Ger man Aerospace Center Transfer Chart Analysis of Iterative OFDM Receivers with Data Aided Channel Estimation Stephan Sand, Christian Mensing, and Armin

Ger manAerospace Center

Transfer Chart Analysis of Iterative OFDM Receivers with Data Aided Channel Estimation

Stephan Sand, Christian Mensing, and Armin Dammann

German Aerospace Center (DLR)

3rd COST 289 Workshop, Aveiro, Portugal, 12th July

2


Outline

System model

Frame structure

Channel estimation (CE)

Extrinisic information transfer (EXIT) Charts

Bit-error rate transfer (BERT) Charts

Comparison of BERT and EXIT charts

Simulation results

Conclusions & outlook

3


System Model: OFDM System with Iterative Receiver

4


Frame Structure

Burst transmission

Rectangular grid

Pilot distance in

frequency direction: Nl=10

Pilot distance between

OFDM symbols: Nk=10

1

1

Nc

Ns

Nk

Nl

data symbol

pilot symbol

frequency

time

5


Channel Estimation (CE)

Initial iteration (i=0) only pilot symbols: Pilot aided channel estimation (PACE)

Afterwards (i>0) additionally data estimates:Pilot and data aided iterative channel estimation (ICE)

Localized estimates for the channel transfer function at pilot or data symbol positions, i.e., the least-squares (LS) estimate:

Replacing unknown Sn,l by the expectations (soft symbol and soft variance):

*, , , ,

, ,( ) ,2, ,,

n l n l n l n ln l i n l

n l n ln l

R R S ZH H

S SS

, ,( )

*, , ,( )

, ,( )

n l i

n l n l in l i

S

R SH

E

6


Channel Estimation (CE)

Filtering localized estimates yields final estimates of the complete CSI:

where ωn’,l’,n,l,(i) is the shift-variant 2-D impulse response of the filter. Tn,l is the set of initial estimates that are actually used for filtering.

Filter design:

Knowledge of the Doppler and time delay power spectral densities

(PSDs)

optimal 2-D FIR Wiener filter

Separable Doppler and time delay PSDs

two cascaded 1-D FIR Wiener filters perform similar than 2-D

FIR Wiener filter

,

, ,( ) ', ', , ,( ) ', ',( ) ,', '

ˆ , , 1, , , 1, , ,n l

n l i n l n l i n l i n l c sn l

H H n N l N

T

T P D

7


EXIT Charts

Benefits

Mutual information flow between inner and outer receiver

Independent computation for inner and outer receiver

Arbitrary combination of inner and outer receiver

Prediction of “turbo cliff“ position and BER possible

Assumptions

Log-likelihood ratio values (L-values): Gaussian distributed random variables

Interleaver depth large: uncorrelated L-values

8


EXIT Charts

A-priori L-values: independent Gaussian random variable

Probability density function of LA

A-priori mutual information

monotonically increasing, reversible function of σA

A A AL c n 2

2A

A 2( , )A A An N

21

1 2 ( | )( ; ) ( | ) log

2 ( | 1) ( | 1)A

A A Ac A A

p C cI C L p C c d

p C p C

22

2

( )2

2

( | )2

A

A

c

AA

ep C c

( ; )A AI C L

9


EXIT Charts

Steps for EXIT chart computation

1. Variance of a-priori L-values from a-priori information

2. A-priori L-value

3. Input a-priori L-value and simulated “channel”-value to component

4. Measure extrinsic information at output of component with histogram estimator

12( ; ) ( ; ) 1 ( | ) log (1 )A A A A A EI C L I C L p C c e d

A A AL c n

21

1 2 ( | )( ; ) ( | ) log

2 ( | 1) ( | 1)E

E E Ec E E

p C cI C L p C c d

p C p C

10


BERT Charts

Benefits

BER flow between inner and outer receiver

Independent computation for inner and outer receiver

Arbitrary combination of inner and outer receiver

Prediction of “turbo cliff“ position and BER possible

Assumptions

Log-likelihood ratio values (L-values): Gaussian distributed random variables

Interleaver depth large: uncorrelated L-values

11


BERT Chart

A-priori L-values: independent Gaussian random variable

Probability density function of LA

A-priori BER

monotonically increasing, reversible of σA

A A AL c n 2

2A

A 2( , )A A An N

0

1

1( ; ) ( | )

2A A Ac

P C L c p C c d

22

2

( )2

2

( | )2

A

A

c

AA

ep C c

( ; )A AP C L

12


BERT Charts

Steps for BERT chart computation

1. Variance of a-priori L-values from a-priori BER

2. A-priori L-value


4. Measure extrinsic BER at output of component by hard decision

1 1( ; ) ( ; ) erfc

2 8A

A A A A AP C L P C L

A A AL c n

,

1

1 sgn( )1( ; )

2

Nn E n

E En

c LP C L

N

13


Comparison of EXIT and BERT Charts

BERT chart computation

1. Variance of a-priori L-values

2. A-priori L-value


4. Measure extrinsic BER / information at output of component

A A AL c n

1( ; )A A AP C L 1( ; )A A AI C L

1

2

1( ; ) ( | )

2

2 ( | ) log

( | 1) ( | 1)

E E Ec

E

E E

I C L p C c

p C cd

p C p C

EXIT chart computation

,

1

1 sgn( )1( ; )

2

Nn E n

E En

c LP C L

N

14


Simulation Results: Scenario

Bandwidth 4.004 MHz

Subcarriers 1001

FFT length 1024

Sampling duration Tspl 3.1 ns

Guard interval TGI 205 Tspl

Subcarrier spacing Δf 4 kHz

OFDM symbols / Frame 101

Modulation QPSK, linear mapping

Coding Conv. code, R=1/2, (23,37)

Information bits 99986

Interleaver length 199980

Interleaver type random

Pilot spacing frequency 10

Pilot spacing time 10

fD,max 0.025Δf ≈ 100 Hz

τmax 20 μs

τrms 0.001τmax

time…

Exponential Channel model with Jakes’ Doppler fading

15


Simulation Results: AWGN Channel BERT

Acronyms:

PCE: perfect channel estimation

DMOD: demodulator

DCOD: decoder

16


Simulation Results: AWGN Channel EXIT

Acronyms:


DMOD: demodulator

DCOD: decoder

17


Simulation Results: Exponential ChannelHistogram of L-values at demodulator output

No Gaussian

distribution of

L-values

18


Simulation Results: Exponential Channel BERT

Acronyms:


ICE: iterative channel estimation

DMOD: demodulator

DCOD: decoder

BERT: DCOD too

pessimistic due to

Gaussian

assumption!

19


Simulation Results: Exponential Channel EXIT

Acronyms:



DMOD: demodulator

DCOD: decoder

ICE system

trajectory dies out:

independence

assumption violated

20


Simulation Results: Exponential Channel BER Plot

Acronyms:

PACE: pilot aided channel estimation



DMOD: demodulator

DCOD: decoder

@ 7dB:

ICE reaches PCE

after 5 iterations

21


Conclusions & Outlook

Iterative receiver including pilot and data aided channel estimation

BERT and EXIT charts:

simpler computation of BERT charts

direct prediction of BERs in BERT charts

Simulation results indicate:

BERT charts too pessimistic due to Gaussian assumption of decoder

EXIT charts more robust against Gaussian assumption

ICE reaches PCE after a few iterations

Outlook:

A-posteriori feedback in ICE to improve convergence

Thank you!

Documents

Ger man Aerospace Center Transfer Chart Analysis of Iterative OFDM Receivers with Data Aided Channel Estimation Stephan Sand, Christian Mensing, and Armin