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nA FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS
CSNDSP 2006
Michael Lunglmayr, Martin Krueger, Mario Huemer
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Contents
Introduction
Simulation Model
Particle Filters
Particle Filters for Equalization
Simulation Results
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Introduction
Particle Filters popular in e.g. image recognition, positioning,...
Aim of this work: Equalization with particle filters
Symbol estimation for GSM/EDGE in a multipath propagation environment
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Simulation Model
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Simulation Model
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Particle Filters
Connection to Equalization: Estimate p(xk|yk) and choose those state with the highest probability
Straight Forward Method: calculate p(xk|yk) for every state
Effort to high for practical systems
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Particle Filters
Connection to Equalization: Estimate p(xk|yk) and choose those state with the highest probability
Straight Forward Method: calculate p(xk|yk) for every state
Effort to high for practical systems
Importance Sampling:Principle: If p(xk|yk) would be known, it could be sampled:
Particles:
then for N:
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Particle Filters
Bad News: p(xk|yk) is not known because it is to be estimated!
But: If we can sample a different probability function:q(xk|xk-1,yk) (importance sampling function) and weight the particles with an importance weight:
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Particle Filters
Bad News: p(xk|yk) is not known because it is to be estimated!
But: If we can sample a different probability function:q(xk|xk-1,yk) (importance sampling function) and weight the particles with an importance weight:
Example: q(xk|xk-1,yk) = p(xk|xk-1)
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PF for Equalization
Probability functions for GSM/EDGE
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PF for Equalization
Probability functions for GSM/EDGE
Until now: Sequential Importance Sampling (SIS)But not very efficient yet!
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Resampling
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Particle Filter Algorithm
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Implementation
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Simulation ResultsGMSK
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Simulation Results
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Conclusion
Particle Filters can outperform existing algorithms
Disadvantage: computational complexity
But: complexity depends only linearly on channel length e.g. Promising use in extremely broadband communication systems with long impulse responses