1. PAPR Reduction Methods for Noncoherent OFDM-MFSK 3rd COST 289 Workshop Aveiro, Portugal, July 12-13, 2006 Matthias Wetz, Werner G. Teich, Jürgen Lindner matthias.wetz@uni-ulm.de http://it.e-technik.uni-ulm.de

2. Information Technology University of Ulm 2 Motivation Fast time variant channels for data transmission to and from high speed trains Security relevant data requires robust transmission scheme Combination of OFDM and noncoherently detected MFSK offers high data rate and robustnes A problem of multicarrier transmission is a high PAPR Use the phases to reduce the PAPR Subcarrier phases for noncoherent OFDM-MFSK are arbitrary

3. Information Technology University of Ulm 3 Outline Motivation Basic OFDM Transmission Model A Robust Transmission Scheme - OFDM-MFSK PAPR Reduction Algorithms Influence on the Spectrum of the Transmit Signal Conclusions

4. Information Technology University of Ulm 4 OFDM Transmission Model COD mo d ser par IDFT cyclic ext. ser par iΔtiΔt s(i) x(k) TF s(t) h(t) Channel AWGN RF iΔtiΔt n(t) g(t) DFT rem. cyclic ext. ser par ser par DET Coding Detection (Decoding)

5. Information Technology University of Ulm 5 OFDM-MFSK … OFDM-Subcarriers (Frequency) ΔfΔf 00 01 11 10 OFDM-4FSK: Subcarriers are grouped into groups of four 4FSK modulation over each group One out of four carriers is occupied Gray coding Coherent and noncoherent detection possible + For noncoherent detection no CSI is necessary + Very robust against time variant channels + Subcarrier phases are arbitrary and can be used for PAPR reduction

6. Information Technology University of Ulm 6 Noncoherently detected OFDM-MFSK Subcarrier phases can be chosen arbitrarily so that PAPR is reduced No side information necessary Peak-to-Average Power Ratio Definition PAPR: Unfavourable superposition of subcarriers in OFDM Very high PAPR of time domain signal Problem: Transmit amplifier has saturation limit Nonlinear distortion (Out of Band Radiation) High backoff necessary (amplifier inefficient)

7. Information Technology University of Ulm 7 PAPR Reduction Goal:Find optimum subcarrier phases for each possible OFDM symbol, so that PAPR is minimum Problem:N=256 and OFDM-4FSK possible OFDM symbols, possibilities to assign phase, if two phases for each subcarrier are considered Exhaustive search impossible Worst case: All subcarrier phases are the same Subcarriers add coherently PAPR = N/M = 256/4 = 18 dB

8. Information Technology University of Ulm 8 PAPR Reduction Methods First approach: Random phases Allow only 0 or π Cumulative Distribution Function (CDF)

9. Information Technology University of Ulm 9 Introduced by Bäuml, Fischer and Huber (´96) Assign random subcarrier phases to each symbol several times Transmit OFDM symbol with lowest PAPR When applied to noncoherently detected OFDM-MFSK, no side information is needed Selected Mapping 567891011 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z=PAPR[dB] CDF(z) random continuous phases [0, 2π) random discrete phases 0 or π Selected Mapping best of 2 symbols Selected Mapping best of 4 symbols Selected Mapping best of 10 symbols with discrete random phases (0 or π) is chosen

10. Information Technology University of Ulm 10 Introduced by Ouderaa et al. (´88) Swapping between time and frequency domain Iterative reduction of PAPR Stop when PAPR is not decreasing any more Parameter: time domain clipping level CL Time-Frequency Domain Swapping random starting phases build spectrum with fixed amplitudes and variable IFFT amplitude clipping in time domain FFT determine phases

11. Information Technology University of Ulm 11 Time-Frequency Domain Swapping (cont´d) 345678910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z=PAPR[dB] CDF(z) random phases 0 or π selected mapping best of 10 symbols CL=0.8 CL=0.95 CL=0.9 swapping algorithm time-frequency domain Good performance Very high complexity: up to several hundred iterations per symbol

12. Information Technology University of Ulm 12 Sequential Algorithm random starting phases IFFT PAPR evaluation flip φ n PAPR new < PAPR ? next subcarrier n PAPR=PAPR new accept φ n discard changes IFFT yes no Subcarrier phases are systematically changed to reduce PAPR Subcarrier phases are flipped sequentially One extra IFFT per occupied subcarrier

13. Information Technology University of Ulm 13 Sequential Algorithm (cont´d) 345678910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z=PAPR[dB] CDF(z) swap algorithm CL=0.9 sequential algorithm random phases 0/π selected mapping best of 65 selected mapping best of 10 Better performance than selected mapping Lower complexity than swapping algorithm good trade off complexity / performance

14. Information Technology University of Ulm 14 Complexity Comparison In general, better performance means higher complexity Remaining problem: PAPR reduction has to be done for each symbol Random Phases: PAPR 6-10.5dB Selected Mapping (best of 10 symbols): PAPR 5.8-7.8dB 10 FFTs in total Sequential Algorithm: PAPR 5.1-6.9dB 1 extra FFT per occupied subcarrier 65 FFTs in total Time-Frequency Domain Swapping (CL=0.8): PAPR 3.8-6.5dB About 200 FFTs in total

15. Information Technology University of Ulm 15 Model of a Nonlinear Transmit Amplifier NLZonal Filter s(t)s‘(t)s‘ BP (t) Nonlinearity causes distortion at harmonic bands of carrier frequency Zonal filter limits signal to be a bandpass signal Nonlinearity can be modeled in the lowpass domain

16. Information Technology University of Ulm 16 Model of a Nonlinear Transmit Amplifier Soft limiter in bandpass domain: amplitude saturates Transformation of the characteristics into lowpass domain 00.511.522.53 0 0.5 1 1.5 00.511.522.53 0 0.5 1 1.5 A in A out

17. Information Technology University of Ulm 17 Transmit Spectrum with Nonlinear Distortion -500-400-300-200-1000100200300400500 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 f/ Δf PSD [dBr] 3dB IBO 6dB 9dB random subcarrier phases 0/π Simulation parameters: Raised cosine transmit filter α=0.2 160 used subcarriers Reference point: Interference in next channel after neighbour channel < -70dBr

18. Information Technology University of Ulm 18 Transmit Spectrum with Nonlinear Distortion Further reduction possible with swapping algorithm but improvement is small

19. Information Technology University of Ulm 19 Summary and Conclusions OFDM-MFSK was presented Noncoherent detection possible Robust transmission scheme Subcarrier phases can be used for PAPR reduction PAPR reduction algorithms were analysed Selected Mapping Time-frequency domain swapping Sequential algorithm Influence on the spectrum of the transmit signal Effects of different PAPR reduction methods were compared