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.