n ear ml d etection of n onlinearly d istorted ofdm s ignals

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.


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.


SYSTEM MODEL (cntd)

• Consider data vector

.• All elements selected from M-point constellation

• .• IDFT of data vector

where


SYSTEM MODEL (cntd)

• Time-domain OFDM symbol

,

with and .

• How to avoid ISI ? Cyclic prefix.


SYSTEM MODEL (cntd)

• exhibits Gaussian-like behavior high PAPR

example

M = 4.


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


DETECTION

• Baseband equivalent received signal

: zero-mean complex Gaussian channel vector.

: additive white complex Gaussian (AWGN) vector.

: convolution between two vectors.


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 .


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.


DETECTION (cntd)

Channel coefficients unknown to the receiver (cntd)• Symbol-by-symbol one-shot detection

.

: Minimum Euclidean distance to the M-point constellation.


DETECTION (cntd)


N-point FFTremove CP

Reciever model

Channel estimation

One-shot detection

DETECTION (cntd)

However

PA is not linear Detection is not ML

Performance Loss!


ML DETECTION

• We take into account the PA transfer function . • ML detection rule:

Complexity !!!

Impractical even for small M and N.


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.


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




N-point IFFTremove CP

Iterative Detection model

Channel estimation

One-shot detection

Hamming-distance-1

setML metric



N = 12, L = 8, M = 2 (BPSK)

Observe: proposed attains ML performance in 1 iteration!



N = 64, L = 17, M = 4 (QPSK), clip level = 0 dB

Observe: Clipping DOES NOT work, don’t employ it!




PA operates in saturation, proposed outperforms all else!




PA operates in linear range, proposed outperforms all else!



N = 16, L = 17, M = 64 (64-QAM)

Even for greater constellation orders the proposed excels!



N = 64, L = 17, M = 4 (QPSK)

Even with channel estimation proposed receiver works great!

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.

n ear ml d etection of n onlinearly d istorted ofdm s ignals

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