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Coding for Noncoherent M-ary Modulation

Coding for Noncoherent M-ary Modulation. Matthew Valenti Shi Cheng West Virginia University Morgantown, WV {mvalenti,shic}@csee.wvu.edu. Motivation. Objective: The objective is to design methods for communicating over a noncoherent (random phase) channel at low E b /N o .

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Coding for Noncoherent M-ary Modulation

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  1. Coding for Noncoherent M-ary Modulation Matthew Valenti Shi Cheng West Virginia University Morgantown, WV {mvalenti,shic}@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) 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. 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 r=2/3 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(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]

  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. 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.

  16. 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.

  17. 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)

  18. 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)

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