IMPROVEMENT OF LTE DOWNLINK SYSTEM PERFORMANCES USING THE LAGRANGE POLYNOMIAL INTERPOLATION

International Journal of Computer Networks & Communications (IJCNC) Vol.6, No.5, September 2014
IMPROVEMENT OF LTE DOWNLINK SYSTEM
PERFORMANCES USING THE LAGRANGE
POLYNOMIAL INTERPOLATION
Mallouki Nasreddine, Nsiri Bechir, Walid Hakimi and Mahmoud Ammar
University of Tunis El Manar, National Engineering School of Tunis, LR99ES21 Lab.
Sys’ Com, ENIT Tunis, Tunisia
ABSTRACT
To achieve a high speed data rate, higher spectral efficiency, improved services and low latency the 3rd
generation partnership project designed LTE standard (Long Term Evolution).the LTE system employs
specific technical as well the technical HARQ, MIMO transmission, OFDM Access or estimation technical.
In this paper we focus our study on downlink LTE channel estimation and specially the interpolation which
is the basis of the estimation of the channel coefficients. Thus, we propose an adaptive method for
polynomial interpolation based on Lagrange polynomial. We perform the Downlink LTE system MIMO
transmission then compare the obtained results with linear, Sinus Cardinal and polynomial Newton
Interpolations. The simulation results show that the Lagrange method outperforms system performance in
term of Block Error Rate (BLER) , throughput and EVN(%)vs. Signal to Noise Ratio (SNR).
KEYWORDS
LTE; MIMO ;OFDM;EVM; Interpolation; Lagrange;
1. INTRODUCTION
In modern world, requirement of high data rate communication has become inevitable.
Applications such as streaming transmission, video images, and World Wide Web browsing
require high speed data transmission with mobility. In order to fulfill these data requirements, the
3rd Generation Partnership Project (3GPP) [1][2][3] introduced Long Term Evolution (LTE), to
provide high speed data rate for mobile communication. The LTE system affords an important
effective bit rate and allows increasing system capacity in terms of numbers of simultaneous calls
per cell. In addition, it has a low latency compared to 3G/3G + networks. It offers a theoretical
speed of 100 Mbits / s in the Downlink and 50Mbits/s in the Uplink transmission. The LTE uses
Orthogonal Frequency Division Modulation (OFDM) and Orthogonal Frequency Division
Modulation multiple access technique (OFDMA) in the downlink transmission [4]. The OFDM
provides the signal transmitted robustness against the multipath effect and can improve the
spectral efficiency of the system [5][6]. On the other hand, the implementation of MIMO system
increases channel capacity and decreases the signal fading by sending the same information at the
same time through multiple antennas [6]. The combination of these two powerful technologies
(MIMO-OFDM) in the LTE system improving thus the spectral efficiency and throughput offered
without increasing resources for base bands and power output.
To best exploit the power of MIMO-OFDM technology, it is imperative to manage at best the
estimation of the channel coefficients; this operation is ensured by the interpolation of pilots.
DOI : 10.5121/ijcnc.2014.6509 129

In this paper, we represent a polynomial interpolation algorithm using the method of Lagrange
[12] which greatly reduces the complexity of the transceiver. The simulation is made on a
‘Vehicular A’ (Veh A) [13].channel through MIMO system using Least Square equalizer (LS).
Section II of this paper give an over view of MIMO-OFDM transmission. In Section III, we
present Lagrange interpolation algorithm. Finally, Section IV provides the numerical results.
130
2. MIMO-OFDM TRANSMISSION
2.1. MIMO OFDM transmissions schemes [3]
In this section, we describe the MIMO OFDM transceiver. A modulation block is used to
modulate the original binary data symbol using the complex constellation QPSK, 16 QAM or 64
QAM according to the LTE standard [8][9]. Pilot insertion is generated according to the LTE
standards, followed by Inverse Fast Fourier Transform operation (IFFT); at the end, a cyclical
prefix is inserted to remedy the phenomenon of the Inter Symbol Interference (ISI) and the Inter
Sub carriers Interference. Transmission is made through a multipath Fast Fading channel over a
multiple antenna system. Multiple antennas can be used in the transmitter and the receiver;
consequently, MIMO encoders are needed to increase the spatial diversity or the channel
capacity. Applying MIMO allows us to get a diversity gain to remove signal fading or getting a
gain in terms of capacity. Generally, there are three types of MIMO receivers, as presented in [1].
At the reception, the cyclical prefix is firstly removed, followed by the Fast Fourier Transform
operation (FFT); after the extraction of pilots, parameters of channel is estimated through the
block interpolation followed by equalization. The method of interpolation chosen is essential to
make the estimation more efficient and to reduce the equalizer complexity.
Figure 1. MIMO-OFDM transmission
2.2. Analysis of standard LTE pilot scattering
In the LTE standards, pilots are placed in a well-defined ways to cover up the frequency and time
domain. The location of pilots for 2x2 MIMO transmissions scheme in LTE system is shown in
the following figures.

131
Time Symbol index Time Symbol index
Figure 2. Pilot structure of Transmitter1&2
It can be seen that, through the first antenna, pilots are disposed in OFDM symbols numbers 1, 5,
8 and 12 while for the second antenna, they are placed in the same OFDM symbols, but in
different subcarriers index. Those positions allow a better coverage of the frequency and time and
reduce the risk of interference in reception [4].
2.3 Error Vector Magnitude (EVM)[7]
Error vector magnitude (EVM) is a measure of modulation quality and error performance in
complex wireless systems. It provides a method to evaluate the performance of software-defined
radios (SDRs), both transmitters and receivers. It also is widely used as an alternative to bit error
rate (BER) measurements to determine impairments that affect signal reliability. (BER is the
percentage of bit errors that occur for a given number of bits transmitted.) EVM provides an
improved picture of the modulation quality as well.
EVM measurements are normally used with multi-symbol modulation methods like multi-level
phase-shift keying (M-PSK), quadrature phase-shift keying (QPSK), and multi-level quadrature
amplitude modulation (M-QAM). These methods are widely used in wireless local-area networks
(WLANs), broadband wireless, and 4G cellular radio systems like Long-Term Evolution (LTE)
where M-QAM is combined with orthogonal frequency division multiplexing (OFDM)
modulation.
EVM is the ratio of the average of the error vector power (Perror) to the average ideal reference
vector power (Pref) expressed in decibels. The averages are taken over multiple symbol periods:

EVM(dB) =10Log(Perror / Pr ef ) (1)
= − (4)
132
You will also see it expressed as a percentage:
EVM(%) = Perro / Pr ef *100 (2)
3. DESCRIPTION OF THE INTERPOLATION ALGORITHM
3.1 Linear Interpolation
In linear polynomial interpolation, the channel coefficients are estimated using the linear
relationship between two successive pilots.
Linear interpolation is given by the following expression:
( ) ( ) ( )
( ) ( )( ) ( 1) ( / )* (1 ( / )) * i i i
k k p p H i d H i d H + = + − (3)
where ( )
k H is the channel coefficient to estimate, ( )
( ) i
k p H and ( )
( )( ) i
( 1) i
p H + two successive pilots, i is
the subcarriers index, k is the OFDM symbol index, p is the pilot index and d is the distance
between two pilots [10].
3.2. Sinus Cardinal Interpolation
Sinus Cardinal (SinC) interpolation is given by the following expression [11]:
n
( ) ( ) sin ( )
S x S k c x k
0
i
=
Where S(k) are the pilots, k is the position of y, S(x) is the Sinus Cardinal interpolation
function. In this work, we use 2 pilots to estimate channel coefficients using Sinus Cardinal
Interpolation. The interpolation is represented as follow:
1-Extract received ( )
i
k p y pilots from received signal ( )
( )( )
i
k y
( )
2-Calculate the channel coefficients of pilots symbols with
Least Square estimator
( ) ( ) ( )
( )( ) ( )( ) ( )( ) / i i i
k p k p k p H = y x (5)
3- Estimate ( )
i
k H with Sinus Cardinal interpolation:
( )
( ) ( ) ( )
( ) 0 ( )( 0) 1 ( )( 1) sin ( )* sin ( )* i i i
k P k P P k P H = c x − x H + c x − x H
(6)
3.3. Newton polynomial Interpolation:
Newton polynomial Interpolation is given by the following expression [12]:

International Journal of Computer Networks Communications (IJCNC) Vol.6, No.5, September 2014
=Õ − (8)
= (11)
=Õ − − (12)
i
k H is the channel
133
n
=
( ) ( )
P x a N x
n i i
0
i
=
(7)
1
( ) ( )
N x x x
0
i
i j
j
−
=
0 [ ................. ] i i a = f x x
(9)
0 1 0 1 0 1 f [x , x ] = ( f [x ]− f [x ]) / (x − x )
0 a ……. n a are the coefficients of Newton polynomial of order n, n P is the polynomial of
Newton and i x are the pilots frequency indexes.
Estimate ( )
i
k H with Newton polynomial:
( )
( )
( )
n
= =
i
k n i i
( ) ( )
H P x a N x
0
i
=
(10)
3.4. Lagrange polynomial Interpolation
Lagrange polynomial allows interpolating a set of points by a polynomial which goes exactly
through these points. The Lagrange polynomial is given by the following expression [12]
n
( ) ( )
P x y L x
0
i i
i
=
( ) ( ) / ( )
L x x x x x
0
n
i i j
=
¹
j
j i
Where i y the pilots, x is the position of y, L is the coefficients of Lagrange and n is the
Lagrange polynomial order.
3.5. Algorithm description
The received signal for MIMO system model consisting of T N transmits antennas and R N
receives antennas can be represented by the following Equation:
( ) ( )
( ) ( ) * i i
k k Y = X H + N (13)
i N N
k NOFDM SYMN Y = y y y is the received vector, ( )
Where ( ) 0
( ) 0 0 _ [ ........... SC ............. SC ]
R
( )
coefficient matrix of the dimensions T N x R N express the channel gain and N= [n1, n2
……n R N ] T is the noise vector.

i
k H to estimate and p0 x , p1 x , p2 x are the frequency indexes of first tree pilots.
134
The matrix ( )
( ) i
k H is written as follow [12][13]:
h ( i ) h ( i ) ............
h
( i
)

( k ) ( k )1,2 ( k )1,
N

h ( i ) h ( i ) ............
h
( i
)

=

( ) ( )2,1 ( )2,2 ( )2,
( )
i k k k N
k
( ) ( ) ( )
( ) ,1 ( ) ,2 ( ) ,
i i ............
i
k N k N k N N
T
T
R R R T
H
M
h h h
(14)
For each reception antennas, after eliminating Cyclical Prefix and Fast Fourier Transform
operation, pilots are extracted and then interpolation block is attacked to estimate the parameter
( )
( ) i
k H of the channel. The interpolation operation is necessary for both frequency and time
domain. In the present work, we use a Lagrange polynomial interpolation for frequency domain
and linear interpolation for temporary. The interpolation algorithm is represented in figure4.
The steps of algorithm are described as follow:
1-Extract ( )
i
k p y pilots from received signal ( )
( )( )
i
k y
( )
2-Calculate the channel coefficients of pilots symbols with
Least Square estimator
( ) ( ) ( )
( )( ) ( )( ) ( )( ) / i i i
k p k p k p H = y x (15)
3-Calculate 0 L …………….. n L Coefficients of Lagrange with n order of Lagrange polynomial
and p index of pilots, we start with n=2. For example for 12 first coefficients to estimate we use 3
first pilots placed respectively at p0 x = 0, p1 x = 6 and p2 x =12 frequency index
0 1 2 0 1 0 2 (( )*( )) / (( )*( )) i p i p p p p p L = x − x x − x x − x x − x (16)
Where 0 L , 1 L and 2 L are the coefficients of Lagrange polynomial of order n=3, i x is the
frequency index of ( )
( )

135
Figure 3. Algorithm of interpolation
4-Estimate ( )
i
k H with Lagrange polynomial:
( )
( ) ( ) ( ) ( )
( ) 0 ( )( ) 1 ( )( 1) 2 ( )( 2) * * * i i i i
k k p k p k p H L H L H L H + + = + + (19)
where ( )
i
k p H , ( )
( )( )
i
k p H + and ( )
( )( 1)
i
k p H + are three successive pilots.
( )( 2)

5- Testing the estimation operation performance by incrementing the polynomial of order n until
having optimal performance in term of Block Error Rate (BLER), Throughput and Error Vector
Magnitude (EVM(%)) vs. SNR.
=Õ − − (20)
=Õ − − (21)
i
k p H and
136
4. SIMULATIONS RESULTS
Our simulations was performed for LTE downlink transmission through a channel which uses the
profile of ITU-Veh A for MIMO system with use of 16 QAM (CQI=7) constellation. This
simulation in divided in 2 parts, firstly we present BLER vs SNR over many values of the order
of Lagrange Polynomial (n) to determinate the optimal one. In the second part, we showed
simulation results for known channel, Lagrange polynomial interpolation algorithm, Sin Cardinal
Interpolation, Newton polynomial interpolation and linear interpolation for optimal n. All
simulations are used over a Least Square equalizer. Simulation results are compared in term of
Block Error Rate (BLER), Throughput and Error Vector Magnitude (EVM(%)) vs. SNR. this
System is simulated using the parameters shown in TABLE I [13][15].
TABLE 1. PARAMETERS SIMULATION.
Transmission Bandwidth 1.4 MHz
Carrier Frequency 2.1 GHz
Data Modulation 16 QAM (CQI 7)
Channel ITU-Veh A
Interpolation
Polynomial interpolation OF LAGRANGE
Polynomial interpolation OF Newton
Sinus Cardinal Interpolation
Linear Interpolation
4.1. Practical Determination of optimal n
One of aim of our adaptive algorithm is to determinate an optimal value of n the order of
Lagrange polynomial. In this part we show how our algorithm determinate n. For that, we choose
4 values of n and we present their performance in term of BLER vs SNR for a MIMO system.
• order of Polynomial n=1(Linear interpolation)
L x x x x
0 0
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
1 1
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
( ) ( ) ( )
( ) 0 ( )( 0) 1 ( )( 1) * * i i i
k k p k p H = L H + L H (22)
Where 0 L and 1 L are the coefficients of Lagrange polynomial of order n=1, i x is the frequency
index of ( )
H i
to estimate, x are the frequency indexes of pilots and ( )
( k )
pj i
k p H , ( )
( )( 0)
( )( 1)
two successive pilots.

=Õ − − (23)
=Õ − − (24)
=Õ − − (25)
=Õ − − (26)
i
k p H ,
=Õ − − (28)
=Õ − − (29)
=Õ − − (30)
=Õ − − (31)
=Õ − − (32)
=Õ − − (33)
137
• order of Polynomial n=3(Cubic interpolation)
L x x x x
0 0
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
1 1
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
2 2
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
3 3
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
( ) ( ) ( ) ( ) ( )
( ) 0 ( )( 0) 1 ( )( 1) 2 ( )( 2) 3 ( )( 3) * * * * i i i i i
k k p k p k p k p H = L H + L H + L H + L H (27)
Where 0 L , 1 L , 2 L and 3 L are the coefficients of Lagrange polynomial of order n=3, i x is the
frequency index of ( )
i
k H to estimate , pj x are the frequency indexes of pilots and ( )
( )
( )( 0)
i
k p H , ( )
( )
( )( 1)
i
k p H and ( )
( )( 2)
i
k p H four successive pilots.
( )( 3)
• order of Polynomial n=5
L x x x x
0 0
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
1 1
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
2 2
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
3 3
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
4 4
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
5 5
0
(( ) /( ))
n
pj p pj
=
¹
j
j i

( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) 0 ( )( 0) 1 ( )( 1) 2 ( )( 2) 3 ( )( 3) 4 ( )( 4) 5 ( )( 5) * * * * * * i i i i i i i
k k p k p k H = L H + L H + L H p + L H k p + L H k p + L H k p
(34)
Where 0 L , 1 L , 2 L , 3 L , 4 L and 5 L are the coefficients of Lagrange polynomial of order n=5, i x
is the frequency index of ( )
i
k p H
=Õ − − (35)
=Õ − − (36)
=Õ − − (37)
=Õ − − (38)
=Õ − − (39)
=Õ − − (40)
=Õ − − (41)
=Õ − − (42)
i
k H to estimate , pj x are the frequency indexes of
i
k p H
138
H i
to estimate , x are the frequency indexes of pilots and ( )
( k )
pj ( )( 0)
, ( )
i
k p H , ( )
( )( 1)
i
k p H , ( )
( )( 2)
i
k p H , ( )
( )( 3)
i
k p H and ( )
( )( 4)
i
k p H four successive pilots.
( )( 5)
• order of Polynomial n=7
L x x x x
0 0
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
1 1
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
2 2
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
3 3
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
4 4
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
5 5
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
6 6
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
L x x x x
7 7
0
(( ) /( ))
n
pj p pj
=
¹
j
j i
( ) * ( ) * ( ) * ( ) * ( ) * ( ) * ( ) * ( ) * ( )
( ) 0 ( )( 0) 1 ( )( 1) 2 ( )( 2) 3 ( )( 3) 4 ( )( 4) 5 ( )( 5) 6 ( )( 6) 7 ( )( 7)
H i = L H i + L H i + L H i + L H i + L H i + L H i + L H i +
L H i
k k p k p k p k p k p k p k p k p
(43)
Where 0 L , 1 L , 2 L , 3 L , 4 L , 5 L , 6 L and 7 L are the coefficients of Lagrange polynomial of
order n=5, i x is the frequency index of ( )
( )
pilots and ( )
i
k p H , ( )
( )( 0)
i
k p H , ( )
( )( 1)
i
k p H , ( )
( )( 2)
i
k p H , ( )
( )( 3)
i
k p H , ( )
( )( 4)
i
k p H , ( )
( )( 5)
i
k p H and ( )
( )( 6)
( )( 7)
are eight successive pilots.

139
-5 0 5 10 15 20
0
10
-1
10
-2
10
Eb-No
BLER
BW= 1.4 MHZ
MIMO-16QAM-Perfect
MIMO-16QAM-n=5
MIMO-16QAM-Linear
MIMO-16QAM-n=3
MIMO-16QAM-n=7
Figure 4. BLER vs. SNR for MIMO Transmission over Veh-A channel, CQI=7.
In Figure 4 the BLER vs SNR of LTE Downlink system over MIMO transmission for different
value of the order of Lagrange Polynomial(n), is showed. We notice that the proposed algorithm
of polynomial interpolation gives the best performances for n=5 which is considered as an
optimal order of polynomial of interpolation. We also see, that for n more than 5(in our case n=7)
we have the same performance in term of BLER vs SNR for these conditions of transmission.
4.2. Simulation results and discussion
To observe the effect of the Lagrange polynomial interpolation compared to linear, Sin Cardinal
and Newton interpolation techniques, we simulate and plot the performance of LTE Downlink
system in MIMO transmission over multipath channel (ITU-Veh A) using an LS equalizer . The
simulations have been carried out for the 16-QAM (CQI=7). The Block Error Rate (BLER),
throughput and Error Vector Magnitude (%) vs. SNR results were study. Figure 5 show Block
Error Rate vs. SNR for known channel, Lagrange polynomial, Sinus Cardinal ,Newton
polynomial and linear interpolations for MIMO transmission.
-5 0 5 10 15 20
0
10
-1
10
-2
10
Eb-No
BLER
BW= 1.4 MHZ
MIMO-16QAM-Perfect
MIMO-16QAM-Lagrange
MIMO-16QAM-Linear
MIMO-16QAM-Sinc
MIMO-16QAM-Newton
Figure 5. BLER vs. SNR for MIMO Transmission over Veh-A channel, CQI=7.
We can see that the proposed adaptive algorithm of Lagrange polynomial interpolation enhances
the performance of downlink LTE system by almost than 2 dB for BLER =10-1 compared to the
Linear and the Sinus Cardinal Interpolations. On the other hand, we also see that performance of

MIMO system using Polynomial Lagrange and Polynomial Newton interpolation gives the same
results in term of BLER vs SNR despite that newton interpolation is more complex.
140
-5 0 5 10 15 20
1.5
1
0.5
0
Eb-No
Throuput(Mbitps)
BW= 1.4 MHZ
MIMO-16QAM-Perfect
MIMO-16QAM-Lagrange
MIMO-16QAM-Linear
MIMO-16QAM-Sinc
MIMO-16QAM-Newton
Figure 6. Throughput vs. SNR for MIMO Transmission over Veh-A channel, CQI=7.
As shown in Figure 6 the throughput of MIMO transmission for CQI=7 over Vehicular A channel
for known channel, Lagrange polynomial, Sinus Cardinal ,Newton polynomial and linear
interpolations are investigated. We can note that the suggested algorithm of polynomial
interpolation improves the throughput compared to the linear and the Sinus Cardinal
interpolation. For example, with throughput=1 MHz we have a gain almost than 1dB for MIMO
systems.
On the other side, performance of LTE Downlink system in term of Throughput vs SNR using
Lagrange interpolation gives the same results compared to the Newton Polynomial interpolation
100
90
80
70
60
50
40
30
20
10
0
-2 0 2 4 6 8 10 12
Eb-No
EVM(%)
BW= 1.4 MHZ
EVM-MIMO-16QAM-Perfect(%)
EVM-MIMO-16QAM-Linear(%)
EVM-MIMO-16QAM-Lagrange(%)
Figure 7. EVM(%) vs. SNR for MIMO Transmission over Veh-A channel, CQI=7.
Figure 7 shows the Error Vector Magnitude vs SNR for LTE Downlink system using Known
Channel, Linear interpolation and Lagrange polynomial interpolation. We note, that the Lagrange
Polynomial interpolation enhances measured EVM (%) compared to the Linear interpolation by
almost 3% for a SNR=8dB.

141
100
90
80
70
60
50
40
30
20
10
0
-2 0 2 4 6 8 10 12
Eb-No
EVM(%)
BW= 1.4 MHZ
EVM-MIMO-16QAM-Perfect(%)
EVM-MIMO-16QAM-Lagrange(%)
EVM-MIMO-16QAM-Newton(%)
Figure 8. EVM(%) vs. SNR for MIMO Transmission over Veh-A channel, CQI=7.
Measured EVM (%) of Lagrange polynomial interpolation and Newton Polynomial interpolation
are investigated in Figure 8, we find that, these two techniques of interpolation have got the same
performance in term of EVM (%)
After studying performance, we find that the Lagrange polynomial interpolation offers a
significant improvement compared to the linear and the Sinus Cardinal Interpolations in term of
BLER, Throughput and EVM(%) vs SNR , as a result of the precision given by using n pilots to
estimate each channel parameter. In fact, the use of n pilots in estimation of the channel
coefficients takes into account the correlation between the pilot subcarriers; which makes this
calculation more accurate and thus enhances the system efficiency.
It is obvious that this polynomial interpolation algorithm is more complex than the linear and
Sinus Cardinal Interpolation, however it significantly improves system performance especially
in the case of a fast fading channel (our case).
On the other hand, the Lagrange Polynomial and the Newton Polynomial interpolation gives the
same performances in term of BLER, Throughput and EVM (%) vs SNR despite the complexity
of the Newton method compared to the Lagrange method.
Finally, this algorithm has the advantage of having an adaptable order of polynomial interpolation
n according to conditions of transmission. For example, in our case, we use a channel ITU-Veh A
in the Bandwidth of 1.4 MHz where we have n = 5 for same Bandwidth but for ITU-PEDISTRIAN-
B channel n = 4.
5. CONCLUSION
In the present work, adaptive polynomial interpolation algorithm was described in relation with
the method of Lagrange for Downlink LTE system. Simulation is achieved through an ITU-Veh
A channel with CQI = 7 and for MIMO system .We conclude that, despite the complexity of this
algorithm (compared to the linear and Sinus Cardinal Interpolation), it offers a considerable
improvement of the performance of Downlink LTE system. In effect, using a maximum number
of pilots to estimate the parameters of the channel against two for a linear and Sinus Cardinal
interpolation optimize considerably the estimation of these parameters. We conclude also, that
despite the complexity of Newton method compared to Lagrange method the performances of
LTE Downlink system using these two techniques of polynomial interpolation are identical.

Another advantage for our adaptive algorithm, that he offers an adaptive order of polynomial n
according to the conditions of system.
142
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Authors
Nasreddine Mallouki, was born in Tunis, Tunisia, on November 1982. From November
2007 until now, he works in National Broadcasting Office, Tunisia. He received the
master degree in telecommunication specialty from the National School of Engineering in
Tunis (ENIT) in Tunisia in 2011. Currently he is a PhD student at the School of
Engineering of Tunis. The research works are realized in Department SYS’COM
laboratory in ENIT. His principal research interests lie in the fields of Wireless and Radio
Mobile Telecommunications engineering such as MIMO OFDM technology and
estimation in radio network planning in LTE system.

143
Bechir Nsiri, was born in Boussalem, Tunisia, on August 1983. From September 2011
until now, he teaches in Higher Institute of Applied Science and Technology Mateur,
Tunisia. He received the master degree in telecommunication specialty from the
National School of Engineering in Tunis (ENIT) in Tunisia in 2011. Currently he is a
PhD student at the School of Engineering of Tunis. The research works are realized in
Department SYS’COM laboratory in ENIT. His principal research interests lie in the
fields of Wireless and Radio Mobile Telecommunications engineering such as MIMO
OFDM technology and scheduling in radio network planning in LTE system.
Walid Hakimi is a Regular Professor of Telecommunications at High Institute of
technology Study, (Rades, Tunis, Tunisia) since September 1999. From September
2011until now, he teaches in Electrical Engineering Department, High School of
technology and Computing, Tunis, Tunisia. He is a member of SYSCOM laboratory
in ENIT. His principal research interests lie in the fields of Wireless and Radio
Mobile Telecommunications engineering. He has received the Dipl.-Ing. Degree in
electrical engineering from the National school of engineers of Tunis (ENIT),
Tunisia. Also, he obtained Doctorat These from University Tunis El Manar, National
School of Engineering in Tunis (ENIT), in 2010, in SYS’COM laboratory with collaboration of Telecom
Bretagne, Brest, Department SC, CNRS TAMCIC, Technople Brest-Iroise in France.
Mahmoud Ammar was born in Korba, Tunisia. Received the Dipl.- Engi. Degree in
electrical engineering from the National School of Engineering in Tunis (ENIT) in
Tunisia. He received the M.S. and Doctorat These degrees in telecommunication
specialty from Bretagne occidental University in 1999, and 2002, respectively. The
research works are realized in Department SC of TELECOM Bretagne, CNRS
TAMCIC, Technople Brest-Iroise in France. He is currently working in University
Tunis El Manar, National School of Engineering in Tunis (ENIT), Department of
communications and information technologies. Also, he is a member of SYSCOM laboratory in ENIT

IMPROVEMENT OF LTE DOWNLINK SYSTEM PERFORMANCES USING THE LAGRANGE POLYNOMIAL INTERPOLATION

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