1. The document analyzes the effect of signal distortion techniques for PAPR reduction like clipping and peak windowing on the bit error rate (BER) performance of turbo and low density parity check (LDPC) coded orthogonal frequency division multiplexing (OFDM) systems. 2. It implements an OFDM system based on IEEE 802.11a standards with turbo and LDPC error correcting codes over additive white Gaussian noise (AWGN) and exponentially decaying Rayleigh fade channels. 3. The results show that LDPC-COFDM performs better than turbo-COFDM in both channels, even with clipping applied. However, turbo-COFDM is better with peak windowing due to

1. The Effect of Signal Distortion
Techniques for PAPR Reduction on
the BER Performance of Turbo and
LDPC Coded OFDM System

2. a) OFDM System
i. System Parameters
ii. System Model Implementation
iii. System Model Assumptions
b) Channel
i. Additive White Gaussian Noise (AWGN) Channel
ii. Exponentially Decaying Rayleigh Fade Channel
c) Orthogonal Frequency Division Multiplexing (OFDM)
d) Peak-to-Average Power Ratio (PAPR)
e) PAPR Problem

3. f) PAPR Solutions for OFDM (Signal Distortion Techniques)
i. Clipping
ii. Peak Windowing
g) Error Correcting Code
i. Turbo Code Encoding & Decoding
ii. Low Density Parity Check (LDPC) Code Encoding &
Decoding
h) Results and Analysis
i) Summary/Conclusion

4. System Parameters (Based from IEEE 802.11a)
System bandwidth: 20MHz
Number of subcarriers: 64
Subcarrier Modulation: Quadrature Phase Shift Keying
(QPSK)
OFDM symbol length/duration: 4μs
IFFT length/duration: 3.2μs
Guard interval: 800ns

5. System Parameters (Based from IEEE 802.11a)
Coding scheme: Turbo & LDPC
Code rate: ½
Signal distortion technique: Clipping & Peak windowing
Window (Peak windowing): Hamming
Maximum amplitude: 8 square root of number of subcarriers
Channel Model: AWGN channel & Exponentially Decaying
Rayleigh Fade model

6. System Model Implementation

7. Assumptions:
In computer simulation:
a) Ideal synchronization in time and frequency
b) Channel is static during the transmission of the
OFDM signal
c) The Eb/No of an AWGN channel is varied by
increasing the signal power making the noise
power constant

8. d) A training sequence is used to identify the state of the
exponentially decaying Rayleigh fade channel
e) The training sequence is equal to one OFDM symbol in
duration
f) The amplitudes of the training sequence are less than or
equal to the maximum clipping amplitude by peak
windowing
g) The training sequence is used to update the coefficient
of the one tap equalizer for each subcarriers.

9. Additive White Gaussian Noise (AWGN)
In this study, the proposed channel model is an AWGN channel
with a mean of zero and a variance of 1.
Exponentially decaying Rayleigh fade channel
Based from the IEEE 802.11-98/156r2 by Chayat Naftali
This channel model has a simple
mathematical description of
multipath and phase change and
its ease of varying the rms delay
spread of the channel. The impulse
response is defined as,

11. 1. Orthogonal Frequency Division Multiplexing
(OFDM)
A multicarrier system that
subdivides the frequency band
into a number of Subchannels
that are arranged orthogonally.

12. a) Peak-to-Average Power Ratio (PAPR)
PAPR equation is defined as.

13. b) PAPR Problem
The major problem with multicarrier modulation is the
relatively high PAPR that is inherent in the transmitted signal.

14. b) PAPR Problem
OFDM Time Domain Signal Illustrating Large Peak Excursions

15. c) PAPR Solutions for OFDM
i. Signal Distortion Techniques: Clipping & Peak
Windowing
Clipping and Peak Windowing are the simplest
method that clips the output to a certain level.
These techniques are actually forcing peaks greater
than the clipping amplitude/level (CL) to be at the
level of the clipping amplitude.
The clipping level (CL) for this study must not
exceed to square root of the number of subcarriers
of OFDM system.

16. i. Clipping
Clips the part of the OFDM signal at transmitter
which are outside the allowable limit.
Clipping Method introduces both in-band
distortion and out-of-band distortion into OFDM
signals.
Drawback: Bit Error Rate (BER) performance
degradation.

17. ii. Peak Windowing
Large signal peak is multiplied with a
certain window.
Like clipping, it also introduces both in-
band distortion and out-of-band distortion
into OFDM signals.
To remedy the out-of-band distortion
problem in clipping.

20. d) Coded OFDM (COFDM)
a system in which the error control coding and
OFDM modulation processes work closely
together.
COFDM systems are able to achieve excellent
performance on frequency selective channels
because of the combined benefits of multicarrier
modulation and coding.

21. 2. Error Correcting Codes
techniques that enable reliable delivery of
digital data over unreliable communication
channels.
the error correcting codes used in this study for
simulation are Turbo and Low Density Parity
Check (LDPC) Code.

22. 2. Error Correcting Code
The likelihood used for M-PSK implemented for the
two codes is expressed in,

23. 2. Error Correcting Code
This study uses Q-PSK and the resulting likelihood is,

24. a) Turbo Code Encoding
The turbo code encoder used in the simulation has a
code generator of (7,5) for both recursive systematic
convolutional encoder.
a 552 Interleaver length from which simile odd-even
helical interleaver (23 rows and 24 columns) is used.

25. a) Turbo Code Encoder

26. a) Turbo Code Decoder
Uses a decoding Algorithm (BCJR Algorithm - Bahl,
Cocke, Jelinek and Raviv) employing max-log map.

27. b) LDPC Code Encoder & Decoder
For the encoding, parity check matrix is used.
A 1104, 522 code with a characteristic of an irregular
LDPC Code.
Uses a decoding algorithm that is based from belief
propagation.
The produced parity check matrix H=[A:B] was
rearranged so that A is non-singular.

33. LDPC-COFDM is better than T-COFDM in an
exponentially decaying Rayleigh fade channel and AWGN
channel. This is also true even with the application of
clipping. The system that performs well in a multipath
channel with the application of peak windowing is the T-
COFDM. T-COFDM performs well in peak windowing
because it only suffers a minimal loss.

34. Among the signal distortion techniques, clipping gives less
performance degradation or peak windowing gives higher
performance degradation to COFDM system.
With the application of peak windowing, the LDPC-
COFDM suffers greater loss than T-COFDM. A 2.8dB loss
is experienced by the LDPC-COFDM whereas only 0.9dB
loss for the T-COFDM.

35. Signal Distortion Techniques
results to an in-band and out-
of-band distortion which is an
additional impairment.