Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE...

Michael LunglmayrParticle Filters for EqualizationPage 1

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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