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Enhancement Orthogonal Frequency Division Multiplexing (OFDM) in Wireless
Communication Network by Using PTS(Partial Transmit Sequences) Technique
Majed M. Albogame and Khaled M. Elleithy
Department of Computer Science and Engineering
University of Bridgeport, Bridgeport, CT 06604, USA
Wireless telecommunications has been significantly
growing due to the need of high data rate during the last
decade. In this paper, OFDM with different scenarios are
experimentally tested and the results demonstrate the
strengths of OFDM technique as a key technology that
fulfils the need of high data rate and high performance in
wireless communication. Furthermore, we demonstrate that
the complexity of OFDM technology can be reduced and
the capacity is increased by using Partial Transmit
Sequences (PTS) method. This method shows the best
performance of OFDM where increased capacity, coverage,
and reliability are clearly evident from the test results
presented in this paper.
Keywords: Orthogonal Frequency Division Multiplexing
(OFDM), FFT (Fast Fourier Transform), BPSK (Binary
Phase Shift keying) and QAM (Quadrature Amplitude
Modulation), PAPR (Peak to Average Power Ratio), Partial
Transmit Sequences (PTS).
Orthogonal Frequency Division Multiplexing (OFDM) is
also known as a multicarrier modulation technique, which
has been the key behind the most advances and
achievements associated with high data rate
communications. OFDM nowadays has become so popular
due to its flexible and efficient management of
inter-symbol interference (ISI). Moreover, OFDM grants
high spectral efficiency and mitigates the multipath
environment effects. OFDM divides the data stream into
multiple sub-streams and sends them through multiple
orthogonal sub-channels. Generally, the overall system
performance and communication link quality is improved
by OFDM technology [1-4].
There is a lot work introduced in literature that focusses
on Orthogonal-Frequency-Division-Multiplexing (OFDM)
technology. In 1960, the parallel data transmission was
proposed to increase data processing and transmission
traffic due to the desired demand of high data rate in
communication networks. Furthermore, Frequency
Division Multiplexing (FDM) was introduced as a
technique in parallel data transmission .
FDM divides the frequency spectrum into slots that are
called transmission channels. Furthermore, each slot
should be assigned to one transmission channel. These
frequency sub-bands cannot be overlapped neither can be
placed adjacently, which means that multicarrier FDM
communication link designers should not only assign non-
overlapped frequency bands for transmission channels but
also leave frequency guard bands in between those
assigned frequency bands . Consequently, multicarrier
modulation technique has two disadvantages. The first one
is the implementation complexity and the second one is the
Weinstein and Ebert proposed a multicarrier system
which works with discrete Fourier Transform (DFT) [14,
15]. DFT was implemented as a part of the modulation and
demodulation process in the multicarrier communication
systems to reduce complexity. Inverse Discrete Fourier
Transform (IDFT) and Discrete Fourier Transform (DFT),
according to Weinstein and Ebert proposed approach, are
used to perform the modulation and demodulation
processes, respectively. Then, many research efforts have
been made to improve multicarrier communication system
complexity even more. The most successful improvement
is the use of Fast Fourier Transform (FFT) and Inverse Fast
Fourier Transform (IFFT) instead of DFT and IDFT
respectively. By that time, both system complexity and
bandwidth inefficiency problems were handled through
modifications being added one after another and the last
one was introduced by Weinstein and Ebert as mentioned
before. Furthermore, OFDM divides the high rate input
data stream into lower rate multiple sub-streams. Then,
those sub-streams are modulated on orthogonal subcarriers
offering high spectral efficiency, frequency flat fading
sub-channels, free ISI communication link, and robust
modulation and multiple access schemes  and .
2. OFDM Concepts
The straightest forward idea of OFDM is to divide the
high rate data stream into lower rate sub-streams and send
them over through multiple parallel sub-channels .
Many advantages, therefore, have been accomplished after
applying the idea of OFDM multi carrier communication
3.1 OFDM Orthogonality
One of the aspects that have made OFDM so popular
multicarrier communication technique is that OFDM
system occupies the frequency spectrum efficiently and
wisely. OFDM satisfies orthogonality of communication
system subcarriers which means that a mathematical
relationship between these subcarriers is developed to allow
these subcarriers to overlap without having any adjacent
sub-channels interference . In any OFDM system, if we
have N equally spaced subcarriers, for instance, we would
satisfy the orthogonality property when we place them
within the specified frequency spectrum with frequency
spacing equals to:
Figure 1: Orthogonality property for five sub carriers .
Where N. Ts = Symbol duration .
This mathematical relationship creates a sine frequency
response for all these N subcarriers where each one of them
has maximum amplitude at a point, whereas others have
nulls . Figure1 shows how OFDM works.
The mathematical proof, which shows there is no
interference between signals if spaced as in equation (1), is
provided in  as the following:
Where, C is constant.
Equation (2) shows that out of 5 OFDM subcarriers,
shown in Figure 1, the amplitude of only one subcarrier can
be non-zero value at a frequency of multiples of 1/(N.Ts)
while the remaining ones should have zero amplitudes.
As a result of this orthogonality aspect, the spectral
inefficiency problem has been taken care of as it has been
shown in Figure 2. Considering that the system frequency
bandwidth is the most valuable component in any
communication system, OFDM system has met the aim of
occupying the communication system spectrum efficiently.
According to [8, 11, 12], OFDM multi carrier system
occupies 50% of the bandwidth that regular FDM
multicarrier system does.
Figure 2: Shows what the differences between the. FDM
and OFDM spectral efficiencies are .
3.2 ISI, ICI, guard time, CP in OFDM system
Another reason why OFDM is preferred over regular
single carrier modulation is the fact that OFDM mitigates
the effects of multipath delay spread significantly. By
dividing the data stream into N sub-streams, the symbol
duration time of each sub-stream is smaller than the
original one by a factor of (1/Ns) . This shorter symbol
duration helps reducing the effects of multipath delay
spread by a factor of (1/Ns) as well.
ISI is unwanted phenomenon which happens during the
communication process when one symbol interferes with
the adjacent symbols, or i.e. when the energy of one
symbol spills over the adjacent symbols . When the
channel delay spread time (τ) is larger than the symbol
spread time (T), ISI becomes severe. In addition, ISI
becomes ever more serious issue with high data rate
communication systems so this phenomenon needs to be
overcome to maintain communication quality. Therefore,
one of the goals that communication link designers were
trying to achieve is handling ISI and supporting high data
rates at the same time. The idea of OFDM that has handled
ISI problem is dividing high data rate stream wanted to be
transmitted into (L) lower rate sub-streams such that each
one has (Ts/L) >> (τ). This property gives almost free ISI
communication, as a result of ISI criterion mentioned
above . Moreover, OFDM handles ISI problem from
another angle to improve the results and eliminate effects
even more. That angle is to insert a guard time slots in
between OFDM symbols as it is shown in Figure 3. These
guard slots should be chosen to be larger than the expected
symbol delay spread time. Doing so, OFDM ensures that
multiple components received of one symbol due to
multipath environment do not interfere with the adjacent
symbols components .
That inserted guard time can be zero content signals.
However, introducing such guard slots raises the effects of
Inter Carrier Modulation (ICI). ICI is the consequences of
losing subcarriers orthogonality in OFDM system and that
happens when the receiver tries to retrieve one of the
subcarriers while a portion from the adjacent symbol is
being added causing ICI . Simply means when OFDM
subcarriers are not properly synchronized, the problem of
ICI would arise, or i.e. when having frequency offset
between OFDM subcarriers as it is illustrated in Figure 4.
That frequency offset causes ICI between adjacent
subcarriers when trying to demodulate one subcarrier
which is not synchronized properly with the adjacent one.
The proposed solution for this problem is adding cyclic
prefix (CP). CP was proposed first in 1980 by Peled and
Ruiz as in . Their idea was to occupy those time guard
slot of any OFDM symbol with the last portion of that
symbol as it is shown in Figure 5, a & b. That portion
duration chosen to have Ng samples. This time duration
should be longer than the longest expected symbol delay
spread. Therefore, the transmitted signal will have (Ng + N)
samples. The advantage of CP is to create an integer
number of cycles of each subcarrier when being passed
through FFT process or simply to maintain subcarriers
As a result of adding CP, energy from one subcarrier will
not interfere with others within FFT process. At the
receiver side, in order to retrieve the original N samples,
the added Ng samples should be excluded out. Doing so
means that the signal to noise ratio (SNR) gets decreased
due to the fact that these samples are being transmitted and
received and they have no useful information. In addition
to the drop in SNR, power consumption is a drawback of
adding CP. That high power consumption takes place
because the transmitter consumes power to transmit CP
samples which contain no useful data.
Figure 3: (a) & (b) show how the guard band is left In
between OFDM symbols .
Figure 4: Shows frequency offset problem which yields
3.1 OFDM frequency flat fading
OFDM has been the most known modulation scheme
candidate for high data rate wireless communications.
OFDM does group high data rate input stream into smaller
lower rate multiple sub-streams to ensure that each
sub-stream would have a flat fading not a frequency
selective one .
Selective frequency fading takes place when having a
wide range of frequencies and some of these frequencies
are more vulnerable to be faded than other frequencies are.
Therefore, when OFDM divides the wideband frequencies
into narrower frequency sub-bands, those narrow bands
experience the same fading effects along that sub-band
which is called flat frequency fading. It is known that flat
frequency fading consequences are lighter and easier to be
taken care of than the selective frequency fading
consequences are. One of the most valued benefits of not
having frequency selective fading is that the receiver no
longer needs complex equalizers and RAKE receivers .
Figure 5: a) Shows CP procedure .
Figure 5: b) Shows how CP is being added 
To be more specific, a communication system with flat
frequency fading needs only simple equalizer at the
receiver side, while the same communication system would
need more than one complex tap equalizers if having
frequency selective fading.
4. PAPR in OFDM
One of the OFDM implementation challenges is peak to
average power ration (PAPR).The major challenge of
implementing OFDM system is the high PAPR. IFFT
procedure in OFDM system involves adding up N
subcarriers which are all sinusoids. This summation of N
subcarriers, at some points gives high peaks values
compared to the average ones and that is well known as
high PAPR. This high PAPR is simply described as an
envelope fluctuation which causes many issues that
degrade the system performance as in , , and .
The most commonly used technique to evaluate the system
PAPR is the cumulative distribution function (CDF). In the
most recent publications, the complementary cumulative
distribution function (CCDF), which can be derived from
the CDF, is also used to evaluate the system PAPR.
5. PTS in OFDM
Partial Transmit Sequences (PTS) is one of the best
techniques that reduce the effect of the peak to average
power ration (PAPR) in OFDM scheme. For this technique,
the input data block is divided into N sub-blocks and each
one of these sub-blocks has multiple subcarriers. For each
sub-block, the subcarriers are weighted by a phase factor.
These phase factors are developed in a way to get the
PAPR of the combined OFDM signal reduced. The block
diagram of PTS is shown in Figure 6.
Simulation results are shown in Figure 7 for OFDM
signals by calculating its PAPR (Peak to Average Power
Ratio) based on different sample points Ns, 64,
128,256,512 and 1024. The x-axis represents the diverse
OFDM values, while y-axis represents the CCDF values.
The simulation in Figure 8 shows that OFDM performs
better when the some partial transmit sequences (PTS) are
chosen for different sub blocks points. The x-axis
represents the PAPR (dB) values, while y-axis represents
the probability of (PAPR > PAPR0) values.
The result of OFDM when PAPR is considered shows
that CCDF (Complementary Cumulative Distribution
Function) increases when the number of chosen points of
OFDM increase which make the system fast and more
applicable. The results illustrated the performance of
OFDM signal in response to using FFT, BPSK and QAM.
Moreover, the CCDF of OFDM signal is more accurate
when the number of OFDM points is increased. Using PTS
of PAPR the OFDM performance has clear improvement
and strong ability. The results show that probability of
(PAPR > PAPR0) increased from 10-4 to 10-1.
Figure 6: PTS system block diagram 
Figure 7: the relation between OFDM and CCDF for
different points with N= 64, 128, 256, 512, and 1024
Orthogonal Frequency Division Multiplexing (OFDM) is
an efficient technique that increases speed, range,
reliability and spectral efficiency for wireless systems. In
this paper we present OFDM using Partial Transmit
Sequences (PTS). The simulation results demonstrate the
improvement in capacity and reliability of OFDM using
PTS. Furthermore, we demonstrate that OFDM signal
becomes more accurate when the number of OFDM points
is increased. Also, using FFT, BPSK and QAM techniques
improve OFDM performance and throughput. Moreover,
OFDM is more efficient and flexible when the PTS PAPR
reduction technique is used.
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Figure 8: the relation of 16 QAM CCDF signal with PTS
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