Peak to Average Power Ratio Reduction of OFDM System using Golay Codes.

Under the guidance of Dr. Amandeep Singh Sappal

Presented by: Harleen KaurRoll no: 11192037

Introduction

• In OFDM a high rate data stream is divided into many low data streams.

• These streams are then multiplied by corresponding carrier frequency signals that are orthogonal to each other.

• A composite signal so formed by multiplexing these modulated signals is called the orthogonal frequency division multiplexed signal.

• Orthogonality: two signals are orthogonal to each other when:

1. Each subcarrier has exactly an integer number of cycles in an interval.

2. The number of cycles between adjacent subcarriers differs by exactly one.

OFDM (contd.)TIME DOMAIN FRQUENCY DOMAIN

SUBCARRIERS IN OFDM

SPECTRA OF THE CARRIERS

ADVANTAGES AND DISADVANTAGES OF OFDM

ADVANTAGES:•Immunity to delay spread•Robustness to channel fading and impulse interference•Eliminate the need for equalizers •Efficient bandwidth usage•Efficient hardware implementations using Fast Fourier Transform (FFT)

DISADVANTAGES:•The problem of synchronization i.e. Symbol synchronization, Frequency synchronization•Sensitive to carrier frequency offset•The problem of high peak to average power ratio (PAPR)

PEAK TO AVERAGE POWER RATIO (PAPR)

• Ratio of peak power to the average power of the OFDM signal.

• PAPR is usually analyzed by using statistical parameter called Complementary Cumulative Distribution Function (CCDF) which shows the probability that PAPR is above a threshold level i.e. P(PAPR > z)= 1 − ((1 − exp(−z)) ^ N

PAPR PROBLEM

When the N sinusoidal signals after modulation by their carriers, adds

mostly constructively the peak envelop power is as much as N times the

mean power. As a result the amplitude of such a signal can have very

large values.

High peak-to-average power ratio:

• Demands the High Power Amplifier (HPA) with large back off.

• Requires the ADC/DAC with large dynamic range.

• Higher power consumption.

• Reduced amplifier efficiency and battery life.

SOLUTION OF PAPR PROBLEM1. Signal distortion techniques which reduce the peak amplitudes

simply by nonlinearly distorting the OFDM signal at or around the peaks. • Clipping• Peak window• Peak cancellation

2. Coding techniques that using a special forward-error correction code • PAPR reduction codes

3. Scrambling techniques are based on scrambling each OFDM symbol with different scrambling sequences and selecting that sequence that gives the smallest PAPR. • Selective mapping (SLM)• Partial transmit sequence (PTS)

CLIPPING AND PEAK WINDOWING

CLIPPING THE SIGNAL• The simplest way to reduce the PAPR• The peak amplitude becomes limited to some desired level• Distorting the OFDM signal amplitude degrades the BER. • Nonlinear distortion increases out-of-band radiation

PEAK WINDOWING• Remedy to the out-of-band problem of clipping• Multiplies large signal peaks by nonrectangular window • To minimize the out-of-band interference, ideally the window should

be as narrowband as possible.• The windows should not be too long in the time domain, because that

implies that many signal samples as affected, which increases the BER.

Selective Mapping (SLM)

• In SLM an OFDM signal of the lowest PAPR is selected from a set of several signals containing the same information data.

• Moderate complexity.• Distortionless technique.• SLM requires large number of IFFT stages in the

transmitter.• Extra bits are required to explicitly represent the

side information.

PARTIAL TRANSMIT SEQUENCE (PTS)

• In PTS the input data block is divided into smaller non-overlapping subblocks.

• Each subblock is multiplied by a phase factor, which is obtained by the optimization algorithm to minimize the PAPR value.

• It introduces additional complexity. • The side information about the phase rotation factors

would be necessary to transmit for correct OFDM symbol recovery.

• There is a small loss in the spectral efficiency due to the insertion of the side information.

CODING

• It needs to find the code words with a lower PAPR and to store the information in a lookup table for encoding and decoding.

• It still is an open problem to construct codes with both low PAPR and short Hamming distance

• Golay and Reed-Muller codes have shown PAPR reduction properties, but at a significant rate reduction.

GOLAY COMPLEMENTARY PAIR

• More than sixty years ago, efforts by Marcel Golay to improve the sensitivity of far infrared spectrometry led to the discovery of complementary sequences

• Golay complementary pairs are sequence pairs for which the sum of auto-correlation function is zero for all delay shifts unequal to zero.

• Aperiodic Auto-Correlation Function (AACF) is given by

• Any sequence which is a member of Golay complementary pair is called a Golay sequence.

Existence of GCP• GCPs are known to exist for all lengths

• The lengths, N < 100, for which GCPs exist are:

2, 4, 8, 10, 16, 20, 26, 32, 40, 52, 64, 80• Primitive GCP is one that cannot be constructed from

any shorter GCP by means of the recursive constructions.

• Primitive GCPs are only known to exist for lengths 2, 10, and 26.

• There is one primitive pair for lengths 2 and 26, and two primitive pairs for length 10.

GCS (contd.)• GCS are potentially deserved candidate for OFDM transmission, but

they do not possess unexceptional essential structure to form a practical coding scheme.

• Golay complementary sequences can be used to achieve more than 3-dB PAPR reduction. Codes with error correcting capabilities can be used to achieve more lower PAPR for OFDM signals by determining the relationship of the cosets of Reed-Muller codes to Golay complementary sequences.

• Sets of binary Golay complementary pairs can be obtained from certain second-order cosets of the classical first order RM code.

• This way the block codes with their exceptionally ingenious encoding decoding and error correcting capabilities were combined with the power control properties of the GCS.

Literature Review

AUTHOR TOPIC STRENGTH WEAKNESS YEAR

Josef Urban [4]

PAPR reduction in OFDM systems by simplified clipping and filtering with bounded distortion

Simplest method of reducing the PAPR

It causes In-Band and Out-of-Band Distortion

2006

K. Kasiri and M.J. Dehghian [5]

A Blind SLM Scheme for reduction of PAPR in OFDM systems

Better PAPR reduction capability than distortion type techniques

Huge Complexity because of many IFFT stages

2009

P.Mukunthan [6]

PAPR Reduction of an OFDM Signal using Modified PTS Combined with Interleaving and Pulse Shaping Method

lowest computational complexity

Better PAPR performance than conventional PTS scheme

2012

Abolfazl Ghassemi and T. Aaron Gulliver [7]

PAPR Reduction of OFDM using PTS and Error-Correcting code subblocking

Better PAPR reduction, no restrictions to the number of the subcarriers

Additional complexity, loss in the spectral efficiency due to side information insertion

2010

Literature Review (contd.)AUTHOR TOPIC STRENGTH WEAKNESS YEAR

Davis, Jedwab and Paterson [8]

Codes, Correlations and Power Control in OFDM

The PAPR of any golay sequence is at most 2, specifies relation between golay sequences and second order reed muller codes

Various open problems are discussed in the end

1998

M.J.E. Golay [10] Complementary seriesPresents the definition, properties and possible applications of complementary sequences

These sequences

does not posses essential

structure to form a practical

coding scheme

1961

Davis and Jedwab [11]

Peak-to-mean Power control in OFDM, GCS and Reed Muller Codes

Provides connection between GCS and RM codes

Provides codes with a restricted length of 2m

1999

Chen and Lian [13]

Construction of 16-QAM and 64-QAM OFDM Codes with Low PAPR and Large Euclidean Distance

Method to construct 16-QAM from two QPSK-GC sequences

2007

Suh and Hwang [14]

Recursive Construction of Golay Sequences

Exhaustive search for GCS is difficult so a recursive method is suggested

No proof for the upper bound of PAPR is given in the paper

2004

Literature Review (contd.)

AUTHOR TOPIC STRENGTH WEAKNESS YEAR

Kenneth G. Paterson [15]

Generalized RM Codes and Power Control in OFDM Modulation

Presents q-ary (with q even) instead of 2h-ary alphabets

Various open problems were left

2000

Masoud Olfat and K. J. Ray Liu [16]

Low Peak to Average Power Ratio Cyclic Golay Sequences for OFDM Systems

Present the concept of cyclic golay codes to reduce PAPR

Causes lower error correction capabilities if higher code rate is required

2004

Hyun Park, Yup Lee et al. [17]

ICI Self Cancellation - Golay Complementary RM Code Scheme for OFDM Systems

Proposed a scheme of ICI self-cancellation along with GCRM codes

Efficient only for low back-off value for TWTA

2004

Rezgui, Jarboui and Grayaa [18]

A PAPR reduction technique based on Golay sequences and Fractional Fourier Transform for OFDM Systems

FRFT block has same complexity as FFT and there is weak correlation of noise and signal for particular time frequency space.

Requires wise choice of golay sequence lengthand FRFT angle

2012

Problem Formulation

From the detailed literature review it has been concluded that PAPR reduction is of main concern in present communication systems. Golay codes can be explored to reduce the PAPR without using extra PAPR reduction techniques, hence resulting in the requirement of less hardware.

Objective of Research

To solve the problem of PAPR in present communication systems using Golay codes. Following objectives have been formulated. These objectives can be modified according to the need of the research.

• To study the problem of PAPR in present day communication systems.

• To study the existing PAPR reduction techniques and to compare their performance.

• To develop PAPR reduction techniques using Golay codes and measure its performance.

Research Methodology

Simulation platform will be developed using MATLAB software. Also for calculation of various parameters Mathematica or Mapple software may be used.

REFERENCES[1] Richard Van Nee, “OFDM for Wireless Multimedia Communications”, Artech House Universal

Personal Communications.

[2] P. Foomooljareona and W.A.C. Fernando, “PAPR Reduction in OFDM Systems”, Thammasat International Journal of Science and Technology, September-December 2002.

 

[3] V. Vijayarangan, Dr. (Mrs.) R. Sukanesh, “An Overview Of Techniques For Reducing Peak to Average Power Ratio and its Selection Criteria for OFDM Radio Systems”, Journal of Theoretical and Applied Information Technology (JATIT), 2005 - 2009.

 

[4] Josef Urban, “PAPR reduction in OFDM systems by simplified clipping and filtering with bounded distortion”, Doctoral Degree Programme, Faculty of Electrical Engineering and Communication Brno University of Technology (FEEC BUT), 2006.

[5] K. Kasiri and M. J. Dehghani, “A Blind SLM Scheme for Reduction of PAPR in OFDM Systems”, World Academy of Science, Engineering and Technology, 2009.

[6] P. Mukunthan , “PAPR Reduction of an OFDM Signal using Modified PTS Combined with Interleaving and Pulse Shaping Method”, European Journal of Scientific Research, pp. 475-486, March 2012.

 

REFERENCES (contd.)[7] Abolfazl Ghassemi and T. Aaron Gulliver, “PAPR Reduction of OFDM Using PTS and Error-

Correcting Code Subblocking”, IEEE Transactions On Wireless Communications, pp. 980 – 989, March 2010.

 

[8] James A. Davis, Jonathan Jedwab and K.G. Paterson, “Codes, Correlations and Power Control in OFDM”, Hewlett Packard Laboratories Technical Report, December 1998

 

[9] Marcel J. E. Golay, “Multislit Spectroscopy”, Journal of the Optical Society of America, 1949.

 

[10] M.J.E. Golay, “Complementary Series,” Institute of Radio Engineers (IRE) Transactions on Information Theory, pp. 82–87, April 1961.

 

[11] J.A. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay Complementary Sequences and Reed-Muller codes”, IEEE Transactions on Information Theory, pp. 2397-2417, November 1999.

[12] J. A. Davis and J. Jedwab, “Peak-to-mean power control for OFDM transmission using Golay sequences and Reed–Muller codes,” Electronic Letters, Vol.33, pp.267-268, 1997

REFERENCES (contd.) 

[13] Chen and Lian, “Construction of 16-QAM and 64-QAM OFDM Codes with Low PAPR and Large Euclidean Distance”, Institute of Electronics, Information and Communication Engineers (IEICE) Transactions on Communication, August 2007.

 

[14] Suh and Hwang, “Recursive Construction of Golay Sequences”, IEEE International Symposium on Information Theory, June-July 2004.

 

[15] Kenneth G. Paterson, “Generalized Reed–Muller Codes and Power Control in OFDM Modulation”, IEEE Transactions on Information Theory, pp. 104 - 120, January 2000.

 

[16] Masoud Olfat and K. J. Ray Liu, “Low Peak to Average Power Ratio Cyclic Golay Sequences for OFDM Systems”, IEEE International Conference on communications, pp. 993 - 997, 2004.

 

[17] Hyun Park, Yup Lee et al., “ICI Self Cancellation - Golay Complementary Reed-Muller Code Scheme for OFDM Systems”,  IEEE International Symposium on Information Theory, June-July 2004.

 

[18] Rezgui, Jarboui and Grayaa, “A PAPR reduction technique based on Golay sequences and Fractional Fourier Transform for OFDM Systems”, IEEE Communications Society, pp. 383 – 386, 2012.

Thank you.