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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