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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

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capacity regions for wireless adhoc networks

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

outline
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

intro
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

system model 1
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

system model 2
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

transmission schemes

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

time division scheduling

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

rate matrices 1

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

rate matrices 2

T1

T2

Rate Matrices, #2
  • Time-division scheduling:

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

transmission protocols basic rate matrices
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

capacity region definition
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

network parameters
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

capacity single hop routing no spatial reuse
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

capacity multi hop routing no spatial reuse
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

capacity multi hop routing with spatial reuse
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

capacity figures
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

fading and mobility increase capacity
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

conclusions
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

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