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Sensing Integrated DFT-Spread OFDM
Waveform and Deep Learning-powered
Receiver Design for Terahertz Integrated
Sensing and Communication Systems
Yongzhi Wu, Graduate Student Member, IEEE, Filip Lemic, Member, IEEE,
Chong Han, Member, IEEE, and Zhi Chen, Senior Member, IEEE
Abstract
Terahertz (THz) communications are envisioned as a key technology of next-generation wireless
systems due to its ultra-broad bandwidth. One step forward, THz integrated sensing and communication
(ISAC) system can realize both unprecedented data rates and millimeter-level accurate sensing. However,
THz ISAC meets stringent challenges on waveform and receiver design, to fully exploit the peculiarities
of THz channel and transceivers. In this work, a sensing integrated discrete Fourier transform spread
orthogonal frequency division multiplexing (SI-DFT-s-OFDM) system is proposed for THz ISAC, which
can provide lower peak-to-average power ratio than OFDM and is adaptive to flexible delay spread of
the THz channel. Without compromising communication capabilities, the proposed SI-DFT-s-OFDM
realizes millimeter-level range estimation and decimeter-per-second-level velocity estimation accuracy.
In addition, the bit error rate (BER) performance is improved by 5 dB gain at the 10-3 BER level
compared with OFDM. At the receiver, a two-level multi-task neural network based ISAC detector is
developed to jointly recover transmitted data and estimate target range and velocity, while mitigating
the imperfections and non-linearities of THz systems. Extensive simulation results demonstrate that the
This work was presented in part at IEEE Vehicular Technology Conference, 2021 [1].
Yongzhi Wu and Chong Han are with the Terahertz Wireless Communications (TWC) Laboratory, Shanghai Jiao Tong
University, Shanghai, China (Email: {yongzhi.wu, chong.han}@sjtu.edu.cn).
Filip Lemic is with the Internet Technology and Data Science Lab (IDLab), University of Antwerpen - imec, Belgium
(Email: filip.lemic@uantwerpen.be).
Zhi Chen is with University of Electronic Science and Technology of China, Chengdu, China (Email: chenzhi@uestc.edu.cn).
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deep learning method can realize mutually enhanced performance for communication and sensing, and
is robust against white noise, Doppler effects, multi-path fading and phase noise.
Index Terms
Terahertz integrated sensing and communication (THz ISAC), Sensing integrated DFT-spread OFDM
(SI-DFT-s-OFDM) waveform, Multi-task neural network (NN).
I. INTRODUCTION
In recent years, exhaustion of spectrum resource in the microwave band has motivated the
adoption of higher and wider spectrum. Following this trend of moving up the carrier frequencies,
the Terahertz (THz) (0.1-10 THz) is regarded as one of the key technologies for supporting the
sixth generation (6G) wireless communication systems. As a highly potential band, 275-450 GHz
has been identified by the World Radiocommunication Conference 2019 (WRC-19) for the land
mobile and fixed services applications [2]. On one hand, the ultra-broad bandwidth in the THz
band enables ultra-fast data rates of up to hundreds of Gbps and even Tbps, and ultra-high
sensing accuracy. On the other hand, due to the short wavelength of THz wave, THz antennas
with small sizes are expected to be implemented and support highly portable and wearable
devices [3]. Moreover, the non-ionization of THz radiation ensures that THz devices are safe to
human body [4].
Meanwhile, along with the trend towards higher frequencies, 6G wireless communication
systems envisage integrating communication and sensing to achieve a promising blueprint,
i.e., all things are sensing, connected, and intelligent [5]. It is expected that the same system
can simultaneously transmit a message and sense the environment by radio signal. Intuitively,
the integration of communication and sensing can enhance spectrum efficiency and reduce
hardware costs [6]. Moreover, when the signal processing modules and the information of the
surrounding environment are shared among communication and sensing, their performance can
be mutually enhanced. Therefore, by realizing Tbps links and millimeter-level sensing accuracy,
the THz integrated sensing and communication (ISAC) is envisioned to guarantee high quality-
of-experience (QoE) for various services and applications, such as autonomous driving in vehicle
networks, wireless virtual reality (VR), and THz Internet-of-Things (Tera-IoT) [4]. In addition,
the THz ISAC can provide diverse sensing services, including sensing, localization, imaging and
spectrogram [7].
3
Despite the great promise of the THz ISAC, stringent challenges are encountered as a result
of the distinctive features of THz wave propagation and devices. First, from the spectrum
perspective, as the free-space propagation loss increases quadratically with frequency, it becomes
much stronger in the THz band than in the microwave band. In this case, directional antennas
are used to provide high gains and compensate for the severe path loss, which reduce the delay
spread and increase the coherence bandwidth of the THz channel [8]. Second, the reflection
and scattering losses of the THz ray depend on the angle of incidence and usually result
in a strong power loss of a non-line-of-sight (NLoS) path, as well as the decrease of the
number of the dominant rays with non-negligible power [9], which can cause a varying delay
spread. Third, from the transceiver perspective, with the increase in the carrier frequency at
the wireless communication transceivers, the overall system performance becomes substantially
sensitive to radio frequency (RF) analog front-end impairments. In particular, the power amplifier
(PA) efficiency of transmitters in the THz band is more sensitive to the peak-to-average power
ratio (PAPR) of the transmit signal, since the saturated output power of PA rapidly decreases
as the carrier frequency increases [10]. In order to maximize the transmit power and power
efficiency, lower PAPR is required to provide higher coverage and promote energy-efficient THz
communications. Fourth, there exist phase noise (PN) effects in the local oscillator during the
up-conversion and down-conversion of the THz transceivers. Since the PN increases by 6 dB
for every doubling of the carrier frequency [11], it becomes significant to consider the increased
PN distortion effect on the THz communications.
A. Related Work
The concept of integrated sensing and communication has been extensively studied in the
literature. Existing papers on integrated sensing and communication can be classified into four
classes according to the level of integration [12]. From bottom up, the first level is the com-
munication and sensing coexistence, where the spectrum crunch encourages to share the same
frequency bands among communication and sensing [13]. A typical scenario at this level is
a communication system sharing spectrum with a co-located radar system [14]–[16]. In this
case, the interference is a major issue for the communication and sensing coexistence and thus,
efficient interference management techniques are required to avoid the conflict of these two
functionalities [13]. Second, in addition to shared spectrum, when the hardware is shared, the
integration of communication and sensing is achieved at a higher level in the dual-functional
4
communication-sensing systems [6]. A direct way to implement such a system is to design a time-
sharing scheme [17] or a beam-sharing scheme [18], which reduces the cost, size and weight of
the system. Alternatively, a common transmitted waveform can be jointly designed and used for
communication and sensing, including integrating communication information into radar [19] and
realizing sensing in communication systems [20]–[23]. The usage of communication waveforms,
such as single-carrier [20], orthogonal frequency division multiplexing (OFDM) [21], [22],
orthogonal time frequency space (OTFS) modulations [23], are applied to radar sensing and
perform as well as the frequency-modulated continuous wave (FMCW) radar in terms of the
sensing accuracy. Moreover, future ISAC systems are expected to enable shared signal processing
modules at the receiver and further prompt communication and sensing to assist each other [24].
The fourth level of integration includes the shared protocol and network design above the physical
layer.
When moving to higher frequencies, i.e., millimeter wave (mmWave) and THz bands, the
directional antenna and beamforming techniques are used to provide high antenna gain and
compensate for severe path loss. In this case, communication and sensing have different require-
ments on beamforming, i.e., sensing requires time-varying directional scanning beams to search
the targets in the environment, while by contrast, communication requires accurately-pointed
beams to support stable links [25]. Furthermore, the information obtained by sensing can be
employed to predict the location of communication receiver in vehicular networks and realize
sensing-assisted beamtracking [26]. In the THz band, a unified framework for vehicular ISAC
with a time-domain duplex (TDD) inspired solution is proposed in [17], essentially at the second
level of integration. Nevertheless, to the best of the authors’ knowledge, there are few attempts on
higher integration levels of THz ISAC. Motivated by this, our work aims at the third integration
level of THz ISAC, by designing a common transmitted ISAC waveform and a multi-task neural
network (NN) powered receiver for THz ISAC systems.
As a popular multi-carrier waveform for ISAC in the microwave band, OFDM is well known
to be highly spectral-efficient and robust to frequency selective channels [27] and also has
good multiple-input-multiple-output (MIMO) compatibility [28]. Nevertheless, with the increased
antenna directivity and reduced delay spread in the THz band, a set of single-carrier waveforms,
such as the discrete Fourier transform spread OFDM (DFT-s-OFDM) and its variants [29], are
preferred by the THz systems. Moreover, low PAPR of the transmit signal is vital for THz
transmitters to guarantee effective transmission power and high energy efficiency [30]. Thus,
5
DFT-s-OFDM with the single-carrier characteristic is more competitive than OFDM for THz
communications. In our work, we investigate the potential of DFT-s-OFDM for THz ISAC
and design a sensing integrated DFT-s-OFDM (SI-DFT-s-OFDM) waveform that is superior to
OFDM. Furthermore, we meet two challenges when designing the joint receiver. First, there exist
strong non-linear distortion effects at the THz transceivers, such as PN effects, which degrade
the link performance [31], especially when using classical signal recovery methods. Second, it is
hard to implement sensing parameter estimation and data detection with one conventional signal
processing method. Nowadays, with a great potential for enhancing performance, deep learning
(DL) has been investigated in terms of its applications to communication systems, such as THz
indoor localization [32] and channel estimation [33]. Furthermore, joint channel estimation and
signal detection in OFDM systems has been implemented by a deep neural network (DNN),
which is more robust to non-ideal conditions than conventional methods [34], [35]. Existing
studies on deep learning for physical layer design focus on either the sensing parameter estimation
or the communication task. Few of them consider integrated signal processing on these two tasks,
which reduces the processing modules and provides potential to enhance their performance.
B. Contributions
In light of the aforementioned features of THz channel and transceivers, the THz waveform
needs to be well designed to yield a low bit error rate (BER) and a high data rate, as well
as to enable accurate sensing capabilities. In this paper, we first propose the SI-DFT-s-OFDM
waveform, which maintains the single-carrier characteristic and provides a lower PAPR than
OFDM. Furthermore, we address the imperfections of the THz systems, including non-ideal
channel conditions and RF impairments, by leveraging the artificial intelligence (AI) techniques,
especially deep learning [36]. To this end, we develop a two-level multi-task artificial neural
network based ISAC receiver for the THz SI-DFT-s-OFDM system, which can realize mutually
enhanced performance for communication and sensing. Remarkably, the proposed waveform and
receiver design for THz ISAC are immune to white noise, Doppler effects, multi-path fading
and phase noise.
The contributions of this work are summarized as follows.
• We propose a SI-DFT-s-OFDM waveform for the THz ISAC system, by taking into
account the peculiarities of the THz channel and transceivers. By designing the frame
structure with the data blocks and reference blocks, function of sensing is integrated into
6
this waveform. Meanwhile, by considering the varying delay spread of THz channels, we
propose a flexible guard interval (FGI) scheme in this waveform, which is able to reduce the
cyclic prefix (CP) overhead and improve the data rate. The proposed waveform with FGI
is able to improve the data rate by tens of Gbps and reduce the PAPR by 3 dB compared
to CP OFDM due to its flexibility and single-carrier characteristic.
• We propose an integrated receiver for the THz integrated sensing and communication
systems, by designing a two-level multi-task artificial neural network. The proposed
neural network is able to realize data recovery and sensing parameter estimation at the same
time with good BER performance and estimation accuracy as well as fast convergence. In
particular, the proposed NN with the subcarrier-wise and block-wise processing mechanism
is composed of shared layers, which extract patterns commonly used for communication
and sensing, and non-shared layers that conduct sensing parameter estimation and signal
recovery, respectively. To the best of our knowledge, this is the first attempt to realize THz
communication and sensing with one integrated algorithm for multi-task implementation.
• We conduct extensive performance evaluation of the SI-DFT-s-OFDM with the NN
method for two THz ISAC modes. The simulation results demonstrate that the proposed
SI-DFT-s-OFDM can provide 5 dB gain at the 10-3 BER level in the THz channel compared
with OFDM. In presence of the non-ideal effects including white noise, Doppler effects,
multi-path propagation effects and phase noise, the NN method achieves better performance
than the classical ones.
The structure of this paper is as follows. THz ISAC systems are described in Section II.
Section III presents the proposed SI-DFT-s-OFDM waveform. Section IV delineates the multi-
task NN-based ISAC receiver. The performance evaluation results are elaborated in Section V.
Finally, the paper is concluded in Section VI.
II. THZ ISAC SYSTEM MODEL
In this section, we describe the key performance indicators (KPI), applications, perception
modes and channel models of THz ISAC systems, which motivate our waveform and receiver
design in this paper.
7
A. Key Performance Indicators
6G in 2030 and beyond foresees key performance indicators in terms of ISAC, including: i)
hundreds of Giga-bit-per-second rates, ii) centimeter-level sensing resolution and millimeter-level
sensing accuracy, iii) 100× improved energy efficiency. The usage of THz bands can open up
new applications for ultra-high data rate communication and high-accuracy sensing scenarios.
To satisfy these demands, we focus on the waveform and receiver design to improve these key
performance metrics of THz ISAC.
B. Active and Passive Perception
At the transmitter (Tx) side, the output signal of the Tx serves for simultaneously enabling
communication and sensing functionalities, which is regarded as a joint communication-sensing
transmitter. According to the identity of the sensing receiver, THz ISAC systems can be classified
into two perception modes, i.e., active and passive perception.
In the active perception mode, the Tx signal propagates either through the communication
channel to the communication receiver, or through the sensing channel back to the sensing
receiver that is collocated with the transmitter. Then the location of the targets can be estimated
from the back-reflected return signal. The self-interference from the Tx to the sensing Rx can be
suppressed by using the full duplex radar technologies [37]. The applications of active perception
includes joint vehicle-to-vehicle communication and radar sensing (Fig. 1(a)), and wireless VR
communication and sensing (Fig. 1(b)), in which the transmitters estimate the distance of targets
around them.
The passive perception system also transmits a signal that is jointly designed and used for
communication and sensing. This is followed by the received communication signal serving as
the sensing signal that carries the information of the transmitter, such as its distance and speed.
The passive perception mode of THz ISAC can be applied to some applications, such as THz
indoor localization (Fig. 1(c)), Tera-IoT (Fig. 1(d)), where the communication receivers sense the
location of transmitters. In such scenarios, the receivers are required to simultaneously perform
two tasks, including recovering data symbols and estimating the target parameters. Motivated
by this, we propose a multi-task neural network to realize these two tasks, which can be also
utilized in the active perception.
8
Communication Beam
Sensing BeamSource Vehicle
Target Vehicle
Recipient Vehicle
(a) Joint vehicle-to-vehicle communication and
radar sensing.
VR Rx
VR Tx
(b) Wireless VR communication and sensing.
THz Access Point 1
THz Access Point 2
UE
(c) THz indoor localization.
Roomrobot
Air conditioner
Mobile phone
THz access point
Vehicles
(d) Integrated sensing and communication in Tera-
IoT.
Fig. 1. Applications of THz ISAC: active perception mode in (a) and (b), passive perception mode in (c) and (d).
C. Channel Models
We introduce the channel models for THz ISAC with a (Nr + 1)-ray communication channel
model and a P -target sensing channel model, respectively as follows. On one hand, the channel
impulse response (CIR) of the (Nr + 1)-ray THz communication channel is [8]
hc(t, τ) =αLoSej2πνLoStδ(τ − τLoS) +
Nr∑i=1
α(i)NLoSe
j2πν(i)NLoStδ(τ − τ (i)
NLoS), (1)
where δ(·) denotes the Dirac delta function, αLoS and α(i)NLoS represent the attenuation for the
LoS ray and ith NLoS ray, respectively. Nr describes the number of NLoS rays. The propagation
delay τLoS for the LoS ray and τ(i)NLoS for the ith NLoS ray can be computed by the equations
τLoS = rLoSc0
and τ(i)NLoS =
r(i)NLoSc0
, where rLoS and r(i)NLoS stand for the LoS path distance and the
ith NLoS path distance, and c0 is the speed of the light. Meanwhile, the time-varying channel
response hc(t, τ) is influenced by the Doppler shift νLoS along the LoS path and ν(i)NLoS along the
9
ith NLoS path, which are calculated by ν = fcvc0
, where v represents the relative speed between
the Tx and the Com Rx along the corresponding path, fc refers to the carrier frequency.
On the other hand, the CIR of the P -target sensing channel is described as
hs(t, τ) =P∑p=1
αpej2πνptδ(τ − τp), (2)
where P is the number of the considered targets, each of which corresponds to one back-reflected
path with the attenuation αp. Due to the two-way propagation, the delay and the Doppler shift
are calculated by τp = 2rpc0
and νp = 2fcvpc0
, where rp and vp stand for the range and relative speed
of the pth target, respectively. The power attenuation of communication rays and sensing echoes
is calculated as [8], [38]
|αLoS|2 = PtGtxGrx
(c0
4πfcrLoS
)2
e−κ(fc)rLoS , (3a)
|α(i)NLoS|
2 = PtG(i)txG
(i)rx
(c0
4πfcr(i)NLoS
)2
e−κ(fc)r(i)NLoSR2
i , (3b)
|αp|2 = PtG(p)tx G
(p)rx
c20σp
(4π)3f 2c r
4p
e−κ(fc)rp , (3c)
where Pt denotes the transmit power, Gtx and Grx refer to the transmit and receive antenna gains,
the molecular absorption coefficient κ(fc) is a function of the carrier frequency, Ri describes the
reflection coefficient and σp stands for the radar cross section (RCS) of the pth sensing target.
In the THz band, directional beams are used to compensate for severe path loss. Sensing
prefers scanning beams to search targets in the active perception, while communication requires
stable beams towards the communication receiver [25]. In this case, a fixed sub-beam for
communication and several time-varying sub-beams for sensing can be generated by using the
THz ultra-massive MIMO (UM-MIMO) and dynamic hybrid beamforming technology [39].
III. SENSING INTEGRATED DFT-S-OFDM
In this section, to reduce the energy efficiency of THz power amplifiers with low saturated
power [10] and integrate high-accuracy sensing into communication, we propose a SI-DFT-s-
OFDM waveform with a lower PAPR compared to OFDM.
A. SI-DFT-s-OFDM with Cyclic Prefix
As illustrated in Fig. 2, we first introduce the Tx digital unit of the SI-DFT-s-OFDM with CP.
At the transmitter, the transmitted data is grouped into multiple data frames. Each data frame
10
𝑁𝑁-point IDFT
Add CP
Subcarrier Mapping
Reference Block
𝐿𝐿-point DFT
Data Block
(a) Tx digital unit of SI-DFT-s-OFDM with CP.
…
Blo
ck si
ze =
𝑆𝑆𝑟𝑟Data block Reference block
(b) Frame design of SI-DFT-s-
OFDM with CP.
Fig. 2. Block diagram of the Tx digital unit and the frame design for the SI-DFT-s-OFDM with CP.
with M blocks consists of MDB data blocks and MRB reference blocks. The input bit streams are
firstly mapped to the data sequences with the Q-ary quadrature amplitude modulation (QAM).
The modulated symbols are grouped into the data blocks xDm = [xm,0, xm,1, · · · , xm,L−1]T ,m =
0, 1, · · · ,MDB − 1, each containing L symbols. Then a L-point DFT is performed on xDm and
produces a frequency domain representation
XDm = WLxDm ,m = 0, 1, · · · ,MDB − 1, (4)
where XDm , [Xm,0, Xm,1, · · · , Xm,L−1]T ∈ CL×1, and WL ∈ CL×L denotes the DFT matrix
with the size L, WL(m,n) , 1√L
exp (−j2πmn/L) ,m, n = 0, 1, · · · , L− 1.
The reference blocks are introduced as the sensing and demodulation reference signals, which
are generated from constant enveloped Zadoff-Chu (ZC) sequence pRm = [p0, p1, · · · , pL−1]T ,m =
0, 1, · · · ,MRB − 1. Then, the frequency domain representation of the reference block is
PRm = WLpRm ,m = 0, 1, · · · ,MRB − 1, (5)
which is a sequence with constant envelope. In a data frame of the frequency domain signal,
the reference blocks are inserted into the data blocks with equi-distance Sr. Thus, the frequency
domain SI-DFT-s-OFDM signal is given by
Xm =
PRq ,m = Sr · q, q = 0, 1, · · · ,MRB − 1,
XDq , q = m− qm, otherwise,(6)
where Xm , [Xm,0, Xm,1, · · · , Xm,L−1]T ∈ CL×1,m = 0, 1, · · · ,M − 1, and qm represents the
number of reference blocks before the mth block in a frame. The insertion of the reference
blocks is used for sensing parameter estimation and signal recovery. Thanks to the ultra-broad
11
bandwidth and ultra-short symbol duration in the THz band, we design the SI-DFT-s-OFDM
frame structure with a number of reference blocks, which can achieve high-accuracy sensing.
Next, the subcarrier mapping assigns each block to a set of L consecutive subcarriers and
inserts zeros into other (N − L) unused subcarriers. As a result, the time domain SI-DFT-s-
OFDM block, xm = [xm,0, xm,1, · · · , xm,N−1]T , is generated by performing an N -point IDFT,
xm = DN
Xm
0(N−L)×1
, (7)
where DN ∈ CN×N refers to the IDFT matrix with size N , DN(m,n) = 1√N
exp (j2πmn/N),
m,n = 0, 1, · · · , N − 1.
In order to avoid the inter-block interference (IBI) caused by the multi-path propagation, a
guard interval between adjacent blocks is required. A popular means of dealing with the IBI effect
over the multi-path channel is to introduce a cyclic prefix part by copying the last samples of the
one block into its front. Let Ncp denote the length of CP. By adding the CP part, the transmitted
blocks become xm = [xm,N−Ncp , · · · , xm,N−1, xm,0, xm,1, · · · , xm,N−1]T . With the rectangular
pulsing shaping and the digital-to-analog conversion, we can further obtain the continuous-time
signal as
x(t) =1√N
M−1∑m=0
L−1∑n=0
Xm,nrect (t−mTo) ej2πn∆f(t−Tcp−mTo), (8)
where ∆f represents the subcarrier spacing, To = Tcp + T refers to the total symbol duration,
T = 1∆f
denotes the original symbol duration, Tcp =Ncp
NT stands for the CP duration, rect(t) is
a rectangular pulse function and equals to 1 for 0 < t < To and 0 otherwise.
B. SI-DFT-s-OFDM with Flexible Guard Interval
In current communication systems, the length of CP is usually set longer than the maximum
delay spread to remove the IBI effect. However, when it comes to the THz band, the delay
spread might fluctuate substantially, e.g., when the signal power of a long NLoS path becomes
too weak to influence the received signal, it can be ignored and thereby causes a shorter delay
spread. In this case, we can use a short guard interval to reduce the overhead and improve
the spectral efficiency. Nevertheless, the insertion of CP is not flexible, since varying its length
may cause different symbol durations and further leads to unfixed frame structure, which makes
various settings incompatible.
12
𝑁𝑁-point IDFT
Subcarrier Mapping
Reference Block
𝐿𝐿-point DFT
Data Block
(a) Tx digital unit of SI-DFT-s-OFDM with FGI.
…
Blo
ck si
ze =
𝑆𝑆𝑟𝑟Data block Reference block
𝐾𝐾𝑝𝑝 reference symbols
(b) Frame design of SI-DFT-s-OFDM with FGI.
Fig. 3. Block diagram of the Tx digital unit and the frame design for the SI-DFT-s-OFDM with FGI.
In order to deal with varying channel delay spread of THz ISAC, we propose the SI-DFT-
s-OFDM with FGI, by modifying part of the Tx digital unit. In contrast with copying samples
of each data block in the CP scheme, the FGI is generated by the fixed reference symbols and
inserted into the data blocks. As shown in Fig. 3, when grouping the modulated symbols into
the data blocks, we insert a fixed sequence into each data block, which is generated from the
tail part of the reference block. In this case, each data block with the block size L is composed
of K data symbols and Kp reference symbols, xDm = [xm,0, xm,1, · · · , xm,K−1, pK , · · · , pL−1]T .
After performing the L-point DFT, subcarrier mapping and N -point IDFT, we obtain the time
domain block xm = [xm,0, xm,1, · · · , xm,N−1]T in which the last KGI = bKpNLc samples are
approximately constant, i.e., xi,n ≈ xj,n, n = N −KGI, · · · , N − 1 for i 6= j.
Based on this feature, we can regard the last KGI samples of the mth block as the approximate
cyclic prefix of the mth block, which is essentially an internal guard interval inside the IDFT
output. Therefore, we do not need extra operation of adding CP. Meanwhile, by flexibly adjusting
the number of data symbols and the length of the fixed sequence with fixed block size, it can
satisfy different requirements of guard interval length for the channel delay spread. Without the
CP part, the continuous time signal of the SI-DFT-s-OFDM is expressed as
x(t) =1√N
M−1∑m=0
L−1∑n=0
Xm,nrect (t−mT ) ej2πn∆f(t−mT ), (9)
where the CP part in (8) is replaced by the FGI part x(t)(mT− KGINT < t < mT,m = 1, · · · ,M)
in (9).
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IV. MULTI-TASK DEEP LEARNING BASED RECEIVER FOR THZ ISAC
A. Signal Pre-processing
Before developing the deep learning method, we perform pre-processing on the received signal.
Since the channel models for active and passive perception have similar forms, we can conduct
similar analysis on each received block by using a unified baseband channel impulse response
h(t, τ) =∑NP−1
l=0 hlej2πνltδ(τ − τl), where NP denotes the number of transmission paths or
targets, hl, τl and νl represent the normalized complex path gain, the path delay and the Doppler
shift of the lth path, respectively.
We derive the received block of the SI-DFT-s-OFDM with CP as follows. The noiseless
received signal r(t) through the communication or sensing channel is given by
r(t) =
∫h(t, τ)x(t− τ)dτ =
NP−1∑l=0
hlej2πνltx(t− τl). (10)
The received noiseless samples of the mth block are expressed as rm = [rm,0, rm,1, · · · , rm,N−1]T ,
where
rm,i = r(t)|t=mTo+Tcp+i TN
=1√N
NP−1∑l=0
αlej2πνlmTo
L−1∑n=0
Xm,nej2πn∆f(i T
N−τl), (11)
where αl = hlej2πνl(Tcp+i T
N ) ≈ hlej2πνlTcp . In the presence of phase noise and additive white
Gaussian noise (AWGN), the noisy received block ym = [ym,0, ym,1, · · · , ym,N−1]T is given by
ym = Qmrm + zm, (12)
where Qm ∈ CN×N refers to the phase noise effect in the THz band and is a diagonal matrix
given by Qm = diag{[ejθm,0 , ejθm,1 , · · · , ejθm,N−1 ]}, where ejθm,n−1 represents the phase noise at
the nth samples of mth received block. Besides, zm denotes the mth AWGN vector.
The phase noise process is modeled as the Wiener process [40], which is given by
θm,n = θm,n−1 + ∆θm,n, (13)
where ∆θm,n follows the real Gaussian distribution, N (0, σ2θ). The variance σ2
θ is calculated by
σ2θ = 2πf3dBTs, where f3dB denotes the one-sided 3-dB bandwidth of the Lorentzian spectrum
of the oscillator at the receiver and Ts represents the sampling duration. With the increase of the
carrier frequencies, phase noise effects in the local oscillator become stronger in the THz band.
14
When the CP part is replaced by the flexible guard interval, we derive the received samples
of the mth block as
rm,i =r(t)|t=mT+i TN
=
NP−1∑l=0
hlej2πνltx(t− τl)|t=mT+i T
N
=1√N
NP−1∑l=0
hlej2πνl(mT+i T
N)
L−1∑n=0
(Xm,nI
(τl 6
i
NT
)+Xm−1,nI
(τl >
i
NT
))ej2πn∆f( i
NT−τl),
(14)
where I (·) refers to the indicator function. We observe that the SI-DFT-s-OFDM with FGI does
not use the perfect cyclic prefix, which may cause weak IBI due to the propagation paths with
long delay.
In order to conduct the sensing parameter estimation and the data detection, we need to perform
N -point DFT operation on ym and subcarrier demapping. As a result, the received frequency
domain signal is written as
Ym =[IL 0L×(N−L)
]WNym, (15)
where Ym , [Ym,0, Ym,1, · · · , Ym,L−1]T . Furthermore, we deduce the frequency domain repre-
sentation of the received reference block and the received data block, respectively as PRm ,
[Pm,0, Pm,1, · · · , Pm,L−1]T and YDm , [Ym,0, Ym,1, · · · , Ym,L−1]T .
B. Analysis of Sensing and Communication Tasks
To perform the sensing task, the channel frequency response (CFR) at the data blocks is
estimated by simply using the least square (LS) channel estimation in OFDM [21]. To this
end, the target range can be extracted from the CFRs at the data blocks by using the sensing
algorithms, such as compressive sensing (CS) [25], multiple signal classification (MUSIC) [41]
and estimation of signal parameters via rotational invariance techniques (ESPRIT) [42]. However,
exploiting the payload signals for sensing is not suitable for the SI-DFT-s-OFDM system. The
frequency domain data blocks at the sensing receiver can be expressed as
Y (s)m,n = Hm,nXm,n +W (s)
m,n,m = 0, 1, · · · ,MDB − 1; n = 0, 1, · · · , L− 1, (16)
where Hm,n denotes the CFR at the data blocks and W (s)m,n refers to the AWGN. The mean square
error (MSE) of least square (LS) channel estimation on Hm,n is given by
E{(Hm,n − Hm,n
)∗ (Hm,n − Hm,n
)}= E
{|W (s)
m,n|2
|Xm,n|2
}. (17)
15
In the OFDM systems, the data symbols are directly modulated on the frequency domain and have
a relative constant envelop. Nevertheless, in the SI-DFT-s-OFDM systems, since the amplitudes
of the frequency domain signal Xm,n vary a lot for different m and n, i.e., Xm,n is very small
at some subcarriers, which causes large MSE of the LS channel estimation. Thus, the sensing
accuracy of this method for SI-DFT-s-OFDM is much worse than that for OFDM. In addition,
in the passive perception, the data symbols are random and not known by the sensing receiver,
and hence they are not ideal for sensing.
In the SI-DFT-s-OFDM system, the reference blocks have a constant envelop in both time and
frequency domains, which can be used for the aforementioned channel estimation based sensing
algorithms. Meanwhile, they are usually generated by a fixed sequence, which is assumed to
be known by both transmitters and receivers. Thanks to the very short symbol duration of THz
waveform, a number of reference blocks can be inserted into a data frame, which contributes to
high sensing accuracy. The received frequency domain reference signals at the sensing receiver
are given by
P (s)m,n = H(s)
m,nPm,n + Z(s)m,n, (18)
where m = 0, 1, · · · ,MRB − 1, and n = 0, 1, · · · , L − 1, Z(s)m,n refers to the AWGN, and H
(s)m,n
denotes the sensing CFR at the nth subcarrier of mth reference block, derived as
H(s)m,n ≈
P∑p=1
αpej2πνpmSrToe−j2πτpn∆f . (19)
Next, we can perform the LS channel estimation and obtain the estimated CFR, which is
expressed as
H(s)m,n =
P(s)m,n
Pm,n= H(s)
m,n +Z
(s)m,n
Pm,n. (20)
The sensing CFR at the reference blocks is then regarded as the sensing processing matrix. Due
to the constant envelop of Pm,n, the LS estimator does not increase the noise variance.
Then, the sensing task is to estimate the delay and Doppler parameters, τp and νp, from
estimated sensing CFR, and calculate the range and velocity parameters. This estimation problem
can be expressed as a problem of spectral estimation from a sum of complex exponential signals
buried in noise. We can regard the sensing CFR as the observation matrix and calculate the
correlation function function of the sensing CFR as RH(∆m,∆n) = E{H
(s)∗m−∆m,nH
(s)m,n+∆n
}.
Furthermore, both the range and velocity can be estimated from this correlation function by using
16
the high-resolution subspace-based methods, such as MUSIC [43]. Alternatively, the DFT-based
method [21] can be invoked as the sensing algorithm, which is the maximum likelihood estimator
and performs DFT on the sensing CFR. Following the derivation in [44], the Cramer-Rao lower
bounds (CRLBs) for range and velocity estimation variance in case of one target using one
SI-DFT-s-OFDM frame are respectively given by
Var [r] >6
σ2 (K2 − 1)KMRB
(c0
4π∆f
)2
, (21)
and
Var [v] >6
σ2 (M2RB − 1)MRBK
(c0
4πSrTofc
)2
, (22)
where σ2 denotes the signal-to-noise ratio (SNR).
At the communication receiver, several steps are implemented to perform the communication
task, including IDFT/DFT operations, channel estimation and channel equalization. In the ISAC
system, the reference blocks are not only used for the sensing parameter estimation, but also
for the frequency domain equalization (FDE) at the communication receiver, including the zero-
forcing (ZF) and the minimum mean square error (MMSE) equalization methods.
The disadvantages of conventional signal processing methods include limited robustness to
non-linear distortions, e.g., PN noise, and difficulty to simultaneously perform sensing and
communication, causing that an integrated receiver for ISAC is challenging. Thus, we delineate
the multi-task NN-based ISAC receiver to estimate the sensing parameters and recover the
communication data in THz SI-DFT-s-OFDM systems at the same time, which can overcome
the above problems.
C. Multi-Task Neural Network Design
In order to design a receiver of THz SI-DFT-s-OFDM system to jointly address the problems
of communication and sensing, we develop a two-level multi-task NN method, which learns the
channel information of the environment and the transmitted communication data. As shown in
Fig. 4, the whole framework consists of the first level and the second level. The first level is used
to extract channel information at the data blocks from the received reference blocks and estimate
the velocity of the target. Then the former output and the received data blocks are concatenated
and make up the inputs of the second level network, which outputs the recovered data symbols
and the target range. Both of the two level networks are composed of the shared layers and
non-shared layers. The former part shares significant knowledge about wireless channel among
17
𝑣𝑣𝑝𝑝
𝑟𝑟𝑝𝑝
Re{𝐘𝐘𝑚𝑚}Im{𝐘𝐘𝑚𝑚}
�𝑷𝑷R𝑚𝑚
�𝒀𝒀D𝑚𝑚
Flatten
Shared Layers
…
…
…
…
…
…
Non-Shared Layers
Reshape
Concatenate
Flatten
Shared Layers
Non-Shared Layers
Recovered data symbols
Reshape
pilot data
Fig. 4. The structure of the proposed two-level multi-task neural network framework for THz ISAC.
communication and sensing and reduces the network parameters, while the latter part contains
the task-specific layers, essentially two sub-networks that optimize communication and sensing
performance, respectively.
Based on the input-output relation of the frequency domain in (16) and (18), we design a
tailored mechanism in the proposed neural network for SI-DFT-s-OFDM, i.e., subcarrier-wise
processing for the first level network and block-wise processing for the second level network,
which is illustrated by the dotted box in Fig. 4. First, subcarrier-wise reference signals are
respectively input into the first level network. In this case, the velocity parameter and the CFR
at the data blocks can be estimated by utilizing the channel Doppler knowledge contained in
the received reference signals along one subcarrier. The communication sub-network in the
first level network works like a 1D linear channel interpolation function. Next, block-wise data
symbols and output vectors from the first level network are concatenated and then input into
the second level network. The range parameter is estimated by employing the channel delay
knowledge within one block and the transmitted data symbols are recovered at the same time.
The communication sub-network in the second level network can be viewed as a function that
integrates the equalization and the IDFT operation.
We compare our proposed neural network with the neural network methods for position
estimation in existing studies from the following aspects. First, we design a multi-task learning
based neural network, i.e., the tasks of our proposed neural network not only include the sensing
18
…
…
…Flatten
Reshape
Re{𝐘𝐘𝑚𝑚}Im{𝐘𝐘𝑚𝑚}
pilot data
Recovered data symbols
𝑟𝑟𝑝𝑝
Fig. 5. The structure of the multi-task neural network for time-invariant channels.
parameter estimation, but also aim at recovery of the transmitted data. Second, we propose a
two-level network architecture to estimate the target velocity in the first level and the target
range in the second level. Third, our neural network is composed of the shared layers and the
non-shared layers with the aforementioned benefits. The neurons in one sub-network of the
non-shared layers are not connected to the other sub-network, which is different from the fully
connected deep neural network, where all the neurons in one layer are connected to the neurons
in the next layer [45].
For the time-invariant channel, the multi-task neural network can be simplified into the second
level by directly regarding the reference blocks as the input of the second level network, as
shown in Fig. 5. Before performing block-wise processing, the reference blocks are copied and
concatenated with adjacent data blocks. In this case, the output of the neural network includes
the target range parameter and recovered data symbols without requiring velocity estimation.
D. Shared Layers
The first level and the second level of the proposed network have the similar network structure
and we describe the common operations of their shared layers and non-shared layers next. The
input layer consists of the received blocks, including the reference and data blocks in (15).
Specifically, the input of the proposed network contains the element-wise real and imaginary
values of the received blocks. Followed by the input layer, we set Nshared hidden layers as the
shared layers for both communication and sensing. Each hidden layer is composed of multiple
neurons, each of which receives input from all neurons of its previous layer and is called a dense
layer. The output of each hidden layer is a nonlinear function of a weighted sum of neurons of
the previous layer with a bias. Let Wi and bi denote the weight vector and the bias vector at
19
the ith hidden layer, respectively. With the forward propagation in the network, the output of the
ith hidden layer oi is given by
oi = fReLU (Wioi−1 + bi) , (23)
where fReLU stands for the activation function of rectified linear unit (ReLU) with fast computa-
tion speed, which is introduced to implement non-linear mapping and expressed as fReLU(x) =
max(0, x). Moreover, the input of the network is defined by o0. In addition, the batch-normalization
(BN) operation is invoked at each hidden layer to prevent overfitting. Meanwhile, we employ
the hard parameter sharing in the shared layers to reduce the possibility of overfitting. Since the
shared layers connect multiple dense layers, the output of the shared layers can be rewritten as
oshared = fReLU(DenseNshared(o0)), (24)
where Dense(·) denotes a fully-connected layer.
E. Non-Shared Layers
The design of the non-shared layers in the proposed network is tailored for the THz ISAC
problem involving with two sub-networks for both the first level and the second level. In Fig. 4,
the output of the shared layers is input into the sensing and communication sub-networks,
respectively. To this end, we invoke separated performance optimization for communication and
sensing. We set Nc layers for the communication sub-network, and Ns layers for the sensing
sub-network. Thus, the output of the communication sub-network is given by
oc = ftanh(DenseNc(oshared)
), (25)
where we choose the hyperbolic tangent function ftanh as the activation function at the commu-
nication output layer, described as ftanh = ex−e−xex+e−x
. The usage of the this function restricts the
output range into [−1, 1], since the real and the imaginary parts of the modulated symbols are
limited to this range. The output of the sensing sub-network is expressed as
os = ftanh(DenseNs(oshared)), (26)
for velocity estimation in the first level and
os = fSigmoid(DenseNs(oshared)), (27)
for range estimation in the second level, where the sigmoid function fSigmoid is used as the
activation function, fSigmoid(x) = 11+e−x
, which maps the output to the interval [0, 1], since the
normalized target distance or path length is non-negative.
20
F. Design of Training Features and Labels
With the proposed neural network, we choose the received samples YDm and PRm in the
frequency domain at the receiver. The features of one data sample in the training set contain the
real and imaginary parts of one transmitted data frame.
For the communication sub-network, the modulated data symbols xDm are chosen as the
training labels. To be precise, the labels are composed of the real and imaginary parts of data
symbols. In order to improve the communication performance, we divide one data block into
several groups and use each group to train a model independently [34]. The outputs of all trained
models are concatenated to the final estimated data block.
For the sensing sub-network, the target distance or the path length rp(p = 0, 1, · · · , P − 1)
is regarded as the training label. We perform the normalization operation on it and map its
value into the interval [0, 1], rp = rprmax
, where rmax refers to the maximum possible value of the
path length. Meanwhile, the target velocity is normalized and mapped into the interval [-1, 1],
vp = vpvmax
, where vmax denotes the maximum possible value of the target velocity.
G. Loss Function, Evaluation Metrics and Optimizer
For the THz ISAC problem, our objective is not only to minimize the BER of the communica-
tion system but also to improve the sensing estimation accuracy. Therefore, we select the MSE to
quantify the distance error between the predicted labels and their real values. We first define two
loss functions. The loss function of communication is defined as Lossc = E{‖xDm − yDm‖22},
where xDm and yDm refer to the true and the estimated label vectors of the communication
sub-network, ‖ · ‖2 denotes the l2-norm. The loss function of sensing is given by Losss =
E {‖r − r‖22} ,, where r and r represent the true and the estimated label vectors of the sensing
sub-network. To minimize the cost of the ISAC receiver, we sum these two losses function as
Loss = a1Lossc + a2Losss, (28)
where a1 and a2 stand for the weights of the communication loss and sensing loss functions,
respectively. We can add the MSE of the target velocity to the loss function of sensing in presence
of Doppler effect.
In addition to the loss functions, we need to define the evaluation metrics that quantify the
communication and sensing performance. Specifically, we demodulate the predicted data symbols
and calculate the BER as the communication performance metric. Moreover, we transform the
21
TABLE I
SIMULATION PARAMETERS
Notation Definition Value Notation Definition Value
fc Carrier frequency 0.3 THz N Subcarrier number 64, 256, 1024
∆f Subcarrier spacing 1.92, 7.68 MHz L Block size 32, 128, 512
T Symbol duration 0.13 µs - Modulation scheme 4-QAM
Tcp CP duration 0.032 µs σ2θ PN variance 10-4 to 10-2
normalized distance and velocity to their absolute values by multiplying them with rmax and
vmax. We select the root mean square error (RMSE) as the sensing performance metric.
The optimizer used for training our network is the adaptive moment estimation (Adam) [46],
which is a combination of root mean square propagation (RMSprop) and stochastic gradient
descent (SGD) with momentum, due to its fast convergence speed and higher computational
efficiency compared to other SGD methods [46].
V. SIMULATION RESULTS
In this section, we investigate the performance of the proposed THz ISAC system with the SI-
DFT-s-OFDM waveform and the NN-powered receiver, in contrast with OFDM and conventional
signal processing methods. The key parameters in simulations are described in Table I. The
subcarrier spacing is set as 15× 2n kHz to be compatible with 4G and 5G numerology [27]. In
addition, we refer to the THz link budget analysis in [47] for other parameters.
A. Generation of the Training Set
The training data set is generated using the channel models introduced in Sec. II-C in the
simulated environment. In particular, for each data sample, we first construct a channel impulse
response by generating several propagation paths with delay that is randomly selected between
zero and guard interval duration and then run a point-to-point communication simulation by
transmitting a data frame. Then, we save the transmitted data symbols, channel parameters and
the received blocks, and build the training dataset. In addition, the AWGN and the phase noise
contributions are further considered to reinforce the robustness of the NN method to these effects.
22
0 2 4 6 8 10 12
PAPR0 [dB]
10-3
10-2
10-1
100
Pr(
PA
PR
>P
AP
R0)
OFDM
SI-DFT-s-OFDM with CP
SI-DFT-s-OFDM with FGI
Fig. 6. Comparison of PAPR between OFDM and SI-DFT-
s-OFDM, L = 12N , Kp = 1
4L, the subcarrier number is 64
for dotted line and 1024 for solid line.
0 5 10 15 20
SNR [dB]
10-4
10-3
10-2
10-1
100
BE
R
OFDM (ZF)
OFDM (MMSE)
SI-DFT-s-OFDM with CP (ZF)
SI-DFT-s-OFDM with CP (MMSE)
SI-DFT-s-OFDM with FGI (ZF)
SI-DFT-s-OFDM with FGI (MMSE)
Fig. 7. Comparison of BER performance between OFDM
and SI-DFT-s-OFDM.
B. PAPR
The PAPR of the transmit signal block is a significant characteristic of the waveform in the
THz band defined as
PAPR{xm} =maxn |xm,n|2
E{|xm,n|2}. (29)
In Fig. 6, we evaluate the PAPR of the SI-DFT-s-OFDM and OFDM signals. The performance
metric is the complementary cumulative distribution function (CCDF) of PAPR, i.e., Pr(PAPR >
PAPR0).
We learn that the SI-DFT-s-OFDM has lower PAPR than OFDM for both cases of CP and
FGI. In particular, the PAPR values of SI-DFT-s-OFDM data block are approximately 2.6 dB
and 3.2 dB lower than OFDM at the CCDF of 1%, when the subcarrier number is 64 and 1024,
respectively. In addition, the PAPR of SI-DFT-s-OFDM with FGI is slightly lower than that
with CP. By reducing PAPR, the power backoff of PA can be decreased and the transmit power
can be maximized when the saturated power of PA is fixed. Thus, SI-DFT-s-OFDM is able to
provide higher coverage and promote more energy-efficient THz communication and sensing
than OFDM.
C. Waveform Comparison
We further compare the BER performance of SI-DFT-s-OFDM and OFDM. In our simulation,
the number of NLoS paths is set to 4 and the reflection loss in dB unit is assumed to be a Gaussian
23
0 5 10 15 20
SNR [dB]
10-4
10-3
10-2
10-1
100
BE
R
OFDM (ZF)
OFDM (MMSE)
SI-DFT-s-OFDM with CP (MMSE)
SI-DFT-s-OFDM with FGI (ZF)
SI-DFT-s-OFDM with FGI (MMSE)
SI-DFT-s-OFDM with CP (ZF)
Fig. 8. Comparison of BER performance between OFDM
and SI-DFT-s-OFDM in presence of phase noise effect, σ2θ
= 2× 10−4.
0 0.05 0.1 0.15 0.2 0.25
Delay Spread [Symbol Duration]
140
150
160
170
180
190
200
Ach
iev
able
Rat
e [G
bp
s]
CPFGI
Fig. 9. Comparison of achievable rate versus channel delay
spread between using CP and FGI, SNR = 20 dB, bandwidth
= 30 GHz.
random variable with the mean -13 dB and the standard deviation 2 dB [9]. The block size and
the number of subcarriers are 128 and 256, respectively.
In Fig. 7, we perform both ZF and MMSE equalization for SI-DFT-s-OFDM and OFDM. We
learn that with the ZF equalization, the SI-DFT-s-OFDM has higher BER than OFDM below
the SNR of 15 dB. However, at high SNR regime, the SI-DFT-s-OFDM can achieve better
BER performance for both two equalization methods. In particular, when using the MMSE
equalization, the SI-DFT-s-OFDM can improve more than 5 dB gain at the 10-3 BER level
compared to the OFDM. The ZF equalizer can amplify the influence of the white noise, especially
through the channels with strong frequency-selectivity. Nevertheless, the reflection loss in the
THz band results in strong power losses of NLoS paths and reduces the frequency-selectivity of
the THz channels. Meanwhile, data symbols are directly modulated on the subcarriers in OFDM
and the frequency domain signal has a constant amplitude when using 4-QAM modulation
scheme. Therefore, the ZF equalization and MMSE equalization have the same BER performance
for OFDM through the THz channels. In the SI-DFT-s-OFDM system, the amplitudes of the
frequency domain signal vary greatly and are smaller than the white noise at some subcarriers.
In this case, the MMSE method can reduce the influence of white noise on SI-DFT-s-OFDM.
In Fig. 8, we consider the phase noise effect on the BER performance in the THz band. When
the phase noise parameter σ2θ equals to 2 × 10−4, we observe that the BER of both SI-DFT-s-
OFDM and OFDM is increased to higher than 10-3 for any SNR below 20 dB, in contrast with
24
0 5 10 15 20
SNR [dB]
10-3
10-2
10-1
100
101
Ran
ge
RM
SE
[m
]
NN (1 target)
NN (2 targets)
NN (3 targets)
MUSIC (1 target)
MUSIC (2 targets)
MUSIC (2 resovlable targets)
CRLB
Fig. 10. Comparison of range estimation accuracy between
NN and MUSIC using one reference block, K = 32.
0 5 10 15 20
SNR [dB]
10-2
10-1
100
101
Vel
oci
ty R
MS
E [
m/s
]
NN (1 target)
NN (2 targets)
MUSIC (1 target)
MUSIC (2 targets)
CRLB
Fig. 11. Comparison of velocity estimation accuracy be-
tween NN and MUSIC using one subcarrier, Mr = 32.
Fig. 7. With such performance degradation, it is concluded that it becomes crucial to consider
the robustness of the data detection algorithms to the phase noise effect in the THz band.
In addition, we calculate the achievable rate of using different guard interval schemes, i.e.,
CP and FGI. The CP duration is fixed as 14T and the FGI duration is adjusted according to the
channel delay spread, which does not require the adjustment of the waveform numerology. In
Fig. 9, it is indicated that the FGI scheme can support higher achievable rates of 30 Gbps than
the CP scheme when the delay spread is 5% of the symbol duration, by reducing the overhead
of the guard interval. The mean value of the achievable rate using the FGI scheme is 174 Gbps,
which is more than that using the CP scheme by approximately 14 Gbps. Since the channel
sparsity in the THz band may lead to small delay spread in many cases, SI-DFT-s-OFDM with
FGI is more promising than that with CP for THz communications.
D. NN-Based Sensing Receiver for Active Perception
Furthermore, we investigate the performance of a single-task NN for THz sensing, which
is tailored for the sensing receiver in the active perception. In Fig. 10, we compare the range
estimation accuracy as a function of SNR, based on the NN and MUSIC algorithms. The target
distances are randomly generated between 0 and c0Tcp
2. The numbers of neurons in each hidden
layers used for NN are 500, 250, 120, 60, respectively. The input vector is composed of the
reals parts and imaginary parts of the received reference block, PRm .
25
0 50 100 150 200
Training Epochs
10-4
10-3
10-2
10-1
100
Lo
ssc
10-5
10-4
10-3
10-2
10-1
Lo
sss
Training Loss (Comm)
Testing Loss (Comm)
Training Loss (Sensing)
Testing Loss (Sensing)
Fig. 12. Convergence evaluation of NN for ISAC receiver.
0 5 10 15 20
SNR [dB]
10-5
10-4
10-3
10-2
10-1
100
BE
R
SI-DFT-s-OFDM with CP (ZF)
SI-DFT-s-OFDM with CP (MMSE)
SI-DFT-s-OFDM with CP (NN)
SI-DFT-s-OFDM with FGI (ZF)
SI-DFT-s-OFDM with FGI (MMSE)
SI-DFT-s-OFDM with FGI (NN)
Fig. 13. Comparison of BER performance versus SNR
among ZF equalization, MMSE equalization and the NN
method.
The simulation results indicate that the RMSE of the range estimation achieves 10-2 m by
employing only one reference block. The sensing accuracy is further improved to millimeter-
level by increasing the size and the number of the reference blocks used for sensing. As shown
in Fig. 10, when single target is estimated, the estimation accuracy of NN is better than MUSIC
below SNR of 15 dB. When considering multiple targets, we observe that the MUSIC algorithm
requires that different targets are resolvable, i.e., the distance difference among the targets is larger
than the resolution of MUSIC. If this condition is not satisfied, MUSIC is not able to distinguish
two targets and hence, estimate their distances incorrectly. By contrast, the NN method is more
robust to the estimation of multiple targets and achieves better range resolution.
Moreover, the velocity estimation accuracy of NN and MUSIC is compared in Fig. 11, in
which the target velocity is randomly generated between -100 km/h and 100 km/h, and the
subcarrier spacing is set as 1.92 MHz. The simulation results indicate that the RMSE of the
velocity estimation achieves the decimeter-per-second level accuracy by employing only one
subcarrier for sensing. In addition, the NN method achieves better velocity resolution than the
MUSIC algorithm.
E. Multi-Task NN-Based ISAC Receiver for Passive Perception
Next, we conduct the performance evaluation of the proposed multi-task NN-based ISAC
receiver, which is tailored for the passive perception. The sizes of the hidden layers in the
26
0 5 10 15 20
SNR [dB]
10-4
10-3
10-2
10-1
100
BE
RSI-DFT-s-OFDM with CP (ZF)
SI-DFT-s-OFDM with CP (MMSE)
SI-DFT-s-OFDM with CP (NN)
SI-DFT-s-OFDM with FGI (ZF)
SI-DFT-s-OFDM with FGI (MMSE)
SI-DFT-s-OFDM with FGI (NN)
Fig. 14. Comparison of BER performance versus SNR
among ZF equalization, MMSE equalization and the two-
level neural network (NN) in presence of Doppler effect.
0 5 10 15 20
SNR [dB]
10-2
10-1
100
Ran
ge
RM
SE
[m
]
SI-DFT-s-OFDM with CP (NN)SI-DFT-s-OFDM with FGI (NN)MUSIC
Fig. 15. The accuracy of estimating the LoS path is
compared between NN and MUSIC.
10-4
10-3
10-2
Phase Noise Parameter 2
10-4
10-3
10-2
10-1
100
BE
R
ZF
MMSE
NN
Fig. 16. Comparison of BER performance versus the phase noise effect among ZF equalization, MMSE equalization and the
NN method, SNR = 20 dB.
shared layers are 500 and 250, respectively. The hidden layer size in the communication sub-
network is 120 and the sensing sub-network uses two hidden layers with the size of 120 and
60. The output layer sizes are 16 for communication and 1 for sensing. The block size and the
number of subcarriers are 32 and 64, respectively.
The convergence of the proposed neural network for ISAC receiver is demonstrated in Fig. 12,
in which the loss functions of communication and sensing for the training set and the testing
27
set are plotted. The curves in Fig. 12 follow an exponential decay in a log scale, which indicate
that the loss function of sensing reduces by three orders of magnitude after 40 epochs and the
loss function of communication decreases by two orders of magnitude after 80 epochs. Thus,
the fast convergence of the proposed deep learning method is verified for both communication
and sensing. In addition, the test time for thousands of transmitted frames is only a few seconds
in the Python environment, i.e., millisecond for one test frame.
The BER is then evaluated based on the classical equalization methods and the deep learning
method. Fig. 13 shows that the NN method is able to achieve the best BER performance at
low SNRs. At high SNRs, the NN method is still better than the ZF method and comparable
to the MMSE method. The MMSE method performs slightly better than the NN because the
second-order statistics of the channels are assumed to be known and used for data detection. In
this case, the advantage of the NN method is that it does not require the knowledge of SNR.
In addition, the BER of SI-DFT-s-OFDM with FGI using NN achieves a magnitude of 10-4.
By contrast, it can provide about 5 dB performance gain at the 10-3 BER level compared with
the ZF equalization, indicating that the NN method can perform better than some conventional
signal recovery methods for THz communications.
When the subcarrier spacing is smaller and the Doppler effect needs to be considered. In
Fig. 14, we evaluate the BER performance of SI-DFT-s-OFDM in presence of Doppler effect.
The subcarrier spacing is set as 1.92 MHz, and the interval of the reference blocks in a frame
Sr equals to 10. The speed along each path is randomly generated between -100 km/h and 100
km/h. In Fig. 14, we learn that the NN method outperforms both ZF and MMSE equalization,
which indicates that the proposed two-level NN method is more robust to Doppler effect than
the conventional channel interpolation method.
Then, we investigate the accuracy of estimating the LoS path to show the effectiveness of the
proposed NN method for passive perception. In Fig. 15, we show that the NN method performs
slightly better than the MUSIC algorithm. Meanwhile, the NN method has stronger robustness to
the AWGN noise than the conventional sensing algorithms. Since the multi-path effect, i.e., the
existence of the NLoS paths, may influence the range estimation of the LoS path, the estimation
accuracy is not as good as the case involving with only one path. Moreover, the NN method is
more robust to the multi-path propagation for THz passive perception.
Finally, the influence of the phase noise in the THz band is studied. We set the phase noise
parameter σ2θ from 10-4 to 10-2, which corresponds to weak phase noise increasing to strong
28
phase noise [48]. We evaluate the BER performance of SI-DFT-s-OFDM with FGI in presence
of phase noise with the NN method. The evaluated NN model is the same as the one trained
using the dataset without considering phase noise. Fig. 16 indicates that the BER increases when
the phase noise becomes stronger. By comparing the NN method with the classical equalization
methods, we state that the proposed NN method has stronger robustness to phase noise and
performs best while experiencing strong phase noise.
VI. CONCLUSION
In this paper, we have proposed a sensing integrated DFT-s-OFDM system for THz ISAC.
We design two types of THz waveforms, i.e., CP based SI-DFT-s-OFDM and FGI based SI-
DFT-s-OFDM, which utilize the specific features of THz channels and take into account the
requirements of THz transceivers. Furthermore, we have developed a two-level multi-task NN
powered receiver to simultaneously perform sensing parameter estimation and signal recovery.
With extensive simulation, the results have demonstrated that the proposed SI-DFT-s-OFDM
can reduce the PAPR by approximately 3.2 dB and enhance 5 dB gain at the 10-3 BER level
in the THz channel, compared to the OFDM system. The proposed SI-DFT-s-OFDM with the
FGI scheme can achieve a mean achievable rate of 174 Gbps and 10-5 BER performance at
the SNR of 20 dB, while realizing millimeter-level range estimation and decimeter-per-second-
level velocity estimation accuracy. In contrast with the conventional ISAC systems, the proposed
NN-based ISAC receiver is more robust to AWGN noise, Doppler effects, phase noise and
multi-path propagation, which is preferred in THz systems. In particular, the NN method in the
SI-DFT-s-OFDM achieves higher accuracy for multiple targets estimation and performs better
BER performance than the classical ZF equalizer. Meanwhile, it is able to reduce processing
modules of ISAC transceiver by integrating sensing parameter estimation and signal recovery.
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