Transcript Cellular Operators in a Shared Spectrum Sivan Altinakar ç

Cellular Operators in a
Shared Spectrum
çSivan Altinakar
Supervisors:
Tinaz Ekim-Asici
ç
Márk Félegyházi
Summary
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S. Altinakar
Introduction
Modeling
Game Theory
Program
Simulations
Results
Further Research
Conclusion
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Introduction
In a given network with non-cooperative
operators on a shared frequency band:
we are interested in optimizing the interference
from the point of view of the network, by setting
each base station's transmission power.
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Modeling
Modeling
Cellular Network

components
• operators
• base stations (BS)
• threshold distance
of interference
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our approach
• shared frequency band
• notion of Interference (related to SINR)
• finite number of power settings
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Definitions
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Signal-to-Interference-plus-Noise-Ratio:
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Interference from one Base Station:
ws,B,A
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Interference from whole Network
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Modeling
First Attempt: edge-deletion
Mutual Disturbance
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Modeling
First Attempt:
edge-deletion
A
p
B
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D
p
p
p
C
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Difficult to
interpret
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Modeling
Second Attempt:
node-deletion
Base Station A
A1
Base Station B
Interference
B1
A2
B2
A3
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B3
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Modeling
Second Attempt:
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node-deletion
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Threshold = 60
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• pairwise threshold
• NP-complete
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Modeling
Early results in first version (IMax):
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quality of a "uniform setting"
( infinite b )
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response by "chunks"
( when decreasing b )
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"almost" equivalent solutions
( N0=0 )
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effect of changing one base station's setting
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coverage constraint & inactive base stations

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introduce second version (SMax)
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Modeling
Final Model
noise factor of B
(w/ setting s)
X
Network
ws,X,B
ws,X,A
ws,X,C
B
ws,A,B
SUM
ws,C,A
ws,B,A
Individual
Interference
of B over A
Interference over A(w/ setting s)
(w/ setting s)
A
C
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ws,A,C
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Modeling
Interference over A
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Game
Theory
Game Theory
Definition
 strategic-form game
No need of
an objective
function
• player
base station
• strategy
power level
• utility function
(based on Interference )
simultaneous
choice of a strategy
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Nash equilibrium
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price of anarchy
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sequential game
(=stable strategy profile)
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Game Theory
Utility functions used (for a base station A ):
related to the
SINR of a
virtual user
very close to
the base
station
(BA)
simulations
(BWFS)
(BPON)
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Program
Program
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Initialization:
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•
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simultaneously:
• play game
• run optimization
heuristic
Result:
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network
upper-bound constraint b (if defined)
initial strategy profile
(=power setting)
objective function
choice of the next base stations
utility function
the final strategy profile reached (result of the game)
the best strategy profile encountered (result of the heuristic)
Procedure:
While a stopping criteria is not met, perform the steps
1. choose a base station
2. choose a strategy for this base station
3. update the best strategy profile encountered (if necessary)
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}
change
of strategy
= MOVE
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Program
Stopping criteria:
• Nash equilibria
• max # of iterations without move
• max # of iterations
Additional fine-tuning capabilities:
• limited range of strategies
• tabu list
Choice of the next base station:
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•
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RAN
SEQ
GTS
DTS
RandomSearch
SequenceSearch
GlobalTabuSearch
DistributedTabuSearch
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Simulations &
Results
Simulations
It's time for a demo…?
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Program
Software & Hardware
• Java 1.5
• Dell with 600MHz Intel Pentium III and 128 MB RAM
• Matlab
Implementation: 3 types of classes
• model representation
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model parameters
base stations, operators, network,…
• algorithms
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brute force search
game
tabu search
• interfaces
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SharedSpectrumSolver
MultipleRunLauncher
SSS
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Simulations
Environment parameters
• N = 0.0001
• a=4
• dthresh = 10 km
Network parameters
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•
b=∞
set of power levels = {6.25, 12.5, 25, 50, 100}
Experiment variables
• objective function
• utility function
• initial setting
• range
• tabu list length
• procedure
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(IMin, SMax)
(Base, BWFS, BPON, g )
(PMin, PMax, PRan)
(free, 1-step)
(no list, 1, 3, 5, 7)
(RAN, SEQ, GTS, DTS)
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Results
NE at the end of the procedure:
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RAN: 99%
SEQ: 100%
GTS: 30-90%
DTS: 65-90%
b= ∞
3 utility functions with
•g
= 0.2
Observations:
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better with structured network
decrease of efficiency with a limited range
iterations average between 10 and 60
unusual behavior with particular utility functions
Reached Nash equilibria:
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usually 1 point:
for g too high:
for limited range:
starting from PMin:
Tabu list length
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PMax
PMaxMin solution(s)
extra Nash equilibria (!)
difficulties, range effect
(free range, PRan)
no effect on RAN
longer=better (-> SEQ)
Random network:
GTS useless for {0,1,3} and DTS for {0,1}
w/ list: DTS better than GTS
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Example
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• tabu
• range
• initial s.
=5
= free
= PRan
Random
Pyramidal
RAN
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SEQ
20
20
GTS
23
18
DTS
50
44
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Results
Objective function value
IMin:
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optimum is PMax
 Nash eq. for almost all utility functions
the game always stabilizes at the optimum
Price of Anarchy = 1
SMax:
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optimum is PMaxMin
 Nash equ. for no utilitiy
good solutions are rare and purely accidental on
the way to PMAX
Price of Anarchy not relevant
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Further
Research
Further Research
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open questions
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effect of b<∞
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new utility functions
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simultaneous strategy choice
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edge- and node-deletion
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Conclusion
Conclusion
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Optimization of the quality of the transmissions in a wireless
communication system.
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We designed several models, defined a game and build a program
for running simulations.
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We observed that:
• usually our utility functions have a unique Nash equilibrium at the
maximum power setting
• the utility functions match perfectly the objective of IMin, but
absolutely not SMax
• other variables such as tabu list length and the range of available
strategies influence a game or an algorithm.
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Further research could be conducted on the proposed open
questions, the influence of b and new utility functions. This could
be done theoretically and by using the developed simulator.
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References
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Félegyházi and Hubaux
Wireless Operators in a Shared Spectrum
(2005)
Halldórsson, Halpern, Li and Mirrokni
On Spectrum Sharing Games
(2004)
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Thank you for your Attention!
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