Evaluation of performance improvement capabilities of PAPR-reducing methods

1
Evaluation of performance improvement
capabilities of PAPR-reducing methods

• Marc Deumal, Ali Behravan, Thomas Eriksson and
  Joan Lluís Pijoan
• Department of Communications and Signal Theory
• La Salle School of Engineering, Ramon Llull
  University, Barcelona, Spain
• Qamcom Technology, Göteborg, Sweden
• Department of Signals and Systems,
• Chalmers University of Technology, Göteborg,
  Sweden

2
Outline

• Introduction
• Theoretical analysis
• OFDM system performance in NL environments
• Peak-to-average power ratio
• Considerations on PAPR-reduction
• Performance of the PAPR-reduced signals
• Conclusions

3
Introduction

• OFDM is a powerful modulation technique being
  used in many new and emerging broadband
  communication systems.
• Advantages
• Robustness against frequency selective fading and
  time dispersion.
• Transmission rates close to capacity can be
  achieved.
• Low computational complexity implementation
  (FFT).
• Drawbacks
• Sensitivity to frequency offset.
• Sensitivity to nonlinear amplification.
• Compensation techniques for nonlinear effects
• Linearization (digital predistortion).
• Peak-to-average power ratio (PAPR) reduction.
• Post-processing.

4
Introduction

• PAPR-reduction techniques
• Varying PAPR-reduction capabilities, power,
  bandwidth and complexity requirements.
• The performance of a system employing these
  techniques has not been fully analyzed
• PAPR is a very well known measure of the envelope
  fluctuations of a MC signal
• Used as figure of merit.
• The problem of reducing the envelope fluctuations
  has turned to reducing PAPR.
• In this paper we ...
• present a quantitative study of PAPR and NL
  distortion
• simulate an OFDM-system employing some of these
  techniques
• Motivation evaluate the performance improvement
  capabilities of PAPR-reducing methods.

5
Theoretical analysis of PAPR and system
performance
Orthogonal Frequency Division Multiplexing

• An OFDM signal can be expressed as

If the OFDM signal is sampled at , the
complex samples can be described as
6
Theoretical analysis of PAPR and system
performance
Peak-to-average power ratio

• Let be the m-th OFDM symbol, then its PAPR
  is defined as

The CCDF of the PAPR of a non-oversampled OFDM
signal is

• CCDF of PAPR increases with the number of
  subcarriers in the OFDM system.
• It is widely believed that the more subcarriers
  are used in a OFDM system, the worse the
  distortion caused by the nonlinearity will be.

7
Theoretical analysis of PAPR and system
performance
In-band and out-of-band distortion

• If N is large enough, the OFDM signal can be
  approximated as a complex Gaussian distributed
  random variable. Thus its envelope is Rayleigh
  distributed

where the variance of the real and imaginary
parts of the signal is

• Bussgang theorem

NL
In particular if ,then
An interesting result is that the output of a NL
with Gaussian input (OFDM) can be written as
8
Theoretical analysis of PAPR and system
performance
In-band and out-of-band distortion (cont.)
attenuation and rotation compensated at the rx.
distortion in the frequency domain
with
introduces an in-band noise that increases the
error probability

• Both the distortion term and a are independent of
  N.
• The envelope of the OFDM signal is also
  independent of N.

is the out-of-band radiation
9
Considerations on PAPR reduction

• In order to improve the system performance, PAPR
  should predict the amount of distortion
  introduced by the nonlinearity
• PAPR increases with the number of subcarriers in
  the OFDM signal.
• The distortion term and the uniform attenuation
  and rotation of the constellation only depend on
  the back-off.
• The effect of a nonlinearity to an OFDM signal
  is not clearly related to its PAPR
• The effective energy per bit at the input of the
  nonlinearity is

• where Eo is the average energy of the signal at
  the input of the nonlinearity, K is the
• number of bits per symbol and ?p is the power
  efficiency.
• There will only be a a BER performance
  improvement when the effect of reducing the
  in-band distortion becomes noticeable and more
  important than the loss of power efficiency.
• This is not taken into account in the majority of
  the PAPR reducing methods.

10
Performance of the PAPR-reduced signals
Active Constellation Extension (ACE)

• In ACE, at each OFDM block, some of the outer
  signal constellation points are extended towards
  outside of the constellation such that the PAPR
  of the resulting block is reduced

• Advantages

• It is transparent to receiver.
• There is no loss of data rate.
• No side information is required.

• Drawbacks

• The increase in the average energy per bit might
  be higher than the NL distortion reduction.
• The larger the constellation size is the lower
  the number of extensible points will be.

11
Performance of the PAPR-reduced signals
Active Constellation Extension (ACE)
Bit Error Rate
Power Spectral Density
PSD rectangular window
12
Performance of the PAPR-reduced signals
Tone Reservation (TR)

• TR consists on reducing the PAPR by reserving a
  few tones (PRT) within the transmitted bandwidth
  and assign them the appropriate values

• Advantages

• No distortion is introduced to the data bearing
  tones
• No side information is required.

• Drawbacks

• Increase in the average energy per bit which
  might reduce the BER performance improvement.
• Loss of spectral efficiency due to tone
  reservation

13
Performance of the PAPR-reduced signals
Tone Reservation (TR)
Bit Error Rate
Power Spectral Density
4.3 of the subcarriers are reserved for
PAPR-reduction
14
Performance of the PAPR-reduced signals
Selected Mapping (SLM)

• In SLM, from the original data block several
  candidate data blocks are generated and the one
  with lowest PAPR is transmitted.
• At the receiver the reverse operation is
  performed to recover the original data block.

• Advantage No distortion is introduced

• Drawback It requires transmitting
  bits of side information per OFDM symbol
• It is crucial that the side information is
  received without errors.
• The side information has to be heavily
  protected.

• SLM has a complexity of U IFFT operations and U
  complex vector multiplications.
• The amount of PAPR reduction depends on U and
  the design of the phase sequences.

15
Performance of the PAPR-reduced signals
Selected Mapping (SLM)
Bit Error Rate
Power Spectral Density
U8 phase sequences are used
16
Performance of the PAPR-reduced signals
Partial Transmit Sequences (PTS)

• The original data block is partitioned into V
  disjoint subblocks. The subcarriers in each
  subblock are rotated by the same phase factor
  such the PAPR of the combination is minimized.
• At the receiver the reverse operation is
  performed to recover the original data block.

• Advantage No distortion is introduced

• Drawback It requires transmitting
  bits of side information per OFDM symbol.
• It is crucial that the side information is
  received without errors.
• The side information has to be heavily
  protected.

• PTS has a complexity of V IFFT operations,
  complex vector multiplications and
  complex vector sums.
• The amount of PAPR reduction depends on V, W and
  the subblock partitioning.

17
Performance of the PAPR-reduced signals
Partial Transmit Sequences (PTS)
Bit Error Rate
Power Spectral Density
V3 subblocks and W4 phase factors are used
18
Conclusions

• In this paper we presented a quantitative study
  of both the PAPR and the performance of an OFDM
  system when a NL is present.
• PAPR-reduction is meant to decrease the
  distortion introduced by the NL.
• We showed that the effect of a NL on an OFDM
  signal is not clearly related to its PAPR.
• In some recent contributions other measures of
  the envelope fluctuations have been proposed.
• The cubic metric Motorola,TechReport,2005
  relies on the fact that major distortion is
  caused by the third order intermodulation
  product.
• The variance of the instantaneous power
  Behravan,VTC,2006 directly reduces the envelope
  fluctuations
• We also compared the BER performance and the PSD
  of a conventional OFDM with that of a
  PAPR-reduced OFDM system.
• Spectral spreading is reduced when applying
  PAPR-reduction.
• BER performance improvement only occurs when the
  effect of reducing the in-band distortion is more
  important than the loss of power efficiency.

19

• Thank you!

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Thank you!
21
High power amplifiers

• Baseband model

HPA

• Operating point

• Input back-off

• Output back-off

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High power amplifiers

• We assume that predistortion is done at the
  transmitter side
• The idea of predistortion is to modify the input
  signal of the HPA so that the output is as close
  as possible to the linearly amplified input signal

PD
HPA

• The AM/AM and AM/PM characteristics of the PD
  satisfy

• After combining the PD and the NL we obtain a SL