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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
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
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.
3Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
SYSTEM MODEL (cntd)
• Consider data vector
.• All elements selected from M-point constellation
• .• IDFT of data vector
where
4Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
SYSTEM MODEL (cntd)
• Time-domain OFDM symbol
,
with and .
• How to avoid ISI ? Cyclic prefix.
5Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
SYSTEM MODEL (cntd)
• exhibits Gaussian-like behavior high PAPR
example
M = 4.
6Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
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.
7
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
SYSTEM MODEL (cntd)
• SSPA conversion characteristics
8
SYSTEM MODEL (cntd)
9
N-point IFFT CP
Transmitter model
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
DETECTION
• Baseband equivalent received signal
: zero-mean complex Gaussian channel vector.
: additive white complex Gaussian (AWGN) vector.
: convolution between two vectors.
10Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
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 .
11Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
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 12
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.
13Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
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 14
DETECTION (cntd)
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos 15
N-point FFTremove CP
Reciever model
Channel estimation
One-shot detection
DETECTION (cntd)
However
PA is not linear Detection is not ML
Performance Loss!
16Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
ML DETECTION
• We take into account the PA transfer function . • ML detection rule:
Complexity !!!
Impractical even for small M and N.
17Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
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.
18Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
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
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos
ITERATIVE NEAR ML DETECTION (cntd)
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos 20
N-point IFFTremove CP
Iterative Detection model
Channel estimation
One-shot detection
Hamming-distance-1
setML metric
ITERATIVE NEAR ML DETECTION (cntd)
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos 21
N = 12, L = 8, M = 2 (BPSK)
Observe: proposed attains ML performance in 1 iteration!
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!
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!
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!
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!
ITERATIVE NEAR ML DETECTION (cntd)
Technical University of Crete Dimitris S. Papailiopoulos and George N. Karystinos 26
N = 64, L = 17, M = 4 (QPSK)
Even with channel estimation proposed receiver works great!
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.