# Exploring the Synergy:
A Review of Dual-Functional Radar Communication Systems

Ali Hanif, Graduate Student Member, IEEE, Sajid Ahmed, Senior Member, IEEE,
Mohamed-Slim
Alouini, Fellow, IEEE, and Tareq Y. Al-Naffouri, Senior Member, IEEE

###### Abstract

This review paper examines the concept and advancements in the evolving
landscape of Dual-functional Radar Communication (DFRC) systems.
Traditionally, radar and communication systems have functioned independently,
but current research is actively investigating the integration of these
functionalities into a unified platform. This paper discusses the motivations
behind the development of DFRC systems, the challenges involved, and the
potential benefits they offer. A discussion on the performance bounds for DFRC
systems is also presented. The paper encompasses a comprehensive analysis of
various techniques, architectures, and technologies used in the design and
optimization of DFRC systems, along with their performance and trade-offs.
Additionally, we explore potential application scenarios for these joint
communication and sensing systems, offering a comprehensive perspective on the
multifaceted landscape of DFRC technology.

###### Index Terms:

Joint Communication and radar/radio Sensing (JCAS), Dual-functional Radar
Communications (DFRC), Integrated Sensing and Communications (ISAC), Wireless
Communications, and Radar.

##  I INTRODUCTION

###  I-A Background and Motivation

The number of worldwide Internet of Things (IoT) and non-IoT connections have
been forecasted to reach over 30 billion and 10 billion respectively by 2025
[1]. Net proceeds of the C-band 5G auction in the US amount to $81.1 billion
in 2021 [2]. With such a drastic increase in the number of users and the cost
of the spectrum, there is an increased research interest in the optimal
utilization of the frequency spectrum. Wireless communications and radar
sensing are two fields that have traditionally been progressing independently
for decades. The first operational use of radar dates back to WW-II when the
‘Chain Home’ radar network was employed by the Royal Air Force to detect enemy
aircraft [3]. Since then, certain portions of the frequency spectrum have been
used exclusively by radars for various operations like airborne radars, Air
Traffic Control (ATC) radars, weather radars, ground surveillance radars,
marine radars,…etc. Thus, spectrum sharing between communications and radars
can help in solving the spectrum congestion problem leading to a better
spectral efficiency. Moreover, joint design of radar and communication systems
can offer other important benefits such as reduced power consumption, form
factor reduction, cost saving, beamforming efficiency, and performance
improvement of both functions via cooperation [4, 5].

Earlier research to solve the spectrum congestion problem focused on the
coexistence of radar and communication systems where both systems can operate
simultaneously in a cooperative fashion without interfering with each other.
Radar-Communication Coexistence (RCC) approaches include [6] opportunistic
spectrum access [7], interference channel estimation [8, 9], precoder design
[10] and optimization based design [11, 12, 13]. However, the efficacy of
these interference cancellation techniques dictates strict requirements on the
mobility of nodes and information exchange, thus, limiting the improvement in
spectral efficiency [5]. Another major drawback of coexistence approaches is
that for efficient cooperation, radar and communication systems have to
exchange side information such as the channel state information, modulation
formats,…etc. [14]. This exchange is usually made possible by a control center
connected to both systems [9], thus, considerably increasing the overall
complexity of the system.

Research on joint Communications and Radar (C&R) systems has been reported
under various names such as Radar-Communications (RadCom), Joint
Communications (Radar)-Radar (Communications) (JCR/JRC), Joint Communication
and radar/radio Sensing (JCAS), Dual-functional Radar Communications (DFRC),
and Integrated Sensing and Communications (ISAC). The interference issue of
coexistence systems can be tackled by using the same signal for communications
and radar sensing. DFRC system refers to the joint systems that use a single
transmit waveform for both functions [6, 4, 15]. The first ever published DFRC
scheme was proposed in [16], in which the communication bits were coded on the
radar pulse interval[6]. A detailed timeline of the evolution of DFRC
techniques can be found in [6].

###  I-B Classification of JCAS Systems

JCAS systems can be classified into three broad categories [5].

####  I-B1 Communication-centric Design or JCR

In JCR systems, design priority is on communications and radar functionality
is added as a secondary feature [17, 18, 19]. Communication waveforms are
exploited to extract sensing information from target echoes. Communication
performance usually remains unaffected, however, sensing performance needs
optimization and is scenario-dependent. Accurate and efficient sensing
parameters estimation algorithms, resolution of clock asynchrony, and full
duplex operation are the key research problems here for improving the
performance of radar functionality [4]. An important advantage of these
systems is in location-aware services and applications like V2X (Vehicle-to-
Everything) network, where they can provide sensing-assisted communications
and considerably reduce the beam training or channel state information
estimation overhead [20, 21].

####  I-B2 Radar-centric Design or JRC

In JRC systems, design priority is on radar sensing and communication
information is embedded in known radar waveforms over time, frequency, code,
or spatial domains [15, 22, 23]. Index modulation (IM) can also be employed
where information is represented by indexes of antennas, frequency or code and
there is no waveform modification involved [24]. Radar performance usually
remains unaffected, however, communication performance is limited by
achievable data rates. One advantage is that long-range communication can be
achieved owing to the high transmission power of radar systems.

####  I-B3 Dual-functional Radar Communications (DFRC)

In DFRC systems, the two functions are jointly designed and optimized from the
start and they are not biased towards communications or radar functionality.
They offer a tunable trade-off between the two functions and aim at meeting
the requirements of the desired application. There is more freedom of design
in this category as it’s not limited by existing radar or communications
systems.

In the rest of the paper, we will use the term JCAS to refer to generic joint
C&R systems and the term DFRC to refer to the joint design and optimization of
dual-functional systems capable of performing both functions simultaneously
utilizing common waveform and hardware.

###  I-C Comparison of Communications and Radar Sensing

To better understand the joint design of C&R systems, first, we need to
compare them to have a look at their similarities and differences. Following
is a comparison between these two functions in terms of signal waveforms,
transmission power, bandwidth, and other specifications [5].

####  I-C1 Signal Waveforms

Radars employ waveforms that are usually simple, unmodulated single-carrier
pulsed or Continuous-Wave (CW) signals occupying large bandwidth. It is
desirable to have radar waveforms that have an ambiguity function with steep
and narrow mainlobes. In contrast, communication signals usually have a
complicated signal structure with advanced modulations comprising unmodulated
(training/pilot) and modulated data symbols. These signals can be
discontinuous over domains of space, time, and frequency.

####  I-C2 Transmitter Power

The transmission power is usually high for pulsed radars to support long-range
operation and comparatively lower for short-range CW radars. Communication
systems normally operate on less power since the coverage range is quite less
as compared to radars. Radar signals aim to have a low peak-to-average-power
ratio for efficient power amplification to achieve long-range operation.

####  I-C3 Bandwidth

In pulsed radars, short pulses of large bandwidths are transmitted, followed
by a silent period for the reception of the targets’ echoes. CW radars
transmit continuous waveforms, such as chirp signals, typically covering a
large range of frequencies. Large bandwidth is desired in radar signals to
improve the range resolution. On the other hand, communication systems usually
operate in a bandwidth-restricted scenario and communication signals have much
smaller bandwidths as compared to radar waveforms.

####  I-C4 Frequency of Operation

Operational frequency bands for radars include L-band (1-2 GHz), S-band (2-4
GHz), C-band (4-8 GHz), X-band (8-12 GHz), Ku-band (12-18 GHz), K-band (18-27
GHz), and Ka-band (27-40 GHz). Automotive radars operate in the W-band
(usually 75-81 GHz). Communication frequencies lie in sub-6 GHz and mmWave
bands. Terahertz frequencies are being employed for 6G.

####  I-C5 Duplex Operation

Pulse radars operate in half-duplex mode while CW radars operate in full-
duplex mode. Communication systems operate either in Time Division Duplex
(TDD) or Frequency Division duplex (FDD) modes.

####  I-C6 Clock Synchronization

In radars, transmitter and receiver clocks are synchronized to avoid ambiguity
in sensing parameters’ estimation. In the case of communications, colocated
nodes may share the same clock but non-colocated nodes usually don’t share the
same clock.

####  I-C7 Performance Metrics

Different performance metrics are used to evaluate the performance of radars
and communication systems. For the case of radars, important metrics are
probabilities of detection and false alarm, maximum range, maximum velocity,
peak-to-sidelobe level ratio, Signal-to-Clutter Ratio (SCR), and resolution
(range, Doppler and angular). Important metrics for wireless communications
are Signal-to-Interference-plus-Noise Ratio (SINR), Bit Error Rate (BER),
outage probability, capacity, latency and throughput.

The majority of the research about joint communication and sensing is focused
on the first two categories of JCAS systems and there is less work addressing
the last category of DFRC systems. In this paper, we will present a detailed
review of the DFRC systems. The paper is organized as follows: The system
model for a generic DFRC system is presented in Section II. Section III
presents different performance bounds for DFRC systems. Section IV provides a
detailed review of the different design aspects of DFRC systems while Section
V discusses key potential application scenarios of the JCAS systems. Resource
allocation in DFRC systems is discussed in Section VI and Section VII
highlights associated challenges and future research directions. The paper is
concluded in Section VIII.

Notations: Bold lower case letters (${\bf x}$) denote vectors and upper case
letters (${\bf X}$) represent matrices. The $(p,q)$th element of a matrix
${\bf X}$ is represented by $x_{p,q}$. The superscripts $(\cdot)^{s}$ and
$(\cdot)^{c}$ will be used to represent sensing and communication signals,
respectively. ${\bf 1}_{N}$ represents an $N\times 1$ vector of ones and the
identity matrix of dimension $N\times N$ is denoted by ${\bf I}_{N}$.
Transpose and conjugate transposition of a matrix are denoted by $(\cdot)^{T}$
and $(\cdot)^{H}$, respectively. The conjugate of a scalar is denoted by
$(\cdot)^{*}$. ${\rm vec}{(\cdot)}$ represents the vectorization operation and
$\mathbb{E}{(\cdot)}$ is the expectation operator.

##  II System Model

In this section, we present a system model for a DFRC platform, aiming to
provide the reader with a better understanding of the subsequent discussions
presented in the following sections. The model presented herein is of a
generic nature, and for details of specific system models pertaining to
individual works, the reader is directed to the relevant references. In the
context of DFRC, we consider a platform equipped with a Uniform Linear Array
(ULA) of $N_{T}$ transmit and $N_{R}$ receive antennas. The inter-element
spacing between adjacent antennas is half of the carrier’s wavelength. The
system serves $K$ communication users by transmitting $L$ symbols per user and
sensing $Q$ targets simultaneously. The transmitted waveforms from different
antennas can be represented as a vector ${\bf
x}(t)=\begin{bmatrix}x_{1}(t)&x_{2}(t)&\ldots&x_{N_{T}}(t)\end{bmatrix}^{T}$
for $0\leq t\leq T_{p}$, where $T_{p}$ is the pulse-repetition interval or
symbol period.

###  II-A Received Signal Model for Sensing

For the purpose of sensing, the transmit and receive antennas are co-located.
The received signal by the target located at a distance $R$ in the direction
$\theta$, ignoring path loss, can be expressed as

$\displaystyle r^{s}(t)={\bf a}_{T}^{T}(\theta){\bf x}(t-\tau),$ (1)

where ${\bf
a}_{T}(\theta)=\begin{bmatrix}1&e^{j\pi\sin(\theta)}&\cdots&e^{j(N_{T}-1)\pi\sin(\theta)}\end{bmatrix}^{T}$
is the transmit steering vector and $\tau=\frac{R}{c}$. The received power at
the target can be written as [25, 26, 27]

$\displaystyle P(\theta,{\bf R})$ $\displaystyle=$
$\displaystyle\mathbb{E}\\{{\bf a}_{T}^{T}(\theta){\bf x}(t-\tau){\bf
x}^{H}(t-\tau){\bf a}_{T}^{*}(\theta)\\},$ $\displaystyle=$ $\displaystyle{\bf
a}_{T}^{H}(\theta){\bf R}{\bf a}_{T}(\theta),$

where ${\bf R}=\mathbb{E}\\{{\bf x}(t-\tau){\bf x}^{H}(t-\tau)\\}$ is the
$N_{T}\times N_{T}$ sample covariance matrix of the waveforms. The signal
model in (1) can be used for beamforming and transmitting information symbols
[28]. The transmitted signal reflects back from the target and the
corresponding signals at the $N_{R}$ receive antennas in vector form can be
written as

$\displaystyle{\bf z}^{s}(t)=\beta e^{j2\pi f_{d}t}{\bf a}_{R}(\theta){\bf
a}_{T}^{T}(\theta){\bf x}(t-2\tau)+{\bf v}^{s}(t).$ (2)

Here, $\beta$ is the reflection coefficient of the target, $f_{d}$ is the
Doppler frequency induced due to the motion of the target of interest, and
${\bf
z}^{s}(t)=\begin{bmatrix}z^{s}_{1}(t)&z_{2}^{s}(t)&\cdots&z_{N_{R}}^{s}(t)\end{bmatrix}^{T}$.
${\bf
a}_{R}(\theta)=\begin{bmatrix}1&e^{j\pi\sin(\theta)}&\cdots&e^{j(N_{R}-1)\pi\sin(\theta)}\end{bmatrix}^{T}$
represent the receive steering vector, and ${\bf
v}^{s}(t)=\begin{bmatrix}v_{1}^{s}(t)&v_{2}^{s}(t)&\cdots&v_{N_{R}}^{s}(t)\end{bmatrix}^{T}$
contains the contribution of noise, interfering signals from other targets,
and clutter. The noise at the $n$th receive antenna can be written as

$v_{n}^{s}(t)=\sum_{q=1}^{Q-1}\beta_{q}e^{j2\pi
f_{d}^{q}t}e^{j\pi(n-1)\sin(\theta_{q})}{\bf a}_{T}^{T}(\theta_{q}){\bf
x}(t-2\tau_{q})+w_{n}(t).$

The received signal in (2) is sampled from $N_{R}$ antennas and can be written
in matrix form as

$\displaystyle{\bf Y}^{s}=\beta{\bf a}_{R}(\theta){\bf a}_{T}^{H}(\theta){\bf
X}_{l_{\tau}}{\cal D}(f_{d})+{\bf V}^{s}.$ (3)

Here, ${\bf Y}^{s}=\begin{bmatrix}{\bf y}_{1}^{s}&{\bf y}_{2}^{s}&\cdots&{\bf
y}_{N_{R}}^{s}\end{bmatrix}^{T}\in{\cal C}^{N_{R}\times L}$ while ${\bf
y}_{n}^{s}=\begin{bmatrix}{y}_{n}^{s}(0)&y_{n}^{s}(1)&\cdots&y_{n}^{s}(L-1)\end{bmatrix}^{T}$,
${\cal D}(f_{d})={\rm diag}\left(1,e^{j2\pi f_{d}},\ldots,e^{j2\pi
f_{d}(L-1)}\right)$, and ${\bf X}_{l_{\tau}}$ is the $l_{\tau}$ samples
delayed version of transmitted signal matrix

$\displaystyle{\bf X}$ $\displaystyle=$
$\displaystyle\begin{bmatrix}x_{1}(0)&x_{1}(1)&\cdots&x_{1}(L-1)\\\
x_{2}(0)&x_{2}(1)&\cdots&x_{2}(L-1)\\\ \vdots&\vdots&\cdots&\vdots\\\
x_{N_{T}}(0)&x_{N_{T}}(1)&\cdots&x_{N_{T}}(L-1)\\\ \end{bmatrix}\in{\cal
C}^{N_{T}\times L}.$

The received signal in (3) serves as a basis for estimating the range, angular
location, and velocity of the target. Relevant literature on parameter
estimation can be found in [29, 30].

###  II-B Received Signal Model for Communication

The transmitted signal from the DFRC system will also be received by multiple
users. The received signal by $k$th user having a single antenna and flat-
faded channel between the transmitter and user can be written as

$\displaystyle r^{c}_{k}(t)={\bf h}_{k}^{T}{\bf x}(t)+{\bf v}^{c}_{k}(t),$ (4)

where ${\bf
h}_{k}=\begin{bmatrix}h^{k}_{1}&h^{k}_{2}&\cdots&h^{k}_{N_{T}}\end{bmatrix}^{T}$.
$h^{k}_{m}$ is the channel gain between the $k$th user and the $m$th transmit
antenna, and ${\bf v}^{c}_{k}(t)$ contains the contribution of noise and
interfering signals from other targets. The signal model given in (4) can also
be used for beamforming and transmitting information symbols. If we have $K$
users and the transmitter transmits $L$ symbols for each user, sampling (4),
the collection of received samples by all users in matrix form can be written
as

$\displaystyle{\bf Y}^{c}={\bf H}_{c}{\bf X}+{\bf V}^{c}.$ (5)

Here, ${\bf Y}^{c}=\begin{bmatrix}{\bf y}^{c}_{1}&{\bf y}^{c}_{2}&\cdots&{\bf
y}^{c}_{K}\end{bmatrix}^{T}\in{\cal C}^{K\times L}$ while ${\bf
y}^{c}_{k}=\begin{bmatrix}y^{c}_{k}(0)&y^{c}_{k}(1)&\cdots&y^{c}_{k}(L-1)\end{bmatrix}^{T}$,
${\bf H}_{c}=\begin{bmatrix}{\bf h}_{1}&{\bf h}_{2}&\cdots&{\bf
h}_{K}\end{bmatrix}^{T}\in{\cal C}^{K\times N_{T}}$, and ${\bf V}^{c}\in{\cal
C}^{K\times L}$ is the noise matrix.

The design of a DFRC system is mainly centered on two signal models as
described in (3) and (5). In the following sections, we will delve into the
latest advancements in DFRC system design.

##  III Performance Bounds for DFRC Systems

To gauge the performance of a DFRC system, it becomes pertinent to understand
and analyze various performance bounds that can be achieved by a joint system
as compared to independent communication and radar systems. In [31], it has
been proposed to employ the sensing Cramér-Rao bound (CRB) and communication
capacity metrics for investigating the fundamental limits of Sensing and
Communication (S&C) performance tradeoff. A Miller-Chang type CRB [32] is
employed for the analysis of the sensing performance. From Fig. 2, we can have
three types of bounds/boundaries of the CRB-rate region namely

  1. 1.

Ideal Scenario and the Outer Bound: The ideal scenario is in which the DFRC
system is able to achieve the maximum communication rate, $R_{max}$, along
with minimum sensing CRB, $\epsilon_{min}$. In this case, there is no tradeoff
between S&C functionalities and both can achieve their optimum without
degrading the other. This ideal boundary is depicted by the boundary B in Fig.
2. The outer bound will be closer to this ideal boundary and is obtained by
letting the coherent sensing period go to infinity[31].

  2. 2.

Inner Bound: This is the lower bound of the CRB-rate region which can be
achieved by using the time-sharing strategy [33] in which the sensing optimal
strategy is applied with probability $p$ and the communication optimal
strategy is applied with probability $1-p$. In this scenario, the integration
of sensing and communication doesn’t provide any additional performance gain.
It is depicted by the boundary A in Fig. 2.

  3. 3.

Actual Boundary: This boundary depicts the actual performance of the DFRC
system depending upon the tradeoffs involved. It is depicted by the boundary C
in Fig. 2. Hence, the DFRC system will offer a performance that lies in
between the ideal and inner boundaries and the aim is to get as close to the
outer bound as possible by optimizing the tradeoffs involved. The S&C tradeoff
is characterized by the two corner points of the CRB-rate region. $P_{CS}$
indicates the minimum achievable CRB constrained by the maximum communication
rate and $P_{SC}$ indicates the maximum achievable communication rate
constrained by the minimum CRB.

The tradeoff between sensing and communication is two-fold and includes the
Subspace Tradeoff (ST) and the Deterministic-Random Tradeoff (DRT) [31, 34] as
discussed below. Depending on these tradeoffs, an outer bound and multiple
inner bounds for the achievable CRB-rate regions have been proposed in [31].

###  III-A Subspace Tradeoff (ST)

The subspace tradeoff depends on the coupling strength between the subspaces
spanned by S&C channels thus balancing the resource allocation between sensing
and communication subspaces. The greater is the coupling between two channels,
the lesser the subspace tradeoff. The coupling strength can be strong,
moderate, or weak as depicted in Fig. 1. Strong coupling occurs between S&C
channels when the target to be sensed is also the communication user. Moderate
coupling is when the sensing target is part of the communication channel and
weak coupling is when both S&C channels are different. Mathematically
speaking, given a specific statistical covariance matrix,
$\widetilde{\boldsymbol{R}}=\mathbb{E}\left(\mathbf{R}\right)$, favorable
communication performance is achieved when its column space is more closely
aligned with the communication subspace, and vice versa.

###  III-B Deterministic-Random Tradeoff (DRT)

It is a well-established fact that communication signals should be as random
as possible to convey maximum information. Contrary to that, radar systems
favor deterministic signals to achieve a stable detection performance. In [31,
34], the authors have explored the fundamental performance limits of a DFRC
system from a rate-distortion perspective employing a vector Gaussian channel
model. Conditional mutual information is used as a performance metric for both
S&C functionalities. The key findings indicate that sensing MI sets a
universal lower limit for any well-defined distortion metrics for sensing and
the distortion lower bound is achieved when the sample covariance matrix of
the DFRC signal is deterministic. Hence, the DFRC system compromises signal
randomness, thereby reducing communication performance, to enhance sensing
performance. This is known as the deterministic-random tradeoff between
sensing and communication performance in the DFRC system. The communication-
optimal point, $P_{CS}$, can be achieved using conventional Gaussian
signalling and the study has provided the lower and upper bounds for the
sensing CRB, $\epsilon_{CS}$, at this point. The communication capacity,
$R_{SC}$, for the sensing-optimal point, $P_{SC}$, can be achieved by a novel
strategy based on uniform sampling over the set of semi-unitary matrices,
i.e., the Stiefel manifold [35].

Figure 1: Coupling between sensing and communication channels [36].

Figure 2: Various performance bounds in the CRB-rate region [31]. Used under
CC license.

##  IV Design of Dual Function Radar Communication Systems

As far as the current literature is concerned, a vague boundary exists between
the DFRC systems and the first two categories (JCR and JRC) of JCAS systems.
However, there is more freedom of design in the case of DFRC, as we are no
longer limited by existing radar and communication standards. We can design
and optimize by considering the application-specific essential requirements
for both functions, thus, leading to a better and more flexible trade-off
between radar and communication performance. In this pretext, joint optimal
waveform design becomes the fundamental problem of interest.

Hardware for DFRC systems can be categorized into phased array, fully digital
Multi-Input Multi-Output (MIMO), and hybrid array architectures with
corresponding beamforming approaches known as analog, digital, and hybrid
analog-digital (HAD) beamforming. These approaches are depicted in Fig. 3. In
the case of analog beamforming, the same signal is fed to all the antennas
through phase shifters, thus, steering a single beam in the desired direction.
It is a simple, power-efficient, and cost-effective solution but can only
generate a single beam and so suffers from beam squint effect for wideband
transmission. For digital beamforming, each antenna is connected to a separate
RF chain and signals are designed in the digital baseband using spatial
precoding as done in MIMO systems. It has more degrees of freedom, can
generate multiple beams in different directions and can support wideband
transmission, however, it is complex, costly and requires more power. HAD is a
compromise between the two approaches in which sub-arrays are formed from a
large array and analog beamforming is used within each sub-array. It can offer
the combined advantages of analog and digital BF while minimizing their
drawbacks. Depending on the hardware architecture being employed for the DFRC
system, we will now be discussing different waveform design and optimization
approaches.

Figure 3: Digital, analog, and hybrid beamforming approaches for DFRC systems.

###  IV-A Waveform Optimization for DFRC Systems with Digital Beamforming

In the case of digital beamforming for fully digital MIMO DFRC systems, the
beampattern depends on the precoding matrix $\mathbf{W}$ such that
$\mathbf{X=WS}$, where $\mathbf{S}$ is the desired constellation symbol
matrix. Hence, the basic optimization problem can be formulated as [4]

$\arg\max_{\mathbf{W}}f(\mathbf{W}),\quad\text{ s.t. some constraints
}\text{,}$ (6)

where $f(\mathbf{W})$ is the objective function. Different waveform
optimization approaches are reported in the literature depending on how you
define the objective function and the constraints. They can be defined
individually for radar sensing or communications or in the form of a weighted
joint function as discussed next.

####  IV-A1 Mutual Information based Optimization

Mutual Information (MI) is well-known for communication systems where the
capacity of a channel is defined as the maximum mutual information between
source and receiver. The first use of MI for radar waveform design for
extended targets appears in [37]. MI for radars refers to the amount of
information obtained about the channel from the signal received at the
receiver. The conditional MI for radar and communication is defined as [38, 4]

$\displaystyle I_{S}\left(\mathbf{H}_{s};\mathbf{Y}_{s}\mid\mathbf{X}\right)$
$\displaystyle=$ $\displaystyle
M\log_{2}\left(\operatorname{det}\left(\frac{1}{\sigma_{z}^{2}}\mathbf{X}^{H}\boldsymbol{\Sigma}_{\mathbf{H_{s}}}\mathbf{X}+\mathbf{I}_{L}\right)\right),$
$\displaystyle I_{C}\left(\mathbf{X};\mathbf{Y}_{c}\mid\mathbf{H}_{c}\right)$
$\displaystyle=$ $\displaystyle
K\log_{2}\left(\operatorname{det}\left(\frac{1}{\sigma_{z}^{2}}\mathbf{H}_{c}^{H}\boldsymbol{\Sigma}_{\mathbf{X}}\mathbf{H}_{c}+\mathbf{I}_{M}\right)\right).$

Here, $\mathbf{H}_{c}$ and $\mathbf{H}_{s}$ are the communication and radar
channels, respectively,
$\boldsymbol{\Sigma}_{\mathbf{H_{s}}}=\mathrm{E}\left[\mathbf{H}_{\mathbf{s}}\mathbf{H}_{\mathrm{s}}{}^{H}\right]/M$,
and
$\boldsymbol{\Sigma}_{\mathbf{X}}=\mathrm{E}\left[\mathbf{X}\mathbf{X}^{H}\right]/L$.
In [38, 39], a weighted sum of these two MIs is used as an objective function
for optimization

$F=\frac{w_{R}}{F_{S}}I_{S}\left(\mathbf{H}_{s};\mathbf{Y}_{s}\mid\mathbf{X}\right)+\frac{1-w_{R}}{F_{C}}I_{C}\left(\mathbf{X};\mathbf{Y}_{c}\mid\mathbf{H}_{c}\right),$
(7)

where $\mathbf{w}_{R}\in[0,1]$ is a weighting factor. $F_{S}$ and $F_{C}$ are
the maximal MI for radar and communications. The objective function in (7) can
be optimized with the Karush-Kuhn-Tucker (KKT) conditions with an optimal
water-ﬁlling type solution.

####  IV-A2 Beampattern Similarity based Optimization

Another approach relies on the optimization of the DFRC waveform with respect
to a benchmark signal having a desired beampattern. The benchmark signal is
usually a known radar waveform having desirable properties for sensing such as
low sidelobe levels and good correlation. This is done in order to minimize
the effect of the randomness of the communication data and channels on the
waveform structure [4] and is achieved by using a waveform/beampattern
similarity metric. Hence, the designed waveform has a beampattern that matches
the desired radar’s beampattern while satisfying the communication
requirements.

In the study conducted by Liu et al. [14], the authors propose closed-form
dual-functional waveform designs for a MIMO system that serves both
omnidirectional and directional radar beampatterns while minimizing the Multi-
User Interference (MUI) for downlink communication users. For instance, to
transmit an omnidirectional beam for sensing and symbol matrix ${\bf S}$ for
communication users, the cost function is defined as

$\displaystyle\min_{\bf X}\|\mathbf{H}_{c}{\bf X}-\mathbf{S}\|_{F}^{2},$
$\displaystyle\text{ s.t. }\frac{1}{L}\mathbf{XX}^{H}=\frac{P_{T}}{M}{\bf
I}_{M},$ (8)

where $P_{T}$ is the total transmit power from all antennas. The authors
derive a closed-form solution for this problem as

${\bf X}=\sqrt{\frac{LP_{T}}{M}}{\bf UI}_{M\times L}{\bf V}^{H}.$ (9)

Here, ${\bf U}\in{\cal C}^{M\times M}$ and ${\bf V}\in{\cal C}^{L\times L}$
are the singular-value-decomposition (SVD) matrices of ${\bf H}_{c}^{H}{\bf
S}$ matrix. In the context of radar systems, efficient focusing of transmitted
power toward specific targets is crucial. Therefore, for the desired
beampattern that depends on the waveform covariance matrix, ${\bf R}_{d}$, Liu
and his colleagues modify the original optimization problem as

$\displaystyle\min_{\bf X}|\mathbf{H}_{c}{\bf X}-\mathbf{S}\|_{F}^{2},$
$\displaystyle\text{ s.t. }\frac{1}{L}\mathbf{XX}^{H}={\bf R}_{d}.$ (10)

By employing the Cholesky decomposition of ${\bf R}_{d}={\bf FF}^{H}$, the
authors successfully derived a closed-form solution for the waveforms as

${\bf X}=\sqrt{L}{\bf F}\tilde{\bf U}{\bf I}_{M\times L}\tilde{\bf V}^{H},$
(11)

where $\tilde{\bf U}\in{\cal C}^{M\times M}$ and $\tilde{\bf V}\in{\cal
C}^{L\times L}$ are the SVD matrices of ${\bf F}^{H}{\bf H}_{c}^{H}{\bf S}$
matrix.

They also proposed weighted optimizations to create dual-functional waveforms
that strike a flexible balance between radar and communication performance.
The trade-off design becomes

$\displaystyle\min_{\mathbf{X}}\rho\|\mathbf{H_{c}X}-\mathbf{S}\|_{F}^{2}+(1-\rho)\left\|\mathbf{X}-\mathbf{X}_{0}\right\|_{F}^{2},$
$\displaystyle\text{ s.t. }\frac{1}{L}\|\mathbf{X}\|_{F}^{2}=P_{T}(\mbox{total
power constraint),}$ or
$\displaystyle\frac{1}{L}\operatorname{diag}\left(\mathbf{X}\mathbf{X}^{H}\right)=\frac{P_{T}}{M}\mathbf{1}\mbox{
(per antenna power constraint).}$

Here, $0\leq\rho\leq 1$ is a weighting factor that determines the performance
weightage for radar and communication, and $\mathbf{X_{0}}$ is the reference
radar waveform. Low complexity algorithms for the solution of (IV-A2) are also
presented. It was shown that a trade-off exists between the probability of
detection and the achievable communication rate. For a fixed probability of
detection, the achievable communication rate increases with the decrease in
the number of users.

The constant modulus constraint is also desirable in practical radar systems
where non-linear amplifiers typically work in a saturation condition,
preventing amplitude modulation in radar waveforms [40]. Waveform design that
minimizes the communication MUI subject to the constant modulus constraint and
similarity constraint, is also proposed in [14]. The optimization problem is
formulated as [14]

$\begin{gathered}\min_{\mathbf{X}}\|\mathbf{H}^{c}{\bf
X}-\mathbf{S}\|_{F}^{2},\\\ \text{ s.t
}\left\|\operatorname{vec}\left(\mathbf{X}-\mathbf{X}_{0}\right)\right\|_{\infty}\leq\eta,\\\
\left|x_{i,j}\right|=\sqrt{\frac{P_{T}}{M}},\forall i,j,\end{gathered}$ (12)

where $\mathbf{X_{0}}$ is the reference radar signal matrix with constant
modulus entries $x_{i,j}$. A branch-and-bound algorithm [41] was developed to
achieve a globally optimal solution, surpassing the performance of the
conventional Successive Quadratic Constrained Quadratic Programming (QCQP)
Refinement (SQR) algorithm [42]. Results of the constant modulus joint
waveform design show that a trade-off exists between 1) communication sum-rate
and radar waveform similarity tolerance (i.e. similarity between achieved and
desired waveform), and 2) communication sum-rate and the radar pulse
compression performance. Moreover, the omnidirectional beampattern design
always outperforms the directional one in terms of communication sum-rate and
symbol error rate.

In [43], the optimization problem aims to achieve a desired radar beampattern
while ensuring that the SINR, $\gamma_{k}$, for $K$ single-antenna downlink
users, remains above a certain threshold $\Gamma_{k}$

$\begin{gathered}\min_{\mathbf{W},\beta}\left\|\mathbf{W}\mathbf{W}^{H}-\beta\mathbf{R}\right\|_{F}^{2},\\\
\text{s. t.}\beta\geq 0,\quad\gamma_{k}\geq\Gamma_{k},\forall
k;\operatorname{diag}\left(\mathbf{WW}^{H}\right)=\frac{P_{T}}{M}\mathbf{1}_{M}.\end{gathered}$
(13)

Here, $\beta$ is a scaling factor. $\mathbf{W}$ is the pre-coding matrix to be
designed, and $\mathbf{R}$ is the covariance matrix of the radar waveform with
the desired beampattern. This non-convex optimization problem is solved in
[43] by using efficient manifold algorithms to obtain a sub-optimal solution.
Another interesting result reported in [43] shows that the jointly designed
waveform outperforms the case where communication and radar signals are
statistically independent of each other.

To attain optimal performance, sensing systems necessitate the repetition of
waveforms at predefined intervals, while communication systems demand waveform
independence. In essence, for peak efficiency, the waveform covariance matrix
must align for sensing and differ for communication systems [31]. Previous
studies, including the cited ones in this paper, have concentrated on waveform
design to optimize both functions. However, these approaches often compromise
one function to enhance the other. Recently, we introduced the concept of
beampattern-invariant covariance matrix design, holding the promise of
maximizing performance for both functions [28]. This approach demonstrates
that different covariance matrices can yield similar beampatterns as long as
the sum of the diagonal elements in these matrices remains constant. Hence,
the additional degrees of freedom can be exploited to convey the communication
information. Mathematically, for a desired beampattern $P(\theta,\textbf{R})$
specified by the positive semidefinite and symmetric $M\times M$ covariance
matrix R, there exists a set $\mathcal{S}_{1}$ of covariance matrices defined
as

$\displaystyle{\cal S}_{1}:=\bigg{\\{}$
$\displaystyle\tilde{\mathbf{R}}^{M\times
M}:\sum_{k=1}^{M-n}\tilde{r}_{k,k+n}=\sum_{k=1}^{M-n}r_{k,k+n}$ (14)
$\displaystyle\quad\text{ for }n=0,1,\ldots M-1,\tilde{\mathbf{R}}\geq
0,\tilde{\mathbf{R}}=\tilde{\mathbf{R}}^{H}\bigg{\\}}$

Then, for all $\tilde{\mathbf{R}}\in\mathcal{S}_{1}$,

$P(\theta,\tilde{\mathbf{R}})=P(\theta,\mathbf{R}).$ (15)

Hence, communication symbols can be transmitted by utilizing various
covariance matrices without compromising the radar functionality. Moreover, an
improved symbol error rate can be achieved by selecting the symbol set, from
various possible symbol sets originating from different covariance matrices,
that maximize the minimum distance among the symbols.

####  IV-A3 Cramér-Rao Bound (CRB) Based Optimization

Accurate estimation of sensing parameters is essential in radar systems. To
achieve optimal sensing, it’s vital to minimize the mean-square estimation
error (MSEE) for parameters like range, angular location, and velocity. Since
Cramér-Rao Lower Bound (CRLB) sets a minimum limit on the MSEE, it serves as a
reliable performance metric for sensing. CRLB is influenced by the transmitted
waveforms, so when designing waveforms for the DFRC system, it’s crucial to
utilize CRLB in the design process. The CRLBs are well-established for radar
signal-based estimates, as documented in [44]. Furthermore, for communication
signals, CRLBs for certain sensing parameters based on beamspace channel
models are also been derived [45].

Due to the nonlinear relationship between the communication and sensing
functions, it becomes challenging to optimize CRLB and mutual information of
the communication system [4]. In [46], for instance, a single-antenna
Orthogonal Frequency-Division Multiplexing (OFDM) DFRC system is considered to
simultaneously improve the range, velocity accuracy, and the channel capacity
for communications. However, due to the multi-objective nature of the
optimization problem, the obtained solutions are not optimal. Another study,
[47], examines waveform optimization by comparing and applying multiple
sensing performance metrics, including MI, CRLB, and an approximated SINR
metric for communications. The work in [47] shows that significant
correlations exist between MI-based and CRLB-based methods, highlighting that
the MI-based approach is both more efficient and less complex compared to the
CRLB-based approach.

The recent work in [48] proposes MIMO beamforming designs for joint radar
sensing and multi-user communications that minimize the CRLB for radar sensing
while ensuring a predefined level of SINR for each communication user. For the
single-user scenario, the authors derive a closed-form solution that optimizes
the beamforming design for both point and extended targets. In the multi-user
scenario, they demonstrate that the optimization problems can be relaxed by
utilizing the semidefinite relaxation approach to obtain globally optimum
solutions. Through simulation results, the authors demonstrate the superiority
of the proposed method over beampattern approximation-based DFRC designs
discussed in Section IV-A2.

###  IV-B Multibeam Optimization for DFRC Systems with Analog Beamforming

In the context of mmWave JCAS systems, digital MIMO systems may not always be
feasible due to their high hardware complexity and cost. Steerable analog or
hybrid arrays are the alternative cost-effective options [49]. Thus, analog
arrays, also the fundamental component of hybrid arrays, are faced with the
challenge of supporting communication and sensing in different directions
required by JCAS systems. To address this challenge with the limitations of
analog array beamforming (BF) capability, a promising solution is the use of
multibeam technology [50, 51, 52]. The multibeam approach involves a fixed
subbeam for communication and a scanning subbeam for sensing that varies its
direction over different communication packets as shown in Fig. 4. Both
subbeams possess identical information and are utilized for both communication
and sensing.

Figure 4: Illustration of multibeam approach for vehicular networks [53]. Used
under CC license.

Two main categories of methods have been proposed for multibeam optimization.
The first category is the subbeam combination method, as described in [50,
51]. To generate the fixed and scanning subbeams, two beamforming vectors,
$\mathbf{w}_{t,c}$ and $\mathbf{w}_{t,s}$, are designed respectively. These
vectors are combined using a phase shifting coefficient and a power
distribution factor to form the BF vector $\mathbf{w}_{T}$ as

$\mathbf{w}_{T}=\sqrt{\rho}\mathbf{w}_{t,c}+\sqrt{1-\rho}e^{j\varphi}\mathbf{w}_{t,s},$
(16)

where $\rho(0<\rho<1)$ is the power distribution factor and $e^{j\varphi}$ is
the phase shifting coefficient. Balancing the communication and sensing
distances typically determines the value of $\rho$. The optimization process
primarily revolves around $\varphi$, as it exerts a significant influence on
the performance of the BF system. When designing the BF vectors for the
subbeams ($\mathbf{w}_{t,c}$ and $\mathbf{w}_{t,s}$), the optimization
primarily focuses on the magnitudes of the desired BF waveform, neglecting the
consideration of phases. The effectiveness of the multibeam is dependent on
how two BF vectors are combined. Through the optimization of $\varphi$, the
coherency between the pre-generated subbeams is ensured, enabling the
formation of a coherent multibeam.

One optimization problem, using the subbeam method, that maximizes the SNR for
communications with constrained beamforming gain on the sensing subbeams, is
formulated as [52]

$\displaystyle\varphi_{\mathrm{opt}}=\arg\max_{\varphi}\frac{\mathbf{w}_{T}^{H}\mathbf{H}_{c}^{H}\mathbf{H}_{c}\mathbf{w}_{T}}{\left\|\mathbf{w}_{T}\right\|^{2}},$
(17) $\displaystyle\text{ s.t.
}\frac{\left|\mathbf{a}_{T}^{T}\left(M,\phi_{i}\right)\mathbf{w}_{T}\right|^{2}}{\left\|\mathbf{w}_{T}\right\|^{2}}\geq
C_{i}^{2}(1-\rho)M,i=1,2,\ldots,N_{s}.$

Here, $\mathbf{w}_{T}$ is the BF vector in (16), $C_{i}$ is the ratio of the
scanning subbeam gain to the maximum possible array gain, i.e., $(1-\rho)M$,
$\varphi_{i}$s are the desired scanning directions, and $N_{s}$ is the total
number of constraints. Closed-form solutions for such problems are derived in
[52].

While the subbeam combination method is simple and efficient for
implementation, it is considered suboptimal due to the separate pre-generation
of BF weights for the two subbeams, combined with only a single variable. The
extent of its performance gap compared to the optimum, and the existence of
the optimum solution remains unclear. To address this issue, global
optimization methods are developed in [52] to directly optimize the BF vector
$\mathbf{w}_{T}$, taking into account the requirements of both communication
and sensing. An example of such global optimization can be as follows, where
the BF vector is optimized to maximize the received signal power for
communication subject to similarity and gain constraints [52]

$\begin{array}[]{c}\mathbf{w}_{t,\text{ opt
}}=\operatorname{argmax}_{\mathbf{w}_{T},\mathbf{w}_{T}^{H}\mathbf{w}_{T}=1}\mathbf{w}_{T}^{H}\mathbf{H}_{c}^{H}\mathbf{H}_{c}\mathbf{w}_{T},\\\
\\\ \text{ s.t.
}\left.\|\mathbf{A}\left(M,\phi_{i}\right)\mathbf{w}_{T}-\mathbf{d}_{v}\right)\|^{2}\leq\varepsilon_{w},\text{
and/or }\\\
\quad\left|\mathbf{a}_{T}^{T}\left(M,\phi_{i}\right)^{T}\mathbf{w}_{T}\right|^{2}\geq\varepsilon_{i},i=1,2,\ldots,N_{s}.\end{array}$
(18)

The first constraint is the similarity constraint between the generated BF
waveform and the desired $\mathbf{d}_{v}$, the second is the BF gain
constraint in the scanning directions, and $\varepsilon_{w}$,
$\varepsilon_{i}$ are the respective thresholds. The optimization problem in
(18) is a non-convex NP-hard problem, which is solved in [52] using the
semidefinite relaxation approach after converting it to a homogeneous QCQP.
Comparison of the global optimization method and the subbeam combination
method (16) highlights the superiority of the former in terms of achieved
received signal power and the MSE of BF waveform. More recent works on
multibeam optimization include [54, 55].

Recent work in [56] introduces energy-efficient and easy-to-design Multi-Beam
Antenna Arrays for DFRC systems. These arrays utilize pre-designed analog
devices, such as lenses or Butler matrix [57], to steer multiple beams with
minimal power consumption. They offer flexible beam synthesis, accurate angle-
of-arrival estimation, and convenient handling of the beam squint effect [56].

###  IV-C Waveform Optimization for DFRC Systems with Hybrid Analog-Digital
(HAD) Beamforming

HAD represents a middle ground between digital and analog beamforming,
creating sub-arrays from a larger array and employing analog beamforming
within each sub-array as depicted in Fig. 3. This approach aims to harness the
benefits of both analog and digital beamforming while mitigating their
respective limitations. In [6], the authors proposed a novel transceiver
architecture for a mmWave massive MIMO DFRC system employing HAD beamforming.
A novel Time-Division Duplex (TDD) frame structure and signal processing
approach was utilized to combine similar radar and communication operations in
three stages of 1) radar target search and communication channel estimation,
2) downlink communication and radar transmit beamforming, and 3) uplink
communication and radar target tracking. A joint receiver design is also
proposed, capable of target tracking while decoding the uplink communication
signals. The system model used in [6] is shown in Fig. 5.

Figure 5: mmWave massive MIMO DFRC system model with HAD beamforming used in
[6]. ©2020 IEEE.

The frame structure and signal processing flowchart, proposed in [6], are
depicted in Fig. 6. In the first stage, orthogonal Linear Frequency Modulation
(LFM) pilot signals are generated from the HAD array for joint channel
estimation and target search. Angle, delay and Doppler, and reflection
coefficient are estimated at the base station (BS) using MUSIC [58], matched
filtering [59], and Angle and Phase EStimation (APES) [60, 29] algorithms,
respectively. In the second stage, analog and digital beamforming matrices are
designed to generate direction beams toward the targets and scatterers while
equalizing the communication channel. In the last stage, target echoes and
uplink data from the user are received at the BS. Target tracking is performed
through peak search in the MUSIC spectrum within
$\left[\hat{\theta}_{k}-\Delta_{\max},\hat{\theta}_{k}+\Delta_{\max}\right]$,
where $\hat{\theta}_{k}$ represents the estimated angles of the targets from
the first stage and $\Delta_{\max}$ is the maximum angular variation. Based on
the updated estimates of the reflection coefficients and angles of targets,
the uplink communication signal is recovered by using the Successive
Interference Cancellation (SIC) approach [61].

Figure 6:  (a) Proposed frame structure and, (b) Signal processing flowchart
used in [6]. ©2020 IEEE.

###  IV-D Waveform Optimization across Time Domain

Different works have also considered the waveform optimization problem across
time and frequency domains apart from the spatial domain approach covered in
sub-sections IV-A to IV-C. Sensing parameters’ estimation accuracy of
communication signals can be improved with waveform optimization in the time
domain. A typical communication frame consists of a preamble followed by a
data payload. In [62], the preamble of a communication frame is used for
sensing, and sparse sensing in the time domain is exploited for the waveform
design. It is shown that non-uniformly placed preambles can achieve better
velocity estimation accuracy as compared to the uniform ones at the cost of a
small drop in communication rate. In [53], a mmWave combined waveform-
beamforming design is proposed for automotive applications with increased
field-of-view. An optimized convolutional compressed sensing technique is
developed that applies carefully designed circulant shifts of the transmit
beamformer at the transmitter for superior radar channel reconstruction in the
Doppler-angle domain using compressed sensing in the space-time domain.
Performance trade-off between radar and communication is evaluated using a
Normalized Mean Square Error metric for radar estimation and a Distortion MSE
metric for communication. In [63], Doppler-resilient Golay complementary
sequences across multiple packets, are constructed to achieve a 20 dB
improvement in range sidelobe suppression over the standard 802.11ad protocol
along with improvement in detection performance for a given SNR.

###  IV-E Coherent Receiver Design for DFRC Systems

In a typical radar system, same waveform is transmitted after each Pulse
Repetition Interval (PRI) and multiple echoes are combined within a Coherent
Processing Interval (CPI) to improve SNR, estimate Doppler, and suppress
clutter [64]. However, the situation changes for the case of a DFRC system
where a single waveform is employed for communication and radar sensing, and
random communication symbols are also transmitted via the same waveform. Owing
to the transmission of different symbol waveforms within a CPI, the output of
the DFRC receiver’s radar unit no longer remains coherent. This non-coherency
can make Doppler estimation and clutter suppression really challenging and can
also lead to weaker targets being masked by the range side lobes [65].

In [66], an iterative adaptation of the least squares mismatch filter approach
is proposed to achieve coherent output response for two waveforms. However,
the coherency is not guaranteed for more than two waveforms. A cascaded filter
design is proposed in [67] to achieve coherency at the expense of increased
range side lobes. In [65], a novel fully coherent closed-form receiver design
for an arbitrary number of waveforms is proposed based on linear and circular
convolution, without degrading the performance of the DFRC system. Within each
PRI (Pulse Repetition Interval), this system enables the transmission of any
of $K$ distinct symbols. The suggested approach involves the creation of $K$
specific matched filters for the various symbols being transmitted. The
challenge is framed as an optimization problem where each filter is designed
to produce an impulse-like response when the corresponding symbol waveform is
inputted while meeting coherent output response constraints for each filter.
This approach maintains the integrity of both communication and sensing
functions without any compromise.

###  IV-F Physical Layer Security of DFRC Systems

Wireless communication systems face inherent security vulnerabilities due to
their broadcast nature. The integration of sensing and communication
exacerbates this vulnerability, hindering the full potential of DFRC systems.
In joint communication and radar sensing scenario, the targets to be detected
could be potential eavesdroppers, especially for defense-related applications.
For radar sensing, the DFRC BS must use high-power signals to gather
information like angle and velocity from target echoes while suppressing side
lobes to minimize clutter. To enable effective joint sensing and
communication, the DFRC BS designs information-carrying signals to create
highly directional sensing beams. However, this exposes the communication
information to potential eavesdropping by malicious targets, making security a
critical consideration in DFRC system design [68, 69]. Artificial Noise (AN)
has been widely exploited in the literature to enhance communication secrecy
[70, 69, 68].

In [69], the authors proposed to enhance the physical layer security of the
DFRC system by formulating fractional programming problems to minimize the
SINR at the eavesdropper with the help of AN, while maintaining a desired SINR
threshold for legitimate user. The downlink cellular users are considered as
legitimate users while the radar targets are regarded as potential
eavesdroppers. By adding artificial noise $\mathbf{N}$ to the transmitted
signal, the transmit matrix $\mathbf{X}$ from a dual-functional MIMO BS can be
written as

$\mathbf{X}=\mathbf{WS}+\mathbf{N},$ (19)

where $\mathbf{S}$ is the desired signal from the BS and $\mathbf{W}$ is the
beamforming matrix. The optimization problem formulated in [69] for minimizing
the SINR at the target is given as

$\begin{array}[]{ll}\min_{\mathbf{W}_{i},\mathbf{R}_{N}}\frac{|\alpha|^{2}\mathbf{a}^{H}\left(\theta_{0}\right)\sum_{i=1}^{K}\mathbf{W}_{i}\mathbf{a}\left(\theta_{0}\right)}{|\alpha|^{2}\mathbf{a}^{H}\left(\theta_{0}\right)\mathbf{R}_{N}\mathbf{a}\left(\theta_{0}\right)+\sigma^{2}},\forall
i\\\ \text{ s.t.
}\quad\left\|\mathbf{R}_{X}-\mathbf{R}_{d}\right\|^{2}\leqslant\gamma_{bp},\\\
\quad\operatorname{SINR}_{i}\geqslant\gamma_{b},\forall i,\\\ \quad
P_{t}=P_{0}.\end{array}$ (20)

Here, $\theta_{0}$ represents the location of targets, $\gamma_{bp}$ is the
threshold that constraints the mismatch between the designed covariance matrix
$\mathbf{R}_{X}$ and the desired $\mathbf{R}_{d}$, $P_{0}$ is the transmission
power budget, $\mathbf{R}_{N}$ is the covariance matrix of artificial noise,
and $\gamma_{b}$ is the required SINR threshold for each legitimate user. By
minimizing the SINR at the target, desired secrecy rate can be achieved.

A more recent work [68] proposes an optimization framework for robust and
secure resource allocation for a DFRC BS by employing variable-length
snapshots of the environment by scanning a pre-defined sector with a sequence
of dedicated beams. By jointly optimizing the duration of each snapshot, the
beamforming vector, and the covariance matrix of the AN, the system sum
secrecy rate $\sum_{k\in\mathcal{K}}R_{k}^{\sec}[m]$ in the $m$-th snapshot is
maximized where $R_{k}^{\mathrm{sec}}[m]$ is the maximum achievable secrecy
rate between the BS and the $k$-th legitimate user given by

$R_{k}^{\mathrm{sec}}[m]=\left[R_{k}[m]-\max_{j\in\mathcal{J}}C_{j,k}[m]\right]^{+}.$
(21)

Here, $R_{k}[m]$ is the achievable rate of legitimate user $k$ in snapshot $m$
and $C_{j,k}[m]$ is the capacity of the channel between the DFRC BS and
potential eavesdropper $j$ in snapshot $m$. Simulation results reported in
[68] indicate that the proposed design can significantly enhance the physical
layer security of the DFRC system compared to other schemes that utilize
single snapshot design.

##  V APPLICATION SCENARIOS FOR JOINT COMMUNICATION AND SENSING

In this section, we will present several key application scenarios where joint
communication and sensing systems demonstrate their utility beyond addressing
spectrum congestion problem.

###  V-A Perceptive Mobile Networks

Present wireless localization methods predominantly adopt a device-centric
approach. In this paradigm, a wireless device, such as a smartphone, is
affixed to the target object. The device’s location is then deduced by
analyzing signal interactions and geometric correlations with other stationed
wireless equipment, such as a base station. Nevertheless, this device-oriented
strategy restricts the range of applicable targets and lacks adaptability
across varied scenarios. By capitalizing on supplementary Doppler processing
and harnessing valuable information from multipath components, JCAS-empowered
cellular networks can enhance localization accuracy in contrast to prevailing
localization technologies [71]. A framework for a Perceptive Mobile Network
(PMN) was first presented in [18]. The idea is to integrate radar sensing into
the current cellular networks by incorporating few modifications so that it
has the ability to perceive the environment via radio vision and inference. In
particular, a Cloud Radio Access Network (CRAN) architecture employing Spatial
Division Multiple Access and OFDMA is considered in [18]. Another possible
architecture proposed for PMNs is utilizing Target Monitoring Terminals (TMTs)
[72]. Direct and indirect sensing schemes based on 1-D compressive sensing
were developed in [18] for sensing parameters estimation. For direct sensing,
the received signal is fed directly to the sensing algorithm, whereas signal
stripping is used in indirect estimation to simplify the signal by removal of
data symbols after demodulation and decorrelation of users using channel
estimation. In addition, a background subtraction method for the suppression
of clutter was also proposed.

Figure 7: Potential applications of PMNs with joint communication and sensing
capabilities.

PMNs can provide unobtrusive and ubiquitous sensing capability (which
otherwise is either impractical or too costly to implement) because of their
large coverage and infrastructure. In addition, they can provide networked
sensing, where the perspectives from multiple sensing nodes can be
collaboratively utilized for sensing the same target. PMNs can enable numerous
new applications related to smart cities, smart homes, IoT, vehicular
networks, smart industry, environmental sensing, drone monitoring and
management, event management, passive sensing, surveillance, and sensing-
assisted communications as depicted in Fig. 7. A detailed survey of the latest
research on PMNs is presented in [73, 74].

###  V-B Autonomous Vehicles

Next generation of autonomous vehicles requires low-latency Gbps data rates
and high-resolution sensing information on the order of few centimeters [75].
Vehicular localization utilizes technologies like Global Navigation Satellite-
based Systems (GNSS), radar, camera, and Light Detection and Ranging (Lidar).
GNSS alone can’t fulfill the localization requirements of the autonomous
vehicles due to its low-resolution, high latency, and coverage holes [75].
GNSS is assisted by dedicated base stations and the on-board sensors mentioned
above but these sensors add to the cost and computational complexity.
Vehicular communication (V2V, V2I, and V2X) uses standards such as Dedicated
Short-Range Communication (DSRC) [76] and the D2D mode of LTE-A. However,
these standards are not able to support the demanding Gbps requirements of
modern autonomous vehicles [77]. In this context, it is argued that 5G mmWave
communication is the only viable solution for vehicular positioning and data
exchange between connected vehicles [77, 75]. One key challenge to the mmWave
vehicular communication is the overhead associated with beam training. In
[77], it has been proposed to utilize the sensing information from the onboard
sensors or DSRC as side information to the mmwave communication link in order
to reduce the beam training overhead. PMNs can address this challenge
effectively as they offer both the functionalities of communication and
sensing. DFRC systems can be employed onboard the autonomous vehicles to offer
both the functionalities of C&R sensing providing a low power, reduced size,
and low-cost solution. Use of DFRC systems in autonomous vehicles can also
address possible interference of mmWave communication with automotive radars
which also operate in the mmWave band. It becomes apparent from the discussion
above that mmWave DFRC systems appear to be a promising candidate for modern
autonomous vehicles.

###  V-C Drones

There is a growing interest in utilizing UAVs as cost-efficient aerial
platforms to deliver UAV-enabled communication services [78] as exemplified by
initiatives like AT&T’s flying COW (Cell on Wings) [79]. These services
include supporting search and rescue efforts, extending coverage to remote
areas, and enhancing services in temporary hotspot areas like concerts,
football games,…etc. However, stringent requirements on SWaP (size, weight,
and power) impose limitations on both fixed-wing and rotary-wing drones,
constraining their communication, sensing, and endurance capabilities. The use
of DFRC systems can significantly help in addressing the SWaP constraints on
drones while fulfilling the communication and sensing requirements. It can
also offer all-weather day/night sensing capabilities in contrast to the
conventional camera sensor utilized by drones. Moreover, radar sensing
capability can be exploited by drone swarms for formation flight and collision
avoidance. Delivery drones, used for the delivery of small packages, can also
benefit from the advantages offered by JCAS systems. From a military point-of-
view, the employment of a joint system on drones can significantly help in
search and rescue, surveillance, and electronic warfare operations by reducing
the payload and radar cross-section of the drone, thus, improving its mobility
and covertness.

A comprehensive overview of UAV-enabled joint communication and sensing is
presented in [80] where authors covered single and multi-UAV-enabled JCAS.
Different application scenarios, emphasizing the benefits of UAV-enabled JCAS,
resulting from the coordination between communication and sensing
functionalities have been discussed under two categories of sensing-assisted
UAV communication and communication-assisted UAV sensing. It is pertinent to
note that, unlike conventional ground-based JCAS systems, in UAV-enabled JCAS
systems, the allocation of resources and the design of waveforms are
significantly impacted by the deployment and trajectory of the UAV. This is
due to the changing angular separations between users and targets as the UAV’s
position changes. Therefore, achieving high-performance sensing and
communication requires a joint design approach that encompasses user
association, transmit beamforming, and route planning [81].

###  V-D Security and Surveillance

JCAS systems can be a good potential candidate for perimeter security and
surveillance of border areas and sensitive installations like military bases,
airports, dams, and grid stations. Radar sensing can offer all-weather
day/night surveillance as opposed to other sensors like cameras. The
information collected by radar sensing can be simultaneously transmitted by
the communication functionality of the JCAS system to the central control
center for initiating countermeasures like the deployment of quick response
forces. This will eradicate the need for installing separate sensor and
communication equipment and laying physical media between various security
posts/towers and the central control center, thus, providing an efficient and
cost-effective solution. As a step further, micro-Doppler signatures can be
extracted and analyzed for activity recognition and classification of various
types of targets for better threat management [82].

###  V-E Smart Homes and Smart Industry

With the rapid pace of technological advancement, concepts like smart home and
smart industry, are becoming a reality. The potential of RF sensing in smart
homes and industries has been well-established by research [83, 84, 85, 86].
However, it contributes to network congestion due to the substantial amount of
wireless traffic in both scenarios. Rather than designing communication and
sensing systems in isolation, joint design can alleviate the strain on
wireless resources. The issue can be addressed from two perspectives 1) to
equip the conventional sensing device with communication functionality and, 2)
to enhance the sensing prowess of WiFi signals by redesigning the packet
format [87].

The integration of joint communication and sensing systems holds immense
promise for a variety of applications within the realm of smart homes. The
localization performance of conventional GPS degrades significantly in indoor
scenarios. Wifi-based localization has emerged as a promising solution for
indoor localization due to its low cost, ubiquitous deployment, and no
additional hardware requirement [88]. Through-wall localization and tracking
enables accurate positioning of individuals even behind physical barriers and
provide a foundation for responsive home automation. Existing Wifi-based
localization either uses propagation-based or fingerprinting techniques [89,
90]. However, propagation-based techniques have low accuracy and they localize
devices instead of users, whereas fingerprinting techniques are sensitive to
human location, body shape, and the ambient environment [90].

JCAS systems can overcome these limitations by embedding sensing
functionalities into the current Wifi systems. These systems can be deployed
in a monostatic or a multistatic configuration like [91]. As a result, human-
centric functionalities in smart homes can be vastly enhanced through these
systems. Micro-Doppler signatures can be extracted for human activity
recognition, health monitoring, and fall detection to ensure the safety and
well-being of occupants [92, 93, 94]. This real-time health insight empowers
remote health management and facilitates early intervention. Gesture
recognition can be employed for the operation and control of smart devices
[95]. The sensing functionality can also be exploited for intrusion detection
and security [91].

In the same context, joint communication and sensing can be used within the
domain of smart industry for localization and tracking of vehicles, equipment,
and workers [96, 97]; object recognition and authentication [98]; surveillance
of designated areas; and gesture recognition for equipment operation [73]. By
seamlessly integrating communication and sensing technologies, industries can
achieve real-time monitoring and precise positioning, leading to enhanced
operational efficiency, streamlined logistics, and improved safety protocols.

###  V-F Replacement/Redundancy of Backhaul Connectivity for Military Radars
and Airborne Warning and Control System (AWACS)

Modern military radars are usually networked together to provide a
comprehensive picture of a country’s airspace at the central command and
control center. This greatly helps in effective decision making and
operational command and control during war-time scenarios. Ground-based radars
usually send their data to the central command and control center via
dedicated optical fiber connectivity whereas AWACS share their radar picture
via dedicated air-to-ground data links. By employing the communication
functionality of radar-centric JCAS systems, this dedicated back-haul
connectivity with the central command and control center is no longer required
(especially in the case of remote and hilly areas), thus saving huge costs.
Even if this back-haul connectivity is not fully replaced, the communication
functionality of JCAS system can act as a backup for this back-haul
connectivity. For the case of AWACS, it can offer another very critical
advantage of weight reduction (resulting from the deletion/reduction of
dedicated data link communication equipment), which leads to enhanced
endurance for the platform.

###  V-G Multipurpose RF Systems for Military

There are various RF systems onboard military ships and aircrafts serving
different purposes of communication, radar, and electronic warfare. The
independent design and development of these systems have led to a significant
increase in the size, weight, and power requirements of the combat platform,
leading to larger radar cross-section and lesser endurance for the platform.
These sophisticated RF systems come with a hefty price tag and require costly
maintenance and complex troubleshooting, resulting in increased downtime of
the combat platform. Additionally, the coexistence of such systems inevitably
causes mutual interference among each other.

In 1996, the Advanced Multi-function Radio Frequency Concept project was
launched by the Defense Advanced Research Projects Agency (DARPA), to design
integrated RF systems utilizing a common set of array architecture, signal and
data processing, signal generation, and display hardware [99]. In 2013, Shared
Spectrum Access for Radar and Communications project [100] was launched by
DARPA. The program aims to improve radar and communications capabilities
through spectrum sharing. In particular, two types of spectrum sharing were
considered for the S-band (2-4 GHz): spectrum sharing between military radars
and military communications systems and spectrum sharing between military
radars and commercial communications systems. An improved version of the
program named Joint Design and Operation of SSPARC was proposed in [101].
Clearly, all these projects aim for the fusion of radar and communication
functionalities and DFRC systems possess the abilities to achieve these
desired outcomes in an efficient way.

##  VI RESOURCE ALLOCATION IN DFRC SYSYTEMS

To achieve optimal Quality of Service (QoS) in DFRC systems, a deep
understanding of radar and communication systems and individual system’s
unique requirements is essential. Optimizing QoS in DFRC systems involves the
strategic allocation of resources to strike a harmonious balance between the
needs of sensing and communication tasks while adapting to changing
requirements. Hence, effective resource management is fundamental to the
seamless operation of these integrated systems across various operational
scenarios.

###  VI-A Memory Management

Radar systems often necessitate substantial memory resources to store critical
data utilized in target localization and tracking. This data includes both
fast-time and slow-time samples, as well as historical information for
tracking purposes. In the context of identifying slow-moving targets, the use
of fast-time samples aids in estimating the target’s range, while slow-time
samples are pivotal for velocity estimation. The combined storage of fast and
slow-time sample data can impose a considerable memory burden. Nonetheless, an
efficient approach can be adopted to minimize memory utilization. The process
begins with the application of a Fast Fourier Transform (FFT) to the fast-time
samples, which facilitates the estimation of target ranges. The indices
corresponding to spectral peaks obtained through this FFT process are then
leveraged to estimate the ranges of different targets within the radar’s
field. Significantly, slow-moving targets exhibit minimal variations in their
ranges over the course of a single CPI. This insight allows us to optimize
memory usage. Specifically, after the initial pulse, the estimated range
indices remain relatively consistent for the duration of a frame.
Consequently, it becomes possible to employ the indices derived after the
first pulse for subsequent pulses during the same frame. This strategic
decision means that only samples associated with the range indices following
the transmission of each pulse need to be preserved for velocity estimation.
By adopting this technique, a substantial reduction in the required memory
capacity can be achieved, without compromising the radar system’s ability to
perform accurate target localization and tracking.

In the case of radar systems, the emphasis is on efficiently storing and
reusing range indices to minimize memory consumption while ensuring precise
target localization and tracking. In contrast, communication units operate on
a frame-by-frame data processing paradigm, which demands a distinct memory
usage pattern compared to radar systems. A desired approach to memory resource
management in DFRC systems ensures that both radar and communication units can
effectively fulfill their respective functions. Therefore, the allocation of
memory resources must be tailored to accommodate the unique requirements of
each task.

In [102], the design of a communication receiver, operating under bit
constraints, is considered for a radar-centric JCAS scenario. Task-based
quantization framework [103, 104, 105, 106] is utilized to facilitate the
operation of communication receiver under bit constraints. The proposed
hybrid/analog receiver design employs a linear analog combiner before the
quantization and digital processing stages. Two different types of analog
combiners are proposed; the spatial-temporal combiner and the spatial
combiner, which are jointly designed with the overall system. The analog
combiner reduces the dimensionality of the input to the analog-to-digital
converters while preserving the dominant eigenmodes of the linear minimum
mean-square error estimate of the transmit symbol vector. The findings
presented in [102] illustrate that the proposed communication receiver yielded
superior performance compared to the task-ignorant quantization system
utilizing the same number of quantization bits. This decrease in quantization
bits can lead to substantial reductions in memory size, hardware expenses, and
overall system complexity.

###  VI-B Processor Allocation

Efficiently managing the processing power of the DFRC system is critical. Take
radars, for instance, which require significant processing capacity to perform
tasks such as determining range, angular location, velocity estimation, and
tracking. In this process, the radar sends out a series of pulses, each
separated by a set interval known as PRI (Pulse Repetition Interval). After
each pulse is transmitted, the radar begins to sample and collect data from
$N_{c}$ pulses, forming what is called a frame. This frame corresponds to a
Coherent Processing Interval (CPI), which serves as the timeframe for radar
processing to commence.

In contrast, communication tasks, especially those involving live video or
audio, necessitate more frequent access to the processing unit. Consequently,
a dynamic allocation strategy becomes crucial, giving priority to
communication processing while periodically releasing resources for radar
processing during predefined intervals. This approach ensures that both radar
and communication tasks are handled efficiently within the DFRC system.

###  VI-C Bandwidth Allocation

Resource allocation in DFRC systems poses a critical challenge due to their
reliance on fixed-bandwidth waveforms for transmission. The bandwidth
allocation in DFRC systems influences two critical aspects: range resolution
(for sensing) and data throughput (for communication). Achieving the optimal
equilibrium in bandwidth allocation becomes imperative to fulfill the unique
demands of sensing and communication within DFRC systems, all while upholding
the stringent QoS standards in place.

There is significant research interest in studying the radar sensing
properties of multi-carrier waveforms, known for their ability to achieve high
communication rates [107]. Frequency-hopping multi-carrier waveforms were used
in [108, 109]. In this approach, the available bandwidth is divided into
multiple sub-bands, and a randomly chosen subset of these sub-bands is paired
with a transmit antenna for each channel use. However, this method utilizes
only a portion of the available bandwidth, degrading target range resolution
and communication rate. Orthogonal Frequency-Division Multiplexing (OFDM)
waveforms for DFRC systems are explored in [39, 110, 111]. In these studies,
non-overlapping subcarriers are allocated to transmit antennas in each channel
use. Contrary to frequency-hopping methods, OFDM approaches make use of the
entire available bandwidth, leading to enhanced range resolution and
communication rate. However, due to the restriction of each antenna to
transmit on specific subcarriers, the communication bandwidth is not fully
exploited.

A bandwidth-efficient DFRC system employing OFDM waveforms is proposed in
[107]. Unlike the OFDM approaches discussed previously, the available
subcarriers in this approach are categorized into two groups: shared and
private. On shared subcarriers, all antennas can transmit simultaneously,
whereas on private subcarriers, only one antenna can transmit at a time.
Subcarrier sharing enables a high communication rate. To address the coupling
of transmitted symbols and sensing parameters in the target echoes, arising
from the shared use of subcarriers, a low complexity target estimation
approach is proposed in [107].

###  VI-D Beampattern Control

The beampattern of transmitted signals holds great significance in DFRC
systems. For sensing purposes, the strength of the reflected signal from the
target relies on the directionality of the transmitted signal toward the
target. Therefore, transmitted signals directed at the target must possess
sufficient power. In contrast, signals directed towards end-users primarily
serve the purpose of information transmission, allowing for lower power
signals in their direction, thereby prioritizing energy efficiency while
upholding QoS standards.

##  VII CHALLENGES AND FUTURE RESEARCH DIRECTIONS

One of the key challenges for the DFRC system is to address the conflicting
beamforming requirements for communications and radar [5]. For radars, we want
to have a wide field-of-view scanning. On the contrary, directive beams are
required for communication at mmWave and sub-Terahertz (THz) band. Moreover,
efficient BF tracking approaches need to be developed for C&R operations with
mobile nodes. Sensing-assisted communication can play a vital role to address
this issue where the sensing capability can be used for tracking the mobile
user and forming predictive communication beams. With the availability of
large bandwidths (BW) at mmWave and sub-THz bands for DFRC systems, the design
of optimal signaling schemes for best utilization of available BW also becomes
an important research area [5].

Efficient channel estimation for highly directional beams in sparse channels
is challenging due to the vast angular search space and limited available
measurements. Existing solutions like compressed sensing are computationally
complex and sensitive to noise, errors in array response, and off-grid issues
[74]. In this regard, the sensing capability of DFRC systems can help by
identifying the locations of key scatterers in the sparse channel, thus
substantially reducing the search space and enhancing estimation accuracy,
especially with limited measurements.

Another interesting research direction is the multichannel system in which
multiple frequency channels are used during a symbol transmission period. By
combining signals from different channels, such systems can offer an overall
large BW required for accurate sensing without increasing the communication BW
[5]. The key challenge here is how to remove the distortions from signals
across multiple channels before stitching them together for sensing and how to
design signals that are easy to concatenate. Readers are referred to [112] for
an example of a work that deals with multichannel signals for passive radar
sensing.

Receiver design for DFRC systems is an emerging research area where little
work has been done until now. A novel joint receiver design is proposed in
[6]. The challenge in receiver design is to discriminate between communication
signals and target echoes in the presence of noise. Machine learning and deep
learning approaches can aid in the receiver design of DFRC systems where they
can be used to distinguish between the two signals based on their independent
statistical characteristics [6]. The situation becomes even more complex in
the case of bistatic or multistatic DFRC configurations where knowledge of the
transmit waveform is not available at the receiver.

Networked sensing presents an important research direction for PMNs [74]. By
leveraging the collaborative use of multiple TMTs, sensing performance can be
enhanced. The primary advantage of networked sensing lies in the macro-
diversity achieved through various TMTs, which can boost the reliability of
target detection, as the likelihood of all TMT perspectives being obstructed
is minimal. However, a significant challenge in networked sensing is tracking
of moving targets. Unlike traditional radar, each TMT’s coverage is limited
and a smooth handover of the sensing task is necessary from one TMT to
another. This challenge becomes more complex in networked sensing when
transitioning between groups of TMTs with possible overlap between them. While
handover is a familiar concept in wireless communication, it differs for
sensing due to several factors which are: the challenging requirement of
synchronization in networked sensing, the handover criteria is dependent on
additional factors including angles and the target’s moving direction, and the
requirement of ”predictive” sensing beams for fast-moving targets [74]. To
address these challenges, machine learning or data-driven approaches may
become more crucial. Graph Neural Networks (GNNs) have shown effectiveness in
solving various wireless network design problems, and they can also be applied
to the handover problem by formulating it as a graph optimization problem
[74].

As far as the military radars are concerned, information about their location,
system parameters, and capabilities is to be kept confidential so that the
adversary is unable to devise countermeasures against these radars. The
security of this information may be compromised by sharing the spectrum with
communication systems. Some notable works in this direction employing physical
layer security are [113, 114, 115, 68]. Another potential implication of using
a joint system for military sensing and communications is that in the event of
a military conflict, the destruction of such a system by the enemy can result
in the loss of both capabilities (sensing as well as communications) within a
particular coverage area, which is of course not a desired scenario.

DFRC system analysis from an information theoretical point of view needs more
work as the current information theoretical foundation for joint systems is
limited [5, 6]. This work is necessary to reveal the performance bounds for
the DFRC systems. Information theoretical analysis for DFRC uplink has been
presented in [116], however, the downlink channel has to be investigated
further.

##  VIII CONCLUSION

DFRC is an emerging research area as it can offer a tunable trade-off between
C&R functionalities. It can tackle the spectrum congestion issue and offer
numerous advantages in terms of power, size, cost, reduced interference,
improved localization accuracy, and beamforming efficiency. Massive MIMO
systems operating in mmWave and sub-THz bands are promising candidates for the
implementation of DFRC systems as they can fulfill the requirements of
accurate sensing and high data rate communications. Hybrid analog-digital
beamforming architecture is suitable for DFRC systems as it can offer the
advantages of both analog and digital BF while minimizing their drawbacks. The
design of an optimal joint waveform that can perform both functionalities of
communication and radar sensing, is the fundamental research problem in DFRC
system design. Challenges arising from the inherent differences between C&R
need to be addressed to maximally benefit from this joint design approach.
This paper provides a comprehensive review of the state-of-the-art research on
DFRC systems covering various design aspects in detail as well as a coverage
of potential application scenarios and future research directions. It can
serve as a good starting point for readers interested in doing research in
this particular area.

## References

  * [1] I. Analytics, “Internet of things (IoT) and non-IoT active device connections worldwide from 2010 to 2025 (in billions) [graph],” Nov 2020, [Online]. Available: https://www.statista.com/statistics/1101442/iot-number-of-connected-devices-worldwide/ (accessed Jul. 21, 2023).
  * [2] 5G midband spectrum: Costs and top winners in the US. [Online]. Available: https://www.rcrwireless.com/20221003/spectrum/5g-midband-spectrum-costs-and-top-winners-in-the-us (accessed July. 6, 2023).
  * [3] A world first – the story of Bawdsey Radar. [Online]. Available: https://www.bawdseyradar.org.uk/a-world-first/ (accessed Jul. 21, 2023).
  * [4] J. A. Zhang, F. Liu, C. Masouros, R. W. Heath, Z. Feng, L. Zheng, and A. Petropulu, “An overview of signal processing techniques for joint communication and radar sensing,” _IEEE Journal of Selected Topics in Signal Processing_ , vol. 15, no. 6, pp. 1295–1315, 2021.
  * [5] K. Wu, J. A. Zhang, and Y. J. Guo, _Joint communications and sensing: From fundamentals to advanced techniques_. John Wiley & Sons, 2022.
  * [6] F. Liu, C. Masouros, A. P. Petropulu, H. Griffiths, and L. Hanzo, “Joint radar and communication design: Applications, state-of-the-art, and the road ahead,” _IEEE Transactions on Communications_ , vol. 68, no. 6, pp. 3834–3862, 2020.
  * [7] L. Wang, J. McGeehan, C. Williams, and A. Doufexi, “Application of cooperative sensing in radar–communications coexistence,” _IET communications_ , vol. 2, no. 6, pp. 856–868, 2008.
  * [8] J. A. Mahal, A. Khawar, A. Abdelhadi, and T. C. Clancy, “Spectral coexistence of MIMO radar and MIMO cellular system,” _IEEE Transactions on Aerospace and Electronic Systems_ , vol. 53, no. 2, pp. 655–668, 2017.
  * [9] B. Li and A. P. Petropulu, “Joint transmit designs for coexistence of MIMO wireless communications and sparse sensing radars in clutter,” _IEEE Transactions on Aerospace and Electronic Systems_ , vol. 53, no. 6, pp. 2846–2864, 2017.
  * [10] A. Babaei, W. H. Tranter, and T. Bose, “A nullspace-based precoder with subspace expansion for radar/communications coexistence,” in _2013 IEEE Global Communications Conference (GLOBECOM)_. IEEE, 2013, pp. 3487–3492.
  * [11] F. Liu, C. Masouros, A. Li, and T. Ratnarajah, “Robust MIMO beamforming for cellular and radar coexistence,” _IEEE Wireless Communications Letters_ , vol. 6, no. 3, pp. 374–377, 2017.
  * [12] B. Li, A. P. Petropulu, and W. Trappe, “Optimum co-design for spectrum sharing between matrix completion based MIMO radars and a MIMO communication system,” _IEEE Transactions on Signal Processing_ , vol. 64, no. 17, pp. 4562–4575, 2016.
  * [13] A. F. Martone, K. A. Gallagher, and K. D. Sherbondy, “Joint radar and communication system optimization for spectrum sharing,” in _2019 IEEE Radar Conference (RadarConf)_. IEEE, 2019, pp. 1–6.
  * [14] F. Liu, L. Zhou, C. Masouros, A. Li, W. Luo, and A. Petropulu, “Toward dual-functional radar-communication systems: Optimal waveform design,” _IEEE Transactions on Signal Processing_ , vol. 66, no. 16, pp. 4264–4279, 2018.
  * [15] A. Hassanien, M. G. Amin, E. Aboutanios, and B. Himed, “Dual-function radar communication systems: A solution to the spectrum congestion problem,” _IEEE Signal Processing Magazine_ , vol. 36, no. 5, pp. 115–126, 2019.
  * [16] R. M. Mealey, “A method for calculating error probabilities in a radar communication system,” _IEEE Transactions on Space Electronics and Telemetry_ , vol. 9, no. 2, pp. 37–42, 1963.
  * [17] P. Kumari, J. Choi, N. González-Prelcic, and R. W. Heath, “Ieee 802.11 ad-based radar: An approach to joint vehicular communication-radar system,” _IEEE Transactions on Vehicular Technology_ , vol. 67, no. 4, pp. 3012–3027, 2017.
  * [18] M. L. Rahman, J. A. Zhang, X. Huang, Y. J. Guo, and R. W. Heath, “Framework for a perceptive mobile network using joint communication and radar sensing,” _IEEE Transactions on Aerospace and Electronic Systems_ , vol. 56, no. 3, pp. 1926–1941, 2019.
  * [19] P. Kumari, S. A. Vorobyov, and R. W. Heath, “Adaptive virtual waveform design for millimeter-wave joint communication–radar,” _IEEE Transactions on Signal Processing_ , vol. 68, pp. 715–730, 2019.
  * [20] N. González-Prelcic, R. Méndez-Rial, and R. W. Heath, “Radar aided beam alignment in mmwave v2i communications supporting antenna diversity,” in _2016 Information Theory and Applications Workshop (ITA)_. IEEE, 2016, pp. 1–7.
  * [21] F. Liu, W. Yuan, C. Masouros, and J. Yuan, “Radar-assisted predictive beamforming for vehicular links: Communication served by sensing,” _IEEE Transactions on Wireless Communications_ , vol. 19, no. 11, pp. 7704–7719, 2020.
  * [22] C. W. Rossler, E. Ertin, and R. L. Moses, “A software defined radar system for joint communication and sensing,” in _2011 IEEE RadarCon (RADAR)_. IEEE, 2011, pp. 1050–1055.
  * [23] K. Wu, J. A. Zhang, X. Huang, Y. J. Guo, and R. W. Heath, “Waveform design and accurate channel estimation for frequency-hopping MIMO radar-based communications,” _IEEE Transactions on Communications_ , vol. 69, no. 2, pp. 1244–1258, 2020.
  * [24] T. Huang, X. Xu, Y. Liu, N. Shlezinger, and Y. C. Eldar, “A dual-function radar communication system using index modulation,” in _2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)_. IEEE, 2019, pp. 1–5.
  * [25] S. Ahmed, J. S. Thompson, Y. R. Petillot, and B. Mulgrew, “Unconstrained synthesis of covariance matrix for MIMO radar transmit beampattern,” _IEEE Transactions on Signal Processing_ , vol. 59, no. 8, pp. 3837–3849, 2011.
  * [26] S. Ahmed and M.-S. Alouini, “MIMO radar transmit beampattern design without synthesising the covariance matrix,” _IEEE Transactions on Signal Processing_ , vol. 62, no. 9, pp. 2278–2289, 2014.
  * [27] T. Bouchoucha, S. Ahmed, T. Al-Naffouri, and M.-S. Alouini, “Dft-based closed-form covariance matrix and direct waveforms design for MIMO radar to achieve desired beampatterns,” _IEEE Transactions on Signal Processing_ , vol. 65, no. 8, pp. 2104–2113, 2017.
  * [28] S. Mazahir, S. Ahmed, and M.-S. Alouini, “Beampattern-invariant MIMO covariance matrices: Synthesis and applications,” _IEEE Transactions on Wireless Communications_ , pp. 1–1, 2023.
  * [29] L. Xu, J. Li, and P. Stoica, “Target detection and parameter estimation for MIMO radar systems,” _IEEE Transactions on Aerospace and Electronic Systems_ , vol. 44, no. 3, pp. 927–939, 2008.
  * [30] S. Jardak, S. Ahmed, and M.-S. Alouini, “Low complexity moving target parameter estimation for MIMO radar using 2d-fft,” _IEEE Transactions on Signal Processing_ , vol. 65, no. 18, pp. 4745–4755, 2017.
  * [31] Y. Xiong, F. Liu, Y. Cui, W. Yuan, T. X. Han, and G. Caire, “On the fundamental tradeoff of integrated sensing and communications under gaussian channels,” _IEEE Transactions on Information Theory_ , vol. 69, no. 9, pp. 5723–5751, 2023.
  * [32] R. Miller and C. Chang, “A modified cramér-rao bound and its applications (corresp.),” _IEEE Transactions on Information Theory_ , vol. 24, no. 3, pp. 398–400, 1978.
  * [33] A. El Gamal and Y.-H. Kim, _Network Information Theory_. Cambridge university press, 2011.
  * [34] F. Liu, Y. Xiong, K. Wan, T. X. Han, and G. Caire, “Deterministic-random tradeoff of integrated sensing and communications in gaussian channels: A rate-distortion perspective,” in _2023 IEEE International Symposium on Information Theory (ISIT)_ , 2023, pp. 2326–2331.
  * [35] M. P. Do Carmo and J. Flaherty Francis, _Riemannian geometry_. Springer, 1992, vol. 6.
  * [36] Technology Innovation Institute (TII). (2023). Information-Theoretic Limits of Integrated Sensing and Communications Under Gaussian Channels. [Online]. Available: https://www.tii.ae/seminar/aidrc-telecom-seminar-prof-fan-liu.
  * [37] M. Bell, “Information theory and radar waveform design,” _IEEE Transactions on Information Theory_ , vol. 39, no. 5, pp. 1578–1597, 1993.
  * [38] X. Yuan, Z. Feng, J. A. Zhang, W. Ni, R. P. Liu, Z. Wei, and C. Xu, “Spatio-temporal power optimization for MIMO joint communication and radio sensing systems with training overhead,” _IEEE Transactions on Vehicular Technology_ , vol. 70, no. 1, pp. 514–528, 2021.
  * [39] Y. Liu, G. Liao, J. Xu, Z. Yang, and Y. Zhang, “Adaptive OFDM integrated radar and communications waveform design based on information theory,” _IEEE Communications Letters_ , vol. 21, no. 10, pp. 2174–2177, 2017.
  * [40] G. Cui, H. Li, and M. Rangaswamy, “MIMO radar waveform design with constant modulus and similarity constraints,” _IEEE Transactions on Signal Processing_ , vol. 62, no. 2, pp. 343–353, 2014.
  * [41] H. Tuy, _Convex analysis and global optimization_. Springer, 2016.
  * [42] O. Aldayel, V. Monga, and M. Rangaswamy, “Successive qcqp refinement for MIMO radar waveform design under practical constraints,” _IEEE Transactions on Signal Processing_ , vol. 64, no. 14, pp. 3760–3774, 2016.
  * [43] F. Liu, C. Masouros, A. Li, H. Sun, and L. Hanzo, “MU-MIMO communications with MIMO radar: From co-existence to joint transmission,” _IEEE Transactions on Wireless Communications_ , vol. 17, no. 4, pp. 2755–2770, 2018.
  * [44] R. Niu, R. S. Blum, P. K. Varshney, and A. L. Drozd, “Target localization and tracking in noncoherent multiple-input multiple-output radar systems,” _IEEE Transactions on Aerospace and Electronic Systems_ , vol. 48, no. 2, pp. 1466–1489, 2012.
  * [45] M. D. Larsen, A. L. Swindlehurst, and T. Svantesson, “Performance bounds for MIMO-OFDM channel estimation,” _IEEE Transactions on Signal Processing_ , vol. 57, no. 5, pp. 1901–1916, 2009.
  * [46] Y. Liu, G. Liao, Z. Yang, and J. Xu, “Multiobjective optimal waveform design for OFDM integrated radar and communication systems,” _Signal Processing_ , vol. 141, pp. 331–342, 2017.
  * [47] Z. Ni, J. A. Zhang, K. Yang, X. Huang, and T. A. Tsiftsis, “Waveform optimization with multiple performance metrics for broadband joint communication and radar sensing,” _arXiv preprint arXiv:2011.10943_ , 2020.
  * [48] F. Liu, Y.-F. Liu, A. Li, C. Masouros, and Y. C. Eldar, “Cramér-rao bound optimization for joint radar-communication beamforming,” _IEEE Transactions on Signal Processing_ , vol. 70, pp. 240–253, 2021.
  * [49] R. W. Heath, N. Gonzalez-Prelcic, S. Rangan, W. Roh, and A. M. Sayeed, “An overview of signal processing techniques for millimeter wave MIMO systems,” _IEEE journal of selected topics in signal processing_ , vol. 10, no. 3, pp. 436–453, 2016.
  * [50] J. A. Zhang, A. Cantoni, X. Huang, Y. J. Guo, and R. W. Heath, “Joint communications and sensing using two steerable analog antenna arrays,” in _2017 IEEE 85th Vehicular Technology Conference (VTC Spring)_. IEEE, 2017, pp. 1–5.
  * [51] Y. Luo, J. A. Zhang, X. Huang, W. Ni, and J. Pan, “Optimization and quantization of multibeam beamforming vector for joint communication and radio sensing,” _IEEE Transactions on Communications_ , vol. 67, no. 9, pp. 6468–6482, 2019.
  * [52] ——, “Multibeam optimization for joint communication and radio sensing using analog antenna arrays,” _IEEE Transactions on Vehicular Technology_ , vol. 69, no. 10, pp. 11 000–11 013, 2020.
  * [53] P. Kumari, N. J. Myers, and R. W. Heath, “Adaptive and fast combined waveform-beamforming design for mmwave automotive joint communication-radar,” _IEEE Journal of Selected Topics in Signal Processing_ , vol. 15, no. 4, pp. 996–1012, 2021.
  * [54] Y. Zhuo, Z. Sha, and Z. Wang, “Multibeam joint communication and radar sensing: Beamforming design and interference cancellation,” _IEEE Communications Letters_ , vol. 26, no. 8, pp. 1888–1892, 2022.
  * [55] J. Suh, J. Kang, K. Han, S. Hong, and G.-T. Gil, “Null space projection-based design of multibeam for joint communication and sensing systems,” _IEEE Communications Letters_ , pp. 1–1, 2023.
  * [56] K. Wu, J. A. Zhang, X. Huang, R. W. Heath, and Y. J. Guo, “Green joint communications and sensing employing analog multi-beam antenna arrays,” _IEEE Communications Magazine_ , pp. 1–7, 2023.
  * [57] Y. J. Guo, M. Ansari, and N. J. Fonseca, “Circuit type multiple beamforming networks for antenna arrays in 5g and 6g terrestrial and non-terrestrial networks,” _IEEE Journal of Microwaves_ , vol. 1, no. 3, pp. 704–722, 2021.
  * [58] R. Schmidt, “Multiple emitter location and signal parameter estimation,” _IEEE transactions on antennas and propagation_ , vol. 34, no. 3, pp. 276–280, 1986.
  * [59] W. Roberts, P. Stoica, J. Li, T. Yardibi, and F. A. Sadjadi, “Iterative adaptive approaches to MIMO radar imaging,” _IEEE Journal of Selected Topics in Signal Processing_ , vol. 4, no. 1, pp. 5–20, 2010.
  * [60] J. Li and P. Stoica, “An adaptive filtering approach to spectral estimation and sar imaging,” _IEEE Transactions on Signal Processing_ , vol. 44, no. 6, pp. 1469–1484, 1996.
  * [61] D. Tse and P. Viswanath, _Fundamentals of wireless communication_. Cambridge university press, 2005.
  * [62] P. Kumari, S. A. Vorobyov, and R. W. Heath, “Adaptive virtual waveform design for millimeter-wave joint communication–radar,” _IEEE Transactions on Signal Processing_ , vol. 68, pp. 715–730, 2020.
  * [63] G. Duggal, S. Vishwakarma, K. V. Mishra, and S. S. Ram, “Doppler-resilient 802.11ad-based ultrashort range automotive joint radar-communications system,” _IEEE Transactions on Aerospace and Electronic Systems_ , vol. 56, no. 5, pp. 4035–4048, 2020.
  * [64] M. A. Richards, J. Scheer, W. A. Holm, and W. L. Melvin, _Principles of modern radar_. Citeseer, 2010.
  * [65] M. Zubair, S. Ahmed, and M.-S. Alouini, “Generalized fully coherent closed-form receiver design for joint radar and communication system,” _IEEE Transactions on Communications_ , vol. 70, no. 11, pp. 7683–7695, 2022.
  * [66] S. D. Blunt, M. R. Cook, and J. Stiles, “Embedding information into radar emissions via waveform implementation,” in _2010 International Waveform Diversity and Design Conference_ , 2010, pp. 000 195–000 199.
  * [67] C. Sahin, J. G. Metcalf, and S. D. Blunt, “Filter design to address range sidelobe modulation in transmit-encoded radar-embedded communications,” in _2017 IEEE Radar Conference (RadarConf)_ , 2017, pp. 1509–1514.
  * [68] D. Xu, X. Yu, D. W. K. Ng, A. Schmeink, and R. Schober, “Robust and secure resource allocation for isac systems: A novel optimization framework for variable-length snapshots,” _IEEE Transactions on Communications_ , vol. 70, no. 12, pp. 8196–8214, 2022.
  * [69] N. Su, F. Liu, and C. Masouros, “Enhancing the physical layer security of dual-functional radar communication systems,” in _2019 IEEE Global Communications Conference (GLOBECOM)_. IEEE, 2019, pp. 1–6.
  * [70] R. Negi and S. Goel, “Secret communication using artificial noise,” in _IEEE vehicular technology conference_ , vol. 62, no. 3. Citeseer, 2005, p. 1906.
  * [71] Y. Cui, F. Liu, C. Masouros, J. Xu, T. X. Han, and Y. C. Eldar, _Integrated Sensing and Communications: Background and Applications_. Springer Nature Singapore, 2023, pp. 3–21.
  * [72] L. Xie, P. Wang, S. Song, and K. B. Letaief, “Perceptive mobile network with distributed target monitoring terminals: Leaking communication energy for sensing,” _IEEE Transactions on Wireless Communications_ , vol. 21, no. 12, pp. 10 193–10 207, 2022.
  * [73] J. A. Zhang, M. L. Rahman, K. Wu, X. Huang, Y. J. Guo, S. Chen, and J. Yuan, “Enabling joint communication and radar sensing in mobile networks—a survey,” _IEEE Communications Surveys & Tutorials_, vol. 24, no. 1, pp. 306–345, 2022.
  * [74] L. Xie, S. Song, Y. C. Eldar, and K. B. Letaief, “Collaborative sensing in perceptive mobile networks: Opportunities and challenges,” _IEEE Wireless Communications_ , vol. 30, no. 1, pp. 16–23, 2023.
  * [75] H. Wymeersch, G. Seco-Granados, G. Destino, D. Dardari, and F. Tufvesson, “5g mmwave positioning for vehicular networks,” _IEEE Wireless Communications_ , vol. 24, no. 6, pp. 80–86, 2017.
  * [76] J. B. Kenney, “Dedicated short-range communications (dsrc) standards in the united states,” _Proceedings of the IEEE_ , vol. 99, no. 7, pp. 1162–1182, 2011.
  * [77] J. Choi, V. Va, N. Gonzalez-Prelcic, R. Daniels, C. R. Bhat, and R. W. Heath, “Millimeter-wave vehicular communication to support massive automotive sensing,” _IEEE Communications Magazine_ , vol. 54, no. 12, pp. 160–167, 2016.
  * [78] Y. Zeng, R. Zhang, and T. J. Lim, “Wireless communications with unmanned aerial vehicles: opportunities and challenges,” _IEEE Communications Magazine_ , vol. 54, no. 5, pp. 36–42, 2016.
  * [79] “When COWs fly: AT&T sending LTE signals from drones,” [Online]. Available: https://about.att.com/innovationblog/cowsfly (accessed Aug. 11, 2023).
  * [80] K. Meng, Q. Wu, J. Xu, W. Chen, Z. Feng, R. Schober, and A. L. Swindlehurst, “UAV-enabled integrated sensing and communication: Opportunities and challenges,” _IEEE Wireless Communications_ , pp. 1–9, 2023.
  * [81] K. Meng, Q. Wu, S. Ma, W. Chen, K. Wang, and J. Li, “Throughput maximization for UAV-enabled integrated periodic sensing and communication,” _IEEE Transactions on Wireless Communications_ , vol. 22, no. 1, pp. 671–687, 2022.
  * [82] A. Hanif, M. Muaz, A. Hasan, and M. Adeel, “Micro-Doppler based target recognition with radars: A review,” _IEEE Sensors Journal_ , vol. 22, no. 4, pp. 2948–2961, 2022.
  * [83] T. Teixeira, G. Dublon, and A. Savvides, “A survey of human-sensing: Methods for detecting presence, count, location, track, and identity,” _ACM Computing Surveys_ , vol. 5, no. 1, pp. 59–69, 2010.
  * [84] F. Adib, H. Mao, Z. Kabelac, D. Katabi, and R. C. Miller, “Smart homes that monitor breathing and heart rate,” in _Proceedings of the 33rd annual ACM conference on human factors in computing systems_ , 2015, pp. 837–846.
  * [85] Y. Zou, W. Liu, K. Wu, and L. M. Ni, “Wi-fi radar: Recognizing human behavior with commodity wi-fi,” _IEEE Communications Magazine_ , vol. 55, no. 10, pp. 105–111, 2017.
  * [86] L. Lubna, H. Hameed, S. Ansari, A. Zahid, A. Sharif, H. T. Abbas, F. Alqahtani, N. Mufti, S. Ullah, M. A. Imran _et al._ , “Radio frequency sensing and its innovative applications in diverse sectors: A comprehensive study,” _Frontiers in Communications and Networks_ , vol. 3, p. 1010228, 2022.
  * [87] Q. Huang, H. Chen, and Q. Zhang, “Joint design of sensing and communication systems for smart homes,” _IEEE Network_ , vol. 34, no. 6, pp. 191–197, 2020.
  * [88] C. Wu, B. Wang, O. C. Au, and K. R. Liu, “Wi-fi can do more: Toward ubiquitous wireless sensing,” _IEEE Communications Standards Magazine_ , vol. 6, no. 2, pp. 42–49, 2022.
  * [89] M. Abbas, M. Elhamshary, H. Rizk, M. Torki, and M. Youssef, “Wideep: WiFi-based accurate and robust indoor localization system using deep learning,” in _2019 IEEE International Conference on Pervasive Computing and Communications (PerCom_ , 2019, pp. 1–10.
  * [90] X. Chen, H. Li, C. Zhou, X. Liu, D. Wu, and G. Dudek, “Fidora: Robust WiFi-based indoor localization via unsupervised domain adaptation,” _IEEE Internet of Things Journal_ , vol. 9, no. 12, pp. 9872–9888, 2022.
  * [91] “Smart home security,” [Online]. Available: https://myhexhome.com/pages/hex-how-it-works (accessed Aug. 16, 2023).
  * [92] Q. Chen, B. Tan, K. Chetty, and K. Woodbridge, “Activity recognition based on micro-Doppler signature with in-home wi-fi,” in _2016 IEEE 18th international conference on E-Health networking, applications and services (Healthcom)_. IEEE, 2016, pp. 1–6.
  * [93] M. Ahmed, H. Hassan, A. Eldeeb, and T. Khattab, “Towards contactless remote health monitoring using ambient rf sensing,” in _2023 21st Mediterranean Communication and Computer Networking Conference (MedComNet)_ , 2023, pp. 135–142.
  * [94] T. Imamura, V. G. Moshnyaga, and K. Hashimoto, “Automatic fall detection by using Doppler-radar and lstm-based recurrent neural network,” in _2022 IEEE 4th Global Conference on Life Sciences and Technologies (LifeTech)_. IEEE, 2022, pp. 36–37.
  * [95] Q. Wan, Y. Li, C. Li, and R. Pal, “Gesture recognition for smart home applications using portable radar sensors,” in _2014 36th annual international conference of the IEEE engineering in medicine and biology society_. IEEE, 2014, pp. 6414–6417.
  * [96] E. Cardillo, C. Li, and A. Caddemi, “Radar-based monitoring of the worker activities by exploiting range-Doppler and micro-Doppler signatures,” in _2021 IEEE International Workshop on Metrology for Industry 4.0 & IoT (MetroInd4.0&IoT)_, 2021, pp. 412–416.
  * [97] R. Cupek, M. Drewniak, M. Fojcik, E. Kyrkjebø, J. C.-W. Lin, D. Mrozek, K. Øvsthus, and A. Ziebinski, “Autonomous guided vehicles for smart industries–the state-of-the-art and research challenges,” in _Computational Science–ICCS 2020: 20th International Conference, Amsterdam, The Netherlands, June 3–5, 2020, Proceedings, Part V 20_. Springer, 2020, pp. 330–343.
  * [98] T. M. Fernández-Caramés and P. Fraga-Lamas, “A review on human-centered IoT-connected smart labels for the industry 4.0,” _IEEE Access_ , vol. 6, pp. 25 939–25 957, 2018.
  * [99] G. Tavik, C. Hilterbrick, J. Evins, J. Alter, J. Crnkovich, J. de Graaf, W. Habicht, G. Hrin, S. Lessin, D. Wu, and S. Hagewood, “The advanced multifunction rf concept,” _IEEE Transactions on Microwave Theory and Techniques_ , vol. 53, no. 3, pp. 1009–1020, 2005.
  * [100] “Shared spectrum access for radar and communications (SSPARC),” [Online]. Available: https://www.darpa.mil/program/shared-spectrum-access-for-radar-and-communications (accessed Aug. 17, 2023).
  * [101] J. R. Guerci, R. M. Guerci, A. Lackpour, and D. Moskowitz, “Joint design and operation of shared spectrum access for radar and communications,” in _2015 IEEE Radar Conference (RadarCon)_ , 2015, pp. 0761–0766.
  * [102] D. Ma, N. Shlezinger, T. Huang, Y. Liu, and Y. C. Eldar, “Bit constrained communication receivers in joint radar communications systems,” in _ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)_ , 2021, pp. 8243–8247.
  * [103] N. Shlezinger, Y. C. Eldar, and M. R. Rodrigues, “Hardware-limited task-based quantization,” _IEEE Transactions on Signal Processing_ , vol. 67, no. 20, pp. 5223–5238, 2019.
  * [104] N. Shlezinger, Y. C. Eldar, and M. R. D. Rodrigues, “Asymptotic task-based quantization with application to massive MIMO,” _IEEE Transactions on Signal Processing_ , vol. 67, no. 15, pp. 3995–4012, 2019.
  * [105] S. Salamatian, N. Shlezinger, Y. C. Eldar, and M. Médard, “Task-based quantization for recovering quadratic functions using principal inertia components,” in _2019 IEEE International Symposium on Information Theory (ISIT)_. IEEE, 2019, pp. 390–394.
  * [106] P. Neuhaus, N. Shlezinger, M. Dörpinghaus, Y. C. Eldar, and G. Fettweis, “Task-based analog-to-digital converters,” _IEEE Transactions on Signal Processing_ , vol. 69, pp. 5403–5418, 2021.
  * [107] Z. Xu and A. Petropulu, “A bandwidth efficient dual-function radar communication system based on a MIMO radar using OFDM waveforms,” _IEEE Transactions on Signal Processing_ , vol. 71, pp. 401–416, 2023.
  * [108] K. Wu, J. A. Zhang, X. Huang, Y. J. Guo, and R. W. Heath, “Waveform design and accurate channel estimation for frequency-hopping MIMO radar-based communications,” _IEEE Transactions on Communications_ , vol. 69, no. 2, pp. 1244–1258, 2021.
  * [109] W. Baxter, E. Aboutanios, and A. Hassanien, “Dual-function MIMO radar-communications via frequency-hopping code selection,” in _2018 52nd Asilomar Conference on Signals, Systems, and Computers_ , 2018, pp. 1126–1130.
  * [110] M. F. Keskin, V. Koivunen, and H. Wymeersch, “Limited feedforward waveform design for OFDM dual-functional radar-communications,” _IEEE Transactions on Signal Processing_ , vol. 69, pp. 2955–2970, 2021.
  * [111] Y. Liu, G. Liao, Y. Chen, J. Xu, and Y. Yin, “Super-resolution range and velocity estimations with OFDM integrated radar and communications waveform,” _IEEE Transactions on Vehicular Technology_ , vol. 69, no. 10, pp. 11 659–11 672, 2020.
  * [112] J. Wei, J. Li, Z. Cao, Q. Chen, C. Song, and Z. Xu, “A passive radar prototype based on multi-channel joint detection and its test results,” in _2020 IEEE 11th Sensor Array and Multichannel Signal Processing Workshop (SAM)_. IEEE, 2020, pp. 1–5.
  * [113] X. Tong, X. Li, F. Dong, W. Wang, and A. Li, “Secrecy rate optimization for dual-functional radar-communication system with energy receiver,” _Transactions on Emerging Telecommunications Technologies_ , vol. 33, no. 12, p. e4617, 2022.
  * [114] R. Wen, Y. Zhang, Q. Li, Y. Tang _et al._ , “Joint secure communication and radar beamforming: A secrecy-estimation rate-based design,” _Wireless Communications and Mobile Computing_ , vol. 2022, 2022.
  * [115] F. Dong, W. Wang, X. Li, F. Liu, S. Chen, and L. Hanzo, “Joint beamforming design for dual-functional MIMO radar and communication systems guaranteeing physical layer security,” _IEEE Transactions on Green Communications and Networking_ , vol. 7, no. 1, pp. 537–549, 2023.
  * [116] A. R. Chiriyath, B. Paul, G. M. Jacyna, and D. W. Bliss, “Inner bounds on performance of radar and communications co-existence,” _IEEE Transactions on Signal Processing_ , vol. 64, no. 2, pp. 464–474, 2015.