorrgmyynuiifiarnn5agnggbud lDDrea4 eebLmmlien4aa Lknnsddin wwksiitthh 6873452 7 4 4 5 3 3 5 FTNTR3iiieoxmmgne3ceerdoe VVgDncfiaaeorrgmyynuiifi4arnnagnggbud lDDr3ea eebLmmli3enaa Lknnsddin wwksiitthh
Stream=1 Stream=2 Stream=3 Stream=4 Stream=1 Stream=2 Stream=3 Stream=4 Stream=1 Stream=2 Stream=3 Stream=4 Stream=1 Stream=2 Stream=3 Stream=4
(a) WiFi over one hop (b) WiFi over two hops (c) WiFi and LTE over one hop (d) WiFi and LTE over two hops
Fig. 7: Community (i): required number of satellite antennas with non-splittable relay to satisfy demands at all time instants.
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