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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