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COPYRIGHT © 2012 IJCIT, ISSN 2078-5828 (PRINT), ISSN 2218-5224 (ONLINE), VOLUME 02, ISSUE 02, MANUSCRIPT CODE: 120111

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Abstract—Orthogonal Frequency Division Multiplexing

(OFDM) is a proficient modulation technique which is used brutally both broadband wired and wireless communication. It brings many advantages. Eliminating Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI), makes efficient use of the spectrum and dividing the channel into narrowband flat fading sub channels are some of them. But it’s not free from disadvantages too. One major disadvantage of OFDM is that the time domain OFDM signal which is a sum of several sinusoids leads to high peak to average power ratio (PAPR). There are many different types of PAPR reduction techniques. Such that Clipping, Windowing, Coding etc. In this paper a new scheme was proposed combining Hadamard transform and Hann peak widowing technique to achieve more novel PAPR reduction. We analyzed performance of the PAPR reduction technique calculating BER. The PAPR reduction performances were analyzed for an OFDM system model containing 64 subcarriers and BPSK modulation technique. All simulations were performed on MATLAB 7.5 platform. The results of MATLAB 7.5 simulation using this scheme show about 5dB PAPR reduction at within decrease of Eb/No at BER.

Index terms —OFDM, PAPR, BER, Hadamard Transform, Hann Windowing.

I. INTRODUCTION

Orthogonal Frequency Division Multiplexing is a great modulation technique. Now-a-days it has been seen rising popularity in wireless applications. For wireless communication an OFDM –based system can provide greater immunity to multi-path fading and reduce the complexity of equalizers [1]. Digital Audio Broadcast (DAB), Digital Video Broadcast (DVB), the IEEE 802.11 Wireless Local Area Network (WLAN) scheme, as well as the IEEE 802.16 Broadband Wireless Access (BWA), particularly, Wireless Metropolitan Area Networks (IEEE 802.16d) WiMAX [2] are some of the enormous applications of OFDM system. Besides this, the major drawback of OFDM signal is its large peak-to-average power ratio (PAPR), which causes poor power efficiency or serious performance degradation in the time of transmitting through power amplifier [3]. Therefore, nonlinearities may get overloaded by high signal peaks, causing inter modulation among subcarriers and, more critical, undesired out-of-band radiation. If RF power

amplifiers are operated without large power back-offs, it is impossible to keep the out-of-band power below specified limits. This leads to very inefficient amplification and expensive transmitters so that it is highly desirable to reduce the PAPR [4]. Several schemes have been proposed to reduce the PAPR. These techniques can mainly be categorized into Signal scrambling techniques and Signal distortion techniques [1]. Signal scrambling techniques are all variations on how to scramble the codes to decrease the PAPR. Coding techniques can be used for signal scrambling [5]. Comparatively signal distortion techniques more straight forward technique. Signal distortion methods distort the high peak valued portion of OFDM signals using different techniques for PAPR reduction. In our proposed new scheme we combine two methods, one is a signal scrambling method, Hadamard Transforms and another is a signal distortion technique, Hann peak windowing. We also analyzed the system performance of our new proposed PAPR reduction scheme in terms of Bit Error Rate (BER).

II. SYSTEM MODEL

A. OFDM System At the starting end binary data is being inputted to the

system. After that this binary data is going through to the process of digital to analog mapping. And this mapped signal is being modulated with proper modulation technique. This modulation signal is than converted into parallel signal by signal to parallel converter. This parallel data is being inputted to the IFFT operation block. This IFFT block converts the frequency domain signal to time domain signal for each subcarrier. Cyclic prefix is being added with the time domain signal. After that this time domain signal is being transmitted through the channel after proper filtering and applications. This transmitted signal is received by receiver and the receiver action is somewhat inverse of transmitter. The starting end of receiver is a synchronizer. It is being used to equalize the received signal to prevent any channel effect and to get the proper signal. Figure 1 shows the transceiver bloc diagram of OFDM system.

B. Peak-to-Average Power Ratio The measurement of a waveform, calculated from the peak

power of the waveform divided by the average power of the waveform is called crest factor or peak-to-average ratio

A New Proposed Scheme for PAPR Reduction of OFDM System Combining Hadamard Transform

and Hann Peak Windowing K. M. Kawsar Pervez, and Md. Mahbub Hossain



(PAR) or peak-to-average power ratio (PAPR) [6]. If we

consider a complex signal , The peak to average power ratio for this signal defined as, PAPR

(1)

Where, the peak or maximum power of the signal is

The average or mean power of the signal is

Corresponding to the conjugate operator = ( )* In the case of OFDM system, we can define PAPR as

follows, PAPR of OFDM system

(2)

We know that, In the case of OFDM system, OFDM signals are the results superposition of many different subcarrier. But as the subcarrier signals are random and the PAPR of OFDM system is totally dependent on those subcarrier signals, so we can understand that the value of PAPR is also random.

OFDM signal is the sum of multiple sinusoidal having frequency separation , where each sinusoidal gets

modulated by independent information . Mathematically, the transmit signal is, [7]

(3)

So, each signal is ; k=0, 1… N-1

(4)

Equation (1) predicts that the PAPR can be defined by the amplitude of output signal. So when output signal exceed a certain value then obviously PAPR also take a higher value.

C. Problem of High PAPR Nonlinearity of power amplifier and high PAPR of OFDM

signals cause severe problems in OFDM implications especially in transmitter. Figure 2 shows a basic characteristics curve of nonlinear power amplifier. In this figure there are two regions. One is for liner response and another is for non-linear response. There are two types of distortion. The explanation of those distortions is given bellow.

D. Out of Band Distortion in OFDM Signal As OFDM signal contains high peak to average power

ratio (PAPR), the peak value of the signal is quite high in comparison with the average signal value. At the time of peak amplitude, the power amplifier operates in its nonlinear region as input of the amplifier is higher at that time. Because of the non linearity of amplifier gain of this region, different frequency components of the OFDM signal amplify with different levels of gain. This creates spreading effect over the frequency bands which cause out-of- band radiation. The frequency components which spread out of the required channels interfered with the side lobes of the subcarrier channels and inter carrier interference take place. These phenomena of interference cause signal distortion which is known as out of band distortion of OFDM system.

Fig. 1. OFDM transceiver block diagram

IFFT

Mapping

S/P

AddCP

[[

FFT

P/S

Sync

Modu-lation

Demod.

Demapping

Data Input

Channel

Data output

Input power

Fig. 2. Characteristics curve of nonlinear power amplifier

Operating region without pre distortion

Operating region with pre distortion

Saturation Linear response

Pout

Pout-pd

Psat

Output



E. In Band Distortion in OFDM signal Again because of the high peak to average power ratio

(PAPR) of OFDM signal, the signal often goes to the nonlinear part of the power amplifier. When the signal goes to the nonlinear part of the power amplifier then the consecutive points of the input signals get amplified with different amount of gains. This prevents the output signals from following the input signals with constant gain and instead of getting an amplified version of input signal we get a distorted version of input signals at output of the power amplifier.

The power efficiency of an HPA can be increased by reducing the PAPR of the transmitted signal. Clearly, it would be desirable to have the average and peak values are as close together as possible in order to maximize the efficiency of the power amplifier. In addition to the large burden placed on the HPA, a high PAR requires high resolution for both the transmitter’s DAC and the receiver’s ADC, since the dynamic range of the signal is proportional to the PAPR. High-resolution D/A and A/D conversion places an additional complexity, cost, and power burden on the system [5].

F. Quantifying PAPR If a random complex variable follows the normal

distribution and its real and imaginary part individually follow the same kind of Gaussian random distribution then the probability distribution of the absolute value of this complex random variable follows the Rayleigh distribution. As our signal amplitude is also the absolute value of normally distributed random complex signal so it will also follow the Rayleigh distribution.

As our main interest is centralized around whether PAPR acrosses a certain value or not it’s more helpful to plot ccdf instead of cdf. For a OFDM signal with N carrier

(5)

III. MATERIALS & MATHODS A. Hadamard Transform

The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of transforms. The Hadamard transform

is a matrix, the Hadamard matrix scaled by a normalization factor that transforms real numbers or complex numbers into real numbers The Hadamard transform can be defined in two ways: recursively, or by using the binary (base-2) representation of the indices n and k [6]. Recursively, we define

(6)

In Hadamard transform scheme, the mapped and modulated data is been Hadamard transformed before IFFT operation and at the receiver end the data can be decoded after demapping , demodulation and FFT operation performing Inverse Hadamard transform.

B. Peak Windowing Peak windowing is a signal distortion technique to reduce

PAPR of OFDM. By this method, we can window a large peak by multiplying it with proper window function. If a signal peak exceeds a certain threshold the peak is then windowed.

Peak windowing gives much better spectral result than that of simple clipping. It gives a smooth peak for the clipped signal in contrast with normal flat top achieved by simple clipping.

C. Hann Window Hann function is defined by

(7) The advantage of the Hann window is very low aliasing,

and the tradeoff is slightly decreased resolution (widening of the main lobe). If the Hann window is used to sample a signal in order to convert to frequency domain, it is complex to reconvert to the time domain without adding distortions [6].

A new scheme for PAPR reduction is been proposed in this paper combining Hadamard transform and Hann windowing. In this scheme, data given inputted has been mapped. This mapped data is then modulated. Modulated data is gone through Hadamard transform. This Hadamard transformed data is then performed through IFFT operation. IFFT operation convert frequency domain signal to time domain signal. This converted time domain signal is the get peak windowed with the help of Hann window. This windowed signal is then transmitted through the channel. The signal is decoded by means of inverse Hadamard transform at the receiver after FFT operation. FFT operation convert time domain signal to frequency domain signal. The block representation of the scheme is given in figure 2. The signal processing algorithm steps are given bellow. Step 1: The sequence of in data, X is transformed by in order Hadamard matrix. (8) Here H is the Hadamard matrix. Step 2: The Hadamard transformed data sequence Y is inputted to the IFFT unit. The time domain signal output of IFFT unit is (9) Step 3: Hann peak windowing is performed over this IFFT output according to following procedure



If then If then Step 4: FFT transform is performed on the received signal that is , Here, (10)

IV. SIMULATION RESULTS To simulate the above OFDM system for PAPR reduction

we used MATLAB 7.5. 32 numbers of data symbol was taken and the subcarrier number were 128. For mapping, PSK modulation technique was performed. BPSK as modulation technique for Hadamard transform scheme and Hann peak windowing and new proposed scheme. Figure 4 shows that Hadamard transform and Hann windowing reduce PAPR at the amount of 3.5 dB and 2 dB respectively while they are working individually than that of original signal. Our proposed new scheme combining Hadamard transform and Hann windowing reduces PAPR at the amount of around 5 dB than that of the original signal. So, certainly proposed new scheme gives comparatively better PAPR reduction. Table I represents the comparative amount of PAPR reduction obtained by using different techniques.

TABLE: I RESULT OF PAPR REDUCTION FOR HADAMARD TRANSFORM,

HANN PEAK WINDOWING AND PROPOSED NEW SCHEME

Techniques used

PAPR of original OFDM

Signal (dB)

After Applying the Techniques

(dB)

Amount of Reduction

(dB)

Hann peak windowing

8.5 7 1.5

Hadamard transform

8.5 5 3.5

New proposed scheme

8.5 3.5 5

Figure 5 shows that Proposed PAPR reduction scheme combining Hadamard transform and Hann peak windowing improve the performance of the system as the BER of the system decreases after using proposed scheme. Here also we use MATLAB 7.5 for simulation. Table II shows that comparative BER performance analysis of new scheme with various techniques. From this figure it is clear that this new scheme is very much effective for BER reduction also.

V. LIMITATIONS

The complexity of Hadamard Transform rises with the increased number of data bit. This may broaden the calculation time causing delay. The windowing process causes self-interference.

VI. FUTURE WORKS

In future this work can be made more elegant by improving the signal distortion techniques along with Hadamard transform so that a more sophisticated and prolific PAPR reduction scheme can be obtained. Figure 4 shows that Proposed PAPR reduction scheme combining Hadamard transform and Hann peak windowing improve the performance of the system as the BER of the system decreases after using proposed scheme. Here also we use MATLAB 7.5 for simulation. Table II shows that comparative BER performance analysis of new scheme with various techniques. From this figure it is clear that this new scheme is very much effective for BER reduction also.

Fig. 3. Block diagram of a baseband OFDM system with proposed new PAPR reduction scheme

Noise

Channel

D/A and HPA

Hann Windowing

IFFT and Add

CP

Data source

QAM/PSK mapping

S/P

Hadamard transform

Remove CP and

FFT

D/A and HPA

Data sink QAM/PSK Demapping

P/S

Inverse Hadamard transform



Fig. 4. Simulation result of PAPR for original OFDM signal and signal after

applying proposed scheme

Fig. 5. Comparison of BER after using different PAPR reduction technique

REFERENCES

[1] A. R. Bahai and B. R. Saltzberg, “Multi-Carrier Digital Communications”.

[2] J.Aktman, B.Z. Bobrovsky and L.Hanzo, "Peak-to-Average Power Ratio Reduction for OFDM Modems", Proc. VTC'2003 (Spring), Jeju,S.Korea, 2003..

[3] H. Rohling, T. May, K. Bruninghaus, and R. Grunheid, “Broadband OFDM radio transmission for multimedia applications,”Proc. IEEE, vol.87,pp.1778-1789,Oct.1999.

[4] Stefan H. Muller and Johannes B. Huber, "A Comparison of Peak Power Reduction Schemes For OFDM", Proc. of IEEE Global Telecom. Conf. GLOBECOM '97, Nov. 1997, Arizona, USA.

[5] Ashraf A. Eltholth, Adel R. Mikhail, A. Elshirbini, Moawad I. Moawad, A. I. Abdelfattah, “Peak-to-Average Power Ratio Reduction in OFDM Systems.

[6] www.wikipidia.com. [7] Jean Armstrong, Senior Member, IEEE, “OFDM for Optical

Communication,” Journal of Light wave Technology, vol. 27, No. 3, February 1, 2009.

A.K.M. Kawsar Pervez was born in Rajshahi, Bangladesh, 26th December, 1989. He got B. Sc Engineering degree in Electronics and Communication in the year of 2011 from Khulna University, Khulna-9208, Bangladesh. Now he was an employee of Augere wireless Broadband Bangladesh Ltd (Qubee). His current research interest is wireless communication, channel coding, all optical networks and antenna design.

SNR (dB)

0 2 4 6 8 10 12 14 16 18 20

BER of OFDM system without

PAPR reduction

0.3909 0.3687 0.3308 0.2893 0.2395 0.1890 0.1292 0.0747 0.0374 0.0132 0.0022

BER of the system with Hadamard Transform

0.0410 0.0161 0.0056 0.0034 0.0029 0.0024 0.0020 0.0015 0.0010 0.0005 0

BER of the system with Hann Peak Windowing

0.3005 0.2356 0.1956 0.1372 0.0903 0.0391 0.0129 0.0032 0.0015 0.0005 0

BER of the system with

Proposed scheme

0.0024 0.0022 0.0020 0.0017 0.0015 0.0012 0.0010 0.0007 0.0004 0.0001 0

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PAPR(dB)

CC

DF(

PA

PR

)

Original SignalAfter Hann WindowingAfter HadamardAfter New Scheme

0 2 4 6 8 10 12 14 16 18 2010-5

10-4

10-3

10-2

10-1

100

Eb/No, dB

Bit

Erro

r Rat

e

Bit error probability curve for BPSK using OFDM

Original signalHadamard transformHann peak windowingProposed Scheme

TABLE: II COMPARATIVE BER PERFORMANCE ANALYSIS OF NEW

SCHME WITH VARIOUS METHODS

a new proposed scheme for papr reduction of … results of matlab 7.5 simulation using this ... a...

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