Double sliding window variance detection-based time-of-arrival estimation in ultra-wideband ranging systems

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 6, December 2022, pp. 6303~6310
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i6.pp6303-6310  6303
Journal homepage: http://ijece.iaescore.com
Double sliding window variance detection-based time-of-arrival
estimation in ultra-wideband ranging systems
Ibrahim Yassine Nouali1
, Zohra Slimane2
, Abdelhafid Abdelmalek1
1
STIC Laboratory, Department of Telecommunications, Faculty of Technology, Tlemcen University, Tlemcen, Chetouane, Algeria
2
STIC Laboratory, Electrical Engineering Department, Belhadj Bouchaib University, Ain Temouchent, Algeria
Article Info ABSTRACT
Article history:
Received Sep 13, 2021
Revised May 28, 2022
Accepted Jun 25, 2022
Ultra-wideband (UWB) ranging via time-of-arrival (TOA) estimation
method has gained a lot of research interests because it can take full
advantage of UWB capabilities. Energy detection (ED) based TOA
estimation technique is widely used in the area due to its low cost, low
complexity and ease of implementation. However, many factors affect the
ranging performance of the ED-based methods, especially, non-line-of-sight
(NLOS) condition and the integration interval. In this context, a new TOA
estimation method is developed in this paper. Firstly, the received signal is
denoised using a five-level wavelet decomposition, next, a double sliding
window algorithm is applied to detect the change in the variance information
of the received signal, the first path (FP) TOA is then calculated according to
the first variance sharp increase. The simulation results using the CM1 and
CM2 IEEE 802.15.4a channel models, prove that our proposed approach
works effectively compared with the conventional ED-based methods.
Keywords:
Energy detection
Ranging
Sliding window
Time-of-arrival
Ultra-wideband
Variance detection
This is an open access article under the CC BY-SA license.
Corresponding Author:
Ibrahim Yassine Nouali
STIC Laboratory, Department of Telecommunications, Faculty of Technology, Tlemcen University
Tlemcen, Chetouane, Algeria
Email: ibrahimyassine.nouali@univ-tlemcen.dz
1. INTRODUCTION
In recent years, ultra-wideband (UWB) technology has been widely used as a viable solution for
indoor position estimation-based applications such as surveillance, navigation, rescue applications,
advertising, crowd-sensing and so on [1]–[6]. The main advantage of this technology is its large bandwidth
that allows a fine time resolution and a high precision ranging and positioning [7]–[10]. Time-based ranging
technique such as time-of-arrival (TOA) estimation is commonly used in UWB ranging systems because it can
take full advantage of UWB characteristics [11], [12]. Then, the position can be calculated by geometric and
trigonometric techniques using at least three ranging measurements in two-dimensional positioning [13], [14].
The accuracy of the TOA-based ranging technique depends strongly on how precisely the first path
(FP) is detected, however, the existence of dense multipath effect and non-line-of-sight (NLOS) condition in
indoor environments can make the detection of the FP quite challenging [15]–[17]. A variety of approaches
have been proposed to overcome these problems, with some attempting to build mathematical models for
range information [18], which is challenging and overly reliant on prior knowledge. Other energy detection
(ED) methods, which are based on low cost and low complexity non-coherent receivers such as the
maximum energy selection method (MES), and some other threshold crossing (TC) methods [19], [20].
These methods consist of, first, squaring the received signal using a square-law device and then, put it into a
finite time integrator to calculate its energy. As shown in Figure 1, the FP TOA is calculated using the
maximum energy block in the MES method; however, under NLOS conditions, the FP may not always be the

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Int J Elec & Comp Eng, Vol. 12, No. 6, December 2022: 6303-6310
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strongest path, so there is a delay between the maximum energy block and the energy block that contains the
FP. As a result, TOA estimation using the maximum energy block leads to significant ranging errors. For TC
methods, the FP TOA is calculated based on the first energy block that exceeds a specific threshold, so
choosing a suitable threshold is critical for these methods. Furthermore, in NLOS conditions, the FP is
sometimes even below the noise level, making detection with traditional thresholds difficult. A variety of
modified methods are proposed to calculate the threshold, but many of them are complex [21], [22], requiring
prior knowledge or costly computations. In addition, the ED receiver has its own issues that impact the
ranging performance such as signal waveform, pulse width, integration interval and noise floor.
Figure 1. Conventional energy detection-based TOA estimation methods
In this paper, with the aim of improving the limitations of the ED-based methods, we propose a new
approach that estimates the FP TOA based on the variance information of the received signal. In this
suggested method, a double sliding window variance detection algorithm is deployed and the FP TOA is
obtained according to the first variance drastic change. The proposed method is tested using the CM1 and
CM2 IEEE 802.15.4a channel models, and the results shows a significant accuracy improvement in
comparison with the conventional ED-based methods.
The rest of the paper is structured as follows. In section 2, we describe the UWB ranging system
model. In section 3, the double sliding window variance detection-based TOA estimation algorithm is
presented. Simulations are done in section 4 to compare the performance of the proposed approach with that
of the ED-based methods. Section 5 concludes the papers.
2. UWB RANGING SYSTEM MODELS
2.1. Ranging signal
Short time pulse is often used in UWB ranging systems because it offers a very high time resolution
with a low energy consumption. Owing to the regulations specified by the Federal Communications
Commission (FCC) for UWB transmissions [23]. The Gaussian pulse and its derivatives are widely used as
transmitted signals in UWB ranging systems. The second derivative of the Gaussian pulse given in (1), is
used as the UWB pulse signal:
𝑠(𝑡) = (1 − 4𝜋
𝑡2
𝛽2) e
(
−2𝜋𝑡2
𝛽2 )
(1)
where 𝛽 = 4𝜋𝜎2
represents the waveform shape factor.
2.2. IEEE 802.15.4a channel model
The IEEE 802.15.4a channel model, as given in [24], is commonly used in the literature for
evaluating the performance of UWB ranging systems, it provides different models for different ranges of
frequency. Considering our research interest, it may be said that the IEEE 802.15.4a CM1 and CM2 channel
models presented in Table 1 may be used to validate the proposed method. Moreover, the IEEE 802.15.4a
channel impulse response follows a clustering structure, cluster arrival times are modelled using a Poisson

Int J Elec & Comp Eng ISSN: 2088-8708 
Double sliding window variance detection-based time-of-arrival estimation in … (Ibrahim Yassine Nouali)
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process and within each cluster, multipath components arrival times are modelled by means of a mixture of
Poisson processes. Mathematically, the IEEE 802.15.4a channel impulse response is given by (2):
ℎ(𝑡) = ∑ ∑ 𝛼𝑘,𝑙
𝐾
𝑘=0
𝐿
𝑙=0 𝑒𝑗𝜙𝑘,𝑙𝛿(𝑡 − 𝑇𝑙 − 𝜏𝑘,𝑙) (2)
where 𝐿 denotes the number of clusters, 𝐾 is the number of multipath components in the 𝑙th cluster, 𝜙𝑘,𝑙 is
the multipath phase distributed uniformly in [0 2π] range and 𝛼𝑘,𝑙 is the multipath gain. 𝜏𝑘,𝑙 is the delay of the
𝑘th
multipath component in the 𝑙th cluster and 𝑇𝑙 is the delay of the 𝑙th cluster.
The received signal is given by (3):
𝑟(𝑡) = 𝑠(𝑡) ∗ ℎ(𝑡) + 𝑛(𝑡) (3)
where 𝑠(𝑡) is the UWB ranging signal, ℎ(𝑡) is the channel impulse response and 𝑛(𝑡) is the additive white
Gaussian noise (AWGN) with zero mean and power spectral density 𝑁0/2. From (1) and (2), the received
signal can be expressed as (4).
𝑟(𝑡) = ∑ ∑ 𝛼𝑘,𝑙
𝐾
𝑘=0
𝐿
𝑙=0 𝑒𝑗𝜙𝑘,𝑙𝑠(𝑡 − 𝑇𝑙 − 𝜏𝑘,𝑙) + 𝑛(𝑡) (4)
Table 1. Description of IEEE 802.15.4a CM1 and CM2 channel models
Channel model number Environment Range
CM1 LOS of indoor residential 7 – 20 m
CM2 NLOS of indoor residential 7 – 20 m
2.3. Ranging system performance
For the performance evaluation of our ranging system, the root-mean-squared-error (RMSE) as
given in (5) is calculated:
𝑅𝑀𝑆𝐸 = √∑ ((𝜏𝑙 − 𝜏𝑇𝑂𝐴
𝑆
𝑙=1 ) ∗ 𝑐)2/𝑆 (5)
where 𝜏𝑇𝑂𝐴 is the true TOA, 𝜏𝑙 is the estimated TOA of each realization, 𝑆 represents the number of
simulations and 𝑐 is the velocity of the electromagnetic wave. Furthermore, according to the literatures [25],
[26] the theoretical accuracy limit of the distance estimation using the TOA method is defined by the Cramer
Rao lower bound (CRLB) given in (6):
𝑉{𝑑
̂} ≥ √
𝑐2
8𝜋2𝛽2𝑆𝑁𝑅
(6)
where 𝛽 and 𝑑
̂ are the effective bandwidth of the UWB ranging signal and the estimated distance using the
TOA method, respectively. It can be noticed from (6) that the accuracy increases with the bandwidth, which
explain the use of UWB signals in ranging systems [27].
2.4. Position calculation
Consider the following scenario: i) a UWB transmitter with unknown location (target node) and
three or more UWB receivers with known locations (reference nodes) are placed in a given area and ii) a
perfect synchronization between the transmitter and the receivers is guaranteed. The position of the target
node is then determined by resolving the (7):
√(𝑥1 − 𝑥𝑡)2 + (𝑦1 − 𝑦𝑡)2 + (𝑧1 − 𝑧𝑡)2 = 𝑑1
̂
√(𝑥2 − 𝑥𝑡)2 + (𝑦2 − 𝑦𝑡)2 + (𝑧2 − 𝑧𝑡)2 = 𝑑2
̂
√(𝑥3 − 𝑥𝑡)2 + (𝑦3 − 𝑦𝑡)2 + (𝑧3 − 𝑧𝑡)2 = 𝑑3
̂ (7)
⋮
√(𝑥𝑛 − 𝑥𝑡)2 + (𝑦𝑛 − 𝑦𝑡)2 + (𝑧𝑛 − 𝑧𝑡)2 = 𝑑𝑛
̂
where (𝑥𝑛, 𝑦𝑛, 𝑧𝑛) are the known coordinates of the 𝑛th reference node, (𝑥𝑡, 𝑦𝑡, 𝑧𝑡) are the target
coordinates and 𝑑𝑛
̂ is the 𝑛th estimated distance between the target node and the 𝑛th reference node.

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3. DOUBLE SLIDING WINDOW VARIANCE DETECTION-BASED TOA ESTIMATION
The key to UWB TOA-based ranging method is to detect the true first path and estimate its time-of-
arrival. The proposed method in this paper aims to capture the change in variance of the received signal to
determine the FP TOA. The difference in amplitude between noise samples and noisy signal samples results
in a noticeable change in variance at the starting point of signal samples. Thus, the FP TOA can be determined
according to the index of the first variance sharp change. In order to achieve this, a double sliding window
variance detection algorithm is deployed. The block diagram of the proposed method is given in Figure 2.
The received signal is first denoised using wavelet decomposition. At this stage, a wavelet
decomposition is performed on the received signal, and the resulting detailed coefficients, which represent
the higher frequency components of the signal at different levels, are thresholder to denoise the signal. There
are several algorithms available to estimate the threshold values; however, due to the ease of implementation
in the simulation software MATLAB, the minimax algorithm was utilized to find the threshold values. Also,
the mother wavelet is vital for improved signal-to-noise separation, and according to [28], standard wavelets
that resemble the signal and its properties are chosen as the mother wavelet. The 'sym4' wavelet closely
resembles the Gaussian doublet employed in our study; hence, it is selected as the mother wavelet in the
denoising process. Following that, the double sliding window variance detection algorithm is employed to
identify changes in the variance information of the received denoised signal. It is important to note that the
windows size is taken to be less than the guard interval to avoid the overlap between frames of the received
signal. The block diagram of the double sliding window algorithm is illustrated in Figure 3, and the detailed
steps of the algorithm are outlined below. The received signal can be expressed as 𝑅𝑘,𝑛, where 𝑘 is the
number of sample and 𝑛 is the number of frames. Firstly, the received signal is denoised using a five-level
wavelet decomposition, the process of denoising is illustrated in Figure 4, where the received signal is
presented in Figure 4(a) and the denoised signal is presented in Figure 4(b).
Figure 2. Block diagram of the proposed method
Figure 3. Block diagram of the double sliding window algorithm
(a) (b)
Figure 4. Illustration of the wavelet decomposition based denoising (CM1 channel, SNR = 10 dB);
(a) received signal and (b) denoised signal

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The detection of the variance change depends on the variance value in the windows, for the 𝑘th
sample in the 𝑛th
frame of the received signal, the variance in the window 𝑎 is given by (8):
𝑎𝑘 =
1
𝑊
∑ (𝑅𝑘,𝑛 − 𝜇)2
𝑊+(𝑘−1)
𝑘=𝑖 , 𝑖 = 1,2 … , 𝐾 (8)
where 𝑊 is the window size, 𝐾 is the number of samples and 𝜇 is the window mean. To simplify the
procedure of detecting the variance change, throughout the entire process of sliding, the variance in the
window 𝑏 is fixed to the variance of a Gaussian random variable 𝑥 with zero mean and a standard deviation
equal to the standard deviation of the received noise, which is estimated from the guard interval. The
variance in the window 𝑏 is given by (9).
𝑏𝑘 =
1
𝑊
∑ (𝑥𝑖)2
, 𝑘 = 1,2 … , 𝐾
𝑊
𝑖=1 (9)
In order to capture the change in variance of the received signal, a decision function is required, and it is
defined as (10).
𝑑𝑘 =
𝑎𝑘
𝑏𝑘
, 𝑘 = 1,2 … , 𝐾 (10)
An illustration of the decision function is given in Figure 5. It can be seen that the decision function
peaks at different instants of the received signal. That is because during the process of sliding, the variance in
the window 𝑎 increases and reach its peak at the TOA of each received multipath component. The number of
the peaks depends primarily on the size of the window and the delay between the received multipath
components, the first peak is a result of the change in variance induced by the FP, and therefore, the FP TOA
can be calculated in accordance with the index of the first decision function peak. Mathematically, the index
of the first peak is determined using the expression below:
𝑘𝑡𝑜𝑎 = 𝐹𝑖𝑟𝑠𝑡 {𝑘|(𝑑𝑘 − 𝑑𝑘−1) ≥ 0 𝑎𝑛𝑑 (𝑑𝑘+1 − 𝑑𝑘) ≤ 0 𝑎𝑛𝑑 𝑑𝑘 > 𝜂 } (11)
𝑘 = 2,3 … , 𝐾
where 𝜂 is the threshold. For the simplicity of implementation, the threshold is set the root mean square
(RMS) of the decision function and it is given by : 𝜂 = √
1
𝐾
∑ 𝑑𝑘
2
𝐾
𝑘=1 . Finally, the first path time-of-arrival can
be calculated using (12):
𝑡̂𝑡𝑜𝑎 = 𝑇𝑠𝑘𝑡𝑜𝑎 − 𝜏𝑔𝑢𝑎𝑟𝑑 (12)
where 𝑇𝑠 is the sampling interval and 𝜏𝑔𝑢𝑎𝑟𝑑 is the guard interval.
Figure 5. Illustration of the decision function (CM1 channel, SNR = 10 dB)

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4. SIMULATION RESULTS AND DISCUSSION
In this section, the performance of the proposed method will be evaluated using the CM1 and CM2
IEEE 802.15.4a channel models. The results presented in Figure 6 were obtained with the following
parameters: the UWB ranging signal used is the Gaussian doublet with a pulse duration of 1 ns and a
bandwidth of 3.1 GHz, the window size 𝑊 is 15 samples and 𝑆 of the RMSE is set to 100 simulations. The
number of frames is 200 with a frame duration of 200 ns and SNR ranges from -10 to 20 dB with a step of
5 dB. As far as the conventional energy detection-based methods (MES, TC), according to the simulations
done in the literature [19], the width of the energy block for both TC and MES methods is set to 4 ns. MES
method selects the center of the maximal energy block as a time-of-arrival and TC method select the center
of the first threshold crossing energy block as a time-of-arrival. The threshold selection in the TC method is
based on a normalized threshold, given the maximum and the minimum energy values, the normalized
threshold is given by (13).
𝜀 𝑛𝑜𝑟𝑚 =
𝜀−min {𝐸𝑛}
max {𝐸𝑛}−min {𝐸𝑛}
(13)
In the simulation, the normalized threshold is fixed to 0.6 and the threshold value 𝜀 can be
calculated from (13). According to the simulation results in Figures 6(a) for CM1 channel and Figure 6(b) for
CM2 channel, in all cases, the performance of the proposed method is better than that of any conventional
ED-based methods (MES, TC), especially, at high SNR (>-5dB), where the ED-based methods hit an error
floor, which is caused by the integration interval. In addition, in NLOS condition, the FP may not be always
the strongest path which can cause a higher error floor and significantly reduce the accuracy of the ED-based
methods.
(a) (b)
Figure 6. SNR vs RMSE of different approaches in AWGN channel: (a) CM1 and (b) CM2
5. CONCLUSION
Energy detection methods are widely used in UWB ranging systems, nevertheless, the presence of
dense multipath effect, NLOS condition, thermal noise and interference can cause large sized errors in the
ranging estimation. In this study, we propose a new TOA estimation method that uses a double sliding
window algorithm to estimate the FP TOA based on the change in the variance of the received signal. The
simulation results with CM1 and CM2 IEEE 802.15.4a channel models proved and confirmed the
effectiveness of our proposed approach as compared to the traditional ED-based methods.
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BIOGRAPHIES OF AUTHORS
Ibrahim Yassine Nouali received his Master degree in Telecommunication at the
University of Tlemcen, (Algeria) in 2018. Currently he is a PhD student at the same University
and a member of STIC laboratory. His doctoral research center around ultra-wideband
technology and indoor positioning techniques. He can be contacted at email:
ibrahimyassine.nouali@univ-tlemcen.dz and nouali.ibrahim.yassine01@gmail.com.

 ISSN: 2088-8708
6310
Zohra Slimane received Magister Diploma (2008), Ph.D. (2012) and HDR
(2017), in Telecommunication from Tlemcen University (Algeria). Since 2008, she has been
researcher at STIC Laboratory and system engineer at Sonatrach Aval Research Group. In
2014, she joined Belhadj Bouchaib University Center (Algeria), where she is currently an
associate and research Professor, responsible for LMD graduation and doctorate training in the
telecommunications sector. Since 2019, she has been involved as project leader dedicated to
indoor localization. Her research interests include location and imaging radars, UWB sensors,
networking, mobile networks, ubiquitous internet and next-generation networks. She can be
contacted at email: zohra.slimane@univ-temouchent.edu.dz and zoh_slimani@yahoo.fr.
Abdelhafid Abdelmalek received the Laurea degree in Telecommunication
Engineering from Institute of Telecommunications Oran (Algeria) in 1991, and Diploma of
deepened studies in optoelectronic at Nancy (France) in 1993. From 1994 to 2000, he worked
as engineer in charge of design and management of ISDN networks at Algerie Telecoms
Company. In 2002, he received Magister Diploma in Signals and systems at Tlemcen
University, Algeria. He subsequently joined the faculty of technology and STIC Laboratory as
research Professor. He received the Ph.D degree in Electronics in 2013. He has participated in
several national research frameworks and projects. His main research activities cover radar,
data communications, mobile networks, security, protocols, and high-speed optical networks.
He can be contacted at email: abdelmalekabdelhafid@gmail.com.

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