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

2 Outline Problem statement 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

3 Problem statement MODCHANNELDEMODDETECTOR bipodal modulation { 1} i.i.d. bits organized into frames PreambleInformation bitsTail Transmitted Signal Model:

4 1x21x(L+1)(L+1)x21x2 Received Signal Model: Symbol-spaced FIR filter Channel model: Multipath fading channel 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 ( ): Channel Estimation Data Estimation Training sequence: LMS, RLS, Kalman filter Classical solutions: Slow fading

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

7 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 algorithm (Duel-Hallen and Heegard, 1989) Fast fading channels ( ): Joint Data-Channel Estimation PSP approach: (Raheli and Polydoros, 1993) Data-aided estimation of the channel (one estimation of the channel coefficients for each survivor path in the trellis) Classical solutions: Fast fading

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

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

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 to limit degeneracy of the algorithm Particle filtering: Joint data-channel estimation 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 Evolution of the particles in a discrete state space:

12 Tree-search algorithm The positions of the particles in the state space are seen as groups of particles. 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 The channel estimation Along each trajectory in the state space the channel is estimated by a Kalman filter. I ) Prediction phase: II ) Correction phase: Estimate at time k Covariance of Particle filtering: Joint data-channel estimation

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

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

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

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

19 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: memory L = 7; Second channel model: HT240

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

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

22 HT240: FER versus Eb/No Simulation results

23 HT240: Complexity versus Eb/No Simulation results

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

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

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 and Fitzgerald reaches the same conclusion)

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

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

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

30 Simulation results Time

31 Simulation results Time

32 Conclusion Possible applications of the PF in digital communications: Discrete state spaceequivalent 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.