1. Capacity of Large Scale Wireless Networks with Directional Antenna and Delay Constraint Guanglin Zhang IWCT, SJTU 26 Sept, 2012 INC, CUHK 1

2. 2 Outline  Background and related works  Unicast capacity for static networks  System model and definition  Main result and sketch of derivation  Multicast capacity for VANETs  Main result and sketch of derivation  Conclusions 2

3. 3 Outline  Background and related works  Unicast capacity for static networks  System model and definition  Main result and sketch of derivation  Multicast capacity for VANETs  Main result and sketch of derivation  Conclusions 3

4. Background 4 “ Broadband's take-up has repeatedly been jumpstarted by must-have applications. Napster drove the shift from dialup to wired broadband. Now Apple's iPhone is playing the same role in triggering explosive growth in the wireless Web. Unless we miss our guess, this dynamic is about to rudely change the subject from net neutrality to a shortage of wireless capacity to meet enthusiastic consumer demand …” [10/14/2009, Wall Street Journal] A Roadmap of Technology Evolution (Borrowed from Junshan Zhang’s slides) iPhone on sale day

5. Background 5 TxRx point-to-point (Shannon 48)  Channel Capacity (Gaussian Channel): Known Rx1 TxRx Tx 1 Tx 2 Rx 2 multiple-access (Alshwede, Liao 70’s) broadcast (Cover, Bergmans 70’s) Shannon 48 Ahlswede 71 Liao 72 Cover 72 Slides partially borrowed from D. Tse’s talk on Information Theory of Wireless Networks

6. 6  Channel Capacity (Gaussian Channel): Unknown D Tx 1 Relay S Tx 2Rx 2 Rx 1 relay (Best known achievable region: Han & Kobayashi 81) (Best known achievable region: El Gamal & Cover 79) Han & Kobayashi 81 El Gamal & Cover79 Background Slides partially borrowed from D. Tse’s talk on Information Theory of Wireless Networks

7. Typical Related Work 7  Capacity in wireless ad hoc network not scalable  In static ad hoc wireless networks with n nodes, the per-node throughput behaves as  Main reason: spatial interference Significant gap between demand and wireless capacity ground breaking work work [1] P. Gupta, P.R. Kumar, The capacity of wireless networks, IEEE Trans. on Information Theory, March 2000. pessimistic result

8. Typical Related Work  Mobility can increase the capacity:  Store-carry-forward communication scheme  Drawback: large delays [2] M. Grossglauser and D. Tse, Mobility Increases the Capacity of Ad Hoc Wireless Networks, IEEE/ACM Trans. on Networking, August 2002. S D R 8

9. Typical Related Work 9  Infrastructure can increase capacity  In static ad hoc network with n wireless nodes and k base stations, the per-node capacity is  Assume that base stations are wired together with unlimited bandwidth, and  Many techniques to increase capacity  Directional antenna, Network coding, MIMO,… [3]Liu, B. and Liu, Z. and Towsley, D., On the capacity of hybrid wireless networks, INFOCOM 2003.

10. Difficulty on Network Capacity Analysis  A large number of potential wireless transmissions  Neighboring transmissions interfere with each other  Dynamic of network topology due to node mobility  Uncertainty of channel quality, e.g., shadowing, pass loss, multi-path  … 10

11. 11 Outline  Background and related works  Unicast capacity for static networks  System model and definition  Main result and sketch of derivation  Multicast capacity for VANETs  Main result and sketch of derivation  Conclusions

12. System Models and Definition  Assumptions  n nodes and m base stations  n nodes randomly placed  m base stations regularly deployed  Random source destination pairs  Base stations are relays 12  Directional Antenna  Every node equipped with directional antenna  Transmitting and receiving range are common  Beam-width:

13. System Models and Definition(Cont’)  Interference Model  Receiver-based Interference model 13  Delay Constraint  Ad hoc mode transmission  Infrastructure mode transmission  Maximum hops form source to destination: L  No interference between ad hoc and infrastructure mode transmission Xk Xl Xi Xj

14. Asymptotic Capacity 14  We say that the per-node capacity is if there exist two constants c and c’ such that  Sustainable: there exists a spatial and temporal scheduling scheme that can achieve such a rate.  Delay: The hops it takes to send packets from source nodes to their destinations.

15. 15 Outline  Background and related works  Unicast capacity for static networks  System model and definition  Main result and sketch of derivation  Multicast capacity for VANETs  Main result and sketch of derivation  Conclusions

16. Main contribution: the capacity of unicast network  Propose an L-maximum-hop delay constraint strategy, and give the closed-form upper bound of the capacity  Provide the transmission schedule strategy and the routing construction to achieve the upper bound of the capacity  Analyze the relations between throughput capacity and system parameters 16

17. Main Results 17  Main theorem : Under the L-maximum-hop resource allocation strategy, by using directional antenna, the throughput capacity of the network is  Proof: sketch Infrastructure Mode Capacity Infrastructure Mode Capacity Hybrid Capacity Ad Hoc Mode Capacity Ad Hoc Mode Capacity Lower Bound Upper Bound

18. Lower Bound: Sketch of derivation  Construct Voronoi Tessellation  Choose points, …,  Spanning  Adjacent Voronoi Cells  Cells have common points  Interfering Neighbors  Distance between cell  : transmission range  : guard zone 18

19. Lower Bound: Sketch of derivation (Cont’)  Number of interfering neighbors 19 Remark: every cell has no more than interfering neighbors, where

20. Lower Bound: Routing and Scheduling  Scheduling  TDMA  Routing  Random chosen destination  Multihop transmission 20 Remark: The scheduling strategy and routing are designed to avoid hot point

21. Lower Bound: Routing and Scheduling  Traffic load  Expectation of traffic load 21 P(the that cross V and can be used to forward packet) E(the number of lines in that cross V and can be used to forward packet)

22. Lower Bound: Ad Hoc Mode Transmission  When, there exists a constant, such that 22  When, we have

23. Upper Bound: Ad Hoc Mode Transmission  When, the upper bound of per-node throughput capacity is 23  When, we have the upper bound per-node throughput capacity Remark: the number of simultaneous transmissions for the whole network is no more than

24. Capacity Scaling Laws 24 Multicast Throughput Capacity in Hybrid Wireless Networks

25. Capacity with respect to L and m 25 Relations with delay constraint L Relations with number of base stations m

26. Capacity with respect to 26 Relations with directional antenna when

27. 27 Outline  Background and related works  Unicast capacity for static networks  System model and definition  Main result and sketch of derivation  Multicast capacity for VANETs  Main result and sketch of derivation  Conclusions

28. System Model and Assumption  Assumption  There are n vehicular nodes and m base stations in the network  At each time slot, n nodes are randomly and uniformly deployed  m base stations are placed regularly  There are k multicast sessions 28  Directional antenna  Delay constraint  Each transmission should be finished within D time slots

29. System Model and Assumption  Mobility model  2D i.i.d. fast mobility model  2D i.i.d. slow mobility model  1D i.i.d. fast mobility model  1D i.i.d. slow mobility model Fit the vehicular mobility 29  Time scale of mobility  Fast mobility The mobility of nodes is at the same time scale as the trans- mission of packets  Slow mobility The mobility of nodes is much slower than the transmission of packets

30. Main Contribution for Multicast VANET 30  We present an asymptotic study of the multicast capacity for the hybrid VANETs, and obtain the closed form formula of the multicast capacity in order of magnitude  We analyze the impact of two mobility models and two mobility time scales on multicast capacity of the VANET, which is not considered in the state-of-the-art research, especially under delay constraint  We analyze the impact of the base stations, the beamwidth of the directional antenna, and delay constraint on the multicast capacity

31. Intuitive Analysis: Multicast Capacity 31 Reliable broadcasting channel Unreliable relay channel Reliable receiving channel Base station Upper bound capacity of hybrid VANET Directional trans-ceiving

32. Main Theorem and Proof Intuition 32  2D i.i.d. fast mobility model Proof: (sketch) Infrastructure mode transmission 2-D i.i.d. fast mobility model the packets have to be transmitted from relays to their destinations the packets have to be transmitted from relays to their destinations Upper bound capacity the packets are directly transmitted from source to their destinations the packets are directly transmitted from source to their destinations 2-D i.i.d. fast mobility model Infrastructure mode transmission Theorem 1: Under the 2D-i.i.d. fast mobility model and delay constraint D, we have the multicast capacity of ad hoc mode transmission

33. Main Theorem and Proof Intuition 33  2D i.i.d. slow mobility model The mobile speed of nodes are much slower than the data transmission 2D i.i.d. slow mobility model Throughput capacity of VANET Proof: (sketch) Theorem 2: Under the 2D-i.i.d. slow mobility model and delay constraint D, we have the number of bits that are successfully delivered to their destinations in T time slots

34. Main Theorem and Proof Intuition 34  1D i.i.d. fast mobility model Proof: (sketch) Lemma 8: Under the 1D-i.i.d. fast mobility model and delay constraint D, we have the number of bits that are successfully delivered to their destinations in T time slots H(B) denotes the minimum distance between the relays that carrying bit B and any of the p destinations.

35. Main Theorem and Proof Intuition 35  1D i.i.d. slow mobility model Proof: (sketch) Theorem 3: Under the 1D-i.i.d. slow mobility model and delay constraint D, we have the number of bits that are successfully delivered to their destinations in T time slots Step 1: Bits transmitted directly from source to destinations By the Cauchy-Schwarz inequality,

36. Proof Sketch 36 Meanwhile, we can have, By the Jansen inequality, Then, we have,

37. Proof Sketch 37 Using similar approach as in step 1, we have, Step 2: Bits transmitted from relay to destinations Step 3: Bits that are successfully delivered to destinations up to time T Step 3: Bits that are successfully delivered to destinations up to time T

38. Main Result: 38 2D i.i.d. fast mobility model ： 2D i.i.d. slow mobility model ： 1D i.i.d. fast mobility model ： 1D i.i.d. slow mobility model ：

39. Capacity Scaling Laws 39 Multicast Throughput Capacity in Hybrid VANET with Directional Antenna and Delay Constraint

40. Conclusions 40 We study the unicast capacity of large scale wireless networks with directional antenna and delay constraint while the nodes are static. The multicast capacity of VANET with different mobility models are investigated and the closed-form formulae are given in order of magnitude. We analyze the impact of system parameters on the capacity scaling laws and provide scheduling strategy and routing construction to achieve the capacity bound.

41. Future Work 41 The capacity of large scale wireless networks with network coding The capacity of heterogeneous network with delay constraint The capacity of wireless networks with social relationship Information theoretic capacity of large scale wireless network

42. Thank You ！