« Particle Filtering for Joint Data-Channel Estimation in Fast Fading Channels »

1. « Particle Filtering for Joint Data-Channel Estimation in Fast Fading Channels » Tanya BERTOZZI Didier Le Ruyet, Gilles Rigal and Han Vu-Thien

2. Classical solutions to the problem: Why the PF (Particle Filtering)? Joint data-channel estimation applying the PF Performance and computational complexity comparison between the PF and the classical solutions Discussion: When is it interesting to use the PF in digital communications? • Conclusion Outline • Problem statement

3. MOD CHANNEL DEMOD DETECTOR Transmitted Signal Model: • bipodal modulation { 1} • i.i.d. bits organized into frames Preamble Information bits Tail Problem statement

4. Channel model: • Multipath fading channel • Symbol-spaced FIR filter Received Signal Model: 1x2 1x(L+1) (L+1)x2 1x2 Problem Statement

5. Purpose of the receiver Estimation of the transmitted sequence in the presence of an unknown channel Classical MLSE solutions • Slow fading channels ( ): Data Estimation Channel Estimation Training sequence: LMS, RLS, Kalman filter Classical solutions: Slow fading

6. Data Estimation: Discrete state space model Viterbi algorithm • Optimal MLSE solution if the channel • coefficients are known • Computational complexity Complexity reduction solutions: M algorithm (Anderson and Mohan, 1984) T algorithm (Simmons, 1990) From one iteration to the next one, it retains only the M best paths, with M less than the total number of states. From one iteration to the next one, it retains a variable number of paths depending on T: Classical solutions: Slow fading

7. Fast fading channels ( ): PSP algorithm (Duel-Hallen and Heegard, 1989) Joint Data-Channel Estimation The memory of the states in the Viterbi trellis is less than L and the terms of residual ISI are corrected along the survivor paths leading to each state. PSP approach: Data-aided estimation of the channel (one estimation of the channel coefficients for each survivor path in the trellis) (Raheli and Polydoros, 1993) Classical solutions: Fast fading

8. Data-aided Channel Estimation Data Estimation • Viterbi algorithm • Complexity reduction algorithms: • M algorithm • T algorithm • PSP algorithm • LMS algorithm Better trade-off between Computational complexity – Performance: • RLS algorithm • Kalman filter algorithm Classical solutions: Fast fading PSP approach: Particle Filtering?

9. Particle Filtering MLSE Detector: Data estimation:Estimation of the Posterior Probability Density (PPD) in a discrete state space Suboptimal solution Optimal solution Approximation of the PPD with particles Exploration of a subset of the possible paths using the SISR algorithm Viterbi algorithm Complexity reduction algorithm Joint data-channel estimation applying the Particle Filtering

10. Observation model: Each state is represented by the L previous information bits because of the channel memory State sequence: Observations: Initial distribution of the particles: , where: L last bits of the preamble Particle filtering: Joint data-channel estimation

11. Selection of the importance function: Minimization of the variance of the importance weights , in order tolimit degeneracy of the algorithm Evolution of the particles in a discrete state space: • At time k-1, several particles are in the same position in the • state space. • At time k, only two values are possible for : +1 and –1. The particles divide in two parts proportionally to the importance function Particle filtering: Joint data-channel estimation

12. Tree-search algorithm +1 +1 -1 +1 +1 -1 +1 -1 -1 +1 The positions of the particles in the state space are seen as groups of particles. -1 -1 Particle filtering: Joint data-channel estimation

13. The channel model • Constant channel: • No a priori knowledge of the speed of the channel • variations: Particle filtering: Joint data-channel estimation

14. Estimate at time k Covariance of Particle filtering: Joint data-channel estimation The channel estimation Along each trajectory in the state space the channel is estimated by a Kalman filter. I) Prediction phase: II) Correction phase:

15. 1 / 2 Bayes Mean: Gaussian Variance: Particle filtering: Joint data-channel estimation Calculation of the importance function

16. Particle filtering: Joint data-channel estimation Calculation of the importance weights Normalisation of the importance weights

17. Particle filtering: Joint data-channel estimation Resampling I) Periodic every L bits: The particles with a weight < T are moved in the group with maximum weight. II) Uniformly according to the importance weights: If the particles are distributed uniformly according to the importance weights.

18. Particle filtering: Joint data-channel estimation Alternative scheme (E. Punskaya, A. Doucet, W.J. Fitzgerald, EUSIPCO, September 2002) +1 +1 -1 -1 At each time only the best M particles are retained +1 +1 -1 +1 -1 -1 +1 +1 -1 +1 -1 +1 -1 close to the M algorithm +1 -1 -1 k-1 k k+1

19. memory L = 7; Simulation results GSM system: the receiver detects only one slot for each TDMA frame; Preamble: 26 known bits for the channel initialisation; Information bits: 58; First channel model: Second channel model: HT240

20. PSP: 8 states PF: 8 particles Simulation results Comparison PSP-Particle filtering First channel model: FER versus Eb/No

21. PF PSP Simulation results First channel model: Complexity versus Eb/No

22. Simulation results HT240:FER versus Eb/No

23. Simulation results HT240: Complexity versus Eb/No

24. M and T PF Simulation results Comparison M-T-Particle filtering First channel model: FER versus Eb/No

25. M T PF Simulation results First channel model: Complexity versus Eb/No

26. Preliminary conclusion If the state space is discrete, the particle filtering technique is equivalent to the classical solutions. When is it interesting to use the particle filtering in digital communications? Joint estimation of discrete and continuous parameters Example: Joint delay-channel-data estimation in DS-CDMA systems. (The paper of Punskaya, Doucet andFitzgerald reaches the same conclusion)

27. LPF RX Joint delay-channel estimation in a DS-CDMA system Data sequence: Spreading sequence: Chip duration: Received signal:

28. DS-CDMA: Joint delay-channel estimation State model: Channel Delay Nearly constant channel coefficients and constant delay: Channel estimation Kalman filter Delay estimation SISR algorithm

29. uniformly between DS-CDMA: Joint delay-channel estimation SISR algorithm for the delay estimation • Initial distribution of the particles: • Selection of the importance function: • Calculation of the importance weights: • Resampling: uniformly according to the importance weights if

30. Simulation results Time

31. Simulation results Time

32. Conclusion Possible applications of the PF in digital communications: Discrete state space equivalent to the classical solutions (M and T algorithms) More interesting: PF for the joint estimation of discrete and continuous parameters Example: Joint delay-channel estimation in a DS-CDMA system The first results are encouraging; this approach can give better performance than the classical solutions.