article Scientifique qui porte sur le suivi des mobiles LTE par filtre de kalman

1. Performance of enhanced LTE OTDOA positioning
approach through Nakagami-m fading channel
Ilham EL MOURABIT, Abdelmajid BADRI, Aicha SAHEL, Abdennaceur
BAGHDAD
EEA&TI laboratory Faculty of Science and Techniques (FSTM), Hassan II University of
Casablanca, BP 146, Mohammedia, Morocco
Elmourabit.ilham@gmail.com
Abstract. Location Based Services (LBS) has known a huge progress with the
4G mobile networks (LTE, LTE-A). Since the LTE introduced a new signal ded-
icated to positioning purposes called Positioning Reference Signal (PRS), many
studies were conducted to use this feature to improve the system performance. In
this context, we have developed a new positioning approach called Adaptive Ob-
served Time Difference of Arrival (A-OTDOA) which is compatible with both
3G and 4G user equipment and respond to the emergency calls accuracy criteria.
In this paper, we will analyze the performance of the A-OTDOA technique in a
propagation environment combining Nakagami-m fading channel, MIMO chan-
nel and additive white Gaussian noise.
Keywords. OTODA, LTE, Nakagami-m, Adaptive OTDOA, AWGN, adaptive
filters, fading channels, positioning.
1 INTRODUCTION
Location Based services (LBS) refers to services that utilizes the position estimate
of a mobile station. LBS are implemented in different areas such as commercial appli-
cations, the public safety and emergency services. The demand to locate a mobile phone
in emergency calls is commonly accepted as the main driving force for LBS regarding
the great benefit of such services in rescuing operations. The estimated position of the
mobile equipment must meet the accuracy standards, generally within 50 to 300 meters
in more than 67% of calls, as mandated by the Federal Communications Commission
(FCC) for E-911 emergency cases [1].
Long Term Evolution or LTE network was introduced as a new standard for mobile
communication networks stepping toward the 4th generation. The majority of its func-
tions were derived from those of the 3rd generation. Moreover, new features were in-
troduced by the LTE as the Orthogonal Frequency Division Multiple Access
(OFDMA), Multiple Input Multiple Output (MIMO) data transmission and the main
special addition related to the positioning domain is the Positioning Reference Signal
(PRS) [2]. This new signal is dedicated only for positioning services, which make its
extraction and processing easier compared to other standards (UMTS, GSM). The aim

2. of cellular positioning approaches is to estimate the position of a user equipment (UE)
in a noisy environment without external assistance. In this context, the positions of the
base stations (eNodeB) are fixed and known while those of the UEs are unknown and
need to be determined [3]. Positioning techniques in cellular networks can be sorted in
three main categories: Handset based (position estimated by the UE), network based
(position estimated by the network units then send to the UE) and hybrid techniques
(collaborative work between the handset and the network units). Since we are interested
in the PRS which is a downlink dedicated positioning signal the second category will
serve our goal and especially the Observed Time Difference of Arrival (OTDOA)
method.
In this work, we will introduce an enhanced version of the OTDOA method called
Adaptive OTDOA. This enhanced version allows us to cancel the noise effect due to
propagation environment, minimize the multipath effect and reach a higher accuracy.
In addition, we will analyze the performance of our approach in a worst case scenario
including a Nakagami-m channel, additive white Gaussian noise and MIMO channel.
In the first section, the proposed approach is presented along with a brief explanation
of the used features. The second section will be dedicated to the modeling of the Nak-
agami-m, white Gaussian noise and MIMO channels. In the third part, the simulation
environment will be discussed along with the obtained results.
2 Enhanced OTDOA or Adaptive OTDOA
2.1 Observed Time Difference of Arrival positioning technique
Observed Time Difference of Arrival is a real time downlink locating technique that
uses the multi-lateration method (hyperbolic positioning) based on timing difference
between the received signals in order to estimate the UE position. It measures the time
of arrival of the PRS signals received from multiple eNodeBs. To perform the meas-
urements, one of the eNodeBs is chosen to be the reference of time, by default is the
one serving the UE at the positioning time. Geometrically, Each TDOA measurement
define a hyperbola and the unknown UE position lays in their intersection. A set of
three eNodeBs, at least, is needed to determine the handset location in a 2-D plan. Since
the time measurements has a certain uncertainty, in reality the intersection will be an
area instead of a single point [4]. The TOA measurements performed by the UE are
related to the geometric distance between the UE and the eNodeBs.
We denote (xi, yi) the known coordinates of the ith eNodeB (the reference eNodeB
is denoted as the 1st one) and (x, y) the unknown coordinates of the UE.
𝑅𝑆𝑇𝐷𝑖,1 =
√(𝑥 𝑖−𝑥)2+(𝑦 𝑖−𝑦)2
𝑐
−
√(𝑥1−𝑥)2+(𝑦1−𝑦)2
𝑐
+ (𝑇𝑖− 𝑇1) + (𝑛𝑖− 𝑛1) (1)
Where (Ti -T1) is the time offset between the two eNodeBs referred to as RTDs (Real
Time Differences), ni and n1 represent the UE Time of Arrival measurement errors and
c is the speed of light.

3. 2.2 Adaptive OTDOA
In reality, the TOA measurements are obtained via performing a cross correlation
between the different versions of the PRS signal issuing from the pairs of eNodeBs, one
of them should be currently serving the mobile user. A peak detection corresponds to
the unknown TOA value.
The received PRS signal at the ith
eNodeB can be written as:
𝑃𝑅𝑆i[n] = Ai PRS[n − τi] + ni[n] (2)
Where, Ai is signal amplitude, PRS[n − τi] is a delayed version of the positioning
reference signal PRS, and ni[n] is the attached propagation noise.
Considering that the 1st
eNodeB is the one actually serving the UE, eventually, it has
the shortest time of arrival among all the other stations. Then, the received PRS signals
equations can be written as:
𝑃𝑅𝑆1[n] = A1 PRS[n] + n1[n] (3)
𝑃𝑅𝑆i[n] = A PRS[n − τ 𝑑] + nd[n] (4)
Where, τd = τ𝑖 − τ1 is the time difference of arrival between the two base stations
(i and 1), and A is the amplitude ratio.
The cross-correlation equation is given as:
R1,2[k] = ∑ PRS1[n] 𝑃𝑅𝑆2[n − k]+∞
n=−∞ (5)
where k is the estimation of TDOA which correspond to a peak detection.
As shown in the previous equations modeling the received PRS signal, an additional
term corresponding to the propagation noise is attached denoted by n[n]. This term af-
fects the time measurements precision if the cross correlation is performed directly on
the received signal, then the positioning accuracy will be also affected. From here came
the idea of pre-filtering the received PRS signal with adaptive filters before performing
the cross correlation or any other signal processing function, so we can minimize the
noise effect to have more accurate position.
Previous work that we carried out aimed to enhance the accuracy of TDOA using
adaptive filters as a noise cancellation system before the TOA estimation via the cross
correlation [5], and so the new method is called Adaptive OTDOA (A-OTDOA). This
kind of filters is controlled by an adaptive algorithm to update the filter's coefficients
in function of the received signal and the error signal.
We have studied the effect of using different kind of these algorithm in order to
choose the more adequate one. As presented in [6] the Normalized Least Mean Square
algorithm was chosen to be the suitable one as it has shown better performances and

4. less complexity comparing to other type of controlling algorithms (LMS and RLS). In
the following, a brief introduction of the NLMS algorithm is given.
2.3 Normalized Least Mean Square Algorithm
In the standard LMS algorithm the filter's coefficients are updated according to the
following equation
w(n + 1) = w(n) + μ e(n) r(n) (6)
μ is the convergence factor, r(n) is the received PRS signal, and e(n) is error signal
defined as e(n) = r(n) - y(n). where y(n) = w(n) r(n-Δ).
The value of the convergence factor has a great importance in the noise cancellation
process. The algorithm experiences a gradient noise amplification problem if the con-
vergence parameter is too big, and a slow convergence rate if it is too small. In order to
solve this difficulty, we can use the NLMS algorithm. The correction applied to the
weight vector w(n) at iteration n+1 is “normalized” with respect to the squared Euclid-
ian norm of the input vector r(n) at iteration n. We may view the NLMS algorithm as a
time-varying step size algorithm [7], defining the convergence factor μ as
μ =
α
c+‖r(n)‖2 (7)
Where α is the NLMS adaption constant, which optimizes the convergence rate of
the algorithm and should satisfy the condition 0< α<2. c is the constant term for nor-
malization and is always less than 1.
So for the NLMS algorithm, the filter weights are updated by the given equation:
w(n + 1) = w(n) +
α
c+‖r(n)‖2 e(n) r(n) (8)
In order to test the performance of our method we decided to try it in a worst case
scenario with no direct line of sight between the UE and the eNodeBs and a multiple
fading channels. The following section introduce the fading models used in our study.
3 Propagation channels
3.1 Nakagami-m fading channel
In communications theory, channel fading was experienced as an unpredictable and
stochastic phenomenon for both user and system planner. However, powerful models
have been developed in order to predict average system behavior accurately. Therefore,
Countermeasures can be planned to avoid system failure, even if the channel exhibits
fade at particular frequencies of particular locations [8].

5. The developed models are based on probability distributions such as Nakagami dis-
tributions, Rician distributions, and Rayleigh distributions which are used to model
scattered signals that reach a receiver by multiple paths. Depending on the density of
the scatter, the signal will present different fading characteristics. Rayleigh and Nak-
agami distributions are used to model dense scatters with no line-of-sight between the
transmitter and the receiver, while Rician distributions model fading with a stronger
line-of-sight. Rayleigh distributions and Rician distributions are special cases of the
Nakagami distributions that’s why the Nakagami model gives more control over the
extent of the fading.
The Nakagami-m probability density function is given as:
𝑓(𝑥) =
2
𝛤(𝑚)
(
𝑚
𝜔
)
𝑚
𝑥2𝑚−1
𝑒−
𝑚𝑥2
𝜔 (9)
Where 𝛤( . )is the Gamma function and 𝜔 = 2𝜎2
= 𝐸{𝑥2}.
With shape parameter m and scale parameter ω > 0, for x > 0. If x has a Nakagami
distribution with parameters µ and ω, then x2
has a gamma distribution with shape pa-
rameter m and scale parameter ω/m [9].
3.2 MIMO channel
Since we are interested in the effect of a Nakagami-m fading channel, we chosen a
simple MIMO channel with additive white Gaussian noise (AWGN). The transmitted
signal Tx reaches the receiver’s antenna via an already set model of the propagation
channel. The MIMO fading channel model emulates the effects of the multipath prop-
agation while The AWGN represents the co-channel interference.
The delay profile chosen is an EPA 5Hz corresponding to a maximum Doppler fre-
quency of 5Hz [10]. The antennas configuration between the eNodeB and the UE is a
2x2 scheme.
4 LTE simulation Environment
In this section, we will present our LTE simulation environment based on Matlab
software. This simulation environment (or simulator) was subject of a published paper
[11]. This tool was designed and tested according to the 3GPP requirements in order to
emulate the behavior of an LTE transmitter, receiver and a MIMO channel for position-
ing purposes (only the Positioning Reference Signal and the Cell Reference Signal were
generated). firstly, we will describe the cellular structure or topology then we will in-
troduce the global structure of the LTE link simulator.

6. 4.1 Network topology
The network cells are designed as a regular hexagonal pattern. The eNodeBs are
placed each in the center of a hexagon with a distance of 500 meters. To avoid an even-
tual underestimation of the total interference in the system a 7-cell topology is chosen
[12] as shown in the following figure.
Fig. 1. Network Topology
4.2 Designed LTE link simulator
The link allowing a wireless communication between the UE and the eNodeBs is
modeled Based on the system-level radio network model presented in [11]. Time meas-
urements obtained by this link will be processed in order to estimate the user position.
The link-level simulator model includes an LTE transmitter, a MIMO communication
and propagation channel and an LTE receiver.
LTE Transmitter Model.
As shown in figure 2, we have two blocks within the transmitter model of our simu-
lator: the transport channel processing block and the physical channel processing block
according to the standards set by the 3GPP [13].
Transport channel.
In this block we perform data generation, Cyclic Redundancy Code (CRC) genera-
tion and attachment, turbo coding and rate matching.

7. Physical channel.
In the physical channel processing block the encoded data is coded and transmitted
to the UE [14]. The main functions of this block are:
a) Scrambling of coded bits
b) Modulation of scrambled bits (here a 16QAM is used)
c) Layer mapping (in our case spatial multiplexing with 2 antenna ports and 2 layers)
d) Pre-coding
e) Mapping to resource elements
f) Generation of Cell Specific Reference Signal (CSR) and the Positioning Reference
Signal (PRS)
g) Generation of the OFDM signal for each antenna port
Fig. 2. LTE Transmitter block diagram.
LTE receiver Model.
At the reception this block performs the inverse functions of these already done by
the transmitter in order to extract the reference signals (PRS and CRS) and the original
sent code words as shown in figure 3.

8. Fig. 3. LTE User Equipment receiver
5 Results Discussion
Computer simulation was done by MATLAB software, using the designed LTE link
simulator and communication toolbox in order to build the channel models.
To evaluate the accuracy parameter of the positioning methods, the Root Mean Square
Error is used, which can be defined as the difference between the estimated and the true
position of the UE as given by the following equation:
RMSE = √
1
N
∑ [xmeasured(k) − xtrue(𝑘)]2N
k=1 (10)
Practically, the geometric solution to estimate the UE position is not applicable that’s
why analytic approaches are needed to solve this problem. Generally, these methods
are based on the Least Square approach to estimate the optimal solution. A comparative
study was conducted in order to determine the best algorithm to work with. This study
was performed on three methods: Gauss-Newton (GN), Steepest Descent (SD) and
Levenberg Marquardt (LM) algorithms. As a result, the LM algorithm showed the best
trade-off between convergence rate and complexity, more details are given by [15].
Figure 4 compare the convergence rate of the three techniques to the optimal perfor-
mance band or as called Cramer Rao Lower Band (CRLB).
In this part, we investigate the accuracy of our method compared with the standard
OTDOA in different propagation conditions. At first, Fig 5 shows the accuracy obtained
by the OTDA technique when the propagation environment is an AWGN channel, a
MIMO channel and a Nakagami channel. The RMSE (or accuracy error) should be
between 50m and 300m for all the developed positioning methods in more than 67% of
calls according to the FCC E-911 criteria.

9. Fig. 4. RMSE vs iteration number k for 𝜎 𝑛
= 200m
Table 1 summarize the obtained results before enhancement for the acceptable error
interval [50m-300m]. The RMSE value decreases with the change of channel from a
simple model (AWGN) to a more complicated one (Nakagami-m). The desired 67%
criteria cannot be obtained even with the higher marge of error (300m) even for the
simplest model.
RMSE (m)
Propagation channels
50 100 300
AWGN 18% 47% 64%
MIMO 13% 28% 51%
Nakagami-m 8% 15% 48%
Table 1. Accuracy values before enhancement

10. Fig. 5. OTDOA RMSE cumulative probability before enhancement.
With the enhancement given to the OTDOA technique by adding the adaptive filter-
ing process (A-OTDOA) method it is clearly shown by figure 6 and table 2 that the
accuracy has reached significantly high levels even for the worst case scenario with the
Nakagami-m fading channel. It was enhanced by 22%, 25% and 22% for 50m, 100m
and 300m RMSE respectively.
RMSE (m)
Propagation channels
50 100 300
AWGN 50% 72% 95%
MIMO 42% 68% 83%
Nakagami-m 30% 40% 70%
Table 2. Accuracy values before enhancement

11. Fig. 6. OTDOA RMSE cumulative probability after enhancement.
6 CONCLUSION
As shown in the study carried out through this paper, OTDOA enhancement based
on adaptive filtering can increase enormously the accuracy of mobile positioning, and
compensate the degradation caused by the propagation noise and multipath. The devel-
oped method for LTE users has shown high performance level through different kind
of propagation channels even in a worst case scenario with no Line-Of-Sight (LOS) as
for the Nakagami-m distributions fading channel. In this paper, the enhancement was
investigated in a fixed and known mobile position in outdoor, ongoing works aim to
improve this technique to take in charge the mobility of users and extend it to indoor
areas.
Acknowledgment. This work falls within the scope of telecommunication projects.
Our sincere thanks to the Faculty of Sciences and Technology, Hassan II University,
Mohammedia, Morocco, for providing us an opportunity to carry out our work in a
well-equipped laboratory (EEA&TI). We are also thankful to all our colleagues who
helped us while working on this project.

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