N EAR ML D ETECTION OF N ONLINEARLY D ISTORTED OFDM S IGNALS
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Transcript of N EAR ML D ETECTION OF N ONLINEARLY D ISTORTED OFDM S IGNALS
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Dimitris S. Papailiopoulos and George N. Karystinos
Department of Electronic and Computer EngineeringTechnical University of Crete
Kounoupidiana, Chania, 73100, Greece
{papailiopoulos | karystinos}@telecom.tuc.gr
NEAR ML DETECTION OF NONLINEARLY DISTORTED
OFDM SIGNALS
1Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
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OVERVIEW
• OFDM signals.
• Nonlinear power amplifiers (PAs).
• Peak to average power ratio (PAPR) + PA nonlinear distortion.
• Iterative receiver.
• Near ML performance.
2Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
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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.
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SYSTEM MODEL (cntd)
• Consider data vector
.• All elements selected from M-point constellation
• .• IDFT of data vector
where
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SYSTEM MODEL (cntd)
• Time-domain OFDM symbol
,
with and .
• How to avoid ISI ? Cyclic prefix.
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SYSTEM MODEL (cntd)
• exhibits Gaussian-like behavior high PAPR
example
M = 4.
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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.
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SYSTEM MODEL (cntd)
• SSPA conversion characteristics
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SYSTEM MODEL (cntd)
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N-point IFFT CP
Transmitter model
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DETECTION
• Baseband equivalent received signal
: zero-mean complex Gaussian channel vector.
: additive white complex Gaussian (AWGN) vector.
: convolution between two vectors.
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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 .
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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.
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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)
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N-point FFTremove CP
Reciever model
Channel estimation
One-shot detection
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DETECTION (cntd)
However
PA is not linear Detection is not ML
Performance Loss!
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ML DETECTION
• We take into account the PA transfer function . • ML detection rule:
Complexity !!!
Impractical even for small M and N.
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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.
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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 vectors19
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ITERATIVE NEAR ML DETECTION (cntd)
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N-point IFFTremove CP
Iterative Detection model
Channel estimation
One-shot detection
Hamming-distance-1
setML metric
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ITERATIVE NEAR ML DETECTION (cntd)
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N = 12, L = 8, M = 2 (BPSK)
Observe: proposed attains ML performance in 1 iteration!
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ITERATIVE NEAR ML DETECTION (cntd)
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos 22
N = 64, L = 17, M = 4 (QPSK), clip level = 0 dB
Observe: Clipping DOES NOT work, don’t employ it!
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ITERATIVE NEAR ML DETECTION (cntd)
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos 23
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)
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos 24
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)
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos 25
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)
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N = 64, L = 17, M = 4 (QPSK)
Even with channel estimation proposed receiver works great!
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CONCLUSION
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos 27
• 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.