Capacity of Wireless Networks Piyush Gupta, P.R. Kumar

1. Capacity of Wireless NetworksPiyush Gupta, P.R. Kumar Presented by Arun Miduthuri 1

2. Notions of capacity in wireless networks Throughput capacity Transport capacity Two models for successful signal reception Protocol model Physical model Results for arbitrary networks Results for random networks Implications Extensions Outline 2

3. For each source-destination pair, it is the average number of bits delivered successfully from the source to the destination For the network, it is the sum of these throughputs over all source-destination pairs Throughput capacity 3

4. Unit of measurement �bit-meter� One bit-meter � 1 bit transported 1m toward destination Transport capacity is the number of bit-meters transported by a network through successful transmissions Transport capacity 4

5. Network of n nodes in a unit area region Location of nodes fixed Each node can transmit at W bps Packets sent from node to node in multi-hop fashion Several nodes can transmit simultaneously For simple exposition, assume transmissions are slotted Setup 5

6. A transmission from node Xi to node Xj is successfully received by Xj if for every other node Xk simultaneously transmitting over the network represents a �guard band� between the two transmitting nodes Protocol Model 6

7. Transmission from Xi successfully received by Xj if T = Subset of nodes Xk transmitting in time slot Pk = Power level of node Xk a = Fading exponent Physical Model 7

8. �Arbitrary� means we have control over the structure of the network n nodes are arbitrarily located in a disk of unit area Each node has arbitrarily chosen destination, and arbitrary rate Hence traffic patterns are also arbitrary Can choose all of these characteristics in an �optimal� way to get upper bounds on performance Arbitrary networks 8

9. If nodes are optimally placed, traffic pattern and transmission range optimally chosen, then transport capacity is of the order In less optimal scenarios, this acts as an upper bound on performance Bound on transport capacity � Arbitrary Networks 9

10. The actual bound on all arbitrary networks is In the optimal scenario, if we also equitably divide transport capacity between all n nodes, then each node attains a transport capacity of Bound on transport capacity � Arbitrary Networks 10

11. Assume nodes are optimally placed, traffic patterns and transmission ranges optimally chosen Assume transport capacity equitably divided between all n nodes Assume each source has its destination unit distance away Then throughput capacity per S-D pair is of the order Bound on throughput � Arbitrary Networks 11

12. Paper shows that bit-meters per second is feasible, while is not, for appropriate c, c� Similar transport capacity bounds for physical model 12

13. Postulates upper bound of order bit-meters per second Proves this for the case in which Where Pmax and Pmin are the max and min powers that transmitters can use Similar transport capacity bounds for physical model 13

14. n nodes independently and identically distributed Not over a circle of unit area, but over a unit area spherical surface Avoids �edge effects� Each node has an independently chosen destination Unit distance away from source on average Throughput requirement of ?(n) bps Random networks 14

15. A throughput of ?(n) bps for each node is feasible if each node can send ?(n) bps on average to its destination under the constraints of The existence of some spatial and temporal scheduling scheme to support it Scheme allows for multi-hop and buffering at intermediate nodes Feasible throughput in random networks 15

16. Throughput capacity is of order T(f(n)) bps if there are constants c, c� such that where T notation in random setting 16

17. Throughput is of order The result is the same for protocol and physical models Results for random networks 17

18. Routing hot spots are not the cause of throughput constriction Rather, each node needs to share its channel with other nodes to accommodate multi-hops Implications 18

19. Networks aimed at smaller numbers of users are better When nodes communicate only with nearby nodes distant, they can transmit at constant bit rate per S-D pair Dividing channel into subchannels does not alter result Larger a (fading exponent) allows greater transport and throughput capacity Implications 19

20. Briefly analyzes use of nodes dedicated solely to relaying If m additional homogenous pure relays are added (random network model), throughput is Number of additional relays per node to be added can be quite large Implications 20

21. Considering the effect of mobility Throughput vs delay tradeoff Use of relays A rate region approach Extensions 21

22. Mobility increases the capacity of wireless ad hoc networks, Grossglauser and Tse Assumes loose delay constraints (eg, email) where network topology changes considerably over time Throughput per S-D pair (time average) can be kept constant as n increases Mobility 22

23. In Gupta and Kumar, nearest neighbor scheme was suggested to achieve this constant throughput This cannot be used in the case of mobility Problem: Fraction of time two nodes are nearest neighbors is of order n-1 Instead, split node�s packet stream and handoff to closest mobile relay; relays handoff to destination when close to destination How to exploit mobility 23

24. [2] Exploiting mobility:Relay scheme � Handoff to relay 24

25. [2] Exploiting mobility:Relay scheme � Handoff to destination 25

26. Throughput-delay tradeoff in wireless networks, El Gamal et al. [3] Throughput and delay influenced by Number of hops Transmission range Node mobility and velocity For a fixed random network, the optimal delay depends on throughput as in Gupta and Kumar: Throughput-delay tradeoff 26

27. In a mobile network as discussed in Grossglauger and Tse, Throughput-delay tradeoff 27

28. Parameterized by a(n), where is the average distance per hop. The optimal throughput-delay tradeoff is Throughput-delay tradeoff 28

29. [3] Throughput-delay tradeoff 29

30. Capacity regions for wireless ad hoc networks, S. Toumpis, A.J. Goldsmith [4] Computes achievable rate regions in a time-division strategy for a number of suboptimal transmission strategies, including Single or multi-hop routing Power control Successive interference cancellation Uses rate matrices (function of nodes transmitting in a time slot, link SINR, transmission strategy) Capacity regions for wireless ad hoc networks 30

31. 31 [4] Capacity regions for wireless ad hoc networks

32. Studies uniform capacity for linear and ring networks Uniform capacity is the maximum sum rate assuming all nodes communicate with all other nodes at a common rate Linear networks show degrading performance as the number of nodes increase Ring networks take advantage of spatial separation; uniform capacity shows limited gains as number of nodes increase Capacity regions for wireless ad hoc networks 32

33. [4] Capacity regions for wireless ad hoc networks 33

34. Analyzes effect of node mobility Models mobility as Brownian walks with a large number of spatial configurations As opposed to modeling nodes as moving continuously Plots convergence of uniform capacity vs the number of spatial configurations Without scheduling across different spatial configurations, it tries to use the current configuration most efficiently, but does not exploit mobility Using scheduling is subject to tolerating large delays Capacity regions for wireless ad hoc networks 34

35. [4] Capacity regions for wireless ad hoc networks 35

36. Use of relaying [5] In the case where only one S-D pair exists and the rest of the nodes are relays, and arbitrarily complex network coding is allowed, can achieve log n bps with n nodes Source broadcasts information to all relays, which use arbitrary cooperation techniques Exploiting cooperative relaying 36

37. Throughput and transport capacity of networks is bounded inversely by the number of nodes in the network The reason is that intermediate nodes use most of their resources to forward other nodes� packets Result pessimistic; mobility, neighborhood communication, broadcast, and relay cooperation can improve throughput Conclusion 37

38. [1] P. Gupta, P.R. Kumar , Capacity of Wireless Networks, IEEE Transactions on Information Theory, Vol. 46, No. 2, March 2000 [2] M. Grossglauser, D. Tse, Mobility increases the capacity of ad hoc wireless networks, IEEE/ACM Transactions on Networking, Vol. 10, No. 4, August 2002 [3] A. El Gamal, J. Mammen, B. Prabhakar, D. Shah, Throughput-delay tradeoff in wireless networks, IEEE Infocom 2004. [4] S. Toumpis, A.J. Goldsmith, Capacity regions for wireless ad hoc networks, IEEE Transactions on Wireless Communications, Vol. 2, No. 4, July 2003 [5] M. Gastpar, M. Vetterli, On the capacity of wireless networks: The relay case, IEEE 2002 Additional references [6] G. Kramer, M. Gastpar, P. Gupta, Cooperative strategies and capacity theorems for relay networks [7] P. Gupta, P.R. Kumar, Towards an information theory of large networks: An achievable rate region, IEEE Transactions on Information Theory, Vol. 49, No. 8, August 2003 References 38