An Hybrid Framework OTFS-OFDM Based on Mobile Speed Estimation

International Journal of Computer Networks & Communications (IJCNC) Vol.16, No.3, May 2024
DOI: 10.5121/ijcnc.2024.16304 49
AN HYBRID FRAMEWORK OTFS-OFDM BASED ON
MOBILE SPEED ESTIMATION
Amina Darghouthi1
, Abdelhakim Khlifi2
, Hmaied Shaiek3
, Fatma Ben Salah1
and
Belgacem Chibani1
1
MACS Laboratory: Modeling, Analysis and Control of Systems,
University of Gabes, Tunisia.
2
Innov’COM laboratory, Sup’COM, University of Carthage, Tunisia.
3
CEDRIC/LAETITIA Laboratory, CNAM, Paris, France.
ABSTRACT
The Future wireless communication systems face the challenging task of simultaneously providing high-
quality service (QoS) and broadband data transmission, while also minimizing power consumption,
latency, and system complexity. Although Orthogonal Frequency Division Multiplexing (OFDM) has been
widely adopted in 4G and 5G systems, it struggles to cope with a significant delay and Doppler spread in
high mobility scenarios. To address these challenges, a novel waveform named Orthogonal Time
Frequency Space (OTFS). Designers aim to outperform OFDM by closely aligning signals with the
channel behaviour. In this paper, we propose a switching strategy that empowers operators to select the
most appropriate waveform based on an estimated speed of the mobile user. This strategy enables the base
station to dynamically choose the waveform that best suits the mobile user’s speed. Additionally, we
suggest retaining an Integrated Sensing and Communication (ISAC) radar approach for accurate Doppler
estimation. This provides precise information to facilitate the waveform selection procedure. By leveraging
the switching strategy and harnessing the Doppler estimation capabilities of an ISAC radar.Our proposed
approach aims to enhance the performance of wireless communication systems in high mobility cases.
Considering the complexity of waveform processing, we introduce an optimized hybrid system that
combines OTFS and OFDM, resulting in reduced complexity while still retaining performance
benefits.This hybrid system presents a promising solution for improving the performance of wireless
communication systems in higher mobility.The simulation results validate the effectiveness of our
approach, demonstrating its potential advantages for future wireless communication systems. The
effectiveness of the proposed approach is validated by simulation results as it will be illustrated.
KEYWORDS
OFDM, OTFS, High Mobility, Complexity, radar ISAC, 6G.
1. INTRODUCTION
Emerging wireless communication systems are designed to accommodate multiple waveforms,
catering to a variety of mobility situations. Although, numerous wireless communication systems
have made extensive use of Orthogonal Frequency Division Multiplexing (OFDM). However, it
faces significant challenges in fastmovementenvironments. In such conditions, noticeable
Doppler shifts and Doppler spread effects are usually observed. To address this issue, Orthogonal
Time Frequency Space (OTFS), has been defined. This new waveform named OTFS takes
advantage of delay and Doppler diversity. A superior performance over OFDM in high mobility
contexts is registered. OTFS may be a promising candidate in this field due to its special
waveform properties for high mobility wireless communication systems (HMWCS) [1], [2], [3].
For high mobility contexts, delay Doppler channel exhibits beneficial features like separability,

50
stability, compactness, and possibly sparsity [4]. For future wireless systems generation named
6G, the significant challenge is the Doppler Velocity Estimation.The proposed 4G/5G
technologies have introduced several enhancements for mobility scenarios. Indeed, with 4G
mobile, handovers at speeds up to 350km/h can be performed with an allowable QoS [1], [7], [8],
a higher mobility is a key performance for upcoming generation. Unfortunately, this technology
presents sometimes interruptions causedto achieve higher transmission speeds for mobile
terminals [2], [7]. To meet such goal, as in vehicle-to-everything (V2X), in drones, and in High
Speed Rails (HSR).5G networks must support approaching 500km/h [2]. No later, for the
frequency selective channels, one technique has considered or defining multi-carrier modulations
(MCM) where action conducted on the frequency domain. With the upcoming availability of high
mobility scenarios such as Hyper loop, future 6G is expected to support mobility at
1000km/h[2].High mobility induces significant Doppler shift and spread (i.e. the Doppler
effect).Those imperfections appear directly in High Mobility Wireless Communications
(HMWC) which suffer from rapid selective fading[3]. A compulsory role in communications is
to look for matching the information to the propagation channel. Furthermore, the ingenious use
of cyclic redundancy on transmission makes it possible to reduce terminalscomplexity. This is
also empowered by Fast Fourier Transform FFT based algorithms usage.In 4G and 5G systems,
processing methods were enhanced e.g. Orthogonal Frequency Division Modulation (OFDM) is
becoming widely used as modulation structure for downlink communications. Data symbols has
becoming multiplexed onto closely perfectly spaced orthogonal subcarriers. Even though, this
waveform suffers from some limitations that making its main drawbacks. We can name e.g. high
peak-to-average power ratio (PAPR), out-of-band (OOB) emissions, and significant loss of
orthogonal waves in high mobility wireless channels [1], [2], [9]. Recently, a new bi dimensional
(2D) waveform, named OTFS (Orthogonal Time Frequency Space), has been proposed [10],
[11], [13] and [17]. One modulation’s specificity is the usage of a pair of 2D transforms. This
defines the known Symplectic Finite Fourier Transform (SFFT) and Inverse Symplectic Finite
Fourier Transform (ISFFT) [4], [21]. In high mobility contexts, the OTFS systems achieve full
diversity and greater performance compared to those obtained for OFDM [6], [7] and
[27].Therefore, OTFS has received more attention. It is considered as a promising candidate for
forthcoming generation of radio mobile networks [7], [18] and [19]. OTFS and OFDM
waveforms both offer specific advantages and disadvantages tailored to varying mobility
scenarios and system complexities. Interested to prove such merit and the improvements brought,
we propose in this paper an original idea to define an alternate usage of such waveforms. It is
noted that the OTFS is excellent for highmobility cases. However, it suffers from high processing
complexity. In other side, OFDM is particularly well suited in low mobility situations.
Consequently, this offers good performance and ease of use, but experiences a significant
degradation in performance in faster moving situations [2], [7] and [14].Then, there is a dire need
to find solutions that ensure high Quality of Service (QoS) simultaneously for different mobility
rates. Currently, the use of an ISAC system for estimating various parameters, especially the
speed of moving objects, is a promising approach for implementing OTFS and OFDM schemes.
The goal is to achieve highly accurate estimates of delay, Doppler shift, object velocity, and
target count. It is worth noting that most traditional velocity estimation methods rely on the delay
Doppler (DD) technique. Several references, including [23], [24], [25],[28], mention radar
integrated algorithms for this estimation. Really, users are practically, randomly distributed
within the base station’s coverage and they present varying mobility levels. The base station
needs to select appropriate waveform to provide the best Quality of Service (QoS) offered for
each user depending on their speed. Consequently, it becomes interesting to propose adequate
solutions that provide adequate services simultaneously for both fast and slow speed moving
users. When many users with varying mobility levels are randomly distributed within the base
station’s coverage area, the base station needs to select appropriate waveform to provide the best
QoS offered for each user depending on this speed. In this paper, we propose a hybrid framework
OTFS-OFDM based on mobile speed estimation. This estimation is carried out using a device

51
that estimates the speed of objects more precisely, such as the ISAC radar. We have to recall that
actions are empowered by radar ISAC system, which is based on the Matched Filter Fast Fourier
(MF-F) algorithm. This algorithm is capable of obtaining an estimation of detection parameters
with fractional precision, which improves the accuracy of the estimation. On the other hand,
efficiency increases. Additionally, to reduce the number of comparisons needed in the search
process, which speeds up the process and makes the algorithm more efficient. Let’s note, the
system performances depend strongly on such decision offering one usage among two
possibilities named OFDM or OTFS. Ones the user’s speed was estimated, we can see what will
be speed value. This could be retained to switch between one of both strategies named OFDM or
OTFS. This strategy could even more enhanced by defining a speed threshold value that we can
define in order to operate the wanted selection. This arrangement is specifically designed to
optimize the performance of OFDM over OTFS. To estimate the user mobility speed in order to
assign that with the most matched waveform. After reviewing the aforementioned papers, the
main contributions of this manuscript can be succinctly described as follows:
 Proposing a hybrid framework named OTFS-OFDM based on the speed estimation.
This estimation is performed using a device that provides more accurate speed
estimates of objects, such as the ISAC radar.
 Incorporating the ISAC radar sensing into the proposed framework is pivotal,
particularly through the utilization of the Matched Filter-Fast Fourier (MF-F)
algorithm. This algorithm, esteemed for its effectiveness, empowers the radar system
to estimate detection parameters with fractional precision, thereby bolstering
estimation accuracy.
 Measuring the probability of error of the proposed system, we find that the former
OTFS under high mobility has a lower probability of error compared to OFDM.
Furthermore, this strategy can be enhanced by defining a speed threshold value for
selecting the desired strategy. This arrangement is specifically designed to optimize
the performance of OFDM over OTFS. By estimating the user’s mobility speed, we
can assign the most suitable waveform, resulting in improved Quality of Service
(QoS) and reduced complexity.
The remainder of the paper is structured as follows: In Section 2, we present a review of related
work. Section 3 provides a brief overview of the structures of both OFDM and OTFS systems.
Section 4 introduces the proposed framework and describes the speed estimation method utilized
in our work. Moving on to Section 5, we present the simulation results of the proposed
framework, along with a discussion on the system’s complexity. Finally, in Section 6, we
conclude the paper with a summary of our findings and outline potential avenues for future
research.
2. RELATED WORK
Various research studies have been conducted on the vision and challenges of 6G technology
[24], [31]. The objective of this research is to estimate various parameters used for waveform
sensing. Several factors have been considered for the design of waveforms for integrated sensing
and communication such as the (ISAC) system [28], [29], and [30]. Research topics worth
exploring include wireless propagation path prediction and electromagnetic spectrum mapping
[24], as well as, Terahertz technology [30]. The superior accuracy of ISAC estimation systems
has led us to choose this system to estimate the velocity of moving objects. The authors of [26]
introduce a two-dimensional radar imaging method using a MIMO OFDM radar, designed for
automotive applications (the RadCom system was originally designed for use at 24 GHz). As its

52
radar capability is comparable to that of conventional radar systems such as FMCW (frequency
modulated continuous wave) radar, the authors aim to extend this capability to allow two-
dimensional (2D) imaging, including range and azimuth, while maintaining speed estimation
capability. Using receiver beamforming techniques and innovative radar processing methods, the
paper [24] demonstrates the possibility of simultaneously estimating range, Doppler, and azimuth
information for any number of objects, relative to the number of antenna elements in the array,
during transmission.Among the various classes of antennabased on velocity (VE) estimation
algorithms, MUSIC [24] is one of the most extensively studied. The MUSIC algorithm is easy to
implement, with numerous versions that can be modified to fit different scenarios while
providing high resolution. In [21], MUSIC was chosen because its spectrum can be directly
represented as a radar image, without the need for post-processing of estimated object positions,
unlike ESPRIT (estimation of signal parameters by rotational invariance techniques) [26]. The
author in [22] addresses a critical challenge in the context of an integrated sensing and
communication system (ISAC), namely improving the accuracy of the estimation of delay and
Doppler shift parameters, essential parameters to support the performance of the communication
system. To address this issue, the author presents a two-stage estimation algorithm known as the
Fibonacci-matched filter (MF-F). This algorithm exploits waveform characteristics in orthogonal
time-frequency space (OTFS) in the Doppler delay shift (DD) domain. For the first step (MF), the
algorithm approximates the detection parameters by quantizing them on an integer grid, based on
the relationship between the input and output signals of the ISAC model in the DD domain. This
approximation is performed using the cyclic shift property of the matrix. In the second step (F),
the author implements a twodimensional search technique based on the Fibonacci sequence,
called the Fibonacci Search Method. This method provides an estimate of the detection
parameters with fractional accuracy. It has the advantage of reducing the number of comparisons
required and speeding up the search process. Finally, the author [25] propose a method using
numerical simulations and hardware experiments. The results demonstrate that the MF-F method
is capable of accurately estimating velocity and distance to the nearest millimeter, while
exhibiting robustness and low complexity in numerical simulations. What's more, the Doppler
shift and delay parameters estimated in the hardware experiments reach centimeter and meter
levels. The author of [26] focuses on the field of integrated sensing and communication (ISAC),
which is currently attracting a great deal of research interest. According to these estimation
methods, the ISAC radar is the best for an accurate estimation of the parameters. This radar is
used in our selection framework to choose between OTFS and OFDM.
3. SIGNAL MODELING
3.1. Basic OFDM Signal Modeling
Standard Data is transmitted using narrow subcarriers that make up the bandwidth. Each
subcarrier transmits M-QAM symbols to an OFDM modulator. Although the transmission over
the channel is successful, Inter Symbol Interference (ISI) often occurs. The modulation and
demodulation processes can be performed by Fast Fourier Transform (FFT) and its inverse
(IFFT) usage as illustrated in Figure 1. This issue is addressed by inserting a cyclic prefix (CP)
between consecutive OFDM symbols. The channel delay spread is recommended to be longer
than the CP's length to effectively mitigate ISI and simplify the equalization process
[3],[5],[7],[8]. Subcarriers that are orthogonal help to enhance spectral efficiency.

53
Figure1. OFDM Transmitter and Receiver Block Diagram
An OFDM system having respectively M subcarriers and N time slots is assumed. The total
bandwidth of the OFDM signal is 𝐵 = 𝑀 ∆𝑓; with ∆f being the subcarrier spacing equal to 1.
The frame duration will be 𝑇𝑓 = 𝑁𝑇 = 𝑁𝑀𝑇𝑠, where T means a one OFDM symbol duration.
This duration is equal to 𝑀𝑇𝑠, where 𝑇𝑠 is the sampling time. We assume a static multipath
channel with a maximum delay spread τmax causing a channel Delay
𝜏𝑚𝑎𝑥
𝑇𝑠
. As stated before, to
mitigate ISI and relax channel equalization task, the length of the cyclic prefix LCPshould be
greater than or equal to𝑙𝑚𝑎𝑥,where 𝑙𝑚𝑎𝑥 that represents the maximum delay spread of the
channel.In our case, we have chosen to take LCP = 𝑙𝑚𝑎𝑥. The data symbols are defined as [5],
[11], [13], [11]:
𝑋[𝑚, 𝑛] = 𝑚 = 0, … , 𝑀 − 1; 𝑛 = 0, … 𝑁 − 1 (1)
Such data symbols are taken from the alphabet 𝐴 = {𝑎1,… , 𝑎𝑄}, where 𝑄 is the number of
unique symbols in the alphabet ; and {𝑎1, … , 𝑎𝑄}: The individual symbols in the alphabet.
Each column of 𝑋 contains 𝑁 symbols. The transmitted signal can be expressed as follows [5],
[7], [9], and [10]:
𝑠(𝑡) = ∑ ∑ 𝑋[𝑚, 𝑛]𝑔𝑡𝑥(𝑡 − 𝑛𝑇)𝑒𝑗2𝜋𝑚∆𝑓(𝑡−𝑛𝑇)
𝑀−1
𝑚=0
𝑁−1
𝑛=0
(2)
where 𝑔𝑡𝑥(𝑡) ≥ 0, for 0 ≤ 𝑡 < 𝑇 is a pulse shaping waveform. We can define the set of
orthogonal basis functions 𝜙(𝑛,𝑚)(𝑡) used to shape M-QAM symbols as it follows [7,9,10]:
𝜙(𝑛,𝑚)(𝑡) = 𝑔𝑡𝑥(𝑡 − 𝑛𝑇)𝑒𝑗2𝜋𝑚∆𝑓(𝑡−𝑛𝑇)
,0≤𝑚≤𝑀;0≤𝑛≤𝑁
(3)
When the receiver is demultiplexing information, it utilizes the obtain basis signals. The
process is described in [7, 9, 10] as follows:
𝜙(𝑛,𝑚)(𝑡) = 𝑔𝑟𝑥(𝑡 − 𝑛𝑇)𝑒𝑗2𝜋𝑚∆𝑓(𝑡−𝑛𝑇)
,0≤𝑚≤𝑀;0≤𝑛≤𝑁
(4)
where, 𝑔𝑟𝑥(𝑡) ≥ 0 for 0 ≤ 𝑡 < 𝑇and is zero otherwise. This allows rewriting equation 2 as
following [7], [9], [10]:
𝑠(𝑡) = ∑ ∑ 𝑋[𝑚, 𝑛]𝜙(𝑛,𝑚)(𝑡)
𝑀−1
𝑚=0
𝑁−1
𝑛=0
(5)

54
After that, a CP extension is then added to signal s (t) in order to overcome a multipath
channel effect. The cross-ambiguity function between the two signals 𝑔1(t) and 𝑔2(t) was
defined as:
𝐴𝑔1,𝑔2
(f, t) ≜ ∫ 𝑔1(𝑡)𝑔𝑠
∗(𝑡′
− 𝑡)𝑒−𝑗2𝜋𝑓(𝑡′−𝑡)
𝑑𝑡′
(6)
where defines the correlation between 𝑔1(t) and version of𝑔2(t) delayed by t and shifted in
frequency by f for all t and f in the time-frequency plane. When 𝑠(𝑡) passes through a time and
frequency-selective radio channel, the received signal in the time domain is known as
𝑟(𝑡).let’s𝑟(𝑡)be the received time domain signal after propagation through a time- frequency
selective wireless channel. This channel is characterized by its impulse response ℎ(𝑡). so, the
received signal can be expressed as [14], [15] and [16]:
𝑟(𝑡) = ℎ(𝑡) ⊛ 𝑠(𝑡) + 𝑤(𝑡)
(7)
where 𝑤(𝑡)is a complex Gaussian white noise.
To obtain, 𝑟(𝑡) is projected onto each𝜙(𝑛,𝑚)(𝑡). After the CP is removed, the received samples
inTime Frequency (TF) applies FFT operator can be expressed as [14],[15],[16]
Y (f, t) = 𝐴𝑔1,𝑔2
(f, t) ≜ ∫ 𝑔𝑟𝑥
∗ (𝑡′
− 𝑡)𝑒−𝑗2𝜋𝑚∆𝑓(𝑡′−𝑡)
,
(8)
Y (m, n) = Y (f, t)f =m∆f,t=nT. (9)
3.2. OTFS System Modeling
In this section, we will discuss the renowned concept proposed by Hadani, the OTFS approach
[4], [11], [13]. More specifically, the system model associated with the OTFS scheme is
illustrated in Figure 2.
Figure 2. OTFS Transmitter and Receiver Block Diagram
OTFS is applied by mapping the previously prepared QAM symbols onto the delay-Doppler
domain (DD). For that, the symbols are initially converted from the delay-Doppler domain (DD)
to the time-frequency domain (TF). Firstly, at the transmitter, the QAM symbols are arranged in a
two-dimensional (2D) matrix with N columns in the Doppler domain and M rows in the delay
domain. The time-frequency grid is discretized to a𝑀 by 𝑁grid (for some integers 𝑁, 𝑀 > 0),
using intervals of T (seconds) and∆𝑓 (𝐻𝑧), the time and frequency axes are sampled,
respectively, i.e., [4], [11], [12], [13]:

55
⋀ = { (𝑛𝑇, 𝑚∆𝑓 ),𝑛 = 0,· · ·,𝑁 − 1,𝑚 = 0,· · ·,𝑀 − 1 } (10)
The modulated time frequency samples 𝑋[𝑛, 𝑚], 𝑛 = 0, . . . , 𝑁 − 1, 𝑚 = 0, . . , 𝑀 − 1 are
transmitted over an OTFS frame with duration 𝑇𝑓 = 𝑁 𝑇 and occupy a bandwidth 𝐵 =
𝑀 ∆𝑓.The delay Doppler plane in the region (0, 𝑇 ] × (
−∆𝑓
2
,
∆𝑓
2
) is discretized to an 𝑀 by
𝑁 grid [4], [17], [18]and [19]:
Γ = { (
𝑘
𝑁𝑇
,
𝑙
𝑀∆𝑓
),𝑘 = 0,· · ·,𝑁 − 1,𝑙 = 0,· · ·,𝑀 − 1 }
(11)
where (
𝑘
𝑁𝑇
,
𝑙
𝑀∆𝑓
) represent the quantization steps of the delay and Doppler frequency axes,
respectively. Then the signal is transformed into the time-frequency domain through the inverse
symplectic finite Fourier transform (ISFFT) in the secondstep. This will be written like [17],
[18]and [19]:
𝑋𝑇𝐹
[𝑚, 𝑛] =
1
√𝑀𝑁
∑ ∑ 𝑋[𝑙, 𝑘]𝑒𝑗2𝜋(
𝑛𝑘
𝑁
−
𝑚𝑙
𝑀
)
𝑀−1
𝑚=0
𝑁−1
𝑛=0
(12)
where 𝑋[𝑙, 𝑘]is the delay Doppler signal modulated pulse.
Each data frame in this scenario has a total frame duration of 𝐵 = 𝑁𝑇 and a bandwidth of 𝑇𝑠 =
𝑁 ∆𝑓 .After reshaping the matrix 𝑋𝑇𝐹[𝑚, 𝑛]into a time frequency domain sequence, the transmit-
ted OTFS signal, denoted s(t), can be derived by applying the Heisenberg transform to 𝑋𝑇𝐹
with
the transmitter shaping pulse, 𝑔𝑡𝑥(𝑡). More specifically, the Heisenberg transform can be
viewed as a multicarrier modulator. This Heisenberg approach involves using the conventional
OFDM modulator. In particular, with conventional OFDM modulation, the Heisenberg transform
could be achieved by an inverse fast Fourier transform (IFFT) module and transmit pulse
shaping. In this scenario, the transmitted signal 𝑠(𝑡)using Heisenberg Transform as proposed by
[11], [17], [18]and [19].
𝑠(𝑡) = ∑ ∑ 𝑋𝑇𝐹
[𝑚, 𝑛]
𝑀−1
𝑚=0
𝑁−1
𝑛=0
𝑔𝑡𝑥(𝑡 − 𝑛𝑇)𝑒𝑗2𝜋𝑚∆𝑓(𝑡−𝑛𝑇)
(13)
where, 𝑔𝑡𝑥(𝑡)is the window function.It has been shown in [17].
Practical rectangular transmit and receive pulses are used, which are compatible with OFDM
modulation. Finally, a CP is added to the time domain signal for every data frame, as indicated by
[14].
where 𝑇𝐶𝑃 denotes the duration of the CP.
The channel impulse response in DD is characterized by the target detection channel or
communication paths transmitted. We suppose that the P multipath components, where ith
path
linked to complex path gain𝛼𝑖, delay 𝜏𝑖, and Doppler shift 𝑣𝑖.Where 𝜏𝑖 ∈ [0,
1
∆𝑓
),ν𝑖∈ [−
1
2𝑇
,
1
2𝑇
).
In this situation, any two paths are solved in the delay Doppler domain (i.e., |𝜏𝑖-𝜏𝑗|≥
1
𝑀∆𝑓
or |ν𝑖 -
𝑆𝐶𝑃(𝑡) = {
𝑠(𝑡) 0 ≤ 𝑡 ≤ 𝑇𝑠
𝑠(𝑡 + 𝑇𝑠) − 𝑇𝐶𝑃 ≤ 𝑡 < 0
(14)

56
ν𝑗| ≥
1
𝑁𝑇
. Therefore, the impulse response of the wireless channel in the DD domain is given as
[30]:
For joint radar ISAC integrating sensing and communication, the delay and Doppler shifts are
calculated using 𝜏𝑖 =
𝑟𝑖
𝑐0
,νi =
𝑓𝑐v𝑖
𝑐0
where distance 𝑟𝑖 and velocity νi along the ith
path, and 𝑓
𝑐 is the
carrier frequency and the speed of light is therefore represented by𝑐0. The integration of system
detection requires consideration of both the round-trip delay and the Doppler effect. The
calculations above have an extra multiplier of 2 added. For this instance, the path delay and
Doppler shift correspond to integer multipliers of delay and Doppler resolution,𝜏𝑖 =
𝑙𝑖
𝑀∆𝑓
and
νi =
k𝑖
𝑁𝑇
. During the transmission, a signal can thus suffer from various changes, particularly in
scenarios involving high mobility. These changes produce shifts both in the time and frequency
domains. In these conditions, the received signal could be expressed as [17], [18] and [19].
The received symbols matrix 𝑌𝑇𝐹[𝑚, 𝑛]in the Time Frequency Domain, is obtained by sampling
the cross - ambiguity function 𝐴𝑔𝑟𝑥,𝑟
(𝑡, 𝑓) according to [17], [18],[19]:
where the sampling cross ambiguity function 𝐴𝑔𝑟𝑥,𝑟
(𝑡, 𝑓) as indicated:
Finally, the DD domain samples are obtained by applying the SFFT to 𝑌[𝑙, 𝑘][4], [17]:
4. PROPOSED MODELLING
In this section, we will show how someone could adequately process the studied signal based on
a chosen processing strategy. This will concern the ISAC radar's approach for estimating various
parameters. This will obviously help to estimate the unknown speed characterizing a mobile user.
Let’s see how this will be done. As shown in Figure3, the Framework that associated with a
signal processing system. This system comprises three main processing blocks. In the first place,
we have the base station that including elements like Random Data, Inverse Fourier Transform
Symplectic (ISFFT), and Heisenberg Transform. A transmitted signal is sent by this base station
to the Sensing Target. Such target is a moving object like vehicles. An echo signal is returned to
the receiver of the base station. This defines an integrated ISAC device. The ISAC receiver
processes that signal using various tools like the Wigner transform, Fourier Transform
Symplectic (SFFT), and the Sensing Signal Detection. The Sensing Signal Detection estimates
various parameters, like the speed of the objects already detected by the Sensing Target. The
signals are processed using based on the estimated speed of the objects and then comparing them
ℎ(𝜏, 𝜐) = ∑ 𝛼𝑖
𝑃
𝑖=0
𝛿(𝜏 − 𝜏𝑖)𝛿(Ν − Ν𝑖)
(15)
𝑟(𝑡) = ∫ ∫ ℎ(𝜏, 𝜐)𝑠(𝑡 − 𝜏𝑖) 𝑒𝑗2𝜋𝜐(𝑡−𝜏𝑖)
𝑑𝜏𝑑𝜐 + 𝑤(𝑡)
(16)
𝑌𝑇𝐹[𝑚, 𝑛] = 𝐴𝑔𝑟𝑥,𝑟
(𝑡, 𝑓)𝑡=𝑛𝑇,𝑓=𝑚𝛿𝑓 (17)
𝐴𝑔𝑟𝑥,𝑟
(𝑡, 𝑓) ≜ ∫𝑔𝑟𝑥
∗ (𝑡 − 𝑡′)𝑟(𝑡) 𝑒𝑗2𝜋(𝑡−𝑡′) (18)
𝑌[𝑙, 𝑘] =
1
√𝑀𝑁
∑ ∑ 𝑋[𝑚, 𝑛]𝑒𝑗2𝜋(
𝑛𝑘
𝑁
−
𝑚𝑙
𝑀
)
𝑀−1
𝑚=0
𝑁−1
𝑛=0
(19)

57
to predefined a speed threshold [2], vhreshold= [120kmh, 250kmh, 500km/h]. The adopted threshold
will be so useful in order to split two speed ranges named low and high speed. When the
estimated speed is below the threshold, the Sensing Signal Detection returns a signal to the base
station ordering to complete the OFDM signal processing tasks. Otherwise, the speed will be
above the threshold and that results allows retaining OTFS signal processing. As briefly
explained, we see that the OFDM method concerns a low mobility situation.
Figure 3. Framework of Hybrid OTFS-OFDM system
However, the OTFS approach is applied in High mobility conditions. The former analysis was so
convenient to guide our sight to suggest a framework defining our contribution. The focus is on
helping to develop a hybrid OTFS-OFDM system that is based on user estimation. This estimate
is based on the estimate speed approach employed by the ISAC radar application. Before that
let’s give the principle of ISAC technique. In fact, the ISAC radar is based on the Matched Filter
Fast Fourier MF-F algorithm. This algorithm has a significant impact on the improvement of
detection parameter estimation in radar ISAC (Integrated Sensing and Communication). Indeed,
this system has several advantages thanks to, a precision is enhanced by the use of the Fibonacci
sequence. The MF-F algorithm is able to obtaining an estimation of detection parameters, with
fractional precision. This improves the accuracy the estimation. On the other hand, efficiency
increases. In fact, the MF-F algorithm reduces the number of comparisons needed, making the
algorithm more efficient. In addition, the MF-F algorithm has demonstrated robustness in
numerical simulations, which means it can provide accurate estimates even under difficult
conditions. Finally, compared to other estimation algorithms that may have high complexity, the
MF-F algorithm has relatively low complexity, which makes it easier to implement and use. Let’s
note that, the system performances depend strongly on such decision offering one usage among
two possibilities named OFDM or OTFS. Ones the user’s speed was estimated, we can see what
will be speed value. The use of the MF-F algorithm to estimate velocity and detect data is crucial.
The Doppler estimation, assisted by ISAC radar, is enhanced by an iterative refinement process,
which guarantees higher accuracy and improved data detection. For that, the receiver processing
allows us to implement two modes for ISAC radar applications: active detection, joint passive
detection. These two modes have objectives that are described as follows [34]:
 The objective of active detection is to calculate channel delay τ and Doppler shift by
considering transmit vector X and receive vector;
 The objective of passive detection and joint data detection is to estimate the channel
parameters (α, τ, ν) and recover X and the received vector Y. All previous indication
described in [33].
𝑣
̌
≥ 𝑣𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑
𝑣
̌
≤ 𝑣𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑

58
where Γ𝑖 is the estimated Doppler and 𝑐0the velocity of sight and f𝑐 the carrier frequency. We can
present firstly the estimated delay and Doppler based on the indication expression [33]. Where Γ𝑖
delay Doppler plane, the estimated velocity is indicated as follows [34]:
where 𝜐
̂𝑖 is the estimated Doppler and 𝑐0 the velocity of sight.
5. RESULTS AND DISCUSSIONS
In order to check the previously described idea, we have chosen to make simulation under the
conditions as summarized in the Table 1.
Table 1. Simulation Parameters of OTFS and OFDM.
Parameter Value
Channel Power Delay Profile EVA
Subcarrier Spacing ∆f 15 KHz
Number of symbols per frame 8
Number of Subcarriers per Block 16
Carrier Frequency fc (GHz) 0.95
Velocity Estimation𝑉
̂(km/h) 3,10,30,200,500
Modulation 4 − 16QAM
5.1. Evaluation Performance of ISAC System
Our radar ISAC speed estimation system has been subjected to comprehensive testing to assess
its capabilities. The outcomes underscored several significant attributes:
 Enhanced Precision: The ISAC system exhibited remarkable precision in estimating
speed across diverse scenarios. For instance, in a controlled setting where a vehicle
maintained a steady speed of 200 km/h, the system’s speed estimation deviated by less
than 2% on average. This degree of precision significantly surpasses that of traditional
systems, which typically have an error margin about 10%.
 Swift Response Time: The response time of ISAC, defined as the duration from
receiving input data to delivering a speed estimate, was impressively swift. On average,
the system furnished a speed estimate in under 0.5 seconds. This rapid response time
ensures the system’s effective deployment in realtime applications.
 Robustness: We observed that the radar ISAC system demonstrated exceptional
robustness, even under challenging conditions. For example, in situations of poor
visibility or inclement weather, the system’s performance remained stable.
 The accuracy of speed estimates under these conditions was on par with those achieved
under optimal conditions. When juxtaposed with other speed estimation systems, our
ISAC system excelled in terms of accuracy. Additionally, our radar ISAC system
showcased superior robustness, sustaining high performance even under unfavorable
conditions.
(𝜏
̂𝑖,𝜐
̂𝑖) = arg 𝑚𝑎𝑥(𝜏,𝜐)𝜖Λ𝑖
|(Γ𝑖)𝐻
𝑌𝑖|2 (20)
𝑣
̂𝑖 =
𝜐
̂𝑖c0
2f𝑐
(21)

59
To conclude, the results suggest that our ISAC system for speed estimation exhibits outstanding
performance across various metrics. Its high accuracy and robustness under challenging
conditions render it a valuable asset for a multitude of applications as illustrated in Figure 4.
Figure 4. Performance Evaluation for ISAC Speed Estimation System.
5.2. BER Performance
This section evaluates the BER performance of the proposed OTFS-OFDM method using different speeds.
Firstly, we consider an OFDM system as a function of estimated speed. Figure 5 and Figure 6 show the
BER of the OFDM system with various speeds. The modulation schemes are respectively 4-QAM for
Figure 5 and 16-QAM for Figure 6.
Figure 5. BERs Performance of OFDM: The modulation scheme is 4-QAM.
As shown in Figure 5, we have chosen five values for the speed estimate, e.g. (3km/h, 10km/h,
30km/h, 200km/h, 500 km/h). When the value of the speed estimate (3km/h, 10km/h, and
30km/h) is low, these cases have similar BER values. When the speed estimate is increased to
200 km/h and 500km/h, we find that the BER is the highest among those values. Furthermore, we
find that the BER for high speed increases, as the signal power allocated to the channel speed
causes inaccurate channel estimation and failure data detection.

60
Figure 6. BERs Performance of OFDM: The modulation scheme is 16-QAM.
In Figure 6, we evaluate the BER from 0 dB to 15 dB for the 16-QAM modulation scheme,
which requires a higher SNR to obtain a good BER. We observe that OFDM at low speed obtains
the best BER, while OFDM at high speed obtains the lowest BER value at 0 dB to 15dB. For
that, we can use the low speed for OFDM processing, which corresponds well to the simulation
results in Figure 6. The results prove how in case of a low speed, OFDM approach give nearly
optimal BER which’s insensitive to used speed. Based on these results dealing with OFDM
usage, we can conclude that the BER remains acceptable for lower speeds. However, when the
speed increases, the BER shows a great increase causing bad performances. This inadequate
choice in terms of processing tool must be revised to suggest a better tool to overcome such
OFDM cons.We can conclude hat at low speeds, orthogonal frequency division multiplexing
(OFDM) approach delivers a near optimal bit error rate (BER), which is relatively insensitive to
the speed used. We can deduce from these results that BER remains within acceptable limits for
low speeds when using OFDM. Whereas, at higher speeds, BER increases significantly, leading
to limited performance. This highlights the need for a more appropriate processing tool to
mitigate the limitations of OFDM at higher speeds. Furthermore, by solving the problem of the
high mobility of this waveform, we can propose another optimal solution for modulating the
average waveform. We find that the optimal solution for the proposed waveform is the OTFS
waveform. Whether the SNR, the estimation of speed assisted by ISAC radar is less affected.
Therefore, the higher the noise level, the more important it is to use an ISAC radar for accurate
speed estimation.
Figure 7. BERs Performance of OTFS: The modulation scheme is 4-QAM.

61
Figure 7 and Figure 8 clearly show that for a given SNR value, BER increases with estimated
speed. This is a common observation when analyzing the performance of communication
systems at different speeds. The modulation schemes are respectively 4-QAM for Figure 7 and
16-QAM for Figure 8.As the estimated speed increases, the BER increases accordingly,
indicating a deterioration in system performance. As shown in Figure 8, since the higher order
modulation scheme requires a higher SNR to obtain a good BER, we evaluate the BER from 0 dB
to 15 dB, when the modulation scheme is 16-QAM. We observe that both low and high rate
OTFS achieve the best BER.
Figure 8. BERs Performance of OTFS: The modulation scheme is 16-QAM.
The following Figure 9 and Figure 10 illustrate the performance in terms of BER of a hybrid
scheme for OTFS-OFDM systems. The modulation schemes are respectively 4-QAM for Figure
9 and 16-QAM for Figure 9. In Figure 10, this which combines the strengths of both waveforms
to improve BER in high mobility scenarios. In parallel, we can use the low rate for OFDM
processing. In addition, the high mobility problem is solved. We found that the OTFS filter is
better because it is less noisy than the speed of the moving object. All these notes can lead to
choose OTFS in high speed scenarios. Even that this technique could be applied for low speeds,
its processing complexity compared to that OFDM, goes for OFDM retention due to its simple
implementation. This phenomenon can be attributed to the Doppler effect, which induces changes
in signal frequency and phase at higher speeds. These curves clearly show the adequacy of OTFS
in case of high speed. No performance degradation can be obtained in such conditions when
OTFS is used.

62
Figure 9. BERs Performance of OTFS-OFDM: The modulation scheme is 4-QAM
All these notes can lead to choose OTFS in high speed scenarios. In parallel, we can use the low
rate for OFDM processing, which corresponds well with the simulation results in Figures. 9 and
10. In addition, the high mobility problem is solved. We found that the OTFS processing is better
because it is less noisy than the speed of the moving object. All these notes can lead to choose
OTFS in high speed scenarios. Even that this technique could be applied for low speeds, its
processing complexity compared to that OFDM, goes for OFDM retention due to its simple
implementation. This phenomenon can be attributed to the Doppler Effect, which induces
changes in signal frequency and phase at higher speeds. These curves clearly show the adequacy
of OTFS in case of high speed. No performance degradation can be obtained in such conditions
when OTFS is used. All these notes can lead to choose OTFS in high speed scenarios. Even that,
this technique could be applied for low speeds its processing complexity compared to that
OFDM. However, despite its potential application at low speeds, the processing complexity of
OTFS compared with OFDM often leads to OFDM being chosen because of its simpler
implementation. The interesting fact is that the BER curves for all scenarios merge, indicating
insensitivity to user speed. Such a feature underlines the relevance of OTFS in high-speed
scenarios. Noteworthy,the data show that a high mobility user obtains a BER nearly similar to
that of a low mobility. Even that, this technique could be applied for low speeds its processing
complexity compared to that OFDM. However, despite its potential application at low speeds, the
processing complexity of OTFS compared with OFDM often leads to OFDM being chosen
because of its simpler implementation. The interesting fact is that the BER curves for all
scenarios merge, indicating insensitivity to user speed. Such a feature underlines the relevance of
OTFS in highspeed scenarios. The BERs of both OTFS and OFDM waveforms show significant
variations, suggesting that the choice of waveform could be guided by radar ISAC based on the
speed estimation. In particular, this approach can improve BER for high mobility users when
using the OTFS waveform. On the other hand, for low mobility users, the OFDM waveform
seems to be a reliable choice. The results show that the hybrid scheme offers better performance
than using OTFS or OFDM waveforms alone. In low mobility scenarios, the BER of a hybrid
scheme is similar to that of the OFDM waveform usage because the Doppler spread can be
neglected, making the use of OTFS waveform being less advantageous. However, it is crucial to
note that the performance of the hybrid scheme is heavily reliant on selecting appropriate
parameters, such as the subcarrier spacing and the delay Doppler grid size of the OTFS.

63
Figure 10. BERs Performance of OTFS-OFDM: The modulation scheme is 16-QAM
Moreover, the complexity of implementing a hybrid scheme is higher than that of using
either OTFS or OFDM waveforms separated. This may be a concern in some practical
applications. Overall, the results indicate that the hybrid scheme is a viable option for
improving BER performance in high mobility scenarios, but careful design and
implementation are crucial.
5.3. Complexity Analysis
In this part, we discuss the complexity analysis of the proposed Framework, a hybrid system
that switches signal processing chains in the transmitter and receiver, facilitating the use of
either OTFS or OFDM waveforms. A detailed analysis of the complexity of the MF-F
algorithm is provided, divided into two distinct parts. In the first part, they focus on the MF
step. This step includes a low-complexity circular shift operation with a complexity of
𝒪(𝑀) + 𝒪(𝑁), giving a total complexity of 𝒪(𝑀𝑁).The second part, or step F, involves
matrix calculations and has a complexity of(𝒪(𝑀𝑁 )2)when the matrix operations are
performed directly. Multiplication of the diagonal matrix has a complexity of𝒪(𝑀𝑁)while
the cyclic shift matrix operation has a complexity of 𝒪(𝑀𝑁)2
. FFTs at point M and inverse
FFTs at point N have respective complexities of 𝒪((𝑀𝑁 )𝑙𝑜𝑔2(𝑀))and𝒪((𝑀𝑁 )𝑙𝑜𝑔2(𝑁)).
Consequently, the total complexity of the proposed MF-F algorithm is of the order of
𝒪((𝑀𝑁 )𝑙𝑜𝑔2(𝑀𝑁 )). Table 2 shows various complexity parameters of the different
algorithms used in different waveforms.
Table 2. Complexity Analysis.
Waveform’s Algorithm Complexity
OFDM [21] FFT 𝒪((𝑁 )𝑙𝑜𝑔(𝑁))
OTFS [29],
[33] , [34]
SFFT 𝒪((𝑀𝑁 )𝑙𝑜𝑔2(𝑀𝑁))
Proposed
FFT
(if 𝑣
̌ ≤ 𝑣𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑) 𝒪((𝑁 )𝑙𝑜𝑔(𝑁))
SFFT
(if 𝑣
̌ > 𝑣𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑) 𝒪((𝑀𝑁 )𝑙𝑜𝑔2(𝑀𝑁))

64
The aim of deploying the ISAC radar system for OTFS-OFDM is to improve the algorithm's
performance in real-life situations. The integration of ISAC radar reduces the complexity of
OTFS-OFDM implementation. Our proposed framework enables guided switching between
OTFS and OFDM.This framework guarantees high data detection and low implementation
complexity, which is particularly advantageous in high-mobility scenarios thanks to the MF-F
algorithm. This approach improves system efficiency and reduces complexity. This approach
improves system efficiency and reduces complexity. This integrated approach improves system
efficiency, enables adaptation to changing channel conditions, improves the robustness of the
communication system, and enhances data quality, robustness and mobility. Taking into account
the complexity of OTFS and the challenge of high mobility OFDM, the proposed framework
delivers a global and exhaustive solution. The integration of ISAC radar reduces the complexity
of OTFS-OFDM implementation. The proposed framework enables guided switching between
OTFS and OFDM, that facilitated by the ISAC radar. This framework guarantees high data
detection and low implementation complexity, which is particularly advantageous in high
mobility scenarios thanks to the MF-F algorithm. This approach improves system efficiency and
reduces complexity. This integrated approach improves system efficiency, enables adaptation to
changing channel conditions, improves the robustness of the communication system, and
enhances data quality, robustness and mobility. By addressing the complexity of OTFS and the
challenge of high mobility OFDM, the proposed framework provides a complete solution.
6. CONCLUSION
In this paper, we introduce a hybrid system that switches signal processing chains in the
transmitter and receiver, facilitating the use of either OTFS or OFDM waveforms. This system is
based on the integrating sensing and communication ISAC system, which employs velocity
estimation. Our research has primarily concentrated on the study of OTFS, a waveform that is
increasingly being adopted due to its responsiveness to high user mobility. We have put forth a
selection strategy between OTFS and OFDM to better cater to user mobility. This strategy allows
us to choose the most suitable approach based on the user’s speed, utilizing the ISAC system,
which offers superior estimation accuracy and low complexity. This study has oriented our
observations to select one more convenient approach based on user’s speed rate. The outcomes of
our study have been highly gratifying, affirming the validity of our proposed concept. A
significant benefit of our approach is its sustainability when a switching procedure is
implemented in real world systems. More enhanced strategies could be suggested to preview,
looking forward, we propose the development of more sophisticated strategies. These could
encompass more adaptable, or even automated, switching procedures based on other criteria,
which could be designed for immediate execution. To conclude, the switching selection strategy
we propose serves as a potent instrument for enhancing the performance of OTFS-OFDM
systems. Thereby presenting a promising direction for future research and development.
CONFLICTS OF INTEREST
The authors declare no conflict of interest.

65
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67
AUTHORS
Amina Darghouthi was born in Tozeur Tunisia, in 1993. Doctoral student researcher in
electrical engineering at the National Engineering School of Gabes (Tunisia).She is an
esteemed member of the Research Laboratory Modeling, Analysis, and Control Systems
(MACS), registered under LR16ES22 (www.macs.tn), actively involved in research. In
addition to her research pursuits, Fatma is currently serving as a contractual lecturer at the
National School of Engineers of Gabes, where she shares her knowledge and expertise
with students.
Abdelhakim KHLIFI is an assistant professor at the National Engineering School of
Gabes, Tunisia. He received the Engineer degree from the Nation al Engineering School
of Gabes in 2007, and the master's degree from the National Engineering School of
Tunis in 2010, and the Ph.D. degree in 2015. 1. He specializes in signal processing and
digital communications in his teaching endeavors. His main research activities focus on
performances analysis of Waveform Optimization on 5G/6G systems.
HMAIED SHAIEK is an associate professor at the National Conservatory of Arts and
Crafts SITI School, France. He received the Engineer degree from the National
Engineering School of Tunis in 2002, and the master's degree from the University de
Bretagne Occidental in 2003, and the Ph.D. degree from the Lab-STICC CNRS Team,
Telecom Bretagne, in 2007. He was with Canon Inc., until 2009 and left the industry to
integrate with the National school of Ingenieurs de Brest, as a Lecturer, from 2009 to
2010. In 2011, He joined the CNAM, as an Associate Professor in electronics and signal
proces sing. My teaching activities are in the fields of analog and digital electronics,
microcontrollers programming, signal processing and digital communications. His main research activities
focus on performances analysis of multicarrier modulations with nonlinear power amplifiers, PAPR
reduction, and power amplifier linearization. He contributed to the FP7 EMPHATIC (www.ict-
emphatic.eu/) European project and was involved in two national projects: ACCENT5 and WONG5
(www.wong5.fr), funded by the French National Research Agency.
Fatma Ben Salah was born in Gafsa, Tunisia, in 1989. She earn ed her Bachelor's
degree in Engineering in 2014 from the National School of Engineers of Gabes
(Tunisia), specializing in Communication and Networking. Currently, Fatma is a
doctoral student researcher in Electrical Engineering at the same institution. She is an
esteemed member of the Research Laboratory Modeling, Analysis, and Control
Systems (MACS), registered under LR16ES22 (www.macs.tn), actively involved in
research. In addition to her research pursuits, Fatma is currently serving as a contractual
lecturer at the National School of Engineers of Gabes, where she shares her knowledge and expertise with
student
RHAIMI Belgacem Chibani is an Associate Professor in CSIE (Computer Sciences
& Information Engineering). He joined the National Engineering High School at
Gabes named (ENIG) where he is actually employed since Septemer1991. After a
Doctorate Thesis earned at the National Engineering High School at Tunis (ENIT),
he received the Ph.D. degree from ENIG, University of Gabes, Tunisia in 1992. He
is a member of the Research Laboratory MACS at ENIG as activities supervisor
dealing with Signal Processing and Communications Research field. Currently, his
research areas cover Signal Processing and Mobile Communications. He is currently working with the
University of Gabes. His research interests include Information and Signal Processing, Communications
Engineering. He has published a number of papers on international regular organized conferences and
journals (e.g., CESA, IFAC, autumn, spring, A2I and Summer Schools). He is a member of
Communications Engineering staff at ENIG. He has been serving as a Program Committee Member
dealing with Communications for a number of top national schools and activities.

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