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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. ICC’05, 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, pp:555-576, 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 SECON’05 [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} ∩ {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 = 0,1}N×M

an,m = 1 iff band m is available for channel n

Constraints C = {ci,j | ci,j = 0,1}N×N

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 0}≧ N×M

un,m = 0 iff band m is not available to channel n

Objective O = {on,m | on,m = 0,1}N×M = argAmax{U}

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 =(V+B,U), it can be treated as a weighted bipartite graph matching problem

b1 b2 b3v1 v2 v3 v4 v5

v1

v2

v3

v4

v5

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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 u3,3+u4,2+u5,1 = 14

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

b1 b2 b3

v1 v2 v3 v4 v5 v1 v2 v3 v4 v5

b1 b2 b3 b1 b2 b3

v1 v2 v3 v4 v5

v1 v2 v3 v4 v5v1 v2 v3 v4 v5

b1 b2 b3 b1 b2 b3

Berge’s 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 E⊂ ℓ’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. c1,2=1, 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 U{i, j}= U{i}+ U{j}

It is easily to get that the perfect matching of U’ is {1,3}+{2,5}+{4}=15 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

b1 b2 b3 b1 b2 b3

v1 v2 v3

v6 v5 v4

{1, 3, 5}{1, 3}, {1, 5}

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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 β Each band can be a candidate of one’s available band set with

probability α 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