Turbo-NFSK: Iterative Estimation, Noncoherent Demodulation, and Decoding for Fast Fading Channels

1
Turbo-NFSK Iterative Estimation, Noncoherent
Demodulation,and Decoding for Fast Fading
Channels

• Shi Cheng and Matthew C. Valenti
• West Virginia University
• Don Torrieri
• U.S. Army Research Laboratory
• This work sponsored by the Xenotran Corporation,
  Glen Burnie, MD

2
Outline

• Iterative M-ary NFSK demodulation and decoding
• ML estimator using EM algorithm
• Performance of iterative estimation, NFSK
  demodulation and decoding
• Methods to reduce the complexity of the estimator
• Conclusions

3
BICM-ID Bit Interleaved CodedModulation with
Iterative Decoding
Binary to M-ary mapping
Binary Encoder
Bitwise Interleaver
M-ary- modulator
Complex flat-fading
AWGN
Soft-In Binary Decoder
LLR Bit Metric Calculation
Receiver front end
Bitwise Deinterleaver
Bitwise Interleaver
Soft-Output Estimates of Coded Bits
4
Noncoherent M-FSKUsing A Priori Probabilities

• Bit LLRs are calculated based on the channel
  observation and the extrinsic information
  feedback from the decoder
• Where

5
BICM ID and CM Capacity
BICM ID Performance using CDMA2000 length 6138
codeword 20 iterations, BER 10-4
Reference M.C.Valenti and S. Cheng, Iterative
demodulation and decoding of turbo coded M-ary
noncoherent orthogonal modulation IEEE Journal
on Selected Areas in Communications, Sept. 2005.
Minimum Eb/No (in dB)
Code Rate R
6
Block Fading Channel

• Fading coefficient is fixed within one block.
• Independent fading from block to block

2
192
3
1
...
0
767
4
8
N
4
1
2
96
...
0
767
8
N
8
CDMA 2000 turbo codeword rate ½ length 1530 with
16-NFSK
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Estimation of One Block

• Channel state information is needed to calculate
  bit LLRs
• Perform estimation of A and B independently block
  by block, where

Soft-In Binary Decoder
LLR Bit Metric Calculation
Bitwise Deinterleaver
Channel Estimator
Bitwise Interleaver
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Channel Estimator with Known Transmitted Sequence

• Form the log-likelihood function based on the
  known sequence d d0,d1,,dN-1 of
• Solving A and B to maximize L
• Where

9
ML Estimator with A Priori Information of the
Sequence

• The sequence d is never known.
• Form log-likelihood function based on the a
  priori information of d
• Too complex to find the solution to maximize this
  function. We resort to EM algorithm.

10
ML Estimator using EM Algorithm

• 0. Select
• 1.
• 2.
• 3.

Normalization factor
Outer Iteration
Inner Iteration
11
BER of 16-ary NFSK in Rayleigh Fading Channel
with Different Block Size
0
10
N32
CDMA2000 Turbo Code, Rate ½, Length
1530 Independent Block Fading Iteration 20
N16
N8
-1
N4
10
N1
-2
10
BER
-3
10
Estimator
-4
Perfect CSI
10
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
Eb/No (dB)
12
BER of NFSK in Rayleigh Fading Channel with
Different Alphabet Size
0
10
CDMA2000 Turbo Code, Rate ½, Length 1530 Data
Rate 24bits/ block
M2
M4
M16
Iteration 20
-1
M64
10
Estimator
-2
10
BER
Perfect CSI
-3
10
-4
10
4
5
6
7
8
9
10
11
12
Eb/No (dB)
13
BER of 16-ary NFSK in Rician Fading Channel
(K10dB)
Estimator
BER
Perfect CSI
CDMA2000 Turbo Code, Rate ½, Length
1530 Independent Block Fading
Iteration 20
Eb/No (dB)
14
Methods to Reduce the Complexity of the Estimator

• 0. Select
• 1.
• 2.
• 3.

Making hard decision
Outer Iteration
Normalization factor
Inner Iteration
Linear approximation of F
15
Methods to Reduce the Complexity of the Estimator

• 0. Select
• 1.
• 2.
• 3.

Making hard decision
Outer Iteration
Linear approximation of F
16
Linear Approximation of F
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Complexity of Different Estimators
7
x 10
3
EM estimator
2.5
CPU Cycles/BICMID iteration
16-ary NFSK, CDMA2000 turbo codeword with rate ½
and length 1530. N4 symbols per block
independent Rayleigh fading

2
Decoder
1.5
Hard Linear EM
Demodulator
1
Linear EM
0.5
0
5.6
5.8
6
6.2
6.4
6.6
6.8
7
Eb/No (dB)
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BER Performance of Low Complexity Estimators
16-ary NFSK, CDMA2000 turbo codeword with rate ½
and length 1530. N4 symbols per block,
independent Rayleigh fading, iteration 20
BER
Eb/No (dB)
19
Conclusions

• Robust noncoherent channel estimator, dealing
  with severe channel conditions.
• The estimator works without needing to know the
  fading statistics model. The only requirement is
  the coherence time of the fading amplitude is
  larger than 4 symbols.
• Although the estimator using the exact EM
  algorithm is complex, linear approximation of
  F(x) I1(x)/I0(x) and hard decision of can
  be used to reduce the comlexity.
• For 16-NFSK, when fading block size is larger
  than 4 symbols per block, the system has
  acceptable BER performance.
• When there are 4 symbols per block, the BER of
  the iterative estimation, demodulation and
  decoding is about 0.60.8dB away from the one
  with perfect CSI.