Spanning Tree Backbone in Multihop Wireless Networks

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Spanning Tree Backbone in Multihop Wireless
Networks

• Mukesh Hira and Fouad Tobagi
• Department of Electrical Engineering
• Stanford University, Stanford, CA

IEEE Globecom 2006 November 28, 2006
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Presentation Outline

• Prior Work on Routing in Multihop Wireless
  Networks
• Our objective
• Numerical Results

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Prior Work on Routing in Multihop Wireless
Networks

• Based on use of additive metrics
• Hop Count Optimized Link State Routing Protocol
  (OLSR), RFC 3626, 2003
• Expected number of Transmissions Couto et. al,
  2005
• Amount of Time used on the medium Awerbuch,
  Holmer and Rubens, 2006
• Computes paths with minimum sum of link costs
  between pairs of nodes
• Paths chosen could possibly include weak links,
  particularly in case of minimum hop count paths

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Our objective Strongest weakest link

• Wireless channel is highly dynamic
• Even with fixed node locations, the quality of a
  wireless link fluctuates rapidly, at a much
  smaller time scale than what a routing protocol
  can react to
• Assuming uniform link quality fluctuation across
  the network, the better the average quality of
  the weakest link, the more robust the path is to
  fluctuations in link quality
• For routing along robust paths, we aim to compute
  paths such that the weakest link along the path
  is the strongest possible

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Our work (contd)

• We show that a Spanning Tree that maximizes sum
  of quality measures of links on the tree provides
  paths with the best possible weakest link between
  all pairs of nodes
• We use Signal to Noise Ratio (SNR) as the link
  metric
• Measure of intrinsic quality of a wireless link
  in a low interference environment
• Spanning Tree that maximizes sum of SNRs is
  referred to as Maximum SNR Spanning Tree (MSST)
• Assumption Symmetrical link SNR

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Distributed Protocol for Computation of MSST

• Each node sends periodic Hello Messages
• SNR of received Hello messages is propagated to
  the routing layer
• Routing layer maintains a moving average of SNR
  per neighbor
• SNRs of links can be used in conjunction with any
  known Distributed Minimum Spanning Tree algorithm
  to compute the MSST (e.g. Gallager, Humblet,
  Spira 1983, Peleg, Garay, Kutten 1993)
• Approach 1 Use link weight 1/SNR
• Approach 2 Modify the protocol to select largest
  link weight at each step where it selects the
  smallest link weight
• Maintenance of MSST is under investigation

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Maximum SNR Spanning Tree (MSST)

• Highest possible Minimum SNR along path between
  any
• pair of nodes

• Proof for nodes adjacent to each other on MSST
• Consider node pair (C, E) adjacent on MSST T
• Assume there exists a path between C and E with
• minimum SNR gt SNR of link L (say path
  C,A,B,D,E)
• At least one link along this path (such as L')
  is not on
• MSST
• Since minimum SNR along path gt SNR of L',
• SNR of L' gt SNR of L
• L' can replace L on T and increase sum of SNRs
• of links on T
• But T is a Maximum SNR Spanning Tree
• Hence, proved by contradiction that there does
  not
• exist a path between C and E with a minimum SNR
  
• gt SNR of L

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Maximum SNR Spanning Tree (MSST) (contd)

• Highest possible Minimum SNR along path between
  any pair
• of nodes

Path between (X, Y) with minimum SNR gt that along
MSST path
B
C
D
A
L2
L3
L1
U
V
X
Y
Path between (X, Y) along MSST
Path between (X, Y) along MSST

• Proof for pair of nodes not adjacent on MSST
• Assume there exists a path between (X, Y) with
  minimum SNR gt minimum SNR
• along MSST path X,U,V,Y
• Say minimum SNR link along MSST path is link
  (U, V)
• gt Minimum SNR along U,X,A,B,C,D,Y,V gt SNR
  of link L2
• But that is not possible since (U,V) are
  adjacent on MSST
• Hence, proved that there does not exist a path
  between (X,Y)
• with minimum SNR gt minimum SNR along MSST

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Maximum SNR Spanning Tree (MSST) (contd)

• Highest value of minimum SNR on Spanning Tree
• among all possible Spanning Trees

• Proof
• Minimum SNR link L on MSST T connects two
  subtrees T1 and T2
• Assume there exists Spanning Tree T ' with higher
  minimum SNR
• L is not on T '
• At least one link in set L,L'', has to be on
• MSST
• SNR of all links from this set that are on T '
• has to be gt SNR of L. Any of these links can
  
• replace link L on T and increase sum of SNRs
• Tree T ' does not exist

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Numerical Results Weakest link selected for
routing

• 12 topologies of 30 randomly located nodes

Transmit Power 15 dBm SNR Threshold 10 dB
Path Loss Model L(d) LFS(d) (0.44d) LFS is
free-space path loss
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Numerical Results Average Minimum SNR along a
path
Minimum SNR along a path, averaged over all pairs
in 20 random topologies for each value of number
of nodes
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Numerical Results Difference in Minimum SNR
along path
Minimum SNR along MSST path compared to Minimum
SNR along Minimum Hop Count Path
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Numerical Results Difference in Minimum SNR
along path
Minimum SNR along MSST path compared to Minimum
SNR along Path with minimum sum of reciprocals of
SNRs
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Numerical Results Difference in Minimum SNR
along path
Minimum SNR along MSST path compared to Minimum
SNR along Minimum Medium Time path
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Numerical Results Minimum SNR on MSST compared
to Minimum SNR on Rooted Spanning Trees

• Rooted Spanning Trees are computed for every
  node as root, with metric 1/SNR
• Minimum SNR is computed on all rooted Spanning
  Trees in a network, and the best and
• worst values of this minimum SNR are compared
  to minimum SNR on MSST

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Some Comments

• Properties proved for Maximum SNR Spanning Tree
  are also valid for Maximum Spanning Trees with
  other choices of link metric, in both wireless as
  well as wired networks
• e.g. if Maximum Link Speed Spanning Trees were
  used in place of Spanning Trees proposed by IEEE
  802.1D, minimum link speed between every pair of
  nodes would be the highest possible

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Thank You

• Questions?