1. Towards the Capacity of Noncoherent Orthogonal Modulation: BICM-ID for Turbo Coded NFSK
Matthew Valenti
West Virginia University
Ewald Hueffmeier and Bob Bogusch
Mission Research Corporation (Monterey)
John Fryer
Applied Data Trends (Huntsville)
11/1/2004

2. Motivation Objective: M-ary Noncoherent FSK Questions:
The objective is to design a link for communicating over a noncoherent fading 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?
11/1/2004

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. 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)

5. Bit Interleaved Coded Modulation
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
The combination of binary encoding, bitwise interleaving, and M-ary modulation
actually yields better performance in fading than symbolwise interleaving and
trellis-coded modulation (Caire 1998).

6. 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:
11/1/2004

7. Turbo Coded Binary NFSK10 -1 10
Performance using
Rate 1/3
UMTS Turbo Code
Full Length: 5114 data bits
16 iterations log-MAP
Capacity limit
is 7.55 dB -2 10 -3 10
BER -4 10 -5 10
0.8 dB from capacity at BER 10-5 -6 10 -7 10 7
7.2
7.4
7.6
7.8 8
8.2
8.4
Eb/No in dB

8. Turbo Coded 16-ary NFSK 10 10 10 10 BER 10 10 10 10 3 3.5 4 4.5 5 5.510 -1 10
Capacity limit
is 2.9 dB -2 10 -3 10
BER -4 10 -5 10
2.2 dB from capacity at BER 10-5 -6 10 -7 10 3
3.5 4
4.5 5
5.5 6
6.5 7
Eb/No in dB

9. BICM-ID: Bit Interleaved Coded Modulation 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
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

10. 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:
11/1/2004

11. 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]
11/1/2004

12. Simplified Expression
The LLR can also be expressed as:
Where:
11/1/2004

13. BER of Noncoherent 16-FSK in Fading with UMTS Turbo Code10
BICM
# iterations = {1, 2, 3, 4, 5, 10, 16}
BICM-ID -1 10
Performance using
Rate 1/3
UMTS Turbo Code
Full Length: 5114 data bits
16 iterations log-MAP -2 10
BER -3 10
capacity = 2.9 dB -4 10
1.5 dB from capacity at BER 10-5 -5 10 3
3.5 4
4.5 5
5.5 6
6.5 7
Eb/No (dB)

14. BICM vs. BICM-ID for NFSK
Performance using
cdma200 Turbo Code
Rates 1/5, 1/4, 1/3, 1/2
6138 data bits
16 iterations log-MAP
Target BER = 10-5

15. Conclusions
Feeding back from decoder to demod can improve the performance of noncoherent M-FSK.
For M=16 and r=⅓ coding, the improvement is 0.7 dB in Rayleigh flat fading.
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
11/1/2004

16. Ongoing and Future Work
Try to close gap further
Optimize interleaver design.
Consider symbol-interleaving and nonbinary codes.
Analysis
EXIT charts to predict waterfall.
Simulation over variety of conditions and parameters:
Constellation size M, rate, code length, channels.
Consider lack of amplitude estimates.
Demodulator with no CSI
Methods to estimate channel
Other applications
Performance in FH systems with partial band jamming.
11/1/2004

17. 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)