Coding for Noncoherent M-ary Modulation

1
Coding for Noncoherent M-ary Modulation

• Matthew Valenti
• Shi Cheng
• West Virginia University
• Morgantown, WV
• mvalenti,shic_at_csee.wvu.edu

2
Motivation

• Objective
• The objective is to design methods for
  communicating over a noncoherent (random phase)
  channel at low Eb/No.
• M-ary Noncoherent FSK
• Coherent reception not always possible
• Rapid relative motion between transmitter and
  receiver.
• Phase noise in local oscillators.
• A natural choice is noncoherent FSK.
• M-ary FSK allows bandwidth efficiency to be
  traded for energy efficiency.
• Questions
• What is the information theoretic limit of M-ary
  NFSK?
• How can we approach that limit in practice?

3
Capacity of M-ary NFSK in AWGN
15
Reference W. E. Stark, Capacity and cutoff rate
of noncoherent FSK with nonselective Rician
fading, IEEE Trans. Commun., Nov. 1985.
Noncoherent combining penalty
10
Minimum Eb/No (in dB)
M2
5
M4
M16
M64
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Rate R (symbol per channel use)
4
Bit Interleaved Coded Modulation
Binary to M-ary mapping
Binary Encoder
Bitwise Interleaver
M-ary- modulator
Random Phase
AWGN
Soft-In Binary Decoder
LLR Bit Metric Calculation
Receiver front end
Bitwise Deinterleaver
Caire G. Caire, G. Taricco, E. Biglieri,
Bit-interleaved coded modulation, IEEE Trans.
Inform. Theory, May 1998 1998
5
M-FSK Noncoherent Channel LLR

• To determine the LLR of bit k, 1 ? k ? log2M
• Let Sk(1) be the set of symbol indices for which
  the kth bit is a one, and Sk(0) the set
  of symbols indices for which the kth bit is a
  zero.
• Assume that the bits other than k are equally
  likely to be 0 or 1.
• Then
• For BFSK this becomes

6
Turbo Coded 16-ary NFSK
0
10
Capacity limit is 2.07 dB
-1
iterations 1, 2, 3, 4, 5, 10, 16
10
Performance using Rate 1/2 cdma2000 Turbo
Code 6138 data bits 16 iterations log-MAP
-2
10
BER
-3
10
-4
10
1.75 dB from capacity at BER 10-5
2
2.5
3
3.5
4
4.5
5
Eb/No(in dB)
7
BICM-ID Bit Interleaved CodedModulation with
Iterative Decoding
Binary to M-ary mapping
Binary Encoder
Bitwise Interleaver
M-ary- modulator
Random Phase
AWGN
Soft-In Binary Decoder
LLR Bit Metric Calculation
Receiver front end
Bitwise Deinterleaver
Li and Ritcey indicate a 1 dB gain from hard
decision feedback in Rayleigh fading for 8-PSK
and r2/3 convolutional coding
Bitwise Interleaver
Soft-Output Estimates of Coded Bits
8
Noncoherent M-FSKUsing A Priori Probabilities

• Earlier we assumed that all modulated symbols
  were equally likely and obtained the bit LLR
• However, we can use the bit probabilities derived
  from the decoder to improve the bit LLRs

9
Computing the A Priori Probabilities

• We want to find p(sick) by using the extrinsic
  bit information from the decoder.
• Let pj be the decoders estimate that the
  probability of the jth bit is a one
• Then if si ? b1i b2i bmi

10
Simplified Expression

• The LLR can also be expressed as
• Where

11
16-NFSK BICM vs. BICM-ID
0
10
BICM
BICM ID
iterations 1, 2, 3, 4, 5, 10, 16
-1
10
Performance using Rate 1/2 cdma2000 Turbo
Code 6138 data bits 16 iterations log-MAP
-2
10
BER
-3
10
-4
10
1.1 dB from capacity at BER 10-5
2
2.5
3
3.5
4
4.5
5
Eb/No(in dB)
12
Convergence Analysis BICM
2.5
Rate 1/2 cdma2000 Turbo Code Gaussian
Approximation for Decoder Output Shown Eb/No
3.8 dB Threshold Eb/No 3.69 dB Capacity Eb/No
2.07 dB
2
1.5
SNR out
1
0.5
0
0
0.5
1
1.5
2
2.5
SNR in
13
Convergence Analysis BICM-ID
1.5
Shown Eb/No 3.2 dB Threshold Eb/No 3.03
dB Capacity Eb/No 2.07 dB
1
SNR out
0.5
0
0
0.5
1
1.5
SNR in
14
16-NFSK BICM vs. BICM-ID
0
10
BICM
BICM ID
-1
10
-2
10
BER
-3
10
-4
10
2
2.5
3
3.5
4
4.5
5
Eb/No(in dB)
15
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16
Conclusions

• Feeding back from decoder to demod can improve
  the performance of noncoherent M-FSK.
• For M16 and r1/2 coding, the improvement is
  0.65 dB in AWGN.
• Other possible benefits
• Reduce number of iterations from 16 to 4
• Reduce signal constellation size from 64 to 16
• The additional complexity is negligible
• No extra iterations needed.
• Only need to update demod metrics during each
  iteration
• Need to perform channel interleaving/deinterleavin
  g during each iteration.

17
Ongoing and Future Work

• Try to close gap further
• Optimize interleaver design.
• Consider symbol-interleaving and nonbinary codes.
• More iterations.
• Fading
• With and without amplitude estimates (CSI).
• Ergodic vs. block fading.
• Other applications
• Cooperative diversity systems for sensor
  networks.
• Performance in FH systems with partial band
  jamming.

18
Capacity of M-ary NFSK in Rayleigh Fading
15
Ergodic Capacity (Fully interleaved) Assumes
perfect fading amplitude estimates available to
receiver
10
M2
Minimum Eb/No (in dB)
M4
5
M16
M64
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Rate R (symbol per channel use)
19
BER of Noncoherent 16-FSK in AWGNwith UMTS Turbo
Code
0
10
BICM
iterations 1, 2, 3, 4, 5, 10, 16
BICM-ID
-1
10
-2
10
BER
-3
10
-4
10
capacity 2.3 dB 5114 bit data word
3
3.5
4
4.5
5
5.5
Eb/No (dB)