Analysis of cyclic prefix length effect on ISI limitation in OFDM system over a Rayleigh-fading multipath

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 11, No. 4, August 2021, pp. 3114~3122
ISSN: 2088-8708, DOI: 10.11591/ijece.v11i4.pp3114-3122  3114
Journal homepage: http://ijece.iaescore.com
Analysis of cyclic prefix length effect on ISI limitation in OFDM
system over a Rayleigh-fading multipath
Sarah Zanafi, Noura Aknin
Information Technology and Modeling Systems Research Unit (TIMS), Abdelmalek Essaadi University,
Tetouan, Morroco
Article Info ABSTRACT
Article history:
Received Jan 2, 2019
Revised Nov 24, 2020
Accepted Jan 13, 2021
In this work, the influence of the cyclic prefix on the performance of the
OFDM system is studied. We worked out an OFDM transceiver using a 16
QAM modulation scheme, a comparison of the BER for various lengths of
the cyclic prefix has been achieved, and the influence of the noise introduced
in the channel has been highlighted, for both a Gaussian and Rayleigh noise.
The simulation was carried out on MATLAB where the curves of the BER
for various lengths of the cyclic prefix are given and compared. We also
adopted as a metric the QAM constellation to show the dispersion of the
carriers as a consequence of the transmission channel, the mitigation of this
effect by the CP is noticeable.
Keywords:
AWGN
CP
ICI
ISI
OFDM
Rayleigh
This is an open access article under the CC BY-SA license.
Corresponding Author:
Sarah Zanafi
Information Technology and Modeling Systems Research Unit (TIMS)
Abdelmalek Essaadi University
Faculty of science, Avenue de Sebta, Mhannech II, 93002 Tetouan-Morocco
Email: s.zanafi@gmail.com
1. INTRODUCTION
One of the major issues in telecommunication is to adapt the information to be passed over a
channel to the channel characteristics [1]. For frequency selective channels, an efficient technique is to use a
multi-carrier modulation in which the blocks of information are modulated by the Fourier transform [2]. This
technique known as orthogonal frequency division multiplexing (OFDM), showed to be very efficient [3].
The information is transmitted on N different sub-carriers [4], every sub-carrier having an interval of time
multiplied by N [5]. By assigning various sets of sub-carriers to various users, the transmitted carriers are
orthogonal between them, Therefore allowing every user to make correspond his symbols of data to the
corresponding sub-carriers. The system is N times more robust against the inter-symbol interference (ISI)
whereas the global rate of transmission remains identical. The spectral efficiency of the OFDM modulation is
thus excellent because sub-carriers can overlap. Nevertheless, the most difficult issue to deal with is the inter
symbol interference (ISI), resulting from the multipath distribution of the signal on the transmission channel
[6], the use of cyclic prefix in the emission allows to reduce the complexity of terminals through the use of
FFT algorithm [7].
The mathematical model of the ISI can be obtained by performing a linear convolution of the
impulse channel response with the bit stream in time domain [8]. The Inter carrier interference (ICI) reflects
the loss of orthogonality between the carrier frequencies as a result of the channel frequency response [9].
The cyclic prefix reduces at the same time ISI and ICI by transforming the linear convolution into a discrete
one by inserting the CP at the beginning of each block [10]. To this end, different ICI cancellation methods
have been proposed in the literature, In [11] authors presented the multilevel soft frequency reuse (SFR)
which aims to limit and manage the inter-cell interference, this method uses cell sectorization, in which each

Int J Elec & Comp Eng ISSN: 2088-8708 
Analysis of cyclic prefix length effect on ISI limitation in OFDM… (Sarah Zanafi)
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sector antenna covers a particular region of the cell, despite its efficiency in reduction ICI, this method
decreases the capacity in the cell. Reducing each customer throughput implies a reduction in spectral
efficiency. Some other studies and techniques like MMSE [12] have been introduced [13] to limit the effects
of ICI and ISI, these approaches require a high complexity in their implementation, whether on transmitter or
receiver side. In [14] a residues coding scheme is designed in order to measure the ICI levels, optimizing
conventional ICI mitigation techniques implemented in MIMO-OFDM. Despite the fact that all the previous
techniques can lead to a significant reduction of the noise ratio, but none of them fully satisfies the criteria of
balancing complexity and efficiency.
In this research we aim to mathematically analyse the effect of CP, and demonstrate its ability to
mitigate the ICI and ISI effects in realistic wideband communication scenarios, the proposed scheme can be
easily implemented because of its low complexity, simplifying the equalization at reception, while increasing
significantly the signal to interference ratio. The rest of the paper is organised as followin section 2, the paper
provides some basic channel models. Section 3 and 4 provide an analysis of the OFDM system. Section 5
describes the multipath effect. Section 6, presents an overview of th cyclic prefix. In section 7, we provide
the simulation results in order to demonstrate the system efficiency and finally the conclusion is provided in
section 8.
2. OFDM CHANNEL MODEL
2.1. AWGN channel
AWGN Channel is the simplest channel [6] and the only parameter is the SNR [7] as shown in Figure 1.
2.2. Rayleigh channel
The channel impulse response of Rayleigh multipath channel could be expressed as [4], and
modelled as illustrated in Figure 2 [6].
ℎ(𝑡, 𝜏) = ∑ 𝑈𝑘𝑒𝑗𝜑𝑘
𝛿(𝑡 − 𝜏𝑘)
𝐿−1
𝑘−1 (1)
where L is the number of paths, 𝜏𝑘 is the delay of the 𝑘𝑡ℎ
path, 𝑈𝑘𝑒𝑗𝜑𝑘
is the gain coefficient.
Figure 1. AWGN channel model Figure 2. Rayleigh channel model
3. OFDM TRANSMISSION SCHEME
Figure 3 depicts a classical OFDM transmission scheme. The input data sequence is baseband
modulated, using modulation schemes such as (BPSK, QPSK, QAM) in our system, 16 QAM method has
been used in order to encode the binary information. The data symbols are converted from serial to parallel,
each of the N parallel substream will modulate a separate carrier via the IFFT modulation block, which
actually generates the OFDM symbol, performing the multicarrier modulation. The inter symbol interference
and inter carrier interference are then dealt with by introducing a cyclic prefix. The cyclic prefix is obtained
by copying the rear part of OFDM symbol and put it at the beginning of the symbol [8]. After Parallel to serial
conversion, we can finally obtain the OFDM symbol [9]. At the receiver, the inverse operations are performed;
starting with the removal of the cyclic prefix [10], the spectral decomposition of the received samples calculated
using the FFT algorithm [15] and finally the demodulation [16], in the case of performing a channel
estimation and additional stage is added to estimate the response of the transmission channel [17].

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 11, No. 4, August 2021 : 3114 - 3122
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Figure 3. The block diagram of an OFDM system
4. SYSTEM DESCRIPTION
4.1. Orthogonality
Consider the time limited complex signals {𝑒𝑗2𝜋𝑓𝑘𝑡}𝑘=0
𝑁−1
which represent the different subcarriers
at𝑓𝑘 =
𝐾
𝑇𝑠𝑦𝑚
the OFDM signal, where 0 ≤ 𝑡 ≤ 𝑇𝑠𝑦𝑚. The signals are defined to be orthogonal if the integral
of the products on their common (fundamental) period is zero. The orthogonality described by (1) is the main
condition characteristic of an ICI free OFDM signal.
1
𝑇𝑠𝑦𝑚
∫ 𝑒𝑗2𝜋𝑓𝑘𝑡
𝑒−𝑗2𝜋𝑓𝑖𝑡
𝑇𝑠𝑦𝑚
0
𝑑𝑡 =
1
𝑇𝑠𝑦𝑚
∫ 𝑒
𝑗2𝜋
𝑘
𝑇𝑠𝑦𝑚
𝑡
𝑇𝑠𝑦𝑚
0
𝑒
−𝑗2𝜋
𝑖
𝑇𝑠𝑦𝑚
𝑡
𝑑𝑡
=
1
𝑇𝑠𝑦𝑚
∫ 𝑒
𝑗2𝜋
(𝑘−𝑖)
𝑇𝑠𝑦𝑚
𝑡
𝑇𝑠𝑦𝑚
0
𝑑𝑡
= {
1, ∀ 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑘 = 𝑖,
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒,
(1)
4.2. OFDM modulation and demodulation
ODFM transmitter codes the bit stream into a sequence of PSK symbols which will be subsequently
parallelized into N streams. This conversion is carried out by different subcarriers. Let 𝑋1[𝑘] denote
𝑙𝑡ℎ
transmit symbol at the 𝑘𝑡ℎ
subcarrier, 𝑙 = 0, 1, 2 … . , ∞, 𝑘 = 0, 1, 2 … , 𝑁 − 1. After the serial-to-parallel
conversion, the duration of transmission time for N symbols becomes 𝑁𝑇𝑠, which forms a single OFDM
symbol with a length of 𝑇𝑠𝑦𝑚(i.e., 𝑇𝑠𝑦𝑚 = 𝑁𝑇𝑠). Let 𝜓𝑙.𝑘(𝑡) be the 𝑙𝑡ℎ
OFDM signal at the 𝑘𝑡ℎ subcarrier,
which is given by:
𝜓𝑙.𝑘(𝑡) = {
𝑒𝑗2𝜋𝑓𝑘(𝑡−𝑙𝑇𝑠𝑦𝑚)
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(3)
Then the pass band and baseband OFDM signals in the continuous-time domain can be expressed
respectively as (4), (5).
𝑋1(𝑡) = 𝑅𝑒
1
𝑇𝑠𝑦𝑚
∑ ∑ 𝑋1[𝑘]𝜓𝑙.𝑘(𝑡)
∞
𝑘=0
∞
𝑙=0 , and (4)
𝑋1(𝑡) = ∑ ∑ 𝑋1[𝑘]𝑒𝑗2𝜋𝑓𝑘(𝑡−𝑙𝑇𝑠𝑦𝑚)
𝑁−1
𝑘=0
𝑁−1
𝑙=0 (5)
The sampling of the continuous time based OFDM signal given in (4) can be carried out at
𝑡 = 𝑙𝑇𝑠𝑦𝑚 + 𝑛𝑇𝑠with 𝑇𝑠 =
𝑇𝑠𝑦𝑚
𝑁
and 𝑓𝑘 =
𝑘
𝑇𝑠𝑦𝑚
to yield the corresponding discrete-time OFDM symbol as (6).
𝑋1[𝑛] = ∑ 𝑋1[𝑘]𝑒
𝑗2𝜋𝑘𝑛
𝑁
⁄
𝑁−1
𝑘=0 , 𝑓𝑜𝑟 𝑛 = 0, 1, … . 𝑁 − 1 (6)
Note that (6) is the N-point IDFT of PSK data symbols 𝑥1[𝑘]𝑘=0
𝑁−1
is performed using the inverse fast
Fourier transform (IFFT) algorithm. Considering the received baseband symbol 𝑦1(𝑡) =
∑ 𝑋1[𝑘]𝑒𝑗2𝜋𝑓𝑘(𝑡−𝑙𝑇𝑠𝑦𝑚)
𝑁−1
𝑘=0 , 𝑙𝑇𝑠𝑦𝑚 < 𝑡 ≤ 𝑙𝑇𝑠 + 𝑛𝑇𝑠, the transmitted symbol 𝑋1[𝑘] can be reconstructed by
the orthogonality among the subcarriers in (2) as:

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𝑌1[𝑘] =
1
𝑇𝑠𝑦𝑚
∫ 𝑦1(𝑡)
∞
−∞
𝑒−𝑗2𝜋𝑘𝑓𝑘(𝑡−𝑙𝑇𝑠𝑦𝑚)
𝑑𝑡
=
1
𝑇𝑠𝑦𝑚
∑ 𝑋1[𝑖]
𝑁−1
𝑖=0
𝑒𝑗2𝜋𝑓𝑖(𝑡−𝑙𝑇𝑠𝑦𝑚)
𝑒−2𝑗𝜋𝑓𝑖(𝑡−𝑇𝑠𝑦𝑚)
𝑒−𝑗2𝜋𝑓𝑘(𝑡−𝑙𝑇𝑠𝑦𝑚)
𝑑𝑡
= ∑ 𝑋1[𝑖]
𝑁−1
𝑖=0
1
𝑇𝑠𝑦𝑚
∫ 𝑒𝑗2𝜋(𝑓𝑖−𝑓𝑘)(𝑡−𝑙𝑇𝑠𝑦𝑚)
𝑑𝑡
𝑇𝑠𝑦𝑚
0
= 𝑋1[𝐾]
(7)
where the effects of channel and noise are not considered. Let 𝑦1[𝑛]𝑛=0
𝑁−1
be the sample values of the received
OFDM symbol 𝑦1(𝑡) at 𝑡 = 𝑇𝑠𝑦𝑚 + 𝑛𝑇𝑠. Then, by integrating (7) in the modulation process the discrete time
form of the signal is obtained:
𝑦1[𝑘] = ∑ 𝑦1[𝑛]𝑒−
𝑗2𝜋𝑘𝑛
𝑁
𝑁−1
𝑛=0
= ∑ {
1
𝑁
∑ 𝑋1[𝑖]𝑒𝑓𝑟𝑎𝑐𝑗2𝜋𝑖𝑛𝑁
𝑁−1
𝑖=0
} 𝑒−
𝑗2𝜋𝑘𝑛
𝑁
𝑁−1
𝑛=0
=
1
𝑁
∑ ∑ 𝑋1[𝑖]𝑒𝑗2𝜋(𝑖−𝑘)𝑛
𝑁
⁄
𝑁−1
𝑖=0
𝑁−1
𝑛=0
= 𝑋1[𝑘]
(8)
As shown in (8) is the N-point DFT of 𝑦1[𝑛]𝑛=0
𝑁−1
which is computed by using the fast Fourier
transform (FFT) algorithm. Diagram in Figure 4 depicts the OFDM modulation and demodulation structure,
for N=6, the frequency domain symbol 𝑋[𝑘] modulates the subcarrier with a frequency of 𝑓𝑘 =
𝑘
𝑇𝑠𝑦𝑚
, and at
the other end of the reception the demodulation is performed by taking advantage of the orthogonally
between subcarriers. The original symbol [𝑘] has duration of 𝑇𝑠, but its length has been extended to
𝑇𝑠𝑦𝑚 = 𝑁𝑇𝑠 by transmitting N symbols in a parallel form. Figure 4 illustrates a realization of orthogonally between
all subcarriers.
Figure 4. Block diagram of OFDM modulation and demodulation of 6 parallel streams
5. EFFECT OF MULTIPATH
In the following section we present the expression of SINR as a function of the following
parameters: symbol length [8], CP length [18], multipath and the thermal noise [16]. The CP length is Δ
seconds. The combined length of the OFDM symbol and the CP is 𝑇𝐺 + 𝑁𝑇𝑠. The function 𝐶(𝜏) is defined as (9).
This is obtained by applying the C function defined in the equation and traduced in time domain as in the
spectrum given in Figure 5.

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𝐶{𝜏} =
{
0, 𝜏 < −𝑁𝑇𝑠
𝑁𝑇𝑠+𝜏
𝑁𝑇𝑠
, − 𝑁𝑇𝑠 < 𝜏 < 0
1, 0 < 𝜏 < 𝑇𝐺
𝑁𝑇𝑠−(𝜏−𝑇𝐺)
𝑁𝑇𝑆
, 𝑇𝐺 < 𝜏 < 𝑁𝑇𝑆 + 𝑇𝐺
0, 𝑁𝑇𝑆 + 𝑇𝐺 < 𝜏
(9)
In the scenario of a N path channels with complex gains 𝛼𝑚, ℎ(𝑡) = ∑ 𝛼𝑚𝛿(𝑡𝜏𝑚),
𝑁 𝑝𝑎𝑡ℎ𝑠
𝑚=1 the SINR
for a channel with transmit signal power 𝜎𝑥
2
per subcarrier and thermal noise of variance 𝜎𝑛
2
per subcarrier,
can be written in terms of signal and interference power.
𝑆𝐼𝑁𝑅 =
𝑃𝑠
𝑃𝑖+
𝜎𝑛
2
𝜎𝑛
2
(10)
where:
𝑃𝑠 = ∑ 𝐶(𝜏𝑚)2
𝐸|𝛼𝑚|2
𝑁𝑝𝑎𝑡ℎ𝑠
𝑚=1 (11)
is the useful signal power after the FFT, and:
𝑃𝑖 = ∑ (1 − 𝐶(𝜏𝑚)2)𝐸|𝛼𝑚|2
= 𝑃ℎ − 𝑃𝑠
𝑚=1 (12)
𝑃ℎ = ∑ 𝐸|𝛼𝑚|2
𝑚=1 is the channel energy. We assume that all subcarriers are occupied, only then
the expression is an approximation of the empirical ICI/ISI power, and useful power. For rays in the tapered
portion of the bias function(𝐶(𝜏) ≤ 𝜏𝑚 < 𝑁𝑇𝑠 + ∆), it can be shown that their interference contribution is:
(1 − 𝐶(𝜏𝑚)2)𝐸|𝛼𝑚|2
=
(𝜏𝑚−𝑇𝐺)
𝑁𝑇𝑠
[1 +
𝑁𝑇𝑠−(𝜏𝑚−𝑇𝐺)
𝑁𝑇𝑠
] 𝐸|𝛼𝑚|2
(13)
In the middle term of this equation, the ‘1’ term is from ISI, while
𝑁𝑇𝑠−(𝜏𝑚−𝑇𝐺)
𝑁𝑇𝑠
term is due to ICI.
For small excess delays, we can consider that the ICI term is approximately equal to the ISI term.
Figure 5. The function 𝐶(𝜏) applied to impulse response
6. CYCLIC PREFIX
To add a cyclic prefix is to extend the OFDM symbol by copying the last samples of the OFDM
symbol into its front [19]. Let 𝑇𝐺 denote the length of CP in terms of samples [20] Then, the extended OFDM
symbols now have the duration of 𝑇𝑠𝑦𝑚 = 𝑇𝑠𝑢𝑏 + 𝑇𝐺. Figure 6 shows two consecutive OFDM symbols [21],
each of which has a CP of length 𝑇𝐺 [22]. Figure 7 illustrates the ISI generated by the multipath effect on
some subcarriers of the OFDM symbol [23]. It can be seen from this figure that if the length of the cyclic
prefix (CP) exceedsthe maximum delay of a multipath channel, the ISI effect of an OFDM symbol (dotted
line) on the next may not affect the FFT of the next OFDM symbol, taken for the duration of 𝑇𝑠𝑢𝑏 [24], this
means that the guard interval must be longer than the maximum delay of the multipath channel in order to
maintain the orthogonality with all other subcarriers over 𝑇𝑠𝑢𝑏, such that [25]:
1
𝑇𝑠𝑢𝑏
∫ 𝑒𝑗2𝜋𝑓𝑘(𝑡−𝑡0)
𝑑𝑡 = 0, 𝑘 ≠ 𝑖
𝑇𝑠𝑢𝑏
0
(14)

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For the first OFDM signal that arrives with a delay of 𝑡0, and;
1
𝑇𝑠𝑢𝑏
∫ 𝑒𝑗2𝜋𝑓𝑘(𝑡−𝑡0𝑇𝑠)
𝑇𝑠𝑢𝑏
0
𝑑𝑡 = 0, 𝑘 ≠ 𝑖 (15)
For the second OFDM signal that arrives with a delay of 𝑡0 + 𝑇𝑠.
Figure 6. OFDM symbol with CP
Figure 7. ISI effect of a multipath channel for each subcarrier
7. SIMULATION AND DISCUSSION
7.1. Parameters of the simulation
To simulation setup details in MATLAB commercial software are shown in Table 1, the OFDM
scheme has 128 sub-carriers using 16 QAM modulation, transmitted over the AWGN and Rayleigh channel,
which depends on two parameters: 𝜏 and the gain on each path.
Table 1. The parameters of the simulation
Number of subcarriers 128
Modulation scheme 16 QAM
Sampling period 1𝑒−5
CP length From 0% to 30%
Number of frames 1000
The delay 𝜏 0, 100𝑒−5
, 3.5 𝑒−5
, 1200𝑒−5
The gains 0, -6, -3, -5
7.2. Simulation
In this work, we carried out a comparative study of the behavior of an OFDM transmission system,
by varying the length of CP values from 0% to 30% of the total duration of the symbol. The metric used for
this evaluation is the BER taking SNR values ranging from -5 to 20 dB. The AWGN channel considers only

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one path between the transmitter and the receiver and only a constant attenuation noise, so no multipath
effect, which makes the transmission immune to ISI. The Rayleigh fading channel instead considers
multipath between transmitter and receiver as shown in Figure 8. Therefore, the communication is affected
by ISI, making its BER higher than that of the AWGN channel for different values of SNR.
The introduction of the CP as shown in Figure 9, reduces the BER of the signal on the Rayleigh
fading channel while the one on AWGN channel remains unchanged. This is fully consistent with the fact
that the AWGN channel does not take the multipath into account, so the introduction of the CP does not
improve the BER for this channel. The Rayleigh fading channel response is more affected by the CP length,
because the main parameters of this channel are the frequency spread spectrum and the delay introduced by
the multipath. We clearly notice that their effect is reduced by the introduction of the CP, as shown on
Figure 10 representing the BER Vs SNR for a signal without CP compared to another with a CP representing
0% to 30% from the inter symbol. We notice that keeping the signal at the same level 0.01 BER requires a
3 dB greater SNR or the introduction of 10% CP. The length of the CP needed to keep the signal at the same
BER level is even more considerable when compared to the 30% CP length where we need a 6 dB SNR, in
comparison to other simple solutions, this almost matches their performance allows the SNR to grow to
45 dB for the blind algorithm [15], and similar performance shown when using equalization [18].
Figure 8. BER performance of OFDM system for
AWGN and Rayleigh fading channel without CP
Figure 9. BER performance of OFDM system for
AWGN and Rayleigh fading channel with varying
CP length
7.3. Constellation
In the constellation diagram for the 16 QAM modulation we depict the error introduced by the
channel and caused mainly by the linear distortions (amplitude ripple, group delay, low carrier-to-noise ratio)
as a dispersion of the symbol points around the theoretical position, for each point of the constellation. This
degradation of the quality of the modulation is given by the MER shown in (15).
𝑀𝐸𝑅 = 10𝑙𝑜𝑔10 [
∑ (𝐼𝑗
2
+𝑄𝑖
2
)
𝑁
𝑗=1
∑ (𝛿𝐼𝑗
2+𝛿𝑄𝑗
2)
𝑁
𝑗=1
] (16)
Assuming that the transmitted data-symbol is represented by the coordinate pair (𝑎𝑘 + 𝑏𝑘). After
reception, the baseband I, Q signals are given by:
𝐼𝑘 = 𝑅𝑒𝑎𝑙[(𝑎𝑘 + 𝑗𝑏𝑘)𝑒𝑗𝜙𝑛]
= 𝑎𝑘 cos(𝜙𝑛) − 𝑏𝑘 sin(𝜙𝑛) + 𝑛𝐼
𝑄𝑘 = 𝐼𝑚𝑎𝑔[(𝑎𝑘 + 𝑗𝑏𝑘)𝑒𝑗𝜙𝑛] (17)
= 𝑎𝑘 sin(𝜙𝑛) + 𝑏𝑘 cos(𝜙𝑛) + 𝑛𝑄
In the Figure 10, for the same snr value the CP length can improve the quality of the MER hence the
quality of the transmission, by limiting this dispersion, and for a lower value of the SNR, the effect of the CP
length is more noticeable.

3121
(a) (b) (c)
(d) (e) (f)
Figure 10. 16QAM constellation for two values of SNR: 20db; (a) CP 0%, (b) CP 10%, (c) CP 30%,
and 40 db, (d) CP 0%, (e) CP 10%, and (f) CP 30%
8. CONCLUSION
In this work, we have discussed the transmission problems in the OFDM transmission scheme, the
effect of CP length has been simulated in terms of BER for AGWN and Rayleigh fading channel. The
AWGN channel considers only one path between the transmitter and receiver, whereas the Rayleigh fading
channel takes into consideration the multipath which is the main reason of the received signal distortion
leading to the ISI. In OFDM system this is avoided by the introduction of the CP. On the simulation we
carried out, we observed that the effect of the multipath decreases with the increasing of the CP length. It
would be easy to assume that the increase of the CP length has always a positive impact on the transmitted
signal, but because the duration of the CP is deducted from the total time dedicated to the data, a trade-off
must be made between the robustness of the signal and the throughput, therefore, there are limits to the size
of the CP. On the other hand, we carried a simulation on the effect of the CP on the dispersion of the
constellation in the Rayleigh channel scenario and it yields that the introduction of the CP could reduce it
considerably.
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BIBLIOGRAPHY OF AUTHORS
Sarah Zanafi, received the license in Electronics Electrotechnics and Automatics (EEA) from
Abdlmelek Essaidi university, faculty of science and Technology, Tangier, Morocco in 2011 and
the Master degree in telecommunication systems engineering (TSE) from faculty of science,
Tetuan in November 2013 and is currently pursuing the Ph.D. degree. His research interests are
new-generation mobile system design, radio network planning and optimization.
Noura Aknin, Professor of Electrical & Computer Engineering at Abdelmalek Essaadi
University since 2000. She received PhD degree in Electrical Engineering in 1998. She is the
Head of Research Unit Information Technology and Modeling Systems. She is R&D project
manager/member related to new technologies and their applications. She was a chair of several
conferences and she has been involved in the organizing and in the Scientific Committees of
several international conferences held worldwide dealing with Information and Communication
technologies. Her research interests focus mainly on mobile and wireless communications, ICT
and their applications. She has authored and co-authored several papers covering different topics
related with the fields cited above.

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