NEAR ML DETECTION OF NONLINEARLY DISTORTED OFDM SIGNALS

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NEAR ML DETECTION OF NONLINEARLY DISTORTED OFDM
SIGNALS
Dimitris S. Papailiopoulos and George N.
Karystinos Department of Electronic and Computer
Engineering Technical University of
Crete Kounoupidiana, Chania, 73100,
Greece papailiopoulos karystinos_at_telecom.tuc.
gr
Technical University of Crete

Dimitris S. Papailiopoulos and George N.
Karystinos
2
OVERVIEW

• OFDM signals.
• Nonlinear power amplifiers (PAs).
• Peak to average power ratio (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

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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.

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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.

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DETECTION (cntd)
Reciever model
N-point FFT
remove CP
One-shot detection
Channel estimation
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DETECTION (cntd)

• However
• PA is not linear Detection 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 (max iterations OR convergence)
• 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
N-point IFFT
remove CP
One-shot detection
Channel estimation
Hamming-distance-1 set
ML metric
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ITERATIVE NEAR ML DETECTION (cntd)

• N 12, L 8, M 2 (BPSK)
• Observe proposed attains ML performance in 1
  iteration!

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ITERATIVE NEAR ML DETECTION (cntd)

• N 64, L 17, M 4 (QPSK), clip level 0 dB
• Observe Clipping DOES NOT work, dont employ it!

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ITERATIVE NEAR ML DETECTION (cntd)

• N 64, L 17, M 4 (QPSK), clip level 0 dB
• PA operates in saturation, proposed outperforms
  all else!

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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!

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ITERATIVE NEAR ML DETECTION (cntd)

• N 16, L 17, M 64 (64-QAM)
• Even for greater constellation orders the
  proposed excels!

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ITERATIVE NEAR ML DETECTION (cntd)

• N 64, L 17, M 4 (QPSK)
• Even with channel estimation proposed receiver
  works great!

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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.