Per-survivor Based Detection ofDPSK Modulated High Rate Turbo Codes

Over Rayleigh Fading Channels

Bin Zhao and Matthew C. Valenti

Lane Dept. of Comp. Sci. & Elect. Eng.

West Virginia University

Morgantown, WV

This work funded by the Office of Naval Research under grant N00014-00-0655

Outline of Talk

Background– Iterative channel estimation and decoding.– Turbo DPSK (Hoeher & Lodge).

“Extended” turbo DPSK – Replace code in turbo DPSK with turbo code.– Analytical tool to predict location of “waterfall”.– Performance in AWGN and fading with perfect CSI– Performance in unknown fading channels using

PSP-based processing. Conclusions

Iterative Channel Estimation

Pilot-symbol filtering techniques:– Valenti and Woerner – “Iterative channel estimation and decoding of

pilot symbol assisted turbo codes over flat-fading channels,” JSAC, Sept. 2001.

– Li and Georghiades, “An iterative receiver for turbo-coded pilot-symbol assisted modulation in fading channels,” Comm. Letters, April 2001.

Trellis-based techniques:– Komninakis and Wesel, “Joint iterative channel estimation and

decoding in flat correlated Rayleigh fading channels,” JSAC, Sept. 2001.

– Hoeher and Lodge, “Turbo DPSK: Iterative differential PSK demodulation and channel decoding,” Trans. Comm., June 1999.

– Colavolpe, Ferrari, and Raheli, “Noncoherent iterative (turbo) decoding,” Trans. Comm., Sept. 2000.

Turbo DPSK Structure

From Hoeher/Lodge. K=6 convolutional code. Block interleaver: 20 frames. Trellis-based APP demodulation of DPSK with perfect CSI. In flat fading channels, per-survivor processing and linear

prediction are applied to estimate the channel information. Iterative decoding and APP demodulation.

RSC channel

Interleaver D P S K

Channel

APP Demod Deint

extrinsic infomation

convolutional decoder

channel Interleaver

input

+ -

- +

output

APP Demodulator for DPSK

Can use BCJR algorithm to coherently detect trellis-based DPSK modulation.– Only 2 state trellis when perfect CSI available.

With unknown CSI apply linear prediction and per-survivor processing to estimate the channel information.– Requires an expansion of the DPSK code-trellis.– Complexity of APP demodulator is exponentially

proportional to the order of linear prediction.– PSP algorithm must be modified to produce soft-outputs.

Construction of Super-Trellis

Use a sliding window to combine multiple adjacent stages of simple DPSK trellis to construct the super-trellis of APP demodulator.

Number of adjacent stages equals the order of the linear predictor.

Complexity of super-trellis is exponentially proportional to the order of linear prediction.

S0

S1

0

1

0

0

1

0

Window 1Window 2

S2

S3

S2

S3

1

0

S0

S1

S0

S1

0

1

0

0

Branch Metric of APP Demodulation in Correlated Fading Channel with PSP

k k

k

k k n k n k n

N

n n n

N k

k k n k n k n

N

n n n

N k

b

z

y b p y b

p ra

y b p y b

p ra

( )~

~ ~

~

~ ~

~

R

S

|||||

T

|||||

1

2

2

1

1

2

2

1

2 1

2 1

= 1

= 0

Channel LLR y and estimated channel input Prediction coefficient and Gaussian noise Prediction residue

pn

bk n

~

2 2 n

11

p rn n

N

Code polynomials (1,23/35) UMTS interleaver for turbo

code. Rate compatible puncturing

pattern. Block channel interleaver. Per-survivor based APP

demodulation for correlated fading channels.

Iterative decoding and demodulation.

RSC

RSC turbo interleaver

Turbo Encoder

PUNT

Channel Interleaver

DPSK

Channel

APP Demod Deint

extrinsic infomation

Turbo decoder

Channel Interleaver

+ - -

+

Extended Turbo DPSK Structure

-6 -4 -2 0 2 4 6 810

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Performance in AWGN Channel with Perfect CSI

Es/No in dB

BE

R

extended turbo DPSKturbo code (coherent BPSK)

1/3

4/7 4/58/9

2.5 dB1 dB

Framesize 1024 bits The energy gap between

turbo code and extended turbo DPSK:

The energy gap decreases as the rate increases except for the rate 8/9 case.

– Why?

Rate Energy Gap

8/9 2 dB

4/5 1 dB

4/7 1.5 dB

1/3 2.5 dB

Analytical Tool: Convergence Box Similar to the “tunnel theory”

analysis.– S. Ten Brink, 1999.

Suppose Turbo decoder and APP demodulator ideally transform input Es/No into output Es/No.

– APP demodulator • DPSK BPSK

– Turbo code decoder • Turbo Code BPSK

Convergence box shows minimum SNR required for converge.

– corresponds to the threshold SNR in the tunnel theory.

convergence box location:

rate Es/No Eb/No

1/2 0.5 dB 3.5 dB

1/3 -1.3 dB 3.5 dB-6 -4 -2 0 2 4 6 8Es/No in dB

10-3

10-2

10-1

100

BE

R

coherentDPSK

BPSK

1 iteration

10 iterations

r =⅓turbo code

Performance in Fading Channel:r = 4/5 case

BT=0.01 Block interleaver

improves the performance of turbo code by about 1.5 dB.

With perfect CSI, the energy gap between turbo code and extended turbo DPSK is 3 dB.

For extended turbo DPSK, differential detection works better than per-survivor based detection

Reason A: 1 local iteration of turbo decoding is sub-optimal.

Reason B: the punctured outer turbo code is too weak.

Performance in Fading Channel: r = 1/3 case

Per-survivor based detection loses about 1 dB to perfect CSI case.

Per-survivor based detection has 1 dB gain over extended turbo DPSK with differential detection.

Increasing the trellis size of APP demodulator provides a decreasing marginal benefit.

Performance in Fading Channel: r = 4/7 case

With perfect CSI, the energy gap between turbo code and extended turbo DPSK is around 2.5 dB.

Per-survivor based detection loses about 1 dB to perfect CSI case.

Per-survivor based detection has 1 dB gain over extended turbo DPSK with differential detection.

Increasing the trellis size of APP demodulator provides a decreasing marginal benefit.

Conclusions

“Extended turbo” DPSK = turbo code + DPSK modulation.– Performs worse than turbo codes with BPSK modulation and

coherent detection.– However, the gap in performance depends on code rate.– Large gap if code rate too low or too high. – “Convergence box” predicts performance.

Extended turbo DPSK suitable for PSP-based detection.– PSP about 1 dB worse than extended DPSK with perfect CSI.– For moderate code rates, PSP is 1 dB better than differential

detection.– However, if code rate too high, PSP can be worse than diff. detection.

• Performance can be improved by executing multiple local iterations of turbo decoding per global iteration (future work).

Future Work

Search for optimal puncturing patterns for extended turbo DPSK. Search for a better modulation structure for turbo codes with a

convergence region comparable or even better than that of BPSK modulated turbo codes.

Further develop analytical tools that leverage the concepts of Gaussian density evolution and convergence boxes of extended turbo DPSK in the error-cliff region.