« Particle Filtering for Joint Data-Channel Estimation in Fast
Fading Channels »
Tanya BERTOZZI
Didier Le Ruyet, Gilles Rigal and Han Vu-Thien
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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
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Problem statementkn
kbMOD CHANNEL DEMOD DETECTOR
kb̂kr
bipodal modulation { 1}
i.i.d. bits organized into frames
Preamble Information bits Tail
Transmitted Signal Model:
4
kkk nFBr
1x2 1x(L+1) (L+1)x2 1x2
Received Signal Model:
Symbol-spaced FIR filter
L
llkf 0,
TT
Channel model:
Multipath fading channel
Problem Statement
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Purpose of the receiver
Estimation of the transmitted sequence in the presence of an unknown channel
Classical MLSE solutions
Slow fading channels ( ):1.0BDTf
Channel Estimation
DataEstimation
Training sequence: LMS, RLS, Kalman filter
Classical solutions:Slow fading
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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)
TLLbest
Viterbi algorithm
Optimal MLSE solution if the channel coefficients are known
Computational complexity L2
Classical solutions:Slow fading
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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 ( ):1.0BDTf
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
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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 fadingPSP approach:
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Joint data-channel estimation applying the Particle Filtering
MLSE Detector:
FRBpB KK
B
K
K
ˆ,maxargˆ111
1
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
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Observation model:
kkk nFBr
Lkkk bbb 1
Each state is represented by the L previous information bits because of the channel memory
State sequence:
Observations:
KkbB kK ,,1;1
KkrR kK ,,1;1
Initial distribution of the particles:
pi NiB ,,1;)(0 , where:
LbbB ,,10 L last bits of the preamble
Particle filtering:Joint data-channel estimation
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Selection of the importance function:
Minimization of the variance of the importance weights , in order to limit degeneracy of the algorithm
ikk
ikkk
iik
kk FBrbpFBRb 111:01
ˆ,,ˆ,,
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.
kb
The particles divide in two parts proportionally
to the importance function
Evolution of the particles in a discrete state space:
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Tree-search algorithm
+1
-1
+1
+1
-1
-1
+1
+1
+1
-1
-1
-1The positions of the particles in the state space are seen as groups of particles.
Particle filtering:Joint data-channel estimation
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The channel model
kkk WFF 1
L
00
00
001
0
Constant channel:
999.0i No a priori knowledge of the speed of the channel
variations:
1i
Particle filtering:Joint data-channel estimation
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The channel estimation
Along each trajectory in the state space the channel is estimated by a Kalman filter.
I ) Prediction phase:
111ˆˆ
kkkk FF
QPP kkkk 111
~~
II ) Correction phase:
11ˆˆˆ
kkkkkkkk FBrGFF
11
~~~ kkkkkkk PBGPP
kkkk RFEF 1
ˆ
Estimate at time k
kkP~
Covariance of
kkkkk FFF ˆ~
Particle filtering:Joint data-channel estimation
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Calculation of the importance function
1 / 2Bayes
ikk
ikkk FBrbp 11
ˆ,,1
kikk
ikk
ikk
ik
ikk
ikk
ikk
ik
bdFBbpFBrp
FBbpFBrp
111
111
ˆ,ˆ,
ˆ,1ˆ,
i
kki
kikk
ik
ikk
ik
FBrpFBrp
FBrp
11
1
ˆ,ˆ,
ˆ,
21
~n
Tiikk
i BPB
GaussianMean:
Variance:
ikk
i FB 1ˆ
Particle filtering:Joint data-channel estimation
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Calculation of the importance weights
ikk
ikk
ik
ik FBrpww 11
*1
* ˆ,
ikk
ik
ikk
ik FBrpFBrp 11
ˆ,ˆ,
Normalisation of the importance weights
pN
j
jk
iki
k
w
ww
1
*
*~
Particle filtering:Joint data-channel estimation
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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.
thresN
i
ik
eff Nw
Np
1
2~1ˆIf the particles are distributed
uniformly according to the importance weights.
Particle filtering:Joint data-channel estimation
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Alternative scheme(E. Punskaya, A. Doucet, W.J. Fitzgerald, EUSIPCO, September 2002)
+1
-1+1
-1
-1
-1
-1
+1
+1
+1
k-1 k k+1
+1
+1
+1
+1
+1
-1
-1
-1
-1
-1
At each time only the best M particles are retained
close to the M algorithm
Particle filtering:Joint data-channel estimation
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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:
07.0,14.0,21.0,28.0,35.0,42.0,49.0,56.070 aa
80,70,60,50,40,30,20,107,0, dd ff
memory L = 7;
sldllk Tkfaf ,, 2cosRe
sldllk Tkfaf ,, 2sinIm
Second channel model: HT240
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Comparison PSP-Particle filteringFirst channel model: FER versus Eb/No
Simulation results
PSP: 8 states
PF: 8 particles
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First channel model: Complexity versus Eb/No
Simulation results
PF
PSP
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HT240: FER versus Eb/No
Simulation results
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HT240: Complexity versus Eb/No
Simulation results
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Comparison M-T-Particle filteringFirst channel model: FER versus Eb/No
Simulation results
M and T
PF
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First channel model: Complexity versus Eb/No
Simulation results
M
T
PF
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Preliminary conclusionIf the state space is discrete, the particle filtering technique is equivalent to the classical solutions.
When is it interesting to use the particle filteringin 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)
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Joint delay-channel estimation in a DS-CDMA system
Data sequence: 1nd
Spreading sequence: 1kc
Chip duration: cT
Received signal:
,0
,
L
lklklkk nsfr
RX
cT2/1
LPF
cT/1
kr
kslk Tlkss
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State model:
Channel lklkllk wff ,,1,
Delay kkk w 1Nearly constant channel coefficients and constant delay:
001.0,999.0 2 ll
001.0,999.0 2
Channel estimation
Delay estimation
Kalman filter
SISR algorithm
DS-CDMA:Joint delay-channel estimation
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SISR algorithm for the delay estimation
Initial distribution of the particles:
Selection of the importance function: i
kkiki
kk pFr 111:1ˆ,,
uplow BB ,uniformly between
Calculation of the importance weights:
ikk
ikk
ik
ik Frpww 1
*1
* ˆ, Resampling:
uniformly according to the importance weights if
thresN
i
ik
eff Nw
Np
1
2~1ˆ
DS-CDMA:Joint delay-channel estimation
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Simulation results
Time
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Simulation results
Time
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ConclusionPossible 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.
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