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Wireless Network Architectures

Local Phy + Global Routing: A Fundamental Layering Principle for Wireless Networks Pramod Viswanath, University of Illinois July, 2011. Wireless Network Architectures. Wireless Networks Cellular Heterogeneous Ad hoc Multiple Layers Cross layer design engineering principles

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Wireless Network Architectures

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  1. Local Phy + Global Routing: A Fundamental Layering Principle for Wireless Networks Pramod Viswanath, University of Illinois July, 2011

  2. Wireless Network Architectures • Wireless Networks • Cellular • Heterogeneous • Ad hoc • Multiple Layers • Cross layer design • engineering principles • We seek for fundamental layering principles • lens of information theory

  3. Information Theory of Wireless Networks • Long standing open question • even for wireline networks • approximate capacity results • scaling law results • Engineering implication unclear • even for known solutions -- complicated(nonlayered) strategies • Goals: • approximate capacity of wireless networks • engineering guidelines

  4. Wireline Networks • Wireline network composed of independentnoisy channels • Layered Design: separate PHY and Network layers • [Koetter, Effros, Medard 2010] Layering is capacity optimal in wireline networks

  5. Layering in Wireline Networks • Layered Design: separate PHY and Network layers • [Koetter, Effros, Medard 2010] Layering is capacity optimal • Capacity is still unknown • Network layer potentially uses network coding

  6. Bit pipe Wireline Networks • Routing • conceptually simple • different traffic flows never mix • practical -- efficient algorithms • Routing is optimal for unicast traffic [Ford Fulkerson, 1956] • max flow = min cut • Network coding required in general • optimal for multicast • Focus of this talk: Multiple unicast traffic

  7. Multiple Unicast in Wireline Networks • Directed graphs • network coding arbitrarily better than routing • min cut far from any efficient algorithm • [Chuzhoy Khanna, 2006] • Undirected graphs • no example of network coding being better than routing • routing close to min cut [Leighton Rao, 1988]

  8. Engineering Implication for Wireline Networks • Separate Phy and Network layers • Routing in network layer

  9. Features of Wireless Channel • Broadcast: one to many • Superposition: many to one • In general both features • Partial Frequency reuse networks • No edge involved in both broadcast and superposition

  10. Partial Frequency Reuse Networks • Cellular Networks • Neighboring cells use different frequencies • Uplink-Downlink design + routing • Enterprise Wi-Fi networks

  11. Wireless Frequency Reuse Networks • No edge involved in both broadcast and superposition • frequency planning • packet erasure networks

  12. Packet Erasure Networks • Communication link is an erasure channel • Broadcast constraint only • Broadcast erasure channel • degraded • time sharing optimal [Dana Hassibi 2005] • very far from min cut

  13. A Non-layered Scheme • Layeringvery suboptimal even forunicast • Do not layer! [Gowaikar et. al. 2003] • global network coding for unicast traffic • wireless network coding = min cut • need to use broadcast feature of medium

  14. Abstraction by Wireline Networks • create detailed bit pipes • multiple multicast traffic • allow general network coding • [Koetter, Effros, Medard, 2010] • Approximate optimality • degree two broadcast and superposition

  15. Reprise • Layering in wireline networks is successful • separation of Phy, MAC, network layers • routing in network layer -- undirected • Reciprocity in wireless channels • Use reciprocity to simultaneously show • separation of Phy and network layers • routing in network layer • This talk: • approximate optimality of separation + routing • multiple unicast traffic

  16. Reciprocity • Wired infrastructure is bidirected • Wireless point-to-point channel is reciprocal • even when scatterers are present • Maxwell equations are reciprocal:

  17. Point to Point Channel is Reciprocal • Reverse source and destination • traffic flow reversed • power capability reversed • Capacity is unchanged • Also true with MIMO • total power across antennas preserved • capacity only depends on singular values [Telatar, 2001]

  18. Uplink Downlink Reciprocity • Broadcast channel -- broadcast • Multiple access channel -- superposition • Channels reciprocal • Communication rates also reciprocal • reciprocal linear strategies • reciprocity of SIC and DPC • Can create a bidirected network

  19. Polymatroidal Networks • Constraints on in/out rates • submodular • rate region is a polymatroid • exact for superposition • approximate for broadcast • Bidirected network • Symmetric inflow and outflow constraints

  20. Unicast in Polymatroidal Networks • Directed polymatroidal network • Various application areas • operations research • Unicast: Max flow = Min cut • [Lawler Martel, 1982] and [Edmonds Giles,1975] • Cut • subset of edges, • removal disconnect source and sink • grouping of edges which share a vertex • value of cut is sum of submodular function on each partition

  21. Main Technical Result • Multiple unicast traffic • Bidirected polymatroidal network, general demands • Max flowMin cut approximation result • generalizes [Leighton Rao, 1988] • Min cut is a fundamental upper bound • information theoretic • Approximation result also true: • directed polymatroidal network, symmetric demands [Klein Plotkin Rao Tardos 1995]

  22. Game Plan: Application in Wireless Networks • Physical layer strategy • use feedback • converts medium into bit pipes • polymatroidal achievable rate region • Cut set bound • typically polymatroidal • achievable scheme is close enough • Wireless Network approximated by polymatroidal network • harness max flow min cut approximation result • Result: local Phy + global Routing is near optimal

  23. Packet Erasure Networks with Feedback • Erasure network with broadcast constraints • Feedback via natural reciprocal channels • Optimal Phy scheme • not time sharing • a form of hybrid ARQ coding [Georghiades Tassiulas 2010] • capacity region now close to min cut • (order log d) • Min cut region is polymatroidal

  24. Layering Principle for Packet Erasure Networks • Critical use of feedback • both in Phy (local) and in routing (global) • Summary: • Local Phy with feedback + Global routing with feedback is near optimal

  25. Gaussian Partial Reuse Networks • Superposition constraint • Capacity rate region is polymatroidal • Capacity equals min cut region • Broadcast constraint • Min cut region is polymatroidal • Capacity (P) contains min cut (P/d) • Thusboth in and out flow constraints are • submodular • symmetric (due to reciprocity)

  26. Gaussian Partial Reuse Networks • Local Phy • superposition coding for broadcast • SIC for multiple access • feedback used for channel state information • Global routing • feedback useful for bidirectional structure • Summary: Local Phy + Global routing nearly achieves min cut

  27. Full Reuse Networks • Every node uses same frequency • interference is a central feature • Begin with specific channel models • fading channels (slow/fast fading) • Geographic Networks • scaling laws; heirarchical MIMO + routing [Niesen, Gupta, Shah 2010]

  28. PHY Layering • Where to draw the line? • Phy ends and routing begins • Treat each hop as separate Phy layer • Phy is over the X channel • multihop routing

  29. X Channel • Every source has independent message for every destination • more general than interference channel • Capacity region unknown • Look for new Phy schemes

  30. Phy Scheme for X Channel • Approach: • consider interference channels • subset of source and destinations • Phy scheme for interference channels • ergodic/real interference alignment • reliable communication at half direct link capacity • Time sharing across all interference channels

  31. Min Cuts in X Channel • Specific cuts lead to polymatroidal constraints • cuts separate one node from rest • General cuts do not fit our framework • Turns out: cuts of interest are essentially minimal • [Niesen 2010]

  32. Feedback • Feedback used in Phy scheme to convey channel state information • Treating each hop as Phy layer leads to a directed network • Need bidirected network • feedback used for efficient global routing

  33. Layering Principle • Local Phy • X channel • Global routing • Main result

  34. Summary • Layering of wireless networks • common engineering practice • Our contribution • Fundamental view of layering • Feedback critically useful in both Phy and Routing • A framework to use good Phy schemes in a network context • No natural place for network coding • Credit: Sreeram Kannan, Adnan Raja, Chandra Chekuri

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