# Peak to Average Power Ratio Reduction in OFDM System by using SLM Technique Rehab Mohamed Elzain Abdulgader Malik

Peak to Average Power Ratio Reduction in OFDM System by using SLM Technique

Rehab Mohamed Elzain Abdulgader Malik, Amin Babiker A/Nabi Mustafa

Faculty of engineering, Alneelain University, Khartoum, Sudan

Corresponding author E-mail: [email protected]

Received :00 December 00

Accepted: 00 February 00

Abstract—Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation technique that offers high spectral efficiency, anti-multipath fading capability and immunity to interference between symbols. It has some drawback, but the major one is high peak to average power ratio (PAPR) of the transmitter’s output signal. There are many techniques used to solve this problem. In this paper, selective mapping (SLM) technique is considered as an effective technique to reduce the PAPR with no increase in power requirement and the performance evaluation is measured by complementary cumulative distribution function (CCDF). the results are simulated using MATLAB 2016a.

Index Terms—Orthogonal Frequency Division Multiplexing (OFDM), Peak to Average Power Ratio (PAPR), Inter-symbol Interference (ISI), Selective Mapping (SLM), Complementary Cumulative Distribution Function (CCDF).

I. INTRODUCTION

W

ith the increase in population in the world and the demand for higher data rate, there has become a huge challenge to increase the speed of communication systems. OFDM has come to the surfers and considered as a special form of multi-carrier modulation techniques. it is a powerful way to minimize multi-bath fading and inter symbol interference (ISI) problems. Where all sub-carriers are orthogonal to each other. OFDM has been used in a different communication application such as digital audio broadcasting, digital video broadcasting, wireless networks, DSL internet access, power line networks, WIMAX, and LTE. OFDM has a lot of advantages such as Makes efficient use of the spectrum due to overlapping, simpler channel equalization, using FFT techniques to modulation and demodulation of the signals, and so many. But it also has disadvantages such as doppler shift sensitivity, sensitivity to frequency synchronization problems, and high peak to average power ratio (PAPR). various methods have been proposed to reduce PAPR, divided into two types. First, signal distortion techniques, such as clipping and filtering 1, peak windowing 2, companding 3. And second, Signal scrambling techniques, such as coding techniques, selective mapping (SLM) 4, partial Transmit sequence (PTS) 5, tone reservation (TR) 6, tone injection (TI) 7, and active constellation extension (ACE) 8.

In this paper, SLM technique is used to reduce the high PAPR.

II. OFDM SYSTEM AND PAPR PROBLEM

A. OFDM system

The idea of OFDM system is to divide the transmission’s information into several sub-streams and sends each one of them on a different frequency known as sub-carrier. These sub-carriers are modulated individually by using either quadrature amplitude modulation (QAM) or phase shift keying (PSK) and then they are simultaneously transmitted as the data stream. So, with the data rate stays the same, the less data rate per sub-carrier, and the longer symbol duration. This reduces the error rate and the amount of ISI 9.

Fig. 1. Block diagram of OFDM system.

As shown in figure 1, the binary stream data shifted into digital modulation block and mapped from bits to symbols and then moved into serial to parallel block. Each group of symbols is moved from IQ plan (frequency domain) to the time domain in IFFT block. The parallel time domain data is rearranged into serial frames. Acyclic prefix extension (guard interval) is added to each frame to combat ISI, then converted from digital to analog signal, now the OFDM signal propagated through a multipath fading channel modulated by impulse response, and finally added to AWGN and transmitted. The opposite method happened in the receiver.

In the discrete time domain with N sub-carrier, the OFDM equation can be expressed as equation (1):

(1)

Where n is the output OFDM signal, and X(k) stands for modulated input symbols and has values of 0,1, 2, …, N-1 4.

B. PAPR Problem

The PAPR in OFDM system is defined as the ratio between the maximum power and the average power of the signal. and it is a major disadvantage in OFDM system, caused by all the carriers that have been added by IFFT operation, which lead to a signal with large peak and dynamic range in the time domain 10. The higher PAPR, the higher complexity of the analog-to-digital and digital-to-analog converters and the lower efficiency of the radio frequency of the power amplifier.

The PAPR is expressed as:

(2)

Where represent an OFDM signal and E{.}stands for the expected value.

When the N signals added up with the same phase at the same time, a peak power will be produced. Which means, the greater the number of sub-carriers, the higher PAPR. This OFDM signal with high PAPR will pass through a non-linear power amplifier in it is saturation region, this signal will cause in-band distortion and out-of-band radiation. which leads to system performance degradation, adjacent channel interference in the neighbor bands and increase bit error rate (BER) at the receiver 11. Therefore, power amplifiers with a

large dynamic range are required for OFDM systems, but these amplifiers are very expensive.

To measure the performance of any PAPR reduction technique, the Complementary Cumulative Distribution Function (CCDF) is used, which denotes the probability that the PAPR of a data block exceeds a predefined threshold z 12 and is given as:

(3)

Where N is the number of sub-carriers and z is the threshold.

With having Rayleigh distribution, the CCDF of the OFDM system is given as:

(4)

A typical OFDM signal without any PAPR reduction technique has about 8 dB to 13 dB PAPR at CCDF. Therefore, when a PAPR reduction technique is applied to the OFDM system, it is expected to reduce the 13 dB PAPR to some lower value. the reduction should be at least 3 dB 13.

III. SLM METHOD

Selective mapping is a distortion less technique that can reduce PAPR efficiently with no increase in power requirement and incur data rate loss. The idea of this technique is based on the phase rotation, the lowest PAPR signal will be selected for transmission from a number of various data blocks (independent phase sequences) that have the same information at the transmitter.

As shown in the figure above, the entire data stream is converted from serial to parallel, then divided into different blocks of N symbols each. Each block is multiplied by U different phase factors to generate U modified blocks and then inserted into IFFT blocks to generate OFDM symbols. PAPR is calculated for each modified block and select the block with the lowest PAPR ratio 14. At the side of the receiver, the side information is required in order to successfully recover the received signals. This information must be transmitted accompanying with the transmitted signal. SLM method effectively reduces PAPR without any signal distortion. This complexity can be less by reducing the number of IFFT block 1516. the probability of PAPR, by approximated N sub-carriers and over-sampling distribution by ?. Reaching the best PAPR 17 is when ?=2.8. The approximation is shown as:

(5)

Where U is the number of phase sequences.

IV. DIGITAL MODULATION SCHEMES

The objective of using digital modulation is to transport digital data from one node to another, or between more than two nodes by adjusting the physical characteristic of the carrier wave. There are three types of digital modulation techniques, frequency shift keying (FSK), phase shift keying (PSK), and amplitude shift keying (ASK).

The benefit of using digital modulation is that the signal can travel along distance, more security and easily detect and correct the noise.

A. Quadrature Amplitude Modulation

QAM is a combination of both amplitude and phase modulation techniques. So, it is a set of M symbols (M-QAM) that has a real and imaginary parts. For example, 16-QAM, 64-QAM, 128-QAM, etc.

Fig. 3. 16-QAM modulation.

Data symbols have different amplitudes and phases according to equation (6).

S(t)=d1(t) cos(2*pi*fc*t) + d2(t) sin(2*pi*fc*t) (6)

Fig. 4. 16-QAM process.

V. RESULTS

Figures 5, 6, 7, 8, and 9 respectively show the performance of peak to average power ratio reduction of threshold selected mapping (SLM) schemes for different values of N subcarriers and U phase sequences using 16-QAM mapping. As shown in the figures that the increase in number of phase sequences, lead to more PAPR reduction. For instance, figure (5) is a plot of PAPR reduction curves for OFDM symbol where N=64. when there is no SLM which is at U=1 threshold needed to get good PAPR reduction performance is 10.5, while for U = 16, only 6.2 is needed to get good PAPR reduction performance.

the oversampling case on SLM where ? =2.8. as shown in figures 10, 11 and 12 respectively, all probability level is almost the same as on Nyquist samples.

Fig. 5. PAPR Reduction for SLM where N = 64.

Fig.6. PAPR Reduction for SLM where N = 128.

Fig.7. PAPR Reduction for SLM where N = 256.

Fig. 8. PAPR Reduction for SLM where N = 512.

Fig. 9. PAPR Reduction for SLM where N = 1024.

Fig. 10. PAPR Reduction for SLM where ? =2.8, N = 64.

Fig. 11. PAPR Reduction for SLM where ? =2.8, N = 128.

Fig. 12. PAPR Reduction for SLM where ? =2.8, N = 256.

VI. CONCLUSION

SLM technique is an effective way to reduce high PAPR. As shown the high phase factor value, the less threshold needed to get a good performance, while applying oversampling on SLM does not make any change. 16 QAM mapping is used because of the low level of distortion.

ACKNOWLEDGMENT

I would like to thank prof Amin Babiker for his help, and the reviewers for their valuable and detailed comments.

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