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N EAR ML D ETECTION OF N ONLINEARLY D ISTORTED OFDM S IGNALS

Dimitris S. Papailiopoulos and George N. Karystinos Department of Electronic and Computer Engineering Technical University of Crete Kounoupidiana , Chania , 73100, Greece {papailiopoulos | karystinos }@ telecom.tuc.gr. N EAR ML D ETECTION OF N ONLINEARLY D ISTORTED OFDM S IGNALS.

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N EAR ML D ETECTION OF N ONLINEARLY D ISTORTED OFDM S IGNALS

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  1. DimitrisS. Papailiopoulos and George N. Karystinos Department of Electronic and Computer Engineering Technical University of Crete Kounoupidiana, Chania, 73100, Greece {papailiopoulos|karystinos}@telecom.tuc.gr NEAR ML DETECTIONOF NONLINEARLY DISTORTED OFDM SIGNALS Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  2. OVERVIEW • OFDM signals. • Nonlinear power amplifiers (PAs). • Peak to average powerratio (PAPR) + PA nonlinear distortion. • Iterative receiver. • Near ML performance. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  3. SYSTEM MODEL ASSUMPTIONS • Transmission of uncoded CP-OFDM sequence. • Single-input single-output. • Arbitrary constellation. • Multipath Rayleigh fading channel. NOTATION • N: sequence length. • M: number of constellation points. • G: size of cyclic prefix. • L : length of channel impulse response. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  4. SYSTEM MODEL (cntd) • Consider data vector . • All elements selected from M-point constellation • . • IDFT of data vector where Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  5. SYSTEM MODEL (cntd) • Time-domain OFDM symbol , with and . • How to avoid ISI ?Cyclic prefix. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  6. SYSTEM MODEL (cntd) • exhibits Gaussian-like behavior high PAPR example M = 4. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  7. SYSTEM MODEL (cntd) • Before transmission, the OFDM sequence is amplified by a nonlinear PA: with and . • Families of PAs - Solid State Power Amplifiers (SSPA): WiFi, WiMAX. - Traveling Wave Tube (TWT): satellite transponders. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  8. SYSTEM MODEL (cntd) • SSPA conversion characteristics

  9. SYSTEM MODEL (cntd) Transmitter model N-point IFFT CP Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  10. DETECTION • Baseband equivalent received signal : zero-mean complex Gaussian channel vector. : additive white complex Gaussian (AWGN) vector. : convolution between two vectors. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  11. DETECTION (cntd) • We remove the cyclic prefix and obtain . • Fourier transform of . : N-point DFT of channel impulse response . : element-by-element multiplication. : zero-mean AWGN vector with covariance matrix . Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  12. DETECTION (cntd) Channel coefficients known to the receiver • Symbol-by-symbol one-shot detection . :Minimum Euclidean distance to the M-point constellation. ML only when PA is linear. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  13. DETECTION (cntd) Channel coefficients unknown to the receiver • Transmit Training sequence . • Best linear unbiased estimator (BLUE) of : with . : diagonal matrix whose diagonal is . : amplified training sequence. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  14. DETECTION (cntd) Channel coefficients unknown to the receiver (cntd) • Symbol-by-symbol one-shot detection . :Minimum Euclidean distance to the M-point constellation. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  15. DETECTION (cntd) Reciever model remove CP N-point FFT One-shot detection Channel estimation Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  16. DETECTION (cntd) However PA is not linearDetection is not ML Performance Loss! Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  17. ML DETECTION • We take into account the PA transfer function . • ML detection rule: Complexity !!! Impractical even for small M and N. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  18. ITERATIVE NEAR ML DETECTION We propose to use the ML decision rule on a reduced candidate set. How to build such a set? 1) Perform conventional detection to obtain and use it as a “core” candidate. 2) Find the closest (in Hamming distance) vectors to and evaluate the ML metric for each one of them. 3) Keep the best neighboring vector, call it , and repeat steps 2-3 until convergence. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  19. ITERATIVE NEAR ML DETECTION (cntd) Conventionally detect . repeat Step 1: define consisting of closest vectors to Step 2: find Step 3: set Step 4: go to Step 1 until (maxiterationsORconvergence) denotes hamming distance of two vectors Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  20. ITERATIVE NEAR ML DETECTION (cntd) Iterative Detection model remove CP N-point IFFT One-shot detection Channel estimation Hamming-distance-1 set ML metric Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  21. ITERATIVE NEAR ML DETECTION (cntd) N = 12, L = 8, M = 2 (BPSK) Observe: proposed attains ML performance in 1 iteration! Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  22. ITERATIVE NEAR ML DETECTION (cntd) N = 64, L = 17, M = 4 (QPSK), clip level = 0 dB Observe: Clipping DOES NOT work, don’t employ it! Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  23. ITERATIVE NEAR ML DETECTION (cntd) N = 64, L = 17, M = 4 (QPSK), clip level = 0 dB PA operates in saturation, proposed outperforms all else! Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  24. ITERATIVE NEAR ML DETECTION (cntd) N = 64, L = 17, M = 4 (QPSK), clip level = 0 dB PA operates in linear range, proposed outperforms all else! Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  25. ITERATIVE NEAR ML DETECTION (cntd) N = 16, L = 17, M = 64 (64-QAM) Even for greater constellation orders the proposed excels! Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  26. ITERATIVE NEAR ML DETECTION (cntd) N = 64, L = 17, M = 4 (QPSK) Even with channel estimation proposed receiver works great! Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

  27. CONCLUSION • Near ML receiver for nonlinearly distorted OFDM signals. • Efficient, bilinear complexity. • Truly near ML, since it exhibits ML behavior! • Much better than conventional. • Works great with channel estimation. Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos

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