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

Outlinea) OFDM System

i. System Parametersii. System Model Implementation iii. System Model Assumptions

b) Channeli. Additive White Gaussian Noise (AWGN) Channelii. Exponentially Decaying Rayleigh Fade Channel

c) Orthogonal Frequency Division Multiplexing (OFDM)d) Peak-to-Average Power Ratio (PAPR) e) PAPR Problem

Outlinef) PAPR Solutions for OFDM (Signal Distortion Techniques)

i. Clippingii. Peak Windowing

g) Error Correcting Codei. Turbo Code Encoding & Decodingii. Low Density Parity Check (LDPC) Code Encoding &

Decodingh) Results and Analysisi) Summary/Conclusion

OFDM SystemSystem Parameters (Based from IEEE 802.11a)

System bandwidth: 20MHzNumber of subcarriers: 64Subcarrier Modulation: Quadrature Phase Shift Keying

(QPSK)OFDM symbol length/duration: 4μsIFFT length/duration: 3.2μs Guard interval: 800ns

System Parameters (Based from IEEE 802.11a)

Coding scheme: Turbo & LDPCCode rate: ½ Signal distortion technique: Clipping & Peak windowingWindow (Peak windowing): HammingMaximum amplitude: 8 square root of number of subcarriersChannel Model: AWGN channel & Exponentially Decaying

Rayleigh Fade model

System Model Implementation

Assumptions:

In computer simulation:a) Ideal synchronization in time and frequencyb) Channel is static during the transmission of the

OFDM signalc) The Eb/No of an AWGN channel is varied by

increasing the signal power making the noise power constant

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.

ChannelAdditive 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 channelBased from the IEEE 802.11-98/156r2 by Chayat NaftaliThis 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,

1. Orthogonal Frequency Division Multiplexing (OFDM)

A multicarrier system that subdivides the frequency band into a number of Subchannels that are arranged orthogonally.

a) Peak-to-Average Power Ratio (PAPR)

PAPR equation is defined as.

b) PAPR Problem

The major problem with multicarrier modulation is the relatively high PAPR that is inherent in the transmitted signal.

b) PAPR Problem

OFDM Time Domain Signal Illustrating Large Peak Excursions

c) PAPR Solutions for OFDMi. Signal Distortion Techniques: Clipping & Peak

WindowingClipping 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.

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.

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.

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.

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.

2. Error Correcting Code

The likelihood used for M-PSK implemented for the two codes is expressed in,

2. Error Correcting Code

This study uses Q-PSK and the resulting likelihood is,

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.

a) Turbo Code Encoder

a) Turbo Code DecoderUses a decoding Algorithm (BCJR Algorithm - Bahl,

Cocke, Jelinek and Raviv) employing max-log map.

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.

Results & Analysis

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.

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.

Why it is not implemented?Signal Distortion Techniques results to an in-band and out-of-band distortion which is an

additional impairment.