1. A Bandwidth Efficient Pilot Symbol Technique for Coherent Detection of Turbo Codes over Fading Channels
Matthew C. Valenti
Dept. of Comp. Sci. & Elect. Eng.
West Virginia University
Brian D. Woerner
Mobile and Portable Radio Research Group
Bradley Dept. of Elect. & Comp. Eng.
Virginia Tech

2. Overview
Turbo codes.
Practical problems over fading channels.
Methods for detecting turbo codes over fading channels.
DPSK-based
Pilot-based
Improved pilot-symbol techniques
Iterative channel estimation
parity-symbol stealing

3. Turbo Codes Features: Parallel Code Concatenation
Can also use a serial concatenation
Nonuniform interleaving
Recursive systematic encoding
Usually RSC convolutional codes are used.
Can use block codes.
Iterative decoding algorithm.
Max-log-MAP
log-MAP
SOVA

4. Recursive Systematic Convolutional
Turbo Encoder
The data is encoded twice by two identical RSC encoders
A nonuniform interleaver changes the ordering of bits at the input of the second encoder.
MUX increases code rate from 1/3 to 1/2.
Systematic Output
Input
Encoder #1
MUX
Parity
Output
Encoder #2
Nonuniform
Interleaver
Length L
Constraint length K
Recursive Systematic Convolutional
(RSC) Encoder

5. Iterative Decoding One decoder for each elementary encoder.
Deinterleaver
Extrinsic
Information
Extrinsic
Information
Interleaver
systematic
data
Decoder #1
Decoder #2
hard bit
decisions
parity
data
DeMUX
Interleaver
One decoder for each elementary encoder.
Estimates the a posteriori probability (APP) of each data bit.
Extrinsic Information is derived from the APP.
Each decoder uses the Log-MAP algorithm.
The Extrinsic Information is used as a priori information by the other decoder.
Decoding continues for a set number of iterations.

6. Turbo Codes for Fading Channels
Many channels of interest can be modeled as a frequency-flat fading channel.
Fading: channel is time-varying
Flat: all frequencies experience same attenuation
Because of the time-varying nature of the channel, it is necessary to estimate and track the channel.
Channel estimation is difficult for turbo codes because they operate at low SNR.
Questions:
How do turbo codes perform over fading channels?
How can the channel be estimated in a turbo coded system?
Goal is to develop channel estimation techniques that take into account the iterative nature of the decoder.

7. System Model transmitter channel receiver turbo encoder channel
Input
data
turbo
encoder
channel
interleaver
symbol
mapper
pulse shaping
filter
transmitter
fading
AWGN
channel
matched
filter
channel
estimator
receiver
symbol
demapper
channel
deinterl.
turbo
decoder
Decoded
data

8. Fading Channel Types Types of channels
X(t), Y(t) are Gaussian random processes.
Represents the scattering component
Autocorrelation: Rc()
A is a constant.
Represents the direct LOS component
Types of channels
AWGN: A=constant and X(t)=Y(t)=0
Rayleigh fading: A=0
Rician fading: A > 0, =A2/22
Correlated fading:
Fully-interleaved fading:

9. Channel Estimation for Turbo Codes
The turbo decoding algorithm requires accurate estimates of channel parameters.
Branch metric:
Noise variance:
Fading amplitude:
Phase: (required for coherent detection)
Because turbo codes operate at low SNR, conventional methods for channel estimation often fail.
Therefore channel estimation and tracking is a critical issue with turbo codes.

10. The Phase Ambiguity Problem
If the receiver is operating at low SNR, accurate estimates of the phase n will not be available.
A proactive solution to the phase ambiguity problem is required.
Use DPSK.
Differential detection
Multiple-symbol differential detection.
Use a pilot.
Pilot tone.
Pilot symbol.

11. DPSK for Turbo Codes One solution is to use DPSK.
When differential detection is used, a severe loss in performance is noted.
~ 4.5 dB loss for turbo codes in Rayleigh fading
Called the noncoherent combining loss.
Not a viable option.
However, multiple-symbol differential detection can be used to approach coherent performance.
Considered for convolutional codes in:
P. Hoeher and J. Lodge, “Iterative encoding/demodulation of coded DPSK systems,” Globecom 98.

12. Multiple-symbol Differential Detection
Can think of a differential encoder as a recursive convolutional code.
Any coded system that uses DPSK can be thought of as a turbo code.
Serially concatenated.
Inner code = the differential encoder.
Outer code = the channel code itself.
Systems using DPSK don’t need pilot symbols.
The decoder can use per-survivor processing to estimate the channel.
However, this is still a differential technique…

13. Coherent Detection using Pilot Symbols
Coherent detection over Rayleigh fading channels requires a pilot.
Pilot tone
TTIB: Transparent Tone in Band
1984: McGeehan and Bateman
Pilot symbols
PSAM: Pilot Symbol Assisted Modulation
1987: Lodge and Moher; 1991: Cavers
PSAM has been shown to be more power efficient than TTIB for turbo codes.
L.-D. Jeng, Y.-T. Su, and J.-T. Chiang, “Performance of turbo codes in multipath fading channels,” VTC 98.

14. Pilot Symbol Assisted Modulation (PSAM)
Pilot symbols:
Known values that are periodically inserted into the transmitted code stream.
Used to assist the operation of a channel estimator at the receiver.
Allow for coherent detection over channels that are unknown and time varying.
segment #1
segment #2
symbol #1
symbol
#Mp
symbol #1
symbol
#Mp
symbol #1
pilot
symbol
symbol
#Mp
symbol #1
pilot
symbol
symbol
#Mp
pilot symbols added here

15. Pilot Symbol Assisted Decoding
Pilot symbols are used to obtain initial channel estimates.
After each iteration of turbo decoding, the bit estimates are used to obtain new channel estimates.
Decision-directed estimation.
Channel estimator uses either a Wiener filter or Moving average.
channel
estimator
Tentative
estimates of
the code bits
matched
filter
symbol
mapper
channel
interleaver
symbol
demapper
channel
deinterl.
turbo
decoder
Final
estimates of
the data

16. Performance of Pilot Symbol Assisted Decoding
Simulation parameters:
Rayleigh flat-fading
Correlated: fdTs = .005
channel interleaving depth 32
Turbo code
r=1/2, Kc =4
1024 bit random interleaver
8 iterations of log-MAP
Pilot symbol spacing: Mp = 8
Wiener filtering: Nc = 30

17. Performance Factors for Pilot Symbol Assisted Decoding
Performance is more sensitive to errors in estimates of the fading process than estimates in noise variance.
Pilot symbol spacing
Want symbols close enough to track the channel.
However, using pilot symbols reduces the energy available for the traffic bits.
Type of channel estimation filter
Wiener filter provides optimal solution.
However, for small fd, a moving average is acceptable.
Size of channel estimation filter
Window size of filter should contain about 4 pilot symbols.

18. Improving the Bandwidth Efficiency of PSAM
Conventional PSAM requires a bandwidth expansion.
Previous example required 12.5% more BW.
This is because all code and pilot symbols are transmitted.
Instead, could replace code symbols with pilot symbols.
“Parity-symbol” stealing
Puncture parity bits at the same rate that pilot symbols are inserted.
Must be careful about how this puncturing is done.

19. Simulation Results for Slow Fading
Simulation Parameters:
Rayleigh fading
fdTs = .005
Turbo code
constraint length K = 4
rate r = 1/2
L = 4140 bit interleaver

20. Performance in Rapid Fading
Rayleigh fading channel
fdTs = .02
Turbo code
K = 4, r = 1/2
L= 4140 bit interleaver

21. Future Work
Compare coherent PSAM technique with multiple-symbol DSPK technique.
In terms of performance and complexity.
Soft vs. hard decision feedback.
Incorporate adaptability
Adaptive estimation filters.
Adaptive pilot-symbol spacing.
Extend the results to higher order modulation and trellis coded modulation.
Extend the results to the problems of symbol-timing estimation and frame synchronization.

22. Conclusions
Pilot symbol assisted decoding can be used to achieve nearly coherent detection/decoding of turbo codes.
Iterative estimation/decoding improves performance.
Good performance even with just hard-decision feedback.
Iterative estimation can also be used for other types of codes.
Main disadvantage of PSAM is loss of bandwidth efficiency.
BW efficiency can be recovered by overwriting parity bits with pilot symbols