Capacity Regions for Wireless AdHoc Networks

1. Capacity Regions for Wireless AdHoc Networks The presentation is based on a paper: S. Toumpis and A. J. Goldsmith: Capacity Regions for Wireless Ad Hoc Networks , IEEE Transactions Wireless Communications , Vol. 2 No. 4, pp 736-748, July 2003 Presented by Antti Tölli antti.tolli@ee.oulu.fi

2. Outline • Introduction • System Model • Transmission Schemes and Schedules • Rate Matrices • Capacity regions • Results for Specific Configurations Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

3. Intro • Lower and upper bounds of capacity of AdHoc NWs defined for large number of nodes (Gupta&Kumar*, Grossglauser&Tse**) • Capacity regions for AdHoc NWs with any number of nodes defined in this article • Although, max achievable rates defined for specific tx protocols (maybe suboptimal) • Impact of power control, multihop routing, spatial reuse, successive interference cancellation, etc. studied • Special Challenges of Ad Hoc Networks • No infrastructure • Decentralized control (power, routing, data rates, etc) • Dynamic topology • Wireless channel impairments *P. Gupta and P. R. Kumar, “The capacity of wireless networks,” IEEE Trans. Inform. Theory, vol. 46, pp. 388–404, Mar. 2000. **M. Grossglauser and D. N. C. Tse, “Mobility Increases the Capacity of Ad Hoc Wireless Networks,” IEEE/ACM Trans. on Networking, vol. 10, no. 4, August 2002, pp. 477-486 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

4. System Model, #1 • nodes : A1 … An • Each Ai • has transceiver with infinite buffer • maximal power output is Pi • canNOT simultaneously send and receive • may send data to any Aj (multihop routing possible) • occupy ALL bandwidth (W) while transmitting • NO broadcast Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

5. System Model, #2 • Channel Gains: G = {Gij}, f(distance, shadowing) • Noise: AWGN, H = [h1 ... hn] • Each node knows “everything”: G, H, P • t  J At is transmitting with power Pt • If Ai (i  J) transmits to Aj (j  J), • SINR: • data rate: Rij = f(gij) pre-agreed for performance; e.g., f(gij) =W log2(1+gij) Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

6. S1 S2 Transmission Schemes T-scheme S : Complete description of information flow betweeen different nodes in the network at a given time instant • all transmit-receive node pairs, and data rates • originating node of data • Example: Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

7. S1 T1 S2 T2 Time Division Scheduling • Network may alternate various schemes • Example • T1 = 0.5S1+0.5S2 or • T2 = 0.75S1+0.25S2 • Resulting info flow: Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

8. S1 S2 Rate Matrices, #1 • For given scheme S, R(S) is n×n matrix such that • Rij= ±r Ajreceives/send r bps originating at Ai Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

9. T1 T2 Rate Matrices, #2 • Time-division scheduling: Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

10. Transmission Protocols & Basic Rate Matrices • Transmission protocol: collection of rules that node must satisfy when transmitting • Transmit own info only, Transmit with max power, Can transmit simultaneously with other nodes, Interference treatment: noise (SIC not allowed) or SIC • Given a protocol, many Tx schemes are possible • Basic rate matrix: each Tx scheme has a rate matrix • The less restrictive Tx protocol, the larger the collection of rate matrices and vice versa Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

11. Capacity Region: Definition • Capacity region: Convex Hull of all basic rate matrices such that the weighted sums have NO negative off-diagonal elements • Describes the net flow of the info in the NW • Uniform Capacity, Cu= Rmax× n(n−1) with Rmaxlargest R given the matrix is in the capacity region: Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

12. Network Parameters • Nodes: 5 uniformly distributed in box [-10m , 10m]×[-10m , 10m] • Gij= K·Sij ·(d0/dij)a, K=10-6, d0 =10m, a=4 • Sij(shadowing) lognormal with µ= 0dB and s= 8 db • Pj= 0.1W ; hj= 10-11 W/Hz • Bandwidth: W = 106 Hz • rij=f(gij) =W log2(1+gij) Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

13. Capacity: Single-Hop Routing, No Spatial Reuse • Only one transmits at a time: # of schemes is Na= n(n−1)+1 • Associated rate matrices : (Ra)i , i= 1 … Na • uniform capacity : 0.83 Mbps • Slice of capacity region (see a) in p. 16) • Only nodes A1 and A3 send data • Straight line – no spatial reuse, transmission only between one source-destination point at any time Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

14. Capacity: Multi-Hop Routing, No Spatial Reuse • Only one transmits at a time • N nodes in the system, each has n-1 different possible receivers and n possible nodes to forward data • # of schemes is Nb= n2(n−1)n+1 • Uniform capacity : 2.85 Mbps (242% increase) • Slice of capacity region (see b in figure, p. 16) • Straight line again – no spatial reuse, transmission only between one source-destination point at any time • Significant capacity increase: multiple hops over favourable channels instead of transmitting directly over paths with small gains Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

15. Capacity: Multi-Hop Routing, with Spatial Reuse • Multiple active connections allowed at any time • # of schemes is • Uniform capacity : 3.58 Mbps (26% increase) • Slice of capacity region (see c in figure, p. 16) • No longer a straight line, NW can use spatial reuse to maintain multiple active transmissions (directly or over multihop) Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

16. Capacity Figures (a) Single-hop, No spatial reuse (b) Multihop, no spatial reuse (c) Multihop, spatial reuse (d) 2-level power cntrl added to (c) (e) Succs. interference cancellation Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

17. Fading and Mobility Increase Capacity • Time varying flat fading channel • Capacity increases as the # of fading states increases • a) % b) one fading state • c) 2 fading states • d) 10 fading states • e) 15 fading states M different fading states Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

18. Conclusions • Mathematical framework developed for finding capacity regions for AdHoc/multihop NWs under time-division routing and given transmission protocol • Network performance shown to be improved by: • Multihop routing, spatial reuse and interference cancellation • Fading and node mobility Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu