1. Coding for Noncoherent M-ary Modulation
Matthew Valenti
Shi Cheng
West Virginia University
Morgantown, WV
11/10/2004

2. Motivation Objective: M-ary Noncoherent FSK Questions:
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?
11/10/2004

3. Capacity of M-ary NFSK in AWGN15
Reference: W. E. Stark, “Capacity and cutoff rate of noncoherent FSK
with nonselective Rician fading,” IEEE Trans. Commun., Nov 10
Noncoherent combining penalty
Minimum Eb/No (in dB)
M=2 5
M=4
M=16
M=64
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

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:
11/10/2004

6. Turbo Coded 16-ary NFSK 10 10 10 BER 10 10 2 2.5 3 3.5 4 4.5 510
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 Coded Modulation 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
r=2/3 convolutional coding
Bitwise
Interleaver
Soft-Output Estimates
of Coded Bits

8. Noncoherent M-FSK Using 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:
11/10/2004

9. Computing the A Priori Probabilities
We want to find p(si|ck’) by using the extrinsic bit information from the decoder.
Let pj be the decoder’s estimate that the probability of the jth bit is a one:
Then if si  [b1i b2i … bmi]
11/10/2004

10. Simplified Expression
The LLR can also be expressed as:
Where:
11/10/2004

11. 16-NFSK: BICM vs. BICM-ID 10 BICM BICM ID 10 10 BER 10 10 2 2.5 3 3.510
BICM
BICM ID -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
1.1 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
11/10/2004
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
11/10/2004
0.5 1
1.5
SNR in

14. 16-NFSK: BICM vs. BICM-ID 10 BICM BICM ID 10 10 BER 10 10 2 2.5 3 3.510
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)

16. Conclusions
Feeding back from decoder to demod can improve the performance of noncoherent M-FSK.
For M=16 and r=1/2 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/deinterleaving during each iteration.
11/10/2004

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.
11/10/2004

18. Capacity of M-ary NFSK in Rayleigh Fading15
Ergodic Capacity (Fully interleaved)
Assumes perfect fading amplitude estimates available to receiver 10
M=2
Minimum Eb/No (in dB)
M=4 5
M=16
M=64
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 AWGN with UMTS Turbo Code10
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)