Cooperative Spectrum Allocation in Centralized Cognitive Networks Using Bipartite Matching

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Cooperative Spectrum Allocation in Centralized
Cognitive Networks Using Bipartite Matching

• Zhao Chengshi, Zou Mingrui, Shen Bin, Kim Bumjung
  and Kwak Kyungsup
• Graduate School of IT and Telecom., Inha
  University, Korea
• GLOBECOM 2008

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Outline

• Introduction
• Network Modeling
• Bipartite Matching Algorithm
• Simulations and Discussions
• Conclusion

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Introduction

• Actual measurements have shown that
• Most of the allocated spectrum is largely
  underutilized
• Traditional fixed spectrum allocation may be very
  inefficient
• Cognitive Radio (CR) is a promising radio design
  method, motivated to increase spectrum
  utilization
• By the method of exploiting unused or low
  utilization spectrum already authorized to
  primary systems
• Secondary Users opportunistically lease spare
  spectrum from Primary Users without disrupting
  their operations

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Previous Work (1)

• In 8-9, it is shown that by mapping each
  channel into a color, spectrum allocation can be
  reduced to a heuristics graph multi-coloring
  (GMC) problem
• The model obtains conflict free spectrum
  assignments that closely approximate the global
  optimum in centralized systems
• In centralized systems, effective and efficient
  coordination heavily depends on fast
  dissemination of control packets among users

8 Zheng, H., and Peng, C, Collaboration and
fairness in opportunistic spectrum access. In
Proc. ICC05, pp 3132-3136 June 2005. 9 Peng,
C., Zheng, H., and Zhao, B. Y. Utilization and
fairness in spectrum assignemnt for opportunistic
spectrum access. Mobile Networks and
Applications, vol. 11, no. 4, pp555-576, Aug,
2006.
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Previous Work (2)

• In 11, through illustrative examples and
  simulation data, authors show that under spectrum
  heterogeneity
• A common channel is rarely available to all
  users, while users do share significant spectrum
  with local neighbors
• In other words, nearby nodes have very similar
  views of spectrum availabilities
• According to this conclusion, we assume that
• Nearby users self-organized into coordination
  groups and use spectrum cooperatively with
  neighbors by exchanging control messages through
  a local common channel in each group
• A group is build up according to 10

10 Cao L, Zheng H. Distributed spectrum
allocation via local bargaining, in Proc. IEEE
SECON05 11 Zhao, J., Zheng, H. and Yang, G.
H., "Spectrum Sharing through Distributed
Coordination in Dynamic Spectrum Access
Networks," Wireless Communications and Mobile
Computing Journal, 2007
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Goal

• In this paper, centralized spectrum allocation is
  considered
• Environmental conditions such as user location,
  available spectrums are static during allocation
• We look upon the target of spectrum allocation is
• To maximize network utilization as well as to
  minimize interference
• Fairness across users is also considered to some
  extent

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Network Modeling

• In this paper, we specify
• Channel is the network link between two users
• Spectrum band is the radio electromagnetic
  frequency range that the channel access to
• we consider that spectrum is orthogonal as FDMA,
  which cuts spectrum into spectrum bands
• Each SU has an available spectrum band list and
  selects one band that avoids interference with
  PUs and other SUs
• Users communicate with each other in a method of
  semi-duplex, uplink and downlink use same
  spectrum band

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Edge-Vertex Transform

• Channels are transformed into vertexes
• Vertexes choose band from intersection of
  neighboring users available band lists
• e.g. band list of 1 band list of I n band
  list of II

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Key Components of the Network Model

• Assume
• A network includes N channels, M spectrum bands
• Key components of the network model include
• Availability A an,m an,m 0,1NM
• an,m 1 iff band m is available for channel n
• Constraints C ci,j ci,j 0,1NN
• ci,j 1 iff channel i and channel j are not
  allowed to access to a same band simultaneously
• Utilities U un,m un,m ? 0NM
• un,m 0 iff band m is not available to channel n
• Objective O on,m on,m 0,1NM argAmaxU
• on,m 1 iff band m is allocated to channel n

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Bipartite Matching Algorithm (1)

• Assume that there are 3 available bands for 5
  channels to choose from, and the utility matrix U
  is assumed as follow
• To get the maximum utility of the graph G
  (VB,U), it can be treated as a weighted
  bipartite graph matching problem

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Bipartite Matching Algorithm (2)

• After perfect matching, we get the result shown
  in following figure
• Utility of the matched network is u3,3u4,2u5,1
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• v1 and v2 did not access to any band, they are
  starved
• In fact, they can access some band by improving
  on the bipartite matching algorithm

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Max Matching

• Berges Theorem
• A matching is maximum if and only if there is no
  more augmenting path
• The edges within the path must alternate between
  occupied and free
• The path must start and end with free edges

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Max-Weight Matching (1)

• A Perfect Matching is an M in which every vertex
  is adjacent to some edge in M
• A vertex labeling is a function l V ? R
• A feasible labeling is one such that
• l(x) l(y) w(x, y), ?x ? X, y ? Y
• The Equality Graph (with respect to l) is G (V,
  El) where
• El (x, y) l(x)l(y) w(x, y)

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Max-Weight Matching (2)

• Theorem Kuhn-Munkres
• If l is feasible and M is a Perfect matching in
  El then M is a max-weight matching
• Algorithm for Max-Weight Matching
• Start with any feasible labeling l and some
  matching M in El
• While M is not perfect repeat the following
• 1. Find an augmenting path for M in El this
  increases size of M
• 2. If no augmenting path exists, improve l to
  l such that El ? El Go to 1

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Sharing and Starvation Consideration

• Sharing Consideration
• v2 can share same band e.g. b1, with v5
• Starvation Consideration
• v1 is still starved

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Solution to Starvation Problem

• In each step of matching, vertexes of set B are
  matched to the starving vertexes first
• this method cannot get an overall optimal
  utility, but starvation is alleviated furthest

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Solution to Sharing Problem (1)

• The allocation is described as follows
• Matching starving vertexes first
• Assume set B0 is matched to starving vertexes
  set
• Delete vertexes V0 delete the connections
  between B0 and confliction vertexes of V0
  according to matrix C
• e.g. c1,21, delete vertex v1 and delete the link
  between b1 and v2
• Considering matrix both C and U to build up
  possible sharing cases and add sharing cases as
  fictitious vertexes in set V
• possible sharing cases are only 1,3, 1,4,
  1,5 and 2,5

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Solution to Sharing Problem (2)

• Delete repeated connections
• e.g. v3 is connected to b1, while 1,3 is
  connected to b1 too, so delete the link between
  v3 and b1
• Describing the figure in a matrix
• The channels competing for same band must be put
  into a column
• Fictitious vertexes that sharing same element
  must be put into a same row

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Solution to Sharing Problem (3)

• U is called as extended utility matrix
• i, j represents a fictitious vertex, and
  utility Ui, j Ui Uj
• It is easily to get that the perfect matching of
  U is 1,32,5415
• Utility is maximized as well as starvation is
  avoided
• To get the overall optimal result, all of the
  feasible extended utility matrix must be ransacked

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Algorithm

1. Derive extended utility matrix U
2. Use K-M algorithm to U, get ONXM
3. If there are other feasible U, turn to 2
4. Compare the results of all ONXM , get the best
   one from them

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Simulation Environment

• Setting
• CR network is assumed by randomly placing users
  on an area
• users within a distance of D will disturb each
  other if they transmit data using same channel
  simultaneously
• each user is within D distance of the other users
  at a probability of ß
• Each band can be a candidate of ones available
  band set with probability a
• For matrix U, uniform random values are produced
  from 1 to 20
• number of overall available bands number of
  users
• Non-Cooperative Case
• There is no band-sharing or starvation-restraining
  
• if confliction happens, the user will be rejected
  to access

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Results
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Conclusion

• Using bipartite graph matching, a spectrum
  allocation algorithm that maximizes system
  utilities and mitigates interference is presented
• Experimental results confirm that user
  cooperation yields significant benefits in
  spectrum allocation