Title: NEAR ML DETECTION OF NONLINEARLY DISTORTED OFDM SIGNALS
1NEAR 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
2OVERVIEW
- 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
3SYSTEM 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
4SYSTEM 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
5SYSTEM 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
6SYSTEM MODEL (cntd)
- exhibits Gaussian-like behavior high
PAPR - example
- M 4.
Technical University of Crete
Dimitris S. Papailiopoulos and George N.
Karystinos
7SYSTEM 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
8SYSTEM MODEL (cntd)
- SSPA conversion characteristics
-
9SYSTEM MODEL (cntd)
Transmitter model
N-point IFFT
CP
Technical University of Crete
Dimitris S. Papailiopoulos and George N.
Karystinos
10DETECTION
- 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
11DETECTION (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
12DETECTION (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.
13DETECTION (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
14DETECTION (cntd)
- Channel coefficients unknown to the receiver
(cntd) - Symbol-by-symbol one-shot detection
- .
- Minimum Euclidean distance to the
M-point constellation. -
15DETECTION (cntd)
Reciever model
N-point FFT
remove CP
One-shot detection
Channel estimation
16DETECTION (cntd)
- However
- PA is not linear Detection is not
ML - Performance Loss!
Technical University of Crete
Dimitris S. Papailiopoulos and George N.
Karystinos
17ML 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
18ITERATIVE 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
19ITERATIVE 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
20ITERATIVE NEAR ML DETECTION (cntd)
Iterative Detection model
N-point IFFT
remove CP
One-shot detection
Channel estimation
Hamming-distance-1 set
ML metric
21ITERATIVE NEAR ML DETECTION (cntd)
- N 12, L 8, M 2 (BPSK)
- Observe proposed attains ML performance in 1
iteration!
22ITERATIVE NEAR ML DETECTION (cntd)
- N 64, L 17, M 4 (QPSK), clip level 0 dB
- Observe Clipping DOES NOT work, dont employ it!
23ITERATIVE NEAR ML DETECTION (cntd)
- N 64, L 17, M 4 (QPSK), clip level 0 dB
- PA operates in saturation, proposed outperforms
all else!
24ITERATIVE NEAR ML DETECTION (cntd)
- N 64, L 17, M 4 (QPSK), clip level 0 dB
- PA operates in linear range, proposed outperforms
all else!
25ITERATIVE NEAR ML DETECTION (cntd)
- N 16, L 17, M 64 (64-QAM)
- Even for greater constellation orders the
proposed excels!
26ITERATIVE NEAR ML DETECTION (cntd)
- N 64, L 17, M 4 (QPSK)
- Even with channel estimation proposed receiver
works great!
27CONCLUSION
- 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.