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 , July 2003
Presented by Antti Tölli

2. 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
Capacity Regions for Wireless Ad Hoc Networks, Univ. of Oulu

3. 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
**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
Capacity Regions for Wireless Ad Hoc Networks, Univ. of Oulu

4. 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
Capacity Regions for Wireless Ad Hoc Networks, Univ. of Oulu

5. 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)
Capacity Regions for Wireless Ad Hoc Networks, Univ. of Oulu

6. 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
Capacity Regions for Wireless Ad Hoc Networks, Univ. of Oulu

7. 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
Capacity Regions for Wireless Ad Hoc Networks, Univ. of Oulu

8. 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
Capacity Regions for Wireless Ad Hoc Networks, Univ. of Oulu

9. Capacity Regions for Wireless Ad Hoc Networks, CWC @ Univ. of Oulu
Rate Matrices, #2
Time-division scheduling: T1 T2
Capacity Regions for Wireless Ad Hoc Networks, 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, 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 Rmax largest R given the matrix is in the capacity region:
Capacity Regions for Wireless Ad Hoc Networks, Univ. of Oulu

12. 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 = W/Hz
Bandwidth: W = 106 Hz
rij=f(gij) =W log2(1+gij)
Capacity Regions for Wireless Ad Hoc Networks, 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, 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, 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, Univ. of Oulu

16. 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
Capacity Regions for Wireless Ad Hoc Networks, 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, Univ. of Oulu

18. 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
Capacity Regions for Wireless Ad Hoc Networks, Univ. of Oulu