Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael Lunglmayr, Martin Krueger, Mario Huemer

Michael Lunglmayr Particle Filters for Equalization Page 2 Contents Introduction Simulation Model Particle Filters Particle Filters for Equalization Simulation Results

Michael Lunglmayr Particle Filters for Equalization Page 3 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

Michael Lunglmayr Particle Filters for Equalization Page 4 Simulation Model

Michael Lunglmayr Particle Filters for Equalization Page 5 Simulation Model

Michael Lunglmayr Particle Filters for Equalization Page 6 Particle Filters Connection to Equalization: Estimate p(x k |y k ) and choose those state with the highest probability Straight Forward Method: calculate p(x k |y k ) for every state  Effort to high for practical systems

Michael Lunglmayr Particle Filters for Equalization Page 7 Particle Filters Connection to Equalization: Estimate p(x k |y k ) and choose those state with the highest probability Straight Forward Method: calculate p(x k |y k ) for every state  Effort to high for practical systems Importance Sampling: Principle: If p(x k |y k ) would be known, it could be sampled:  Particles: then for N   :

Michael Lunglmayr Particle Filters for Equalization Page 8 Particle Filters Bad News: p(x k |y k ) is not known because it is to be estimated! But: If we can sample a different probability function: q(x k |x k-1,y k ) (importance sampling function) and weight the particles with an importance weight:

Michael Lunglmayr Particle Filters for Equalization Page 9 Particle Filters Bad News: p(x k |y k ) is not known because it is to be estimated! But: If we can sample a different probability function: q(x k |x k-1,y k ) (importance sampling function) and weight the particles with an importance weight: Example: q(x k |x k-1,y k ) = p(x k |x k-1 ) 

Michael Lunglmayr Particle Filters for Equalization Page 10 PF for Equalization Probability functions for GSM/EDGE

Michael Lunglmayr Particle Filters for Equalization Page 11 PF for Equalization Probability functions for GSM/EDGE Until now: Sequential Importance Sampling (SIS)  But not very efficient yet!

Michael Lunglmayr Particle Filters for Equalization Page 12 Resampling

Michael Lunglmayr Particle Filters for Equalization Page 13 Particle Filter Algorithm

Michael Lunglmayr Particle Filters for Equalization Page 14 Implementation

Michael Lunglmayr Particle Filters for Equalization Page 15 Simulation Results GMSK

Michael Lunglmayr Particle Filters for Equalization Page 16 Simulation Results

Michael Lunglmayr Particle Filters for Equalization Page 17 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