1. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 1 PAPR Reduction of OFDM by Unitary Transformations Je Woo Kim TeleCIS Wireless, Inc. jewkim@telecis.com

2. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 2 Contents Background for PAPR Reduction in OFDM Delta Frequency Autocorrelation OFDM (DFA- OFDM) by Unitary Transformation Simulation Conclusion References

3. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 3 Background for PAPR Reduction in OFDM PAPR is one of the major issues for OFDM systems Most of PAPR reduction schemes require side information or suffer from performance degradation : e.g., PTS, SLM, Clipping, etc. PAPR in OFDM can be better than or equal to that of Single-Carrier Modulation without BER performance loss ?

4. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 4 DFA-OFDM by Unitary Transformation PAPR Reduction –Minimize the power variation of unfiltered time domain signals –Minimize the PAPR after LPF Minimum power variation in time domain signals –Constant power in time domain; this means “delta autocorrelation” in frequency domain (DFA) by Wiener-Khinchine Theorem Minimum PAPR after LPF –Avoid zero crossing as possible with constellation rotation –Results in better than or at least equal to Single-carrier in PAPR

5. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 5 DFA-OFDM by Unitary Transformation System Block Diagram Figure 1. DFA OFDM block diagram S/P d(j) DFA Trans U(i,j) a IFFT P/S GI b c c GR r(t) Inv. DFA Trans U(i,j) a FFT S/P P/S d(j) H

6. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 6 Assumptions – M-point IFFT/FFT –TX signal : d(j) (j=0,1,2,…) –input vector : Unitary matrix U Transformed output b is given by DFA-OFDM by Unitary Transformation

7. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 7 permutation matrix i times permutation of U Transformed signal with U(i) : DFA-OFDM by Unitary Transformation

8. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 8 The autocorrelation of b is given as If there is a U that results in the delta autocorrelation of b (i.e., ), the time domain signal can be made constant in power : This U is a DFA transformation For BPSK/QPSK modulation (where is one of the ), the sufficient condition for is and For QAM, it is difficult to have DFA transforms, but similar concept can be applied DFA-OFDM by Unitary Transformation

9. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 9 Typical U matrix for DFA transform Similar Vandermonde matrix is used in [7] using carrier interferometry with DFA-OFDM by Unitary Transformation

10. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 10 Further PAPR Reduction by Constellation Rotation –With the U matrix (DFA-OFDM), we can make the time domain power constant before LPF, but it may still have high PAPR after LPF. –Find the U(i,j) matrix by constellation rotation that results in minimum PAPR after LPF –This U(i,j) matrix can be found by row and/or column permutation of the given U matrix DFA-OFDM by Unitary Transformation

11. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 11 Simulation Environment Initial U matrix [7] and P(i) matrix U(i,j)=P(i)UP(j) : DFA Transformation with Constellation Rotation

12. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 12 Simulation Environment & Results M=64 BPSK/QPSK/16QAM/64QAM 2,000 OFDM symbols for each modulation 39 tap FIR filter Time domain waveforms PAPR BER performance at multi-path fading channel (RMS delay spread = 50ns, 802.11g model)

13. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 13 Simulation results (a) OFDM waveforms(b) DFA-OFDM(i=j=0) waveforms Figure 2. Time domain waveforms (QPSK)

14. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 14 Simulation results (a) PAPR of QPSK DFA-OFDM (i=0,j=0) (b) PAPR of 16QAM DFA-OFDM (i=0,j=0) Figure 3. PAPR changes before/after LPF

15. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 15 Simulation results Figure 4. PAPR properties (a) BPSK modulation(c) QPSK modulation

16. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 16 Simulation results Figure 4. PAPR properties (cont’d) (c) 16-QAM modulation(d) 64-QAM modulation

17. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 17 Simulation results Figure 5. BER characteristics (multi-path channel: rms delay spread = 50 ns)

18. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 18 Conclusions DFA transformation -> constant time domain power for BPSK/QPSK modulations Constellation Rotation -> Further reduce the PAPR after LPF This concept can be extended to QAM modulation PAPR in OFDM can be better than that of Single- Carrier Modulation without BER performance loss : –3dB better at BPSK –0.5dB better at QPSK, 16QAM and 64QAM

19. doc.: IEEE 802.11-670r0 Submission November 2002 Je Woo Kim, TeleCIS WirelessSlide 19 References 1.A. D. S. Jayalah, C. Tellambura and H. Wu, “Reduced complexity PTS and new phase sequences for SLM to reduce PAP of an OFDM signal,” VTC 2000 2.H. Ochiai and H. Imai, “Performance analysis of deliberately clipped OFDM signals”, IEEE Trans. Comm. Vol. 50, No. 1, Jan. 2002 3.S.G. Kang, J.G. Kim and E.K. Joo, “A novel subblock partition scheme for partial transmit sequence OFDM,” IEEE Trans. Broadcasting, Vol. 45, No. 3, September 1999. 4.L.J. Cimini,, Jr. and N.R. Sollenberger, “Peak-to-average power ratio reduction of an OFDM signal using partial transmit sequences,” IEEE Comm. Letter, Vol. 4, No. 3, March 2000. 5.G.R. Hill, M. Faulkner and J. Singh, “Reducing the peak-to-average power ratio in OFDM by cyclically shifting partial transmit sequences,” Electronics Letter, Vol 36, No. 6, March 2000. 6.V. Tarokh and H. Jafarkhani, “On the computation and reduction of the peak-to-average power ratio in multicarrier communications,” IEEE Trans. Comm., Vol.48, No. 1, pp. 37-44, Jan. 2000. 7.D. A. Wiegandt, C. A. Nassar and Z. Wu, “Overcoming peak-to-average power ratio issues in OFDM via carrier-interferometry codes,” IEEE Proc. 2001 8.B. T. Shim, H. J. Lee, J. H. Park, J. W. Kim and K. O. Kim, "On the implementation of spread spectrum MODEM for wireless LAN," Journal of Korean Institute of Communication Sciences (KICS), Jan. 1995. 9.J. H. Woo, J. W. Kim et al., “A Study on the PAR Reduction for CDMA Reverse Link,” KICS, May 1999.