Towards the Capacity of Noncoherent Orthogonal Modulation: BICM-ID for Turbo Coded NFSK

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)

2. Motivation • Objective: • 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?

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) M=2 5 M=4 M=16 M=64 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. Capacity of M-ary NFSK in Rayleigh Fading 15 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 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)

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:

7. Turbo Coded Binary NFSK 0 10 -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 0 10 -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 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 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-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:

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]

12. Simplified Expression • The LLR can also be expressed as: • Where:

13. BER of Noncoherent 16-FSK in Fadingwith UMTS Turbo Code 0 10 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

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.

17. 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)