Table Of Content

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 7 tinhcerebaasnindgw.iCdtohnsruemqueirrsemdeemntanfodruInPin-btearsreudpTteVdsceornvtiecnetwiisthraaphidiglhy ATVcq cuoisnittieonnt IP/CMoPreLS DNistertiwbuotrikon NAectwceosrsk FTTx 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 problems 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 relays 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 communities 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. obtained for fixed peak TV demands in Fig. 5, all with non- References splittablerelays.Fig.5suggeststhatformulationsconsidering the time-varying demands, instead of per-user peak demands, [1] X. Hei, C. Liang, J. Liang, Y. Liu, and K. W. Ross, “A measurement can lead to a higher cost saving in two-hop and LTE cases. study of a large-scale P2P IPTV system,” IEEE Trans. Multimedia, vol.9,no.8,pp.1672–1687,Dec.2007. Forthetwocasesconsideredwithfixedpositioningofsatellite [2] K. Kerpez, D. Waring, G. Lapiotis, J. B. Lyles, and R. Vaidyanathan, antennas with configurable and non-reconfigurable relays, we “IPTV service assurance,” IEEE Commun. Mag., vol. 44, no. 9, pp. obtained the same results for all the combinations studied. 166–172,Sep.2006. This suggests that fixed positioning of satellite antennas and [3] K. Brunnstro¨m, B. Ahlgren, C. Lagerstedt, M. Kihl, and A. Novak, proper selections of relay routing are sufficient for an optimal “Future media distribution: An innovation agenda for digital media distribution,”Mar.2015. distribution topology. [4] Gary Kim, “How much does rural fiber really cost?” http://blog.performantnetworks.com/2012/11/ 7. Conclusion how-much-does-rural-fiber-really-cost.html,Nov.2012. [5] Clarke Richard N., “Costs of neutral/unmanaged ip networks,” Review ofNetworkEconomics,vol.8,no.1,pp.61–89,Mar.2009. We provide an all wireless solution to deliver live TV [6] J. Baliga, K. Hinton, and R. S. Tucker, “Energy consumption of the services. Some service providers now have the benefit of Internet,”inProc.COIN-ACOFT,June2007. [7] homewyse,“Costtoinstallasatellitedish,”http://www.homewyse.com/ leveraging multiple access technologies to distribute live TV services/cost to install satellite dish.html,accessed:2016-07-28. content (e.g. satellite, WiFi and LTE). We capitalize on [8] M. Wittig, “Satellite onboard processing for multimedia applications,” this opportunity to create a distribution infrastructure that IEEECommun.Mag.,vol.38,no.6,pp.134–140,Jun.2000. is optimized to serve large residential neighborhoods with a [9] Y.Xiao,X.Du,J.Zhang,F.Hu,andS.Guizani,“Internetprotocoltele- vision (IPTV): The killer application for the next-generation internet,” minimal number of TV content injection points. We solve IEEECommun.Mag.,vol.45,no.11,pp.126–134,Nov.2007. multicommodityoptimizationflowproblemstomodelvarious [10] Y. Liu, Z. Liu, X. Wu, J. Wang, and C. C. Y. Yang, “IPTV system scenarios.UsingrealdatafromanationalTVserviceprovider, design:AnISP’sperspective,”inProc.CyberC,Oct.2011. [11] A.Abdollahpouri,B.E.Wolfinger,andJ.Lai,“Unicastversusmulticast we show that our proposed architecture can save provisioning for live TV delivery in networks with tree topology,” in Proc. WWIC, costs by between 75% to 90%. We experiment using four ACM,2010. different representative residential neighborhoods with time- [12] J. She, F. Hou, P. H. Ho, and L. L. Xie, “IPTV over WiMAX: varying traffic demands. Our investigation shows that there Key success factors, challenges, and solutions [advances in mobile multimedia],” IEEE Commun. Mag., vol. 45, no. 8, pp. 87–93, Aug. is an optimum strategy for placing the satellite dish antennas 2007. combinedwithanappropriateselectionofWiFiroutestomeet [13] H.Singh,C.Y.Kwon,S.S.Kim,andC.Ngo,“IPTVoverwirelesslan: the time-varying demand of subscribers/households. Promisesandchallenges,”inProc.IEEECCNC,Jan.2008. [14] E. Shihab, L. Cai, F. Wan, A. Gulliver, and N. Tin, “Wireless mesh networksforin-homeIPTVdistribution,”IEEENetwork,vol.22,no.1, pp.52–57,Jan.2008. [15] K. H. Lee, S. T. Trong, B. G. Lee, and Y. T. Kim, “QoS-guaranteed IPTVserviceprovisioninginhomenetworkwithIEEE802.11ewireless LAN,”inProc.NOMSW,Apr.2008. [16] M. Gidlund and J. Ekling, “VoIP and IPTV distribution over wireless meshnetworksinindoorenvironment,”IEEETrans.Consum.Electron., vol.54,no.4,pp.1665–1671,Nov.2008. [17] M. Garcia, J. Lloret, M. Edo, and R. Lacuesta, “IPTV distribution network access system using WiMAX and WLAN technologies,” in Proc.UPGRADE-CN,ACM,2009. [18] K. Pahlavan and A. Levesque, Wireless Information Networks. NJ: Wiley,1995. [19] X.Li,“Collaborativelocalizationwithreceived-signalstrengthinwire- less sensor networks,” IEEE Trans. Veh. Technol., vol. 56, no. 6, pp. 3807–3817,Nov.2007. [20] E.PerahiaandR.Stacey,NextGenerationWirelessLANs:802.11nand 802.11ac. CambridgeUniversityPress,2013. [21] Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer(PHY)Specification,IEEEStd.802.11,2012. [22] TechnicalSpecificationGroupRadioAccessNetwork;EvolvedUniversal TerrestrialRadioAccess(E-UTRA);BaseStation(BS)radiotransmis- sionandreception(Release10),3rdGenerationPartnershipProjectStd. 3GPPTS36.104V10.2.0(2011-04),2011. [23] P. Mogensen, W. Na, I. Z. Kovacs, F. Frederiksen, A. Pokhariyal, K. I. Pedersen, T. Kolding, K. Hugl, and M. Kuusela, “LTE capacity comparedtotheShannonbound,”inProc.IEEEVTC,Apr.2007. [24] L.Gouveia,“Multicommodityflowmodelsforspanningtreeswithhop constraints,”EURJOPERRES,vol.95,no.1,pp.178–190,1996. [25] M.GrantandS.Boyd,“CVX:Matlabsoftwarefordisciplinedconvex programming,version2.1,”http://cvxr.com/cvx,Mar.2014. [26] Michael Grant and Stephen Boyd, “Graph implementations for nons- moothconvexprograms,”inRecentAdvancesinLearningandControl. Springer-VerlagLimited,2008,pp.95–110.