BEHAVIOUR OF OFDM SYSTEM AND REDUCTION OF ITS PAPR BY USING SELECTIVE MAPPING IN MATLAB

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International Journal of Electronics and Communication Engineering & Technology
(IJECET)
Volume 7, Issue 3, May–June 2016, pp. 11–17, Article ID: IJECET_07_03_002
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ISSN Print: 0976-6464 and ISSN Online: 0976-6472
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BEHAVIOUR OF OFDM SYSTEM AND
REDUCTION OF ITS PAPR BY USING
SELECTIVE MAPPING IN MATLAB
Pankaj Kumar
Assistant Professor, Electronics and Communication Deptt,
MIT, Meerut, (U.P), India
Paridhi Sharma, Shivangi Gupta, Tripti Bisht, Pallavi Mittal
B. Tech Student, Electronics and Communication Deptt,
MIT, Meerut, (U.P), India
ABSTRACT
The OFDM technique divides the total bandwidth into many narrow sub-
channels and sends data in parallel. It has various advantages, such as high
spectral efficiency, immunity to impulse interference and, frequency selective
fading without having powerful channel equalizer. But one of the major
drawbacks of the OFDM system is high PAPR. OFDM signal consists of lot of
independent modulated subcarriers, which created the problem of PAPR. It is
impossible to send this high peak amplitude signals to the transmitter without
reducing peaks. So we have to reduce high peak amplitude of the signals
before transmitting. Communication is one in all the numerous features of
existence. A new DSI-SLM method for PAPR reduction in OFDM system state
that the phase sequence and dummy sequences added to the signal improves
the PAPR reduction in OFDM signals whereas less hardware resources and
less time are required to achieve the desired result.
Key words: OFDM, ISI, SLM, Reimann Matrix, Distortion, AWGN
Cite this Article: Pankaj Kumar, Paridhi Sharma, Shivangi Gupta, Tripti
Bisht and Pallavi Mittal. Behaviour of OFDM System and Reduction of Its
PAPR by Using Selective Mapping In Matlab, International Journal of
Electronics and Communication Engineering & Technology, 7(3), 2016, pp.
11–17.
http://www.iaeme.com/IJECET/issues.asp?JType=IJECET&VType=7&IType=3
1. INRODUCTION
OFDM is a multicarrier modulation technique, which employs several carriers, within
the allocated bandwidth, to convey the information from source to destination. The

Pankaj Kumar, Paridhi Sharma, Shivangi Gupta, Tripti Bisht and Pallavi Mittal
OFDM concept is based on spreading the data to be transmitted over a large number
of carriers, each being modulated at a low rate. The carriers are made orthogonal to
each other by appropriately choosing the frequency spacing between them. A
multicarrier system, such as FDM
(Frequency Division Multiplexing), divides the total available bandwidth in the
spectrum into sub-bands for multiple carriers to transmit in parallel. It combines a
large number of low data rate carriers to construct a composite high data rate
communication system. Orthogonality gives the carriers a valid reason to be closely
spaced with overlapping without ICI.
2. OFDM
The OFDM concept is based on spreading the data to be transmitted over a large
number of carriers, each being modulated at a low rate. The carriers are made
orthogonal to each other by appropriately choosing the frequency spacing between
them. A multicarrier system, such as FDM (Frequency Division Multiplexing),
divides the total available bandwidth in the spectrum into sub-bands for multiple
carriers to transmit in parallel. It combines a large number of low data rate carriers to
construct a composite high data rate communication system. Orthogonality gives the
carriers a valid reason to be closely spaced with overlapping without ICI.
3. QAM
Quadrature Amplitude Modulation or QAM is a form of modulation which is widely
used for modulating data signals onto a carrier used for radio communications. It is
widely used because it offers advantages over other forms of data modulation such as
PSK, although many forms of data modulation operate alongside each other.
When using QAM, the constellation points are normally arranged in a square grid
with equal vertical and horizontal spacing and as a result the most common forms of
QAM use a constellation with the number of points equal to a power of 2 i.e. 4, 16, 64
. . . .
By using higher order modulation formats, i.e. more points on the constellation, it
is possible to transmit more bits per symbol. However the points are closer together
and they are therefore more susceptible to noise and data errors.
Normally a QAM constellation is square and therefore the most common forms of
QAM 16QAM, 64QAM and 256QAM.The advantage of moving to the higher order
formats is that there are more points within the constellation and therefore it is
possible to transmit more bits per symbol. The downside is that the constellation
points are closer together and therefore the link is more susceptible to noise. As a
result, higher order versions of QAM are only used when there is a sufficiently high
signal to noise ratio.
Figure 1 Constellation Diagram of 64 QAM

Behaviour of OFDM System and Reduction of Its PAPR by Using Selective Mapping In
Matlab
4. BER Vs SNR
A bit error rate is defined as the rate at which errors occur in a transmission system.
This can be directly translated into the number of errors that occur in a string of a
stated number of bits.
The signal to noise ratio is the ratio between the wanted signal and the unwanted
background noise.
It is more usual to see a signal to noise ratio expressed in a logarithmic basis using
decibels:
If all levels are expressed in decibels, then the formula can be simplified to:
Bit error rate BER is a parameter which gives an excellent indication of the
performance of a data link such as radio or fibre optic system. As one of the main
parameters of interest in any data link is the number of errors that occur, the bit error
rate is a key parameter. A knowledge of the BER also enables other features of the
link such as the power and bandwidth, etc to be tailored to enable the required
performance to be obtained.
Figure 2 BER vs. SNR Plot
As we can conclude from the above plot that the theoretical points and simulated
values overlap each other resulting in correct simulation and description of OFDM
system in our MATLAB function.
The Value of Bit error rate or in this case symbol error rate are given on the y-axis
and the values for signal to noise ratio are plotted on the x-axis. The scale is plotted
on a logarithmic one and the axis coordinates are defined accordingly on the upper
right corner.
5. PAPR
The peak-to-average power ratio (PAPR) is the peak amplitude squared (giving the
peak power) divided by the RMS value squared (giving the average power). It is the
square of the crest factor:

When expressed in decibels, crest factor and PAPR are equivalent, due to the way
decibels are calculated for power ratios vs amplitude ratios.
The PAPR is most used in signal processing applications. As it is a power ratio, it
is normally expressed in decibels (dB).
6. PROBLEMS RELATED TO PAPR
1. Power Peaks: In order to accommodate this peak in power, the radio's RF power
amplifier (PA) must provide gain without compression for every peak power level. In
other words, the PA will provide less RF power between peaks, by an amount given
by the PAPR.
Not only does this imply that the power amplifier must be oversized in terms of its
average power requirement, it also means that the efficiency of the PA will suffer
dramatically, since its DC power consumption is determined by the peak power level.
Since the DC power consumption of the PA represents a significant portion of the
total DC power for a radio, traditionally designed OFDM modems are not power
efficient.
2. Non linearity: For higher-level modulations such as a 64 quadrature amplitude
modulation (QAM) scheme, these constellation clouds can contribute to an increase in
bit errors for each carrier. Even a modest increase in bit error rate (BER) for each
carrier can result in a dramatic increase in the cumulative error rate over a packet.
Thus, in an OFDM modem design, linearity must be carefully controlled.
3. Image Rejection: The latest trend in receiver design is to reduce or eliminate the
intermediate frequency (IF) stage in order to eliminate costly additional filtering
circuitry. While this streamlines the receiver, it makes it more difficult to control
image rejection, because designers cannot make use of external RF and IF filtering.
At best, insufficient image rejection in an OFDM modem reduces the carrier-to-noise
ratio available for the demodulator. At worst, it allows another signal to interfere with
the OFDM signal, resulting in a catastrophic increase in error rate.
4. Phase Distortion: OFDM provides a selection of modulation constellations for
each carrier. For example, the 802.11a standard provides for individual carrier
modulation up to 64 quadrature amplitude modulation (QAM). Although signal
impairments due to multi-path are eliminated through the use of a cyclic prefix guard
interval (during which no demodulation is performed in the receiver), the closeness of
the constellation points can result in significant errors due to dispersion. This
dispersion can be caused by motion of the radio units or from motion of any other
object in the channel. It can also be caused by phase variation with frequency in the
radio antennas, filters, and other components.
7. REMOVAL OF PAPR
A. SLM
The Riemann matrix [17] is obtained by removing the first row and first column of
the matrix R, where:

Matlab
Using This Equation , Riemann Matrix (A) of order 4 can be written as:
The SLM technique was first described by Bauml In the SLM, the input data
sequences are multiplied by each of the phase sequences to generate alternative input
symbol sequences. Each of these alternative input data sequences is made the IFFT
operation, and then the one with the lowest PAPR is selected for transmission. Figure
shows the block of the SLM technique. Ak is the OFDM data block, Bu is the phase
vectors and Au is the modified data vectors in the frequency domain.
Figure 3 Selective Mapping
So the time domain signal
Where u=1, 2… U and N is length of A, also the number of sub-carriers. Among
the modified data blocks, the one with the lowest PAPR is selected for transmission.
The amount of PAPR reduction for SLM depends on the number of phase sequences
U and the design of the phase sequences.

8. RESULTS
PAPR before Implementing SLM technique:
PAPR after Implementing SLM technique:
REFERENCES
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Matlab
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