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

Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu Outline Introduction System Model Transmission Schemes and Schedules Rate Matrices Capacity regions Results for Specific Configurations 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu 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 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu 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 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu 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) 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu 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: S1 S2 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

Time Division Scheduling Network may alternate various schemes Example T1 = 0.5S1+0.5S2 or T2 = 0.75S1+0.25S2 Resulting info flow: S1 S2 T1 T2 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu Rate Matrices, #1 For given scheme S, R(S) is n×n matrix such that Rij= ±r  Aj receives/send r bps originating at Ai S1 S2 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu Rate Matrices, #2 Time-division scheduling: T1 T2 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

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 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

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 Rmax largest R given the matrix is in the capacity region: 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu 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) 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

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 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

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 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

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) 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu 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 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

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 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu

Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu 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 8.12.2018 Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu