PAPR Reduction of OFDM by Unitary Transformations

1
PAPR Reduction of OFDM by Unitary
Transformations

• Je Woo Kim
• TeleCIS Wireless, Inc.
• jewkim_at_telecis.com

2
Contents

• Background for PAPR Reduction in OFDM
• Delta Frequency Autocorrelation OFDM (DFA-OFDM)
  by Unitary Transformation
• Simulation
• Conclusion
• References

3
Background for PAPR Reduction in OFDM

• PAPR is one of the major issues for OFDM systems
• Most of PAPR reduction schemes require side
  information or suffer from performance
  degradation e.g., PTS, SLM, Clipping, etc.
• PAPR in OFDM can be better than or equal to that
  of Single-Carrier Modulation without BER
  performance loss ?

4
DFA-OFDM by Unitary Transformation

• PAPR Reduction
• Minimize the power variation of unfiltered time
  domain signals
• Minimize the PAPR after LPF
• Minimum power variation in time domain signals
• Constant power in time domain this means delta
  autocorrelation in frequency domain (DFA) by
  Wiener-Khinchine Theorem
• Minimum PAPR after LPF
• Avoid zero crossing as possible with
  constellation rotation
• Results in better than or at least equal to
  Single-carrier in PAPR

5
DFA-OFDM by Unitary Transformation

• System Block Diagram

Figure 1. DFA OFDM block diagram
6
DFA-OFDM by Unitary Transformation

• Assumptions
• M-point IFFT/FFT
• TX signal d(j) (j0,1,2,)
• input vector
• Unitary matrix U
• Transformed output b is given by

7
DFA-OFDM by Unitary Transformation

• permutation matrix
• i times permutation of U
• Transformed signal with U(i)

8
DFA-OFDM by Unitary Transformation

• The autocorrelation of b is given as
  
• If there is a U that results in the delta
  autocorrelation of b
• (i.e., ), the
  time domain signal can be made constant in power
  This U is a DFA transformation
• For BPSK/QPSK modulation (where is one of
  the ), the sufficient condition
  for is
• and
• For QAM, it is difficult to have DFA transforms,
  but similar concept can be applied

9
DFA-OFDM by Unitary Transformation

• Typical U matrix for DFA transform
• Similar Vandermonde matrix is used in 7 using
  carrier interferometry with

10
DFA-OFDM by Unitary Transformation

• Further PAPR Reduction by Constellation Rotation
• With the U matrix (DFA-OFDM), we can make the
  time domain power constant before LPF, but it may
  still have high PAPR after LPF.
• Find the U(i,j) matrix by constellation rotation
  that results in minimum PAPR after LPF
• This U(i,j) matrix can be found by row and/or
  column permutation of the given U matrix

11
Simulation Environment

• Initial U matrix 7 and P(i) matrix

• U(i,j)P(i)UP(j) DFA Transformation with
  Constellation Rotation

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Simulation Environment Results

• M64
• BPSK/QPSK/16QAM/64QAM
• 2,000 OFDM symbols for each modulation
• 39 tap FIR filter
• Time domain waveforms
• PAPR
• BER performance at multi-path fading channel (RMS
  delay spread 50ns, 802.11g model)

13
Simulation results
(a) OFDM waveforms
(b) DFA-OFDM(ij0) waveforms
Figure 2. Time domain waveforms (QPSK)
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Simulation results
(a) PAPR of QPSK DFA-OFDM (i0,j0)
(b) PAPR of 16QAM DFA-OFDM (i0,j0)
Figure 3. PAPR changes before/after LPF
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Simulation results
(a) BPSK modulation
(c) QPSK modulation
Figure 4. PAPR properties
16
Simulation results
(c) 16-QAM modulation
(d) 64-QAM modulation
Figure 4. PAPR properties (contd)
17
Simulation results
Figure 5. BER characteristics (multi-path
channel rms delay spread 50 ns)
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Conclusions

• DFA transformation -gt constant time domain power
  for BPSK/QPSK modulations
• Constellation Rotation -gt Further reduce the PAPR
  after LPF
• This concept can be extended to QAM modulation
• PAPR in OFDM can be better than that of
  Single-Carrier Modulation without BER performance
  loss
• 3dB better at BPSK
• 0.5dB better at QPSK, 16QAM and 64QAM

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References

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