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June 21, 2007 [email protected]
Minimum Interference Channel Assignment in Multi-Radio Wireless Mesh Networks
Anand Prabhu Subramanian, Himanshu Gupta and Samir Das
Stony Brook University, NY, USA
June 21, 2007 [email protected]
Wireless Mesh Network
Internet
Capacity problem due to
Wireless Interference
Objective: Reduce Interference
June 21, 2007 [email protected]
Using different forms of diversities Improve spatial reuse
Use Transmit Power Control Use directional communication
Use multiple channels Single Radio Approach Multi-Radio Approach
How to reduce Interference?
Our Approach
June 21, 2007 [email protected]
Single Radio Approach
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3
Challenges:
1) Channel switching latency (in order of milliseconds)2) Coordination between sender and receiver
June 21, 2007 [email protected]
Multi-Radio Approach
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Advantage:
1) No need to switch channels in “packet time scale.”2) No need for synchronization between communicating nodes3) Can work with commodity 802.11 Hardware
Challenge:
Efficient channel assignment to links such that interference is minimized as much as possible
June 21, 2007 [email protected]
Modeling Interference
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Network Graph:
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1 - 2
2 - 3
4 - 5
2 - 5
3 - 6
5 - 6
Conflict Graph:
Models Interference between a pair of links
Two-hop interference model
Weighted Graph to model variabletraffic and fractional interference
June 21, 2007 [email protected]
Channel Assignment Problem
Network Graph:
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64 5
3
K (=3) different channels
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64 5
31 - 4
1 - 2
2 - 3
4 - 5
2 - 5
3 - 6
5 - 6
Conflict Graph:
June 21, 2007 [email protected]
1 - 4
1 - 2
2 - 3
4 - 5
2 - 5
3 - 6
5 - 6
Max-K-Cut Problem
Maximize edges between nodes with different color
1 - 4
1 - 2
2 - 3
4 - 5
2 - 5
3 - 6
5 - 6
Minimize edges between nodes with same color
June 21, 2007 [email protected]
5 64
1 2 3
Interface Constraint
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2 - 3
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2 - 5
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Channel Assignment Problem
Max-K-Cut problem with Interface Constraint
June 21, 2007 [email protected]
Our Contribution
Design efficient heuristic algorithms (Upper bound on interference) Tabu search based centralized algorithm Distributed greedy algorithm
Establish lower bound on interference using Semi-definite Programming (SDP)
Show the bounds are close by simulation
June 21, 2007 [email protected]
Tabu Search Based Centralized Algorithm – Phase I
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1 - 2
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4 - 5
2 - 5
3 - 6
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1 - 2
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5 - 62 - 5
4 - 5
1 - 4
Start from the random solutionIn each iteration, generate certain number of neighboring solutionsPick the solution with least interferenceRepeat until no improvement for certain number of iterations
June 21, 2007 [email protected]
First phase could result in interface constraint violation in some nodes
Tabu Search Based Centralized Algorithm – Phase II
A
B
C
D
4 channels and 2 Interfaces Violation at node D
June 21, 2007 [email protected]
Merge 2 colors into 1 at node D
Tabu Search Based Centralized Algorithm – Phase II
A
B
C
D
4 channels and 2 Interfaces
June 21, 2007 [email protected]
Propagate color change to entire connected component
Tabu Search Based Centralized Algorithm – Phase II
A
B
C
D
4 channels and 2 Interfaces
June 21, 2007 [email protected]
Greedy Heuristic Takes the interface constraint right from the start
Initially, color all the nodes in the conflict graph with same color
In each iteration choose the node-color pair that minimizes interference (not violating the interface constraint) the most and change the color
Repeat untill interference decrease monotonically
Can be distributed/localized as interference is local
June 21, 2007 [email protected]
Lower Bound using SDPTechnique to optimize a linear function of a
symmetric positive semi-definite matrix subject to linear constraints
Max-K-cut has a good approximate solution using SDP
Add interface constraint to get a lower bound for the channel assignment problem
Can be solved in polynomial time (theoretically)Public domain solvers to solve SDP (DSDP 5.0)
June 21, 2007 [email protected]
Performance with Random Graph
0
0.1
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Number of radio interfaces per node
Fra
cti
on
al N
etw
ork
In
terf
ere
nc
e
Random CLICA-SCE Dist. Greedy Tabu Based SDP
Fractional no. of monochromatic edges in conflict graph (edges outside the cut)
Random disk graphs. Dense - average node degree 10. Interference range = 2 x Transmission range 802.11 interference model (with RTS/CTS) 12 channels.
June 21, 2007 [email protected]
0
0.1
0.2
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2 3 4 5 6 7 8 9 10 11 12
Number of radio interfaces per node
Fra
cti
on
al N
etw
ork
In
terf
ere
nce
Random CLICA-SCE Dist. Greedy Tabu Based SDP
Performance with Random Graph
Fractional no. of monochromatic edges in conflict graph (edges outside the cut)
Random disk graphs. Sparse – barely connected Interference range = 2 x Transmission range 802.11 interference model (with RTS/CTS) 12 channels.
June 21, 2007 [email protected]
0
0.1
0.2
0.3
0.4
0.5
0.6
2 3 4 5 6 7 8 9 10 11 12
Number of radio interfaces per node
Fra
cti
on
al N
etw
ork
In
terf
ere
nce
Random CLICA-SCE Dist. Greedy Tabu Based SDP
Performance with Random Graph
Fractional no. of monochromatic edges in conflict graph (edges outside the cut)
Little improvement beyond a certain no. of interfaces. Saturation reached with smaller no. of interfaces for sparser networks Tabu is generally better than greedy except with for small no. of interfaces (the merging technique is inefficient).
June 21, 2007 [email protected]
Non-Orthogonal Channels
Channel Overlap Factor:
0.2714
2
00.00540.03750.72721Overlap
54310Distance
2402 2407 2412 2417 2422 2427 2432 2437 2442 2447 2452 2457 2462 2467 2472 MHz
1 6 11
2
3
4
5
7
8
9
10
802.11b2.4GHz
June 21, 2007 [email protected]
Performance using Overlapping channels
0123456789
10
1 2 3
Number of radio interfaces per node
Sa
tura
tio
n T
hro
ug
htp
ut
Tabu-11 Channels Dist. Greedy-11 Channels
Tabu-3 Channels Dist. Greedy-3 Channels
Single Channel
Use of overlapped channels advantageous
Both Tabu and Greedy perform well with 11 channels compared to 3 channels
June 21, 2007 [email protected]
Practicalities
Can implement algorithms centrally. Not a problem for managed networks. Collect average load information periodically
from links.
Conflict graph is an input to the problem. How to determine?
Use Standard models (Protocol, Physical…) Based on measurements
June 21, 2007 [email protected]
Summary
Formulated the channel assignment problem to minimize interference
Two efficient algorithms for channel assignment in multi-radio mesh networks
Lower bounding techniques using SDP
Future work: Approximation algorithms, Joint routing