1 Joint Transmit and Receive Beamforming Design in Full-Duplex Integrated Sensing and

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Joint Transmit and Receive Beamforming Design in

Full-Duplex Integrated Sensing and

Communications

Ziang Liu, Sundar Aditya, Member, IEEE, Hongyu Li, Student Member, IEEE, and Bruno Clerckx, Fellow, IEEE

Abstract—Integrated sensing and communication (ISAC) has

been envisioned as a solution to realize the sensing capability

required for emerging applications in wireless networks. For a

mono-static ISAC transceiver, as signal transmission durations

are typically much longer than the radar echo round-trip times,

the radar returns are drowned by the strong residual self

interference (SI) from the transmitter, despite adopting sufﬁcient

SI cancellation techniques before digital domain - a phenomenon

termed the echo-miss problem. A promising approach to tackle

this problem involves the ISAC transceiver to be full-duplex (FD),

and in this paper we jointly design the transmit and receive

beamformers at the transceiver, transmit precoder at the uplink

user, and receive combiner at the downlink user to simultaneously

(a) maximize the uplink and downlink communication rate, (b)

maximize the transmit and receive radar beampattern power

at the target, and (c) suppress the residual SI. To solve this

optimization problem, we proposed a penalty-based iterative

algorithm. Numerical results illustrate that the proposed design

can effectively achieve up to 60 dB digital-domain SI cancellation,

a higher average sum-rate, and more accurate radar parameter

estimation compared with previous ISAC FD studies.

Index Terms—Integrated sensing and communication, full-

duplex, self-interference suppression, transmit/receive beamform-

ing.

I. INTRODUCTION

Next generation wireless communication networks are ex-

pected to support high data transmission rates, high-quality

wireless connectivity with massive devices, and highly accu-

rate and robust sensing capability [1], [2]. To realize these

requirements, integrated sensing and communication (ISAC),

which uniﬁes the signal processing procedures and hardware

framework between sensing and communication systems, is

widely viewed as a promising solution to efﬁciently utilize

the available spectral, hardware and energy resources.

Challenge: Echo miss.In the existing ISAC literature, many

studies assume that the sensing takes place in mono-static

mode [3]–[7] due to its relative simplicity compared to other

sensing conﬁgurations (e.g., multi-static). In a mono-static

ISAC system, the transmit (TX)/receive (RX) antennas are

co-located, resulting in the transmit (dual-function) waveform

being known at the receiver. Hence, the receiver can use

the transmit waveform as a reference waveform to extract

The authors are with the Communications & Signal Processing (CSP)

Group at the Dept. of Electrical and Electronic Engg., Imperial Col-

lege London, SW7 2AZ, UK. (e-mails:{ziang.liu20, s.aditya, c.li21,

b.clerckx}@imperial.ac.uk).

target information from the radar echo, thereby saving on

the overhead associated with reference sharing. However, the

transmit waveform is also expected to serve communications

users in parallel, and typically communication frames are

much longer than the radar echo round-trip times (RTTs).

For example, in the 5G NR speciﬁcations [8], a standard

radio frame has 10ms duration. For a target located at 100-

1000m from the radar, its echo RTT is of the order of 1-10µs

- orders of magnitude smaller than even the minimum unit

of data scheduling (i.e., 1 slot = 0.5ms). Hence, the radar

echo is drowned by the severe self interference (SI) from the

transmitter, which causes receiver saturation, where the power

of the received signal exceeds the analog-to-digital converter

(ADC) dynamic range. Even if there is no ADC saturation

due to the use of sufﬁcient SI cancellation techniques before

quantization, the radar echo may still be difﬁcult to detect

because it is masked by strong residual SI. We term this

phenomenon the echo-miss problem. Thus, it is important to

sufﬁciently suppress the residual SI to manageable levels.

To address the echo-miss problem and suppress the SI, one

straightforward method is to physically separate the TX and

RX antennas. The measurement-based study [9] shows that

limited isolation capability can be achieved by a combina-

tion of directional isolation, absorber, and cross-polarization.

Speciﬁcally, in the experiments, a 35cm separation between the

TX and RX antennas, along with an absorber, was shown to

realize 45dB passive suppression. However, the power level of

the self interference (SI) can be large (i.e., up to 100dB larger

than the receiver thermal noise ﬂoor [10], [11]). Thus, physical

separation of TX and RX antennas may not entirely solve the

echo-miss problem. Consequently, to integrate communication

and sensing functions, the transceiver should work in the full-

duplex (FD) mode to simultaneously transmit a dual-functional

signal, receive the echo signal, and suppress the SI, caused

by the leakage of the transmit signal to the receiver. Some

attempts have been made for ISAC in the FD context, with

[12] concentrating on waveform design by utilizing the waiting

time of conventional pulsed radars to transmit communication

signal in a single-antenna setup. For the multi-antenna case,

[13] jointly optimizes relay beamformer, receive ﬁlter, and

transmit power of the radar for a FD ISAC relay system,

wherein the residual SI is assumed to be cancelled in advance

by SI cancellation techniques. However, for the most part,

the SI cancellation problem is underestimated by many ISAC

studies [4], [5], [7], [14]–[16], which assume either ideal

isolation between TX and RX or rely on the radar-function-

arXiv:2210.10904v2 [eess.SP] 13 May 2023

focused SI cancellation method in [17].

Previous Approaches for SI Cancellation. The SI can-

cellation problem has been actively studied in FD wireless

communication systems [18]–[20] (i.e., without the additional

sensing functionality). In general, SI cancellation techniques

can be adopted in the propagation [21], analog [22]–[24],

and digital domains [25], [26]. As shown in Fig. 1, the

propagation-domain cancellation aims to minimize the cou-

pling between the transmit and receive direct paths. This kind

of cancellation is achieved by techniques based on path loss,

cross-polarization, and antenna directionality [9]. Beyond this,

the analog-domain cancellation aims to suppress SI before the

ADC, where a negative copy of the transmit waveform gen-

erated by the canceller circuit is subtracted from the received

signal [20], [22], [23], [27]. Finally, as the last defense against

SI, the digital-domain cancellation block utilizes either linear

or non-linear adaptive ﬁlters to generate the negative of the

residual SI [25], [26], and add it to the digital signal after the

ADC.

The above SI cancellation techniques for communications

rely on the uncorrelated nature between the SI (e.g., downlink

data stream) and the signal of interest (SoI) (e.g., the uplink

data stream); thus, the SI can be suppressed by adding its

negative to the received signal without impairing the SoI.

However, since the SoI in ISAC consists of uplink commu-

nications data and radar echoes that are correlated with the

SI, it is challenging to effectively suppress the SI without

distorting the radar echoes. To tackle this problem, utilizing the

time-of-arrival (ToA) difference or the spatial angle-of-arrival

(AoA) difference between the SI and echo are two promising

approaches. With respect to the ﬁrst approach, the early study

[17] utilizes the temporal difference to generate a negative

counterpart of the SI signal before the ADC (cf. Fig. 1 (b)),

based on a gradient-learning method. Apart from adding this

negative counterpart, an adaptive ﬁlter is also employed to

generate a negative in digital domain to cancel the residual

SI (cf. Fig. 1 (a)). In practice, many factors (e.g., RF taps,

adaptive ﬁlter taps, and update algorithms) affect the accuracy

of the generated negatives in both domains, which in turn,

have a huge impact on the SI cancellation performance. If the

SI signal is fast-changing, this approach may fail in tracking

and can have high computational complexity.

In multi-antenna systems, an alternative way to suppress SI

in ISAC is by employing the spatial AoA difference between

the SI and SoI. In [28], the SI cancellation based on TX and

RX beamforming design is adopted in the digital domain (cf.

Fig. 1a). Speciﬁcally, the TX beamformer is the weighted sum

of two separate beams probing at a downlink communication

user and a radar target, whose power allocation is controlled

by a parameter. In terms of the RX beamformer, the null-space

projection (NSP) based on pseudoinverse operation is used to

generate nulls in the angles of the downlink communication

beam and SI. In [29] and [30], the NSP method is utilized to

design hybrid TX and RX beamformer for sensing the target

and communicating to a downlink user (cf. Figs. 1a and 1b).

However, in these studies, the TX and RX beamformers are

separately designed and only the RX beamformer is used for

TABLE I

NOVELTY COMPARISON WITH EXISTING FD ISAC LITERATURE

Our work [12] [13] [17] [28]–[30]

Relay X

Analog hardware design X

Waveform design X

Tx/Rx beamformers NSP design X

Tx/Rx beamformers joint design X X

Uplink user X X

Downlink user X X X X

Multi-antenna at users X

Radar performance X X X X X

Communication performance X X

SI cancellation. Recently, intelligent reﬂecting surfaces (IRS)

have emerged as a means to boost the SoI, and thus reduce

the effect of SI [31], [32], but this approach cannot actively

cancel SI, and induces additional hardware and beamforming

design complexity.

Thus, the potential of joint ISAC TX-RX beamformer design

at transceiver to further suppress the SI has not been explored.

In addition, the uplink communication performance in the FD

ISAC system has not been analyzed. Given that the research

on FD ISAC is still in its infancy (cf. Table I), we consider a

mono-static FD ISAC multiple input multiple output (MIMO)

system. In this system, (a) the TX-RX beamformers at the

transceiver, (b) transmit precoder at the uplink user, and (c)

receive combiner at the downlink user are jointly optimized.

The aim of the optimization is to simultaneously (a) maximize

the uplink and downlink rate, (b) maximize the transmit and

receive radar beampattern power at the target, and (c) suppress

the residual SI. Inspired by research adopting the penalty-dual

decomposition (PDD) method (e.g., for FD mmWave hybrid

beamforming [33], and IRS [34]), a penalty-based iterative

algorithm is proposed to solve the optimization problem. Our

proposed scheme can work when the received signal exceeds

ADC dynamic range by adopting effective SI cancellation

techniques before quantization.

Contributions and Overview of Results. In this paper, our

contributions are summarized as follows:

•We ﬁrst model a FD ISAC mono-static system to capture

the echo-miss problem.

•To suppress the residual SI and preserve the two types of

SoI (e.g., radar echo and uplink data), we formulate the

joint TX-RX beamformer design problem for FD ISAC,

where the objective function incorporates (a) uplink and

downlink rates as the communications metric, (b) the

transmit and receive radar beampattern power at a target

as the sensing metric, and (c) the post-beamforming SI

residual as a penalty term. Based on the equivalence

between the rate maximization and the mean square

error (MSE) minimization [35], [36], and inspired by

the PDD method, an iterative algorithm with guaran-

teed convergence and acceptable complexity is developed

using block coordination descent (BCD) methods. As

seen in Table I, in contrast to the existing literature,

our optimization framework concentrates on joint TX-RX

beamformer design and directly cancel residual SI.

Direct

Paths

Target

Reﬂected

Paths

SoI

Total

TX chains

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LNA

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RX chains

ADC

DAC

(b) Analog Domain

(a) Digital Domain

HPA

(Analog)

Canceller

Circuit

Digital Interference

Cancellation

RF Chain

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chains

UL user

Precoder

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chains

DL user

RF Chain

Combiner

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FD ISAC Transceiver

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Hsi

Fig. 1. Full-duplex integrated sensing and communication system, and illustration of the boundaries and contents of the SI suppression in the propagation,

analog, and digital domains for multi-antenna conﬁgurations.

•The performance of the designed beamformers is val-

idated via simulations, which show that up to 60dB

residual SI can be effectively suppressed with better sum-

rates for the uplink and downlink users and better radar

parameter estimation performance (i.e., range-velocity

and AoA detection) compared with the NSP method [28]–

[30]. As shown in Table I, the performance of uplink

communications, in particular, has not been thoroughly

investigated in FD ISAC literature.

Organization of This Paper. The rest of the paper is or-

ganized as follows. The FD ISAC system model and the

optimization framework for the joint ISAC TX-RX beam-

formers design is introduced in Section II. In Section III,

the problem reformulation and the proposed joint ISAC TX-

RX beamformers design algorithm are provided based on the

BCD method. The convergence and complexity analysis of

the proposed algorithm is given in Section IV, and numerical

evaluations are presented in Section V. Finally, we conclude

this work in Section VI.

Notation. The set of reals, integers, and complex numbers are

denoted by R,Z, and C, respectively. <(x)and =(x)denote

the real and imaginary part of x∈C, respectively. Continuous

signals and discrete sequences are expressed by x(t), t ∈R

and x[k], k ∈Z, respectively. Matrices, vectors and scalars are

written in capital boldface, small boldface and normal fonts,

respectively. [X]i,:and [X]:,j denote the i-th row and j-th

column of the matrix X.[X]i,j denotes the entry of the matrix

Xat index (i, j). Similarly, [x]ifor vector x.XH,X>and X†

are used to denote conjugate-transpose, transpose and pseudo

inverse of matrix X, respectively. We use E(·),|·|, and k·k2

to denote statistical expectation, absolute value and Euclidean

norm.

II. SYSTEM MODEL

A. Signal Model

As shown in Fig. 1, we consider a single-cell narrowband

FD MIMO ISAC transceiver equipped with Nttransmit anten-

nas and Nrreceive antennas. All antenna arrays are assumed to

be uniform linear arrays (ULA) with half-wavelength spacing

between adjacent antenna elements. The transceiver simultane-

ously serves one uplink user with Nuantennas, one downlink

user with Ndantennas, and probes a target direction.

Let sd∈Cdenote the ISAC downlink transmit symbol, and

su∈Cthe uplink symbol. We assume both sdand suhave

unit power. The received signal yd∈CNd×1at the downlink

user is given by

yd=Hdpsd+nd,(1)

where p∈CNt×1denotes the transmit precoder at the

transceiver, Hd∈CNd×Ntthe downlink communication

channel, nd∈CNd×1the independent and identically dis-

tributed (i.i.d) additive complex Gaussian noise (i.e., nd∼

CN(0, σ2

dINd)). At the downlink user, an estimate of sd,

denoted by bsd, is obtained by ﬁltering ydby a combiner

ud∈CNd×1, as follows:

bsd=uH

dyd=uH

dHdpsd+uH

dnd.(2)

At the FD ISAC transceiver, the received signal incorporates

the SoI (i.e., the radar echo and the uplink symbol, su), along

with residual SI. We assume that the received signal has no

clipping error due to sufﬁcient SI cancellation techniques in

propagation and analog domains, and a high ADC dynamic

range1, of the order of 80dB, which can be achieved by a

variety of ways, e.g., logarithmic ADC [37], modulo ADC

[38], [39]). Hence, the received signal at the transceiver is

given by

yu=Huωusu+Hpsd+nu,(3)

where ωu∈CNu×1denotes the precoder vector of the uplink

user, Hu∈CNr×Nuthe uplink communication channel,

1The dynamic range is deﬁned by the ratio between the largest and smallest

possible values of the input signal, which are respectively the residual SI and

radar echo in our system model. From our link budget simulation, the ratio

between the residual SI and radar echo is 134.15dB, thus we assume that

the SI cancellation techniques before digital domain can achieve larger than

54.15dB SI cancellation.

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1JointTransmitandReceiveBeamformingDesigninFull-DuplexIntegratedSensingandCommunicationsZiangLiu,SundarAditya,Member,IEEE,HongyuLi,StudentMember,IEEE,andBrunoClerckx,Fellow,IEEEAbstractIntegratedsensingandcommunication(ISAC)hasbeenenvisionedasasolutiontorealizethesensingcapabilityrequiredforemergin...

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