1 Bidirectional Integrated Sensing and Communication Full-Duplex or Half-Duplex

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Bidirectional Integrated Sensing and

Communication: Full-Duplex or Half-Duplex?

Zhaolin Wang, Graduate Student Member, IEEE, Xidong Mu, Member, IEEE,

and Yuanwei Liu, Fellow, IEEE

Abstract—A bidirectional integrated sensing and communica-

tion (ISAC) system is proposed, in which a pair of transceivers

carry out two-way communication and mutual sensing. Both full-

duplex and half-duplex operations in narrowband and wideband

systems are conceived for the bidirectional ISAC. 1) For the

narrowband system, the conventional full-duplex and half-duplex

operations are redesigned to take into account sensing echo sig-

nals. Then, the transmit beamforming design of both transceivers

is proposed for addressing the sensing and communication (S&C)

tradeoff. A one-layer iterative algorithm relying on successive

convex approximation (SCA) is proposed to obtain Karush-Kuhn-

Tucker (KKT) optimal solutions. 2) For the wideband system, the

new full-duplex and half-duplex operations are proposed for the

bidirectional ISAC. In particular, the frequency-selective fading

channel is tackled by delay pre-compensation and path-based

beamforming. By redesigning the proposed SCA-based algorithm,

the KKT optimal solutions for path-based beamforming for char-

acterizing the S&C tradeoff are obtained. Finally, the numerical

results show that: i) For both bandwidth scenarios, full-duplex

mode may not always be preferable to half-duplex mode due to

the presence of the sensing interference; and ii) For both duplex

operations, it is sufﬁcient to reuse communication signals for

sensing in the narrowband system, while an additional dedicated

sensing signal is required in the wideband system.

Index Terms—Beamforming design, full-duplex, half-duplex,

integrated sensing and communication.

I. INTRODUCTION

The peak data rate of next-generation wireless networks

is expected to be at least one terabit per second [2], which

requires very high spectral efﬁciency. To this end, full-duplex

communication, which allows overlap of downlink (DL) and

uplink (UL) communications over the same time-frequency

resource, is a promising candidate technique in next-generation

wireless networks [3]. Theoretically, the full-duplex technique

is capable of doubling the communication capacity. How-

ever, the main obstacle to the full-duplex technique is self-

interference (SI) caused by strong power leakage between

adjacently deployed transmitter and receiver, which typically

overwhelms the desired communication signals [4]. Thus,

SI cancellation techniques are critical for full-duplex tech-

niques. With the advanced SI cancellation techniques in the

propagation domain, analog domain, and digital domain [5]–

[10], the strong SI can be suppressed to the receiver noise

level, which makes the practical implementation of full-duplex

communication systems possible.

An earlier version of this paper was presented in part at the IEEE

International Conference on Communications, Rome, Italy, June 2023 [1].

The authors are with the School of Electronic Engineering and Com-

puter Science, Queen Mary University of London, London E1 4NS,

U.K. (e-mail: zhaolin.wang@qmul.ac.uk, xidong.mu@qmul.ac.uk, yuan-

wei.liu@qmul.ac.uk).

Furthermore, the next-generation wireless networks are en-

visioned not only to enhance the wireless communication

performance, but also to provide sensing services to emerging

sensing-based applications such as virtual reality, Internet of

Vehicles, and Metaverse. Therefore, integrated sensing and

communication (ISAC) techniques have been regarded as one

of the key enablers of next-generation wireless networks [11]–

[13]. In ISAC, radio-frequency sensing and wireless communi-

cation functionalities are carried out simultaneously by sharing

the same frequency spectrum and hardware facilities, thus

enhancing resource efﬁciency. Moreover, based on the widely

deployed wireless infrastructures, ubiquitous sensing can be

realized by exploiting the advanced ISAC techniques [11]–

[13], which are capable of capturing the environment data for

building ubiquitous intelligence and bridging the virtual and

physical worlds.

A. Prior Works

1) Studies on Full-duplex Communication: The existing

research contributions of full-duplex communication may be

classiﬁed into two categories: full-duplex for DL/UL com-

munication [14]–[17] and full-duplex for relaying [18]–[21].

Firstly, for the full-duplex DL/UL communication, the authors

of [14] conceived a classical bidirectional topology, where a

pair of full-duplex terminals communicate with each other.

Moreover, an explicit residual SI model under the limited

dynamic range was proposed. As a further step, the authors

of [15] extended the full-duplex bidirectional communica-

tion system into the wideband orthogonal frequency division

multiplexing (OFDM) systems, where the residual SI model

in the frequency-domain was derived. By considering the

DL/UL communication in the cellular networks, the authors

of [16] jointly optimized the frequency channel pairing and

power allocation to guarantee spectral efﬁciency and user

fairing. Moreover, multi-objective optimization was invoked in

[17] for jointly minimizing the downlink and uplink transmit

power in the full-duplex communication systems. Next, for

the full-duplex relay, a classical full-duplex relay topology

with a pair of transmitter and receiver was studied in [18].

Furthermore, the authors of [19] proposed a full-duplex hybrid

relay system, where the resource allocation and scheduling

are jointly optimized. For maximizing the end-to-end signal-

to-noise ratio (SNR) of the full-duplex relay system, several

antenna selection schemes were designed to reduce the system

complexity. Finally, the authors of [21] investigated a multipair

full-duplex relay system, where the optimal power allocation

for maximizing energy efﬁciency was obtained.

2) Studies on ISAC: The transmit waveform design plays

a key role in implementing dual functions in ISAC systems,

arXiv:2210.14112v2 [cs.IT] 3 Jan 2024

which has attracted extensive attention [22]–[25]. The authors

of [22] reused the communication signals for carrying out

target sensing and investigated the sensing and communica-

tion (S&C) tradeoff under several design criteria of sensing

beampattern. To achieve the full degrees-of-freedom (DoFs) of

sensing, the authors of [23] proposed to exploit the composite

transmit signal, where an additional dedicated sensing signal is

added together with the communication signals. It was shown

that the composite transmit signal is capable of achieving bet-

ter sensing beampattern than the communication-only signal.

As a further advance, a ﬂexible beamforming approach is

proposed in [24] for guaranteeing the desired levels of S&C

performance. Furthermore, the authors of [25] developed a

holographic beamforming scheme that employs more densely

deployed radiation elements in an antenna array to realize ﬁner

controllability of the S&C beams. However, only considering

the waveform design at the transmitter cannot catch the overall

sensing performance. As such, some works also considered

the sensing performance metrics at the receiver [26]–[28].

Speciﬁcally, the authors of [26] jointly optimized the transmit

waveform and the ﬁlter at the receiver to maximize the signal-

to-interference-plus-noise ratio (SINR) of the sensing echo

signal. To characterize the parameter estimation accuracy at

the receiver, the fundamental Cram´

er-Rao bound (CRB) was

exploited as the sensing performance metric in [27] and [28].

Most recently, there are growing research contributions to the

new modulation techniques for ISAC. For example, the authors

of [29] conceived an ISAC framework based on the orthogonal

time frequency space (OTFS) modulation technique. In OTFS,

the communication symbols are multiplexed in the delay-

Doppler domain, which well matches the parameter estima-

tion in the sensing function. Moreover, the authors of [30]

proposed a novel delay alignment modulation (DAM)-aided

ISAC framework to guarantee high Doppler shift tolerance

and low peak-to-average-power ratio (PAPR).

B. Motivations and Contributions

As mentioned above, full-duplex communication has been

studied in diverse scenarios, but there is still a paucity of

research contributions on integrating the sensing function into

full-duplex communication systems. It is well known that

compared with half-duplex mode, full-duplex mode can almost

double the communication capacity by utilizing advanced SI

cancellation techniques. However, we note that in full-duplex

communication systems, the SI consists of two components,

namely direct-path interference and reﬂected-path interference

[4]. When integrating the sensing function into the full-duplex

communication systems, the reﬂected-path interference cannot

be totally eliminated since it also includes the useful sensing

echo signal reﬂected by the target of interest. In other words,

part of the SI, i.e., the sensing echo signal, needs to be

preserved to guarantee the sensing performance. In this case,

an interesting question arises, does full-duplex mode with the

preserved sensing echo signal still outperform half-duplex

mode?

To answer this question, we propose to integrate the sensing

function into the classical bidirectional communication system

[4], [14], which is referred to as a bidirectional ISAC system.

In this system, a pair of dual-functional transceivers carry

out two-way communication and mutual sensing. Then, we

investigate the full-duplex and half-duplex operations for the

bidirectional ISAC system in both narrowband and wide-

band scenarios. The corresponding transmit beamforming is

optimized for characterizing S&C tradeoff regions achieved

by both full-duplex and half-duplex operations, which are

compared to provide answers to the raised question. It is

suggested that full-duplex mode may not always outperform

half-duplex mode.

The primary contributions of this paper are as follows:

•We propose a bidirectional ISAC system, where a pair

of transceivers communicate with each other and sense

each other’s direction. Then, we design the corresponding

full-duplex and half-duplex operation protocols, which

are distinguished by whether the communication signals

are transmitted and received at the same time or not,

for both narrowband and wideband systems. Based on

these protocols, we further study the S&C tradeoff by

optimizing the transmit beamforming.

•For the narrowband system, we redesign the conven-

tional full-duplex and half-duplex operations for the

bidirectional ISAC system. Then, for both operations,

we formulate a joint beamforming optimization problem

for maximizing the weighted sum of the communication

achievable rate and the sensing CRB, which characterizes

the S&C tradeoff. To solve it, we develop a one-layer

successive convex approximation (SCA)-based algorithm

to obtain Karush-Kuhn-Tucker (KKT) optimal solutions.

•For the wideband system, we propose the new full-

duplex and half-duplex operation protocols by exploiting

different delays in communication and sensing echo sig-

nals. Moreover, the DAM technique is used to address

frequency-selective communication channels based on

delay pre-compensation and path-based beamforming.

Furthermore, we redesign the proposed SCA-based al-

gorithm to obtain the KKT optimal solutions to the S&C

tradeoff optimization problem.

•Our numerical results reveal that when the line-of-sight

(LOS) component of the communication channel is not

dominated, full-duplex and half-duplex operations are

superior in the communication-prior regime and sensing-

prior regime, respectively. When the communication

channels become LOS-dominated, half-duplex always

outperforms full-duplex due to the strong interference

caused by sensing. It is also shown that the proposed

wideband system requires an additional dedicated sensing

signal for fulﬁlling the sensing performance, but reusing

the communication signal is sufﬁcient in the narrowband

system.

C. Organization and Notations

The rest of this paper is organized as follows. Section II

presents the half-duplex and full-duplex transmission schemes

for the narrowband bidirectional ISAC system and the S&C

tradeoff optimization problem. Then, an SCA-based algorithm

Transceiver A Transceiver B

S&C

channel

Fig. 1: Illustration of the bidirectional ISAC system.

is proposed to obtain the KKT optimal solutions to this

problem. In Section III, the half-duplex and full-duplex trans-

mission schemes for the wideband bidirectional ISAC system

are proposed. The KKT optimal solution to the corresponding

S&C tradeoff optimization problem is obtained by redesigning

the SCA-based algorithm. Our numerical results are presented

in Section IV comparing the half-duplex and the full-duplex,

which is followed by our conclusions in Section V.

Notations: Scalars, vectors, and matrices are denoted by

the lower-case, bold-face lower-case, and bold-face upper-

case letters, respectively; CN×Mand RN×Mdenotes the

space of N×Mcomplex and real matrices, respectively; a∗

and |a|denote the conjugate and magnitude of scalar a;aH

denotes the conjugate transpose of vector a;diag(a)denotes

a diagonal matrix with same value as the vector aon the

diagonal; A⪰0means that matrix Ais positive semideﬁnite;

tr(A)denote the trace of matrix A;E[·]denotes the statistical

expectation; Re{·} denotes the real component of a complex

number; CN(µ, σ2)denotes the distribution of a circularly

symmetric complex Gaussian random variable with mean µ

and variance σ2.

II. NARROWBAND BIDIRECTIONAL ISAC SYSTEMS

We focus our attention on integrating the sensing function

into the typical bidirectional communication system [4], [14],

which is referred to as a bidirectional ISAC system. In this

system, two dual-functional transceivers, denoted by the set

K=A, B, have the dual objectives of establishing commu-

nication between each other and concurrently sensing each

other’s direction. Each of these transceivers is equipped with a

total of Mtransmit antennas and a single receive antenna. The

bandwidth of this system is denoted by W, which corresponds

to a symbol period Ts= 1/W . In this paper, we consider

both narrowband and wideband transmission schemes for the

bidirectional ISAC system. The key differences between these

two transmission schemes are summarized as follows. On the

one hand, in narrowband systems, the communication channel

is characterized as frequency-ﬂat, whereas, in wideband sys-

tems, the channel exhibits frequency-selective behavior. On

the other hand, the delays in both communication and sensing

signals can be neglected in the narrowband systems due to

the relatively large value of Ts. However, this simpliﬁcation

is not applicable in the context of wideband systems. In

subsequent sections, we delve into the study of the narrowband

Signal A (1)

CPI

Full-duplex

Half-duplex

time

Signal A (1)

Echo A (1)

Signal B (2)

Echo A (1)

Signal B (1)

Signal A (2)

Echo A (2)

Signal B (2)

Fig. 2: Half-/full-duplex protocols for narrowband system (the view

from transceiver A).

bidirectional ISAC system in Section II, and we address the

more intricate wideband system in Section III.

In the narrowband system, the integration of a sensing func-

tion into the established bidirectional communication system

[citeday2012full, sabharwal2014band] allows for the direct re-

design of corresponding full-duplex and half-duplex operation

protocols, as depicted in Fig. 2. Speciﬁcally, we focus on

one coherent processing interval (CPI) of length 2N, during

which communication channels and target parameters remain

approximately constant. For the half-duplex mode, transceiver

Atransmits the joint S&C signal to transceiver Bin the

ﬁrst half of the CPI. Subsequently, both Transceivers B and

A, during the same time period, receive the communication

signal and the sensing echo signal, respectively. Following

this, transceiver Bassumes the role of transmitting the joint

S&C signal to transceiver Aduring the second half of the

CPI, repeating a similar sequence of events. For the full-

duplex mode, transceivers Aand Btransmit the joint S&C

signals simultaneously throughout the entire CPI. Thus, each

transceiver receives superimposed communication and sensing

echo signals.

Based on the above operating protocol, we divide the CPI

into two time intervals of equal duration, denoted as P1=

{1, ..., N}and P2={N+ 1, ..., 2N}. Within this context, we

denote xk,i[n]∈CM×1as the normalized joint S&C signal

transmitted by the transceiver kat time nwithin the interval

Pi. The transmit signal covariance matrix is thereby deﬁned

as Qk,i =E[xk,i[n]xH

k,i[n]] ∈CM×M, with the constraint

Qk,i ⪰0ensuring that it is a positive semideﬁnite matrix.

We further consider an average power constraint that applies

across the entire CPI at each transceiver, and it is expressed

as follows:

i=1

E∥xk,i[n]∥2=

i=1

tr(Qk,i)≤2.(1)

To facilitate the full-duplex and half-duplex modes, the fol-

lowing constraints must be met in the narrowband system:

Full-duplex: QA,1=QA,2,QB,1=QB,2,(2a)

Half-duplex: QA,2=0M×M,QB,1=0M×M.(2b)

In the narrowband system, each communication channel expe-

riences frequency-ﬂat fading, allowing for representation by a

single ﬁlter tap [31]. Consequently, we denote hk∈CM×1as

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1BidirectionalIntegratedSensingandCommunication:Full-DuplexorHalf-Duplex?ZhaolinWang,GraduateStudentMember,IEEE,XidongMu,Member,IEEE,andYuanweiLiu,Fellow,IEEEAbstract—Abidirectionalintegratedsensingandcommunica-tion(ISAC)systemisproposed,inwhichapairoftransceiverscarryouttwo-waycommunicationandmutua...

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