1. June 21, 2007 anandps@cs.sunysb.edu Minimum Interference Channel Assignment in Multi-Radio Wireless Mesh Networks Anand Prabhu Subramanian, Himanshu Gupta and Samir Das Stony Brook University, NY, USA

2. June 21, 2007 anandps@cs.sunysb.edu Wireless Mesh Network Internet Capacity problem due to Wireless Interference Objective: Reduce Interference

3. June 21, 2007 anandps@cs.sunysb.edu  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

4. June 21, 2007 anandps@cs.sunysb.edu Single Radio Approach 1 2 6 4 5 3 Challenges: 1)Channel switching latency (in order of milliseconds) 2)Coordination between sender and receiver

5. June 21, 2007 anandps@cs.sunysb.edu Multi-Radio Approach 1 2 6 4 5 3 Advantage: 1) No need to switch channels in “packet time scale.” 2) No need for synchronization between communicating nodes 3) Can work with commodity 802.11 Hardware Challenge: Efficient channel assignment to links such that interference is minimized as much as possible

6. June 21, 2007 anandps@cs.sunysb.edu Modeling Interference 1 2 6 4 5 3 Network Graph: 1 - 4 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 variable traffic and fractional interference

7. June 21, 2007 anandps@cs.sunysb.edu Channel Assignment Problem Network Graph: 1 2 6 4 5 3 K (=3) different channels 1 2 6 4 5 3 1 - 4 1 - 2 2 - 3 4 - 5 2 - 5 3 - 6 5 - 6 Conflict Graph:

8. June 21, 2007 anandps@cs.sunysb.edu 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

9. June 21, 2007 anandps@cs.sunysb.edu 5 6 4 1 23 Interface Constraint 1 - 4 1 - 2 2 - 3 4 - 5 2 - 5 3 - 6 5 - 6 Channel Assignment Problem Max-K-Cut problem with Interface Constraint

10. June 21, 2007 anandps@cs.sunysb.edu 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

11. June 21, 2007 anandps@cs.sunysb.edu Tabu Search Based Centralized Algorithm – Phase I 1 - 4 1 - 2 2 - 3 4 - 5 2 - 5 3 - 6 5 - 6 1 - 2 2 - 3 3 - 6 5 - 62 - 5 4 - 5 1 - 4  Start from the random solution  In each iteration, generate certain number of neighboring solutions  Pick the solution with least interference  Repeat until no improvement for certain number of iterations

12. June 21, 2007 anandps@cs.sunysb.edu  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

13. June 21, 2007 anandps@cs.sunysb.edu  Merge 2 colors into 1 at node D Tabu Search Based Centralized Algorithm – Phase II A B C D 4 channels and 2 Interfaces

14. June 21, 2007 anandps@cs.sunysb.edu  Propagate color change to entire connected component Tabu Search Based Centralized Algorithm – Phase II A B C D 4 channels and 2 Interfaces

15. June 21, 2007 anandps@cs.sunysb.edu 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

16. June 21, 2007 anandps@cs.sunysb.edu Lower Bound using SDP  Technique 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)

17. June 21, 2007 anandps@cs.sunysb.edu Performance with Random Graph 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.

18. June 21, 2007 anandps@cs.sunysb.edu 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.

19. June 21, 2007 anandps@cs.sunysb.edu 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).

20. June 21, 2007 anandps@cs.sunysb.edu Non-Orthogonal Channels Channel Overlap Factor: 0.2714 2 00.00540.03750.7272 1 Overlap 54310Distance 2402 24072412241724222427243224372442244724522457246224672472 MHz 1611 2 3 4 5 7 8 9 10 802.11b 2.4GHz

21. June 21, 2007 anandps@cs.sunysb.edu Performance using Overlapping channels  Use of overlapped channels advantageous  Both Tabu and Greedy perform well with 11 channels compared to 3 channels

22. June 21, 2007 anandps@cs.sunysb.edu 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

23. June 21, 2007 anandps@cs.sunysb.edu 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