# Deep Learning-based Target-To-User Association in Integrated Sensing and
Communication Systems

Lorenzo Cazzella, Marouan Mizmizi, Dario Tagliaferri, Damiano Badini, Matteo
Matteucci,
and Umberto Spagnolini

###### Abstract

In Integrated Sensing and Communication (ISAC) systems, matching the radar
targets with communication user equipments (UEs) is functional to several
communication tasks, such as proactive handover and beam prediction. In this
paper, we consider a radar-assisted communication system where a base station
(BS) is equipped with a multiple-input-multiple-output (MIMO) radar that has a
double aim: (i) associate vehicular radar targets to vehicular equipments
(VEs) in the communication beamspace and (ii) predict the beamforming vector
for each VE from radar data. The proposed target-to-user (T2U) association
consists of two stages. First, vehicular radar targets are detected from
range-angle images, and, for each, a beamforming vector is estimated. Then,
the inferred per-target beamforming vectors are matched with the ones utilized
at the BS for communication to perform target-to-user (T2U) association. Joint
multi-target detection and beam inference is obtained by modifying the you
only look once (YOLO) model, which is trained over simulated range-angle radar
images. Simulation results over different urban vehicular mobility scenarios
show that the proposed T2U method provides a probability of correct
association that increases with the size of the BS antenna array, highlighting
the respective increase of the separability of the VEs in the beamspace.
Moreover, we show that the modified YOLO architecture can effectively perform
both beam prediction and radar target detection, with similar performance in
mean average precision on the latter over different antenna array sizes.

###### Index Terms:

Radar-aided communications, Multi-target detection, Deep Learning, Target-to-
User association

##  I Introduction

INTEGRATED sensing and communication (ISAC) are poised to be a fundamental
technology for the forthcoming 6G era [1]. This revolutionary concept combines
advanced wireless communication capabilities with pervasive sensing, paving
the way for unprecedented levels of connectivity and intelligence in future
networks [2, 3, 4]. Moreover, exploiting higher frequency bands in 6G, e.g.,
millimeter waves (mmWaves), enables finer sensing resolutions, expanding
ISAC’s potential. This amalgamation propels advancements in domains such as
autonomous systems, smart cities, and healthcare, revolutionizing the
interaction with technology. The fusion of communication and sensing
transcends mere opportunity, becoming an imperative for harnessing the full
potential of 6G networks.

The design of ISAC technology consists of trading between sensing and
communication performance, leaning towards one or the other depending on the
target application. The complexity of the tradeoff depends on the level of
integration between the two functionalities [5], stemming from colocation,
where sensing and communication shares partially the hardware, to co-design,
where they share the same space-time-hardware resources. The work herein can
be framed within the communication-centric ISAC framework [1], where we
explore sensing as a secondary function to support communication for beam
management in a multi-vehicular scenario.

Beam management poses significant challenges that hinder the deployment of 5G
new radio (NR) at mmWave frequencies [6], which becomes even more complex when
considering Vehicle-to-Everything (V2X) applications [7]. Efficient beam
management is critical for maintaining reliable and stable connections in
dynamic environments. Factors such as link blockages [8] and multi-path
propagation create hurdles for beam alignment, tracking, and handover [9].

Beam management solutions encompass three main classification methods: blind
techniques (e.g., [7, 10]), side information-based methods (e.g., [11, 12]),
and ISAC approaches (e.g., [3, 4]). Blind solutions use pre-designed beam
training sequences and exploit the statistical properties of the channel to
estimate the optimal beamforming direction iteratively. However, blind
techniques introduce significant overhead and can be inefficient. Side
information techniques utilize the transmitter and receiver location
information for optimal beamforming direction estimation. While these methods
can be effective, they require a pre-established link for information sharing.

ISAC approaches have emerged as a promising alternative that attracted
significant attention recently. In the context of beam management, the authors
in [4] introduced radar-aided beam alignment in mmWave V2I communications
exploiting side information gathered from a radar mounted at the
infrastructure to select the beams of the communication system. A deep
learning-based beam prediction solution has been recently introduced in [3],
which studies the impact of different preprocessed raw radar
measurements—i.e., range-angle maps, range-velocity maps, and radar cube—on
the network predictive capabilities. The proposed method is evaluated on real-
world mmWave radar and communication data acquired in vehicular environments,
showing high accuracy, significant reduction in beam training overhead, and
leading performance when using range-angle radar maps as conditioning inputs.

To exploit radar sensing for beam management, two key steps must be addressed:
target detection (TD) and target-to-user (T2U) association. TD involves
distinguishing the relevant targets from the clutter in the received radar
image. On the other hand, the T2U association focuses on determining the
correspondence between the detected targets in the radar images and the
communication users. The association step is fundamental in establishing the
appropriate beamforming direction for each user based on the radar
information. By successfully addressing both TD and T2U association, radar
sensing can effectively contribute to efficient beam management in wireless
communication systems.

TD is a central and challenging problem in computer vision, playing a
fundamental role in several applications. A remarkable breakthrough in TD
performance has emerged with the proposal of region-based convolutional neural
network (R-CNN) architecture, which extracts hierarchical features from CNNs
and utilizes region proposals for TD [13]. R-CNN is a two-stage detector,
which (i) proposes a set of object bounding boxes, and (ii) predicts for each
proposed bounding box the presence of an object and its class. By contrast,
one-stage detectors, e.g., Single Shot Detector (SSD) [14] and YOLO [15],
complete the TD task in a single step. Fundamental milestones in two-stage
deep learning-based TD are represented by the introduction of spatial pyramid
pooling networks (SPPNet) [16], Fast R-CNN [17], Faster R-CNN [18], and
Feature Pyramid Networks (FPNs) [19].

The You Only Look Once (YOLO) architecture has been proposed in [15] as the
first single-stage object detection model. Renowned for its efficiency, the
YOLO model infers bounding boxes in parallel for separate image regions.
Nevertheless, it experiences lower localization accuracy compared to the two-
stage detectors. Several YOLO versions have been developed to overcome this
limitation, leading to the recently proposed YOLOv8 [20], which represents the
state-of-the-art model for both efficiency and accuracy. We refer the
interested reader to [21] for an exhaustive survey on TD models.

YOLO-based multi-target detection algorithms have been successfully applied to
radar sensing in the automotive field. A method for simultaneous detection and
classification of radar targets in automotive scenarios based on YOLOv3 is
proposed in [22]. In [23], the authors design a lightweight CNN leveraging
dense connections, residual connections, and group convolution and compose it
with the YOLO architecture to build a lightweight model for the detection of
marine ship objects in radar images, showing good mean average precision (mAP)
over two experimentally acquired datasets. A multi-data source YOLO-based TD
is in [24], where the authors fuse the information derived from a mmWave radar
and a camera to improve the detection performance.

The T2U association is a key operation in ISAC systems, but research in this
area remains limited. In realistic scenarios, T2U association poses
significant challenges due to: i) the presence of multiple users and targets,
potentially resulting in a non-empty set difference; ii) differing resolutions
in sensing and communication information—for example, sensing provides angle,
range, and Doppler, while communication yields beam and received power data;
iii) practical considerations, where vehicles, treated as extended targets,
undergo geometric distortions known as foreshortening and overlay [25] when
illuminated by a sensing apparatus positioned at heights of base station (BS).
These distortions introduce biases in target position estimation, leading to
mismatches between communication and sensing information. The most notable
works addressing this topic are [26, 27, 25]. In [26], the focus is on
sensing-aided vehicular communications, where the challenge lies in
associating vehicle ID with detected targets using radar and GPS data. The
authors utilize the Kullback-Leibler divergence as a similarity metric to
solve the constrained data association problem. Nevertheless, the accuracy and
reliability of the proposed approach can be affected by environmental factors
and by the need for an active low-rate uplink channel for GPS data exchange.
On the other hand, [27] proposes a different approach that overcomes the
aforementioned limitations. They utilize ISAC-only data for multi-vehicle
tracking and perform ID association based on the Kullback-Leibler divergence
between estimated and predicted vehicle states (range, velocity, and angle).
In a more recent work [25], the authors introduce reconfigurable intelligent
surfaces (RIS) mounted on vehicles’ roofs and strategically configured to
reflect the sensing signal towards the radar with a known pattern, enabling
accurate T2U association and improving TD.

The abovementioned works require additional hardware [25] or side information
[26]. The work in [27], instead, operates on the assumption of successful TD,
which is a particularly challenging task for extended targets in highly
dynamic scenarios. Differently from the current state of the art, in the
context of ISAC systems, our paper proposes a unified framework for multi-user
TD and T2U association to enhance beam management. Indeed, when the
association between observed radar target and communication equipment is known
at some time steps, beam prediction for a VE can be naturally conditioned on
the radar target.

In this paper, we propose the following contributions:

  * •

Considering a hybrid MIMO communication system and a mmWave MIMO radar, we
employ the latest version of the YOLO architecture (YOLOv8 [20]) to jointly
achieve real-time radar multi-target detection and analog beam prediction at
the BS for each detected radar target. We model the beam prediction problem as
a multi-class classification task over a fixed-size codebook of beamforming
vectors, and we integrate the beam classification within the YOLO prediction
heads. The resulting model is trained and evaluated over realistic simulated
radar range-angle images and accurate ray-tracing wireless channel data. We
show that YOLO achieves considerable detection and classification performance
on both radar target detection and beam prediction tasks.

  * •

Leveraging the beam prediction obtained from YOLOv8, and the beamforming
vectors selected for each VE at the BS, we tackle the radar target-to-user
(T2U) association problem in the beamspace, showing that the probability of
correct association significantly increases with the antenna array size at the
BS—which highlights the related increase in the separability of the VEs in the
beamspace required for effective association.

  * •

We design a framework for the simulation of radar images and wireless
communication channels at the communication infrastructure. Dynamic vehicular
simulations are achieved integrating the Simulation of Urban Mobility (SUMO)
[28] vehicular traffic simulator, and the EM simulation software Remcom
Wireless InSite [29] and Remcom WaveFarer [30]—used, respectively, for high-
fidelity wireless channel and radar channel simulations.

The paper is organized as follows: Section II presents the reference
communication system, channel model, and radar signal models; Section IV
introduces the proposed beamspace Target-to-User association method relying on
DL-based radar target detection and beam prediction; Section V details the
simulation framework and shows the achieved results, while Section VI reports
the conclusions.

### Notation

Matrices are denoted by bold upper-case letters, while lower-case letters
describe column vectors. $\mathbf{A}^{\mathrm{T}}$, $\mathbf{A}^{*}$,
$\mathbf{A}^{\mathrm{H}}$ and $\left\lVert\mathbf{A}\right\rVert$ indicate,
respectively, the matrix transpose, conjugate, conjugate transpose and
Frobenius norm. A Gaussian multi-variate circularly complex random variable
$\mathbf{a}$ is denoted With
$\mathbf{a}\sim\mathcal{CN}(\boldsymbol{\mu},\mathbf{C})$ with mean
$\boldsymbol{\mu}$ and covariance $\mathbf{C}$. $\mathbb{R}$ and $\mathbb{C}$
represent the sets of real and complex numbers, respectively.

##  II System Model

(a)

(b)

Figure 1: ISAC system with co-located mmWave radar sensor and communication
base station. (a) provides a front view representation of the system, showing
analog communication beams on the vertical direction at the BS, and
highlighting the radar slant-range plane used for radar imaging. (b) shows a
top view of the system, depicting analog communication beams on the horizontal
direction at the BS.

Let us consider the downlink ISAC system depicted in Fig. 1, where a BS is
equipped with a mmWave MIMO radar for sensing and a hybrid sub-connected MIMO
array for communication. Fig. 1 depicts the ISAC system over two different
views, highlighting the radar placement and the analog communication beams at
the BS. In the following, we detail the model of the communication system and
of the radar system.

###  II-A Communication system model

Figure 2: Hybrid MIMO sub-connected Tx. architecture.

We consider a hybrid mmWave MIMO system where the BS is equipped with a planar
antenna array with $N_{T}=N_{T}^{h}\times N_{T}^{v}$ antenna elements (along
horizontal and vertical directions, respectively) and $N_{T}^{\mathrm{RF}}$ RF
chains and is using $N_{S}$ data streams to communicate with $K$ VEs. Each VE
is equipped with a planar antenna array with $N_{R}=N_{R}^{h}\times N_{R}^{v}$
antenna elements and $N^{\mathrm{RF}}_{R}$ RF chains. A sub-connected hybrid
MIMO configuration is considered, where the antennas are grouped into sub-
arrays of $N_{T}^{B}=N_{T}/N_{T}^{\mathrm{RF}}$ and
$N_{R}^{B}=N_{R}/N_{R}^{\mathrm{RF}}$ antenna elements at the BS and at the
VEs, respectively. The transmitted $N_{S}$ complex-valued symbols are such
that $\mathbf{s}\in\mathbb{C}^{N_{S}\times
1}\sim\mathcal{CN}\left(\mathbf{0},\mathbf{I}_{N_{S}}/N_{S}\right)$, and they
are spatially precoded using the cascade of digital and analog precoders
$\mathbf{F}=\mathbf{F}_{\mathrm{RF}}\;\mathbf{F}_{\mathrm{BB}}$, where
$\mathbf{F}_{\mathrm{BB}}\in\mathbb{C}^{N^{\mathrm{RF}}_{T}\times N_{S}}$ is
the base-band digital precoder and
$\mathbf{F}_{\mathrm{RF}}\in\mathbb{C}^{N_{T}\times N^{\mathrm{RF}}_{T}}$ is
the RF analog counterpart, obtaining the time-discrete transmitted signal

$\mathbf{x}=\mathbf{F}\;\mathbf{s}.$ (1)

We assume analog precoding $\mathbf{F}_{\mathrm{RF}}$ implemented with phased
shifters. Hence, its elements are constrained to have the same norm, i.e.,
$[\mathbf{F}^{(i)}_{\mathrm{RF}}\mathbf{F}^{(i),\mathrm{H}}_{\mathrm{RF}}]_{k,k}=1/N_{T}$.
Moreover, the Tx total power constraint is enforced by designing
$\mathbf{F}_{\mathrm{BB}}$ such that
$\left\lVert\mathbf{F}_{\mathrm{RF}}\mathbf{F}_{\mathrm{BB}}\right\rVert^{2}=N_{S}$
[31]. In the sub-connected hybrid configuration, depicted in Fig. 2, the
analog precoding matrix $\mathbf{F}_{\mathrm{RF}}$ is block-diagonal

$\mathbf{F}_{\mathrm{RF}}=\begin{bmatrix}\mathbf{f}^{(1)}_{\mathrm{RF}}&\mathbf{0}&\cdots&\mathbf{0}\\\
\mathbf{0}&\mathbf{f}^{(2)}_{\mathrm{RF}}&\cdots&\mathbf{0}\\\
\vdots&\vdots&\vdots&\vdots\\\
\mathbf{0}&\cdots&\mathbf{0}&\mathbf{f}^{(N_{T}^{RF})}_{\mathrm{RF}}\end{bmatrix},$
(2)

where $\mathbf{0}\in\mathbb{C}^{N_{T}^{B}\times 1}$ is a vector with zero-
elements and $\mathbf{f}^{(n)}_{\mathrm{RF}}\in\mathbb{C}^{N_{T}^{B}\times
1}$, $n=1,\dots,N_{T}^{RF}$ denotes the precoding vector for the $n$-th Tx
sub-array.

After time-frequency synchronization, the received signal at the $k$th VE can
be expressed as

$\mathbf{y}_{k}=\mathbf{H}_{k}\mathbf{x}+\mathbf{n}_{k},$ (3)

where $\mathbf{H}_{k}\in\mathbb{C}^{N_{R}\times N_{T}}$ is the spatially
sparse and block-faded MIMO channel between the BS and the $k$th VE, while
$\mathbf{n}_{k}\sim\mathcal{CN}\left(\mathbf{0},\sigma_{n}^{2}\,\mathbf{I}_{N_{R}}\delta_{k-u}\right)$
denotes the additive white noise, spatially uncorrelated across the antennas
and among different VEs. The channel at mmWave follows the block-fading
spatially sparse model [32]:

$\mathbf{H}_{k}=\frac{1}{\sqrt{\rho_{k}}}\sum_{p=1}^{P}\;\alpha_{p}e^{j2\pi\nu_{p}t}\;\mathbf{a}_{UE}(\boldsymbol{\vartheta}_{p})\;\mathbf{a}_{BS}^{\mathrm{H}}(\boldsymbol{\varphi}_{p})$
(4)

where $\rho_{k}$ denotes the average power path-loss of the $k$th UE, $P$ is
the number of paths, $\alpha_{p}\sim\mathcal{CN}(0,\sigma_{p}^{2})$ denotes
the Rayleigh distributed complex amplitude of the $p$th path, such that
$\sum_{p}\sigma_{p}^{2}=1$, $\nu_{p}$ is the Doppler shift of the $p$th path,
$\boldsymbol{a}_{BS}$ and $\boldsymbol{a}_{UE}$ are, respectively, the BS and
UE antenna array response vectors, functions of directions of arrival
$\boldsymbol{\vartheta}_{p}$ and directions of departure
$\boldsymbol{\varphi}_{p}$.

At the receiver, the $k$th VE applies the cascade of analog and digital
combiners
$\mathbf{w}_{k}=\mathbf{W}^{k}_{\mathrm{RF}}\;\mathbf{w}^{k}_{\mathrm{BB}}$,
with $\mathbf{W}^{k}_{\mathrm{RF}}\in\mathbb{C}^{N_{R}\times
N^{\mathrm{RF}}_{R}}$ and
$\mathbf{w}^{k}_{\mathrm{BB}}\in\mathbb{C}^{N_{R}^{\mathrm{RF}}\times 1}$.
Similarly, the analog combiner $\mathbf{W}_{RF}$ is subject to the same
constraint of $\mathbf{F}_{RF}$, i.e.,
$[\mathbf{W}^{(j)}_{RF}\mathbf{W}^{(j),\mathrm{H}}_{RF}]_{l,l}=1/N_{R}$. The
received symbol can be expressed as

$\begin{split}\hat{s}_{k}&=\mathbf{w}_{k}^{\mathrm{H}}\;\mathbf{H}_{k}\;\mathbf{x}+\mathbf{w}_{k}^{\mathrm{H}}\;\mathbf{n}\\\
&=\mathbf{w}_{k}^{\mathrm{H}}\;\mathbf{H}_{k}\;\mathbf{f}_{k}\;s_{k}+\underbrace{\sum_{i\neq
k}\mathbf{w}_{k}^{\mathrm{H}}\;\mathbf{H}_{k}\;\mathbf{f}_{i}\;s_{i}}_{\mathrm{Intra-
Cell\,Interference}}+\underbrace{\mathbf{w}_{k}^{\mathrm{H}}\;\mathbf{n}}_{\mathrm{Noise}}\\\
\end{split}$ (5)

where $\mathbf{f}_{k}\in\mathbb{C}^{N_{T}\times 1}$ is the cascade of digital
and analog precoders of the $k$th UE. Herein, we propose a DL approach in the
ISAC context to predict analog precoders $\mathbf{F}_{RF}$. Derivation of
$\mathbf{F}_{BB}$, $\mathbf{W}_{BB},\mathbf{W}_{RF}$ is based on state-of-the-
art methods, e.g., [33].

###  II-B Radar signal model and image synthesis

We consider a frequency-modulated continuous wave (FMCW) MIMO radar at the BS
side. In the general case, the MIMO radar is equipped with $L_{\mathrm{Tx}}$
Tx antennas and $L_{\mathrm{Rx}}$ Rx ones, for a total of
$L=L_{\mathrm{Tx}}L_{\mathrm{Rx}}$ of virtual measurement channels (Tx-Rx
pairs). The 3D positions of the Tx and Rx antennas forming the $\ell$-th
channel are denoted by $\mathbf{p}_{\mathrm{Tx},\ell}$ and
$\mathbf{p}_{\mathrm{Rx},\ell}$, respectively. We assume that the MIMO radar
operates in time-division multiplexing, thus each Tx antenna emits a modulated
chirp signal, centered around carrier frequency $f_{0}$, of bandwidth $B_{s}$
and periodic by the pulse repetition interval (PRI) $T_{P}$ [34]111The
waveforms at the $L_{\mathrm{Tx}}$ Tx antennas are orthogonal in time, but we
drop the antenna index and the pulse delay among the antennas for simplicity.

$\displaystyle x_{s}(t)=\begin{cases}A\,e^{j(2\pi f_{0}t+\pi\mu t^{2})}&0\leq
t\leq T_{c}\\\ 0&T_{c}\leq t\leq T_{P}\end{cases}$ (6)

where $A$ is the amplitude of the Tx signal, $\mu=B_{s}/(2T_{c})$ denotes the
chirp rate, $T_{c}$ denotes the chirp duration, during which the carrier
frequency is linearly increased from $f_{0}$ up to $f_{0}+B_{s}$. Within the
coherent processing interval (CPI)222The CPI is defined as the time interval
within which the Doppler shift of the target (thus its velocity) does not
change, thus the Rx echoes can be coherently processed., the Rx signal for the
$\ell$-th measurement channel, pertaining to the $k$-th PRI, after
demodulation and mixing with the conjugate chirp $e^{-j(2\pi f_{0}t+\pi\mu
t^{2})}$, is:

$\begin{split}y^{k}_{\ell}(t)&=\sum_{q=1}^{Q}\underbrace{\beta^{k}_{q,\ell}\,e^{-j(2\pi
f_{0}\,\tau_{q,\ell}-\pi\mu\tau_{q,\ell}^{2}+2\pi\mu\tau_{q,\ell}t)}}_{s_{\ell}^{k}(t;\mathbf{p}_{q})}+z^{k}_{\ell}(t)\end{split}$
(7)

where (i) the number of targets in the environment is denoted by $Q$; (ii)
$\beta^{k}_{q,\ell}$ is the complex scattering amplitude the $q$th target,
comprising the path-loss, the reflectivity of the target (radar cross section,
RCS) and the target’s proper scattering phase (i.e., the phase modeling the
interaction of the EM wave with the target); (iii) $\tau_{q,\ell}$ is the two-
way delay from the Tx antenna to the target and back to the Rx antenna, while
(iv)
$z^{k}_{\ell}(t)\sim\mathcal{CN}(0,\sigma_{z}^{2}\delta_{\ell-m}\delta(t))$ is
the additive noise, uncorrelated in time and space (across channels). We
denote with $s_{\ell}^{k}(t;\mathbf{p}_{q})$, for convenience, the Rx signal
due to the $q$-th target located in $\mathbf{p}_{q}$. The delay is

$\tau_{q,\ell}=\frac{\|\mathbf{p}_{q}-\mathbf{p}_{\mathrm{Tx},\ell}\|+\|\mathbf{p}_{\mathrm{Rx},\ell}-\mathbf{p}_{q}\|}{c}.$
(8)

The model of the scattering amplitude is

$\beta^{k}_{q,\ell}=\sqrt{\frac{(4\pi)^{-4}\lambda_{0}^{2}G_{\ell}(\boldsymbol{\vartheta}_{q,\ell})G_{\ell}(\boldsymbol{\vartheta}_{q,\ell})}{\|\mathbf{p}_{q}-\mathbf{p}_{\mathrm{Tx},\ell}\|^{2}\|\mathbf{p}_{\mathrm{Rx},\ell}-\mathbf{p}_{q}\|^{2}}\Gamma_{q}}\;e^{j(\delta_{q}+2\pi\nu_{q}kT_{P})}$
(9)

where $\lambda_{0}=c/f_{0}$ is the carrier wavelength,
$G_{\ell}(\boldsymbol{\vartheta}_{q,\ell})$ is the power gain of the single
radar antenna element in the direction of the $q$th target
$\boldsymbol{\vartheta}_{q,\ell}$, $\Gamma_{q}$ is the radar cross section
(RCS) of the target, $\nu_{q}=2V_{q}/\lambda_{0}$ is the Doppler shift of the
$q$th target, the function of its radial velocity $V_{q}$ and
$\delta_{q}\sim\mathcal{U}[0,2\pi)$ is an additional random phase term
modeling unknown phase terms pertaining to the Tx/Rx circuitry as well as to
the target. In (7), the $q$th target manifests with a time-invariant term
comprising the propagation phase $2\pi f_{0}\tau_{q,\ell}$ as well as a
quadratic phase term w.r.t. the delay $-\pi\mu\tau_{q,\ell}^{2}$333The
quadratic phase term $-\pi\mu\tau_{q,\ell}^{2}$ is sometimes referred to as
”video phase” in the radar jargon, and it usually negligible for short-range
radars (up to few tens to a hundred of meters in range) compared to the
propagation phase [REF]. and a time-varying linear phase term whose frequency
is proportional to the delay $\tau_{q,\ell}$.

Radar image synthesis: The Rx data (7) is then processed to generate radar
images. A radar image is a 2D or 3D map of the complex reflectivity of the
environment, that shall be characterized by the highest possible resolution,
i.e., the capability of distinguishing two closely spaced point targets. The
image at the $k$ PRI is synthesized by back-projection (BP) on a pre-defined
grid of pixels $\\{\mathbf{x}\\}$. BP consists of a 2D correlation (over time
$t$ and channels $\ell=1,...,L$) between the gathered radar data
$y^{k}_{\ell}(t)$ and the theoretical (noiseless) response of a fictitious
target located in a given location in space $\mathbf{x}$, i.e.,
$s_{\ell}^{k}(t;\mathbf{x})$:

$I_{k}(\mathbf{x})=\sum_{\ell}\int_{T_{P}}y^{k}_{\ell}(t)s_{\ell}^{k,*}(t;\mathbf{x})\;dt$
(10)

where $I_{k}(\mathbf{x})\in\mathbb{C}$ denotes the complex image value at
pixel $\mathbf{x}$. The BP technique for image synthesis is based on the
wavefield migration integral extensively used in remote sensing to find the
location of one or more targets [35], and it describes the matched filtering
operation along space and time of the environment composed of $Q$ point
scatteters.

The image formation procedure (10) is split into range compression (RC) and
focusing. Range compression is the matched filter along time, and, for FMCW
radars, it consists of (i) a Fourier transform over time (ii) a frequency
scaling factor $f=\mu t$ (iii) a phase rotation to remove the video phase
$e^{-j\pi\mu\tau^{2}}$. The RC Rx signal is:

$\begin{split}y^{k}_{\mathrm{RC},\ell}(t)&=\int_{T_{P}}y^{k}_{\ell}(t)e^{-j2\pi
ft}\,dt\bigg{\rvert}_{f=\mu t}\times e^{j\pi\mu t^{2}}=\\\
&=\alpha\sum_{q=1}^{Q}\beta^{k}_{q,\ell}\,\mathrm{sinc}\left[B_{s}(t-\tau_{q,\ell})\right]e^{-j2\pi
f_{0}\tau_{q,\ell}}+n_{\ell}^{k}(t)\end{split}$ (11)

where $\alpha=T_{c}B_{s}A$, $\mathrm{sinc}[x]=\sin(\pi x)/(\pi x)$ and
$n_{\ell}^{k}(t)$ denotes the noise after RC. The result by (11) is a linear
combination of scaled ad delayed sinc pulses, multiplied by the propagation
phase term $e^{-j2\pi f_{0}\tau_{q,\ell}}$. After RC, focusing refers to the
matched filtering along space, i.e., the available measurement channels. The
image $I_{k}(\mathbf{x})$ is finally formed as:

$\begin{split}I_{k}(\mathbf{x})&=\sum_{\ell}y^{k}_{\mathrm{RC},\ell}(t=\tau_{\ell}(\mathbf{x}))\,e^{+j2\pi
f_{0}\tau_{\ell}(\mathbf{x})}\\\ &\simeq\alpha
L\sum_{q=1}^{Q}\widetilde{\beta}_{q}^{k}\,H_{q}(\mathbf{x}-\mathbf{p}_{q})+W_{k}(\mathbf{x})\end{split}$
(12)

where (i) $\widetilde{\beta}_{q}^{k}$ is the complex amplitude of the $q$-th
target in the final image, (ii) the two-way delay between $\ell$-th channel
and pixel location $\mathbf{x}$ is

$\tau_{\ell}(\mathbf{x})=\frac{\|\mathbf{x}-\mathbf{p}_{\mathrm{Tx},\ell}\|+\|\mathbf{p}_{\mathrm{Rx},\ell}-\mathbf{x}\|}{c}$
(13)

(iii) $H_{q}(\mathbf{x})$ is the spatial signature of the $q$-th target
evaluated over the grid of pixels $\\{\mathbf{x}\\}$ while (iv)
$W_{k}(\mathbf{x})$ is the noise in the spatial domain444$H_{q}(\mathbf{x})$
is sometimes referred to as spatial impulse response function, meaning the
image of a point target (impulse in the spatial domain) obtained with a
specific setup, i.e., array aperture and employed bandwidth. For monostatic
setups with linear arrays of antennas, $H(\mathbf{x})$ is the mapping in
Cartesian coordinates of a 2D sinc in polar coordinates (range and angle).. BP
is a generalization of the conventional DFT-based image synthesis, accounting
for any curvature of the wavefront and employed bandwidth, thus it is
inherently suited for image synthesis when employing very large arrays, wide
bandwidths, and/or non-regular array geometries. Moreover, differently from
DFT-based image synthesis, that provides the image in range-angle(s) domain,
BP allows choosing the pixel grid $\\{\mathbf{x}\\}$ on which to generate the
image, accomplishing different imaging possibilities (on both slant planes,
i.e., tilted as the radar, and/or ground-level planes). The BP consists of
three steps: 1) interpolation of RC sampled data in
$t=\tau_{\ell}(\mathbf{x})$, 2) a phase rotation to compensate for the carrier
propagation phase by $e^{+j2\pi f_{0}\tau_{\ell}(\mathbf{x})}$ and 3) the
summation (integration) over the available measurement channels. Image (12),
as any matched filter, can be also cast as an operation that provides the
likelihood of the targets’ positions in space, from which it follows their
estimation by maximum likelihood approaches as described in [36].

##  III YOLO-based Multi Target Detection

YOLOv8 [20] is a real-time multi-target detection and classification model. It
has proven an extremely flexible architecture providing state-of-the-art
performance over complex target detection benchmarks. The architecture is
proposed in multiple model scales that flexibly adapt to heterogeneous
application scenarios. YOLOv8 relies on the successful architectures of the
previous YOLO versions and introduces new advancements to improve performance
and flexibility [20]. As a result, it leads to state-of-the-art detection and
classification accuracy while keeping real-time prediction performance. Its
architecture is depicted in Fig. 3 and can be decomposed into backbone, neck,
and prediction heads.

Backbone: The objective of the YOLOv8 backbone is to perform feature
extraction from the input image. It leverages Cross-Stage Partial (CSP)
connection blocks [37] to improve the CNN performance and lower the
computational complexity. YOLOv8 introduces the C2f module, improving YOLOv5’s
C3 module by means of the ELAN design adopted also in [38]. Moreover, YOLOv8
reduces the number of blocks in each stage and the last backbone stage uses
the SPPF module, an improved version of SPP [16].

Neck: YOLOv8 performs a multi-scale fusion of features by means of Feature
Pyramid Network (FPN) [19] and Path Aggregation Network (PAN) [39]
architectures, introduced to counteract the reduction in object location
information emerging in deep convolutional networks, and the information loss
over small objects resulting from the high number of convolution operations.
As presented in Fig. 3, the architecture neck fuses features learned at
different scales.

Figure 3: YOLOv8 architecture utilized for target class and beam indices
prediction (upper-left block). The remaining blocks expand the layer
components depicted in the architecture graph. Conv2D denotes a 2-dimensional
convolution, BN indicates batch normalization, U describes an upsampling
layer, and SiLU represents a Sigmoid Linear Unit activation function.

Head: YOLOv8 is anchor-free, i.e., it directly infers the bounding boxes’
centers instead of the offset from the center of a known anchor box. Each
prediction head is further split into two separate branches for detection and
classification. In Fig. 3, the two separate prediction heads are shown within
the Detection sub-module. The YOLO architecture proposes a set of detection
bounding boxes and, for each of them, the inferred object classes. During
model training, the matching of the model predictions to the ground truth
values is performed by means of the Task Aligned Assigner proposed in [40],
which evaluates the alignment between inferred information and target labels
relying on the weighted scores of bounding box regression and targets
classification:

$a=p^{\lambda}\cdot r^{\mu},$ (14)

where $p$ is the predicted score for the label target class, $r$ is the
intersection-over-union (IoU) score between the predicted bounding box and the
ground truth one, and $\lambda$, $\mu$ are tunable hyperparameters. At
inference time, the inferred bounding boxes are post-processed using Non-
Maximum Suppression (NMS), aimed at merging bounding boxes that may belong to
the same object. NMS is a fundamental step in modern object detection
algorithms to improve the detection performance.

The YOLOv8 model is divided into multiple detection branches operating on
representations learned from the input image at different scales, to be able
to detect objects of different sizes in the image and to allow effective
processing of images of different sizes. Each branch is, in turn, split into
separate regression and classification heads. The classification heads employ
the binary cross-entropy (BCE) loss

$\mathcal{L}_{BCE}=-w(y_{n}\log x_{n}+(1-y_{n})\log(1-x_{n})),$ (15)

where $w$ is the weight, $y_{n}$ is the labelled value, and $x_{n}$ if the
value predicted by a YOLOv8 classification head. The BCE loss is commonly used
for multi-class classification as it deals with the targets’ classes
separately and allows to provide during inference a classification score for
each possible class

Bounding box regression heads are endowed with Distribution Focal Loss (DFL)
and Complete IoU (CIoU) losses. Focal loss accounts for the class imbalance
problem common in object detection tasks. Distribution Focal Loss [41] is a
special case of Generalized Focal Loss, which has been shown to flexibly model
the underlying distribution of bounding boxes, leading to more informative and
accurate bounding box locations. DFL aims to focus on enlarging the
probabilities of the values around target $y$ (i.e., $y_{i}$ and $y_{i+1}$).
It is defined by

$\mathcal{L}_{DFL}(P_{i},P_{i+1})=-((y_{i+1}-y)\log(P_{i})+(y-y_{i})\log(P_{i+1})),$
(16)

with

$P_{i}=\frac{y_{i+1}-y}{y_{i+1}-y_{i}};\;P_{i+1}=\frac{y-y_{i}}{y_{i+1}-y_{i}}.$
(17)

We refer the reader to [41] for an extensive description of DFL and its
derivation from the Generalized Focal Loss continuous framework.

Complete IoU (CIoU) and Distance IoU (DIoU) metrics have been recently
introduced in [42] as a possible solution to the slow convergence and
inaccurate regression problems of IoU and generalized IoU (GIoU) losses. DIoU
incorporates the normalized distance between the centers of the predicted and
the ground truth bounding boxes, showing much faster convergence in training
concerning IoU and GIoU losses. CIoU considers in addition the aspect ratios
of the predicted and target boxes, leading to still faster convergence and
better performance. CIoU is defined by

$\mathcal{L}_{CIoU}=1-IoU+\frac{d^{2}(\mathbf{b},\mathbf{b}^{gt})}{c^{2}}+\alpha
v,$ (18)
$v=\frac{4}{\pi^{2}}\left(\arctan\frac{w^{gt}}{h^{gt}}-\arctan\frac{w}{h}\right)^{2},$
(19) $\alpha=\frac{v}{(1-IoU)+v},$ (20)

where $d(\mathbf{b},\mathbf{b}^{gt})$ is the Euclidean distance between the
central points of bounding boxes $B$ and $B^{gt}$, $c$ is the diagonal length
of the smallest enclosing box covering the two boxes, $v$ compares the
predicted and target bounding boxes aspect ratios, and $\alpha>0$ is a
parameter giving higher relevance to the overlap area factor.

##  IV Proposed method

Figure 4: Proposed method for the integration of deep learning-based radar
multi-target detection and beam prediction aimed at T2U association. A
sequence of RA radar images is provided to a modified YOLOv8 model to jointly
infer radar targets’ positioning and classification information and the per-
target beamforming vectors’ classes. The predicted beam indices are then
matched with the ones used at the BS to perform T2U association.

In this section, we provide an overview of the proposed method for the
integration of deep learning-based radar multi-target detection and beam
prediction aimed at T2U association. The proposed method is sketched in Fig.
4. To clarify the aim of the depicted pipeline, we here briefly describe the
proposed processing steps. The system inputs are radar range-angle (RA) image
and a set of analog precoding beamforming vectors $\mathbf{f}$ selected at the
BS for each vehicular target in the scene. The two inputs are assumed to be
synchronized. In the following, we assume that the targets are vehicles
crossing the scenario and that each vehicle is equipped with a VE as described
in Section II-A. Hence, we investigate the identification of radar targets
within RA images, the distinguishability of the corresponding VEs in the
beamspace, and the association of radar targets to VEs. A description of the
considered hybrid sub-connected communication architecture is provided in
Section II-A, along with a specification of the considered analog beamforming
codebook. We refer the reader to Section V for a thorough description of the
simulation framework, post-processing steps, and radar RA images generation.

For radar target detection, we consider the latest version of the YOLO deep
learning model, i.e., YOLOv8 [20], detailed in Section III. We integrated the
YOLOv8 model to simultaneously infer targets’ bounding boxes, classes, and
analog beam indices, as detailed in Section IV-A. To perform T2U association,
the analog codebook beam indices inferred through YOLOv8 are compared with the
beam indices observed during communication, as detailed in Section IV-B.

###  IV-A Deep Learning-based Joint Beam Prediction and Radar Multi-Target
Detection

####  IV-A1 Radar multi-target detection

We consider the problem of multi-target detection of vehicular radar targets
over radar images. Range-Angle (RA) images have been shown in [3] to enhance
beam prediction accuracy with respect to radar cube (i.e., tensors aggregating
radar RA images at different velocity values) or Range-Velocity maps data,
highly reducing computational complexity with respect to radar cube inputs
owing to the considerably lower data dimensions. Therefore, in the following,
we consider sequences of RA radar images as inputs to the YOLOv8 model.

We denote the sequence of contiguous input radar RA images by $I_{t}$, where
$t=1,\cdots,T$ indicates the sampling time step and $T$ is the total number of
RA radar images in the sequence. Each vehicular target $k$ is represented by
its bounding box $B_{t,k}$, and its class $c_{t,k}\in 1,\cdots,C$, with $C$
denoting the total number of target classes. We will refer to generic bounding
boxes by omitting the time and object subscripts. In this paper, we consider
three different vehicular target classes ($C=3$), i.e., sedan, hatchback, and
truck. A bounding box is described by $B_{t,k}=(x,y,w,h)$, where $(x,y)$ are
the bounding box center coordinates, $w$ and $h$ are, respectively, the
bounding box width and height within the image, and $k$ indexes an object in
the radar image. Bounding box center position, width, and height are assumed
to be normalized with respect to the radar image $I_{t}$ dimensions, i.e.,
$x,y,w,h\in[0,1]$.

####  IV-A2 Beam prediction

We discretize the analog beam prediction problem as the inference of the beam
index within a fixed-size beamforming codebook, whose features are specified
in Section II-A. Therefore, the analog beam prediction problem can be
naturally defined as a multi-class classification problem over the set of
indices of the vectors within the precoding analog beamforming codebook. We
denote with $(f_{t,k}^{h},f_{t,k}^{v})$ the indices within the horizontal and
vertical beamforming codebooks of the beamforming vectors
$(\mathbf{f}_{t,k}^{h},\mathbf{f}_{t,k}^{v})$, used by the BS for analog
precoding towards its VE, where $f_{t,k}^{h}\in 1,\cdots,N_{T}^{h}$,
$f_{t,k}^{v}\in 1,\cdots,N_{T}^{v}$, and $N_{T}^{h}$, $N_{T}^{v}$ is as
described in Section II-A. In the following, we will refer to these indices as
beam indices.

In the YOLOv8 model, the classification head output is extended to contain the
beam indices’ classes besides the vehicular target classes. The beamforming
codebook can be split into two separate codebooks over the horizontal and
vertical antenna array directions. Therefore, we divide the beam prediction
choice over the horizontal beam indices
$\\{f_{i}^{h}\\}_{i=1,\cdots,N_{T}^{h}}$ and vertical beam indices
$\\{f_{j}^{v}\\}_{j=1,\cdots,N_{T}^{v}}$. The resulting total number of
additional beam prediction classes per object is

$C_{beam}=N_{T}^{h}+N_{T}^{v}$ (21)

instead of $N_{T}^{h}\cdot N_{T}^{v}$ of the whole beamforming vectors when
the array horizontal and vertical directions are jointly considered. This
considerably reduces the computational effort by indexing each beamforming
vector through the inferred horizontal and vertical coordinates, i.e.,

$\mathbf{f}_{\hat{i},\hat{j}}=\mathbf{f}_{\hat{i}}^{h}\otimes\mathbf{f}_{\hat{j}}^{v},$
(22)

where $\hat{i}=\hat{f}^{h}$ and $\hat{j}=\hat{f}^{v}$ are, respectively, the
inferred horizontal and vertical beam indices, and the analog precoding
beamforming vector is provided by the Kronecker product of the beamforming
vectors over the horizontal and vertical array directions, respectively.

We assume that a set of ground truth azimuth and elevation beam prediction
labels are collected for training at the BS and that the matching between beam
prediction labels and sensed radar targets is known. In the simulation results
proposed in Section V, this is achieved by matching the ray-tracing wireless
channel and radar sensing simulations. In a real deployment, the same result
may be achieved by collecting synchronized wireless channels and positioning
information from cooperative vehicles crossing the urban scenario in the
neighborhood of the BS.

We consider the BCE loss in eq. (15) to perform optimization over both target
classes and beam prediction classes. Then, the total number of classes becomes
$C=C_{target}+C_{beam}$. The most relevant target classes and beam prediction
classes are separately determined by applying a threshold $\gamma_{class}$ on
the inferred classification scores.

We notice that, with respect to position-based methods proposed in the
literature, e.g., [12], the proposed method based on the YOLOv8 architecture
end-to-end optimizes the beam prediction task considering the whole radar
image as conditioning input and, therefore, the joint knowledge of the objects
present in the image. Then, both global information on relative positioning of
the perceived targets and local details on their state are available for the
inference of the beam indices at the BS. This provides the possibility to take
into account also anomalous conditions—e.g., dynamic blockage—that may depend
on relative vehicular motion patterns, or to predict the availability of relay
communication links that can be used when no line-of-sight (LoS) links are
available.

###  IV-B Beamspace T2U Association

We propose here to associate radar targets to VEs in the beamspace leveraging
the knowledge of the precoding beam indices selected for communication at the
BS and the per-target beam indices inferred through the YOLOv8 architecture
described in Section IV-A.

Considering a fixed observation time step, the selected horizontal and
vertical beam indices for a VE are denoted, respectively, by one-hot encoded
vectors $\textbf{y}^{h}\in\\{0,1\\}^{N_{T}^{h}}$, and
$\textbf{y}^{v}\in\\{0,1\\}^{N_{T}^{v}}$. The beam indices
$\hat{\mathbf{y}}^{h}\in\mathbb{R}^{N_{T}^{h}}$ and
$\hat{\mathbf{y}}^{v}\in\mathbb{R}^{N_{T}^{v}}$ represent the beam prediction
logits output from the YOLOv8 classification head for the detected radar
targets. The classification scores are processed by a softmax function

$\sigma(\mathbf{z})_{i}=\frac{e^{\mathbf{z}_{i}}}{\sum_{j=1}^{N}e^{\mathbf{z}_{j}}}$
(23)

to transform the output logits into discrete probability distributions over
the horizontal and vertical codebook beam indices. The selected beam indices
and the predicted ones are then compared by means of categorical cross-
entropy:

$\mathcal{L}_{CCE}=-\sum_{i=1}^{N_{T}^{h}}\mathbf{y}_{i}^{h}\log\sigma(\hat{\mathbf{y}}_{i}^{h})-\sum_{j=1}^{N_{T}^{v}}\mathbf{y}_{j}^{v}\log\sigma(\hat{\mathbf{y}}_{j}^{v}),$
(24)

where the softmax function $\sigma$ in the two sums is computed over
$N_{T}^{h}$ and $N_{T}^{v}$ classes, respectively.

In this context, the BCE loss is used as a metric to build the association
cost matrix $C^{T2U}$. The resulting assignment problem is represented by the
following linear minimization problem:

$\min_{X}\sum_{k=1}^{K}\sum_{v=1}^{V}C_{k,v}^{T2U}X_{k,v},\\\ $ (25)

where $X_{k,v}\in\\{0,1\\}$ represents an element of the assignment matrix
$X\in\mathbb{R}^{K\times V}$, $K$ is the total number of detected radar
targets, and $V$ is the total number of active VEs at the observation time
step. The linear assignment problem (25) is then solved by means of the
Hungarian algorithm.

The performance of T2U association is evaluated in terms of the probability of
correct association between radar targets and VEs, provided by the ratio of
correctly performed associations over the total number of targets in the scene
averaged over simulation time steps.

##  V Simulation results

In this section, we present the simulation results achieved by the proposed
methods. After introducing the utilized V2X channel simulation and radar
imaging framework, we present the results achieved over the tasks of radar
multi-target detection, beam prediction, and beamspace T2U association.

TABLE I: Simulation parameters Task | Parameter | Value
---|---|---
Ray-tracing communication channel | BS carrier frequency |  $28$ GHz
Communication bandwidth |  $100$ MHz
BS height from the ground |  $5$ m
VEs height from vehicles’ rooftops |  $0.2$ m
Max. reflection, diffraction, scattering | $(7,6,1)$
| Number of ray-tracing paths | $25$
Ray-tracing sensing channel | Radar carrier frequency |  $28$ GHz
Radar bandwidth |  $800$ MHz
Radar height from the ground |  $5$ m
Max. reflection, diffraction | $(2,1)$
Number of ray-tracing paths | $2\cdot 10^{5}$
Number of azimuth antennas | $128$
Number of elevation antennas | $4$

For simulations in vehicular environments, we selected the three urban
scenarios depicted in Fig. 6. Below each scenario, we report a RA radar
imaging sample acquired during vehicles motion. The chosen scenarios lead to
different traffic vehicular patterns: in Scenario A, the ISAC system laterally
observes a single road bidirectionally crossed by multiple vehicles; Scenario
B contains a roundabout, which includes rotational motion patterns that are
not present in the simplified Scenario A; Scenario C contains both
intersections and curved trajectories, resulting in different vehicle motion
patterns with respect to Scenarios A and B.

###  V-A Simulation framework

The developed simulation framework is depicted in Fig. 5, which highlights the
utilized simulation software and its use in relation to the tasks examined in
this paper. Table I shows the simulation parameters selected for the three
chosen scenarios. We detail here the simulation workflow depicted in Fig. 5.

Data acquisition and pre-processing: Building structures and road traffic
networks data are exported from OpenStreetMap[43] for the selected urban
scenarios depicted in Fig. 6. The collected map data are post-processed
through the Blender [44] 3D modeling software and the Blender-OSM [45] plugin
to extract the buildings’ 3D structures required for wireless propagation
simulations. We considered three different vehicle types, i.e., sedan,
hatchback, and truck, which have varied geometric features and impact
differently on wireless propagation.

Vehicular traffic simulation: Vehicular traffic networks are extracted from
the OpenStreetMap data and a set of realistic vehicular trajectories is
generated for each scenario by means of the Simulation of Urban Mobility
(SUMO) microscopic vehicular traffic simulator [28]. Random generation of
vehicular traffic has been defined by selecting the vehicles’ density per lane
km to obtain a regular traffic flow through the networks. Vehicles have been
generated at the fringe of the maps and crossed the scenarios according to
randomly generated routes. For each discrete simulation time step $t$, and for
each simulated vehicle at time $t$, we collected information on the state of
the vehicle, i.e., position, heading angle, and speed. Vehicular traffic
simulations have been performed using a simulation time step of $0.1$ s, with
a simulation duration of $60$ s for each considered scenario.

Figure 5: Communication and sensing channel simulation framework.

Communication channel simulation: The mmWave communication channel has been
simulated using Remcom Wireless InSite [29]. Owing to channel sparsity in the
space and time domains, ray-tracing is one of the most accurate techniques for
the simulation of propagation environments at high frequencies [46]. Indeed,
electromagnetic (EM) propagation at mmWaves strictly depends on the
geometrical features of the environment and is widely explained by a few
different types of physical interactions with the environment, including
reflection, refraction, diffraction, transmission, and scattering.

Frame-by-frame dynamic simulation is achieved by changing the position and
orientation of the vehicles’ 3D meshes within the Wireless InSite 3D
environment according to the vehicular trajectories generated by SUMO. We
consider a VE on the rooftop of each simulated vehicle while the BS is
positioned as represented in Fig. 6. Isotropic antennas are set for both the
BS and the VEs to collect the rays from the BS to the VEs over the simulation
time steps. For each VE and for each simulated ray-tracing path, we collect
from Remcom Wireless InSite the direction of departure (DoD), direction of
arrival (DoA), received power, phase, and delay. We report the communication
channel simulation parameters in Table I.

Figure 6: Considered urban scenarios (top row) with FOV of the radar
sensor—represented as a shaded area,—and radar image samples (bottom row)
showing vehicular targets crossing the scenario. Bounding boxes indicate the
vehicles’ positions and extensions within the radar images.

Analog precoding beam training: The analog beamforming vectors to be selected
for communication, among the ones in the precoding codebook, are determined
through a beam training procedure exhaustively spanning the combinations of Tx
and Rx beams. During simulations, VEs are equipped with a $2\times 2$
rectangular antenna array lying on the vehicle rooftop, while rectangular
antenna arrays from $2\times 2$ to $64\times 64$ antennas are considered at
the BS. Beam training is performed in different signal-to-noise ratio (SNR)
per antenna conditions, starting from -55 dB to -10 dB. The YOLO-based beam
prediction method proposed in Section IV is trained over analog precoding beam
indices determined at -10 dB SNR per antenna, while the performance of the
model is examined over all the considered communication SNRs range.

Radar sensing channel simulation: The mmWave radar sensing channel has been
simulated by means of Remcom WaveFarer [30]. Differently from Remcom Wireless
InSite—which simulates the leading propagation paths for communication channel
modeling purposes,—Remcom WaveFarer generates a high number of propagation
paths to achieve the resolution required for accurate radar sensor simulation
at high frequencies. As for the communication channel simulation, we perform a
frame-by-frame ray-tracing simulation moving vehicles according to the
trajectories generated by means of SUMO. Separate EM materials are assigned to
different vehicle parts to increase the radar sensing simulation accuracy
(i.e., PEC for vehicle body and rims, glass for windows, and rubber for
tires). Besides direction of departure (DoD), direction of arrival (DoA),
received power, phase, and delay, we collect from Remcom WaveFarer the
positions of the interaction points of the propagation rays with the
environment. The sensing channel simulation parameters are reported in Table
I.

Radar targets’ bounding boxes computation: Since the radar sensing channel can
be enriched by a variety of interactions with the environment (e.g., owing to
reflections and diffractions), it is crucial to effectively distinguish a
radar target from the environment and provide a suitable definition of the
object’s boundaries. In a radar image, this task is not as immediate as for
camera images owing to the different image formation process. Indeed, the
transmitted radar signal can undergo multiple interactions with the
propagation environment, resulting in distortions of target images. We employ
a heuristic approach to determine these boundaries exploiting the availability
of detailed propagation information from the Remcom WaveFarer sensing channel
simulator. Therefore, we divide the bounding boxes computation into three
steps:

  1. 1.

Identification of the interaction points lying on the target or strictly
related to the latter, achieved evaluating the orthogonal distance of the
wireless propagation interaction points with respect to the vehicle oriented
3D mesh and selecting the points belonging to the related propagation rays
(derived from the WaveFarer ray-tracing procedure).

  2. 2.

Filtering of the identified points by power and by target distance, where the
filtering is applied to take into consideration interaction points near to the
target that are sufficiently important (e.g., near-to-target ground
reflections); this phase allows to include points that can be relevant for the
detection training process but do not extend the bounding box to non-
representative target dimensions.

  3. 3.

Spherical projection onto the radar slant-range plane of the filtered points
and generation of the bounding box enclosing the projected points.

###  V-B Radar Multi-Target Detection and Beam Prediction

We present here the results obtained performing radar multi-target detection
by means of YOLOv8 using 5-fold cross-validation. Results are averaged among
the three considered scenarios depicted in Fig. 6. Radar target detection has
been performed from $512\times 512$ RA radar images. As described in Section
IV-A, we jointly perform radar target detection and analog beam prediction for
each detected target. We selected YOLOv8 small model size (YOLOv8s) as a
trade-off between detection/classification performance and real-time
efficiency. The fixed-size model performance is examined over a selection of
rising planar array dimensions at the BS, resulting in increasing beamforming
resolution and number of beam indices for classification. We trained the
YOLOv8s models on a Linux server accelerated by NVIDIA RTX 6000 GPUs. Training
has been performed according to the hyperparameters specified in Table IV.
Early stopping after a patience window of $50$ epochs has been considered. The
trained models converged activating the early stopping condition within $300$
epochs.

Table II reports the detection and classification performance of the trained
YOLOv8 model for different rectangular antenna array sizes at the BS. The
array sizes are indicated in the form $N_{T}^{h}\times N_{T}^{v}$. The antenna
array size determines the size of the codebooks for analog precoding along the
horizontal and vertical antenna array dimensions, as reported in Section II-A.
The classification performance is shown in terms of the precision, recall, and
F1 metrics. Detection performance is measured by mean average precision with
an IoU threshold of $0.5$ (mAP50), and by the mean of mean average precision
mAP50-95 determined by averaging mAP at $10$ different IoU thresholds between
$0.5$ and $0.95$ (extremes included). The detection and classification
performance is provided over both the radar targets classification task (i.e.,
whether the vehicular targets belong to the sedan, hatchback, or truck
classes) and on beam prediction.

TABLE II: Mutli-target detection performance on the three considered scenarios (5-fold cross-validation) for a selection of antenna array sizes at the BS. Precision, recall and F1-score provide the classification performance, while mAP50 and mAP50-95 account for both classification and detection. The metrics are separately evaluated on the targets classification and beam prediction tasks. | Targets classification | Beam prediction
---|---|---
Array size | Precision | Recall | F1 | mAP50 | mAP50-95 | Precision | Recall | F1 | mAP50 | mAP50-95
$2\times 2$ | 0.90 | 0.78 | 0.80 | 0.92 | 0.79 | 0.91 | 0.79 | 0.81 | 0.92 | 0.79
$4\times 4$ | 0.90 | 0.76 | 0.78 | 0.90 | 0.76 | 0.84 | 0.70 | 0.69 | 0.86 | 0.73
$8\times 8$ | 0.89 | 0.77 | 0.79 | 0.89 | 0.76 | 0.80 | 0.70 | 0.69 | 0.84 | 0.71
$16\times 16$ | 0.88 | 0.77 | 0.79 | 0.89 | 0.76 | 0.76 | 0.65 | 0.63 | 0.79 | 0.67
$32\times 32$ | 0.89 | 0.77 | 0.79 | 0.90 | 0.77 | 0.73 | 0.61 | 0.58 | 0.74 | 0.64
$64\times 64$ | 0.88 | 0.79 | 0.81 | 0.89 | 0.77 | 0.69 | 0.55 | 0.51 | 0.67 | 0.59

(a)  (b)  (c)  (d)

(e)  (f)  (g)  (h)

Figure 7: YOLOv8 detection and classification 5-fold cross-validation performance over radar target classification (top row) and beam prediction (bottom row). Results are provided in terms of precision/recall, precision/confidence, recall/confidence and F1-score/confidence curves for a selection of antenna array sizes at the BS. TABLE III: Comparison of the YOLOv8s, Faster R-CNN and SSD object detection models over scenario C (Fig. 6). Detection model | Precision | Recall | mAP50 | mAP50-95
---|---|---|---|---
YOLOv8s | 0.96 | 0.77 | 0.89 | 0.70
Faster R-CNN | 0.83 | 0.88 | 0.82 | 0.66
SSD | 0.79 | 0.90 | 0.79 | 0.53

We provide in Table III a performance comparison of the selected YOLOv8s model
with two widespread deep learning-based object detection models, i.e., Faster
R-CNN [18] and SSD [14], over the radar vehicular target detection and
classification task. We select a ResNet101[47] pre-trained backbone and an FPN
neck for the Faster R-CNN model, while the SSD model is equipped with a pre-
trained VGG16 [48] backbone. We notice that, while Faster R-CNN is a two-stage
detector—which separates the regions proposal phase from their
classification,—both YOLOv8 and SSD are single stage detectors. The three
methods are compared on the scenario C depicted in Fig. 6, which is the one
exhibiting the most varied vehicular patterns among the simulated
environments. The hyperparameters have been manually tuned to achieve high
detection performance. Setting the maximum number of training epochs to 300,
the highest mAP validation performance has been achieved at 56 epochs for
YOLOv8s, 30 epochs for Faster R-CNN and 99 epochs for SSD. The training and
validation of the two methods over the radar images dataset has been performed
by means of the MMDetection benchmarking library[49]. We refer the reader to
[18] and [14] for a thorough description of the Faster R-CNN and SSD
architectures.

While providing notable detection and classification performance over the
considered scenario, YOLOv8s presents a higher computational efficiency and a
considerably lower number of model parameters with respect to both the
considered Faster R-CNN and SSD architectures. The selected configurations
lead to $\approx 11.2\cdot 10^{6}$ model parameters for YOLOv8s, $\approx
60.7\cdot 10^{6}$ for Faster R-CNN, and $\approx 24.7\cdot 10^{6}$ for SSD.
Moreover, Faster R-CNN showed a higher detection performance with respect to
SSD. This behaviour of Faster R-CNN and SSD over radar images is similar to
the one obtained in [50], where the authors show a comparable gap between SSD
and Faster R-CNN for training over real-world acquired data. Nevertheless, we
notice that this behavior can depend on the choice of several model features,
e.g., the backbone type or the radar image pre-processing steps, and that, to
the best of our knowledge, a thorough architectural comparison on the radar
target detection task over the available deep learning object detection models
is missing in the specific literature. The proposed comparison aims to show
that the radar target detection task can be effectively learned by diverse
deep learning-based object detection architectures originally designed (and
partially pre-trained) for camera data.

We notice that the performance under radar target classification is minimally
affected by the number of additional classes (i.e., $N_{T}^{h}+N_{T}^{v}$)
owing to the beam prediction task, with a $\approx 2.5\%$ loss in mAP50-95
between the $2\times 2$ and the $64\times 64$ antenna array size cases. We
show that the classification and detection metrics over horizontal and
vertical beams prediction depend instead on the beamforming codebook size,
resulting in the highest performance for the $2\times 2$ antenna array case up
to $\approx 25\%$ loss in mAP50-95 for a $64\times 64$ antenna array.

Fig. 7 presents the YOLOv8s performance by means of precision-recall (PR),
precision-confidence (PC), recall-confidence (RC), and F1-confidence (FC)
graphs for both the target classification (Figs. 7a to 7d) and beam prediction
(Figs. 7e to 7h) tasks. The YOLO model performance is summarily described by
the area under the proposed curves. The results reflect the same behavior
presented in Table II. Indeed the metrics related to the targets
classification task are almost unaffected by the precoding codebook size,
whereas the metrics evaluated on the beam prediction task show decreasing
performance owing to the increase in the output inference space over the same
YOLOv8 model size.

Figure 8: Beam prediction top-$k$ accuracy over different rectangular antenna
array dimensions at the BS.

The top-$k$ classification accuracy for the beam prediction task is provided
in Fig. 8. The classification accuracy is evaluated as the average between the
horizontal and the vertical beam classification top-$k$ accuracy. The proposed
model shows significant top-$1$ accuracy over the considered antenna array
dimensions at the BS, with a $\approx 9.4\%$ performance loss for a $64\times
64$ antenna array at the BS with respect to a $2\times 2$ antenna array.
Moreover, the model presents a similar top-$k$ accuracy increase over the all
the considered antenna array sizes, showing an average enhancement of $\approx
5.7\%$ from top-$1$ to top-$5$ accuracy over $64\times 64$ antenna arrays.

TABLE IV: Model hyperparameters. Model | Hyperparameter | Value
---|---|---
Radar multi-target detection (YOLOv8) | Input images size | $512\times 512$
Max. number of epochs | $500$
Max. number of detections | $300$
Confidence threshold | $0.25$
IoU threshold | $0.7$
Batch size | $16$
Optimizer | SGD

###  V-C T2U Association

We present here the results achieved applying the T2U association procedure
described in Section IV-B to match the detected radar targets to VEs in the
beamspace. Radar target detection and per-target beam prediction are performed
by means of the YOLO architecture proposed in Section IV-A according to the
hyperparameters specified in Table IV. Analog precoding beam training is
performed at the BS by an exhaustive span of the Tx. and Rx. beamforming
codebooks at each simulation time step, as described in Section V-A. We assume
that the vehicular targets can be sensed by the BS and that each target is
equipped with a VE.

We assess in Fig. 9 the performance of the proposed T2U association method.
The association performance is provided in terms of the probability of correct
association between radar targets and VEs averaged over the three considered
urban scenarios, as described in Section IV-B. We evaluate the association
procedure over increasing SNR per antenna values and we compare the
performance on different antenna array dimensions at the BS. Probability of
correct association converges to a plateau with the increase of the SNR per
antenna. The SNR per antenna can highly influence the beamspace patterns that
enable T2U association. Indeed, faster convergence to the plateau is achieved
for larger antenna arrays at the BS, which is expected owing to the greater
beamforming gain counteracting lower SNRs per antenna. The achieved
probability of correct association plateau rapidly increases with the number
of antennas at the BS. This is in accordance with the capability of larger
antenna arrays to more accurately resolve different targets in the beamspace.
As a result, massive antenna arrays show higher resilience to low SNR
conditions owing to their significant beamforming gain while providing notable
performance in probability of correct association.

Figure 9: Probability of correct association for varying SNR per antenna
utilized to determine the horizontal and vertical analog precoding beam
indices selected at the BS. Performance is averaged over the three considered
scenarios.

Fig. 10 studies the variation of the probability of correct association over
different dynamic clutter conditions. We consider the association between the
detected radar targets and 2 sensed VEs crossing the environment. The
remaining vehicles in the scene are treated as dynamic clutter, i.e.,
(possibly) detected vehicular radar targets which are not active VEs. The
association performance shows a decreasing behavior over an increasing number
of clutter vehicles in the scene, highlighting the limits of lower dimensional
antenna arrays in distinguishing the VEs in the beamspace. Indeed, the
probability of association performance significantly improves over increasing
sizes of the antenna array utilized at the BS, with an improvement of $\approx
48.7\%$ between $2\times 2$ and $32\times 32$ antenna arrays when 5 clutter
vehicles within the sensed environment are considered. Over the simulated
vehicular scenarios, no relevant gain in probability of correct association
has been observed beyond the $32\times 32$ antenna array size.

Figure 10: Probability of correct association at -20 dB SNR per antenna for
varying number of clutter vehicles and considering association between the
detected radar targets and 2 active VEs in the scenario. Performance is
averaged over the three considered scenarios.

In Fig. 11, we provide a matrix showing the probability of correctly
associating VEs to vehicular radar targets for a varying number of VEs (from 1
to 4) and of vehicles inducing dynamic clutter in the scene. The matrix is
presented for an antenna array of dimensions $8\times 8$ at the BS, and -20 dB
SNR per antenna. The first column of the matrix corresponds to the case in
which only vehicular targets which are also VEs are crossing the scenario. It
represents an upper bound for the following columns. In general, a decreasing
behavior in the probability of correct association is observed for an increase
in the number of clutter vehicles in the environment. A similar behavior can
be observed over the matrix rows for an increasing number of VEs in the
scenario. Therefore, as expected, the uncertainty in the matching raises with
the number of both VEs and clutter vehicles present in the scene. We observed
an equivalent behavior for the remaining antenna array dimensions ($2\times
2$, $4\times 4$, $16\times 16$, $32\times 32$, $64\times 64$) considered in
Figs. 9 and 10. In particular, the decreasing trend is more marked for lower
dimensional antenna arrays, as envisaged by Fig. 10. We observed an analogous
attitude over different SNRs per antenna between -55 dB and -10 dB. In the
latter case, the values in the matrix experience a heavy reduction when
approaching lower SNRs per antenna. The same behavior can be observed in Fig.
9.

Figure 11: Probability of correct association at -20 dB SNR per antenna for
varying number of clutter vehicles considering association between the
detected radar targets and a varying number of active VEs (from 1 to 4) in the
scenario. The antenna array dimension is set to $8\times 8$. Performance is
averaged over the three considered scenarios.

##  VI Conclusion

In this paper, we addressed target-to-user (T2U) association in next-
generation V2I ICAS systems presenting a DL-aided method to associate
vehicular radar targets to communication users in the communication beamspace.
We modeled the beam prediction problem as a classification task over a fixed-
size codebook of beamforming vectors, and we modified the renowned YOLO
architecture to infer both the radar targets’ classes and the beamforming
vectors’ classes for each detected target. We trained the YOLO model over
recurring vehicular motion patterns—and, therefore, VEs’ patterns in the
beamspace—within the sensed urban scenario. The aim of the proposed method is
to provide the communication system with information on the matching between
sensed radar targets and communication users, which is essential to
extensively take advantage of the ICAS system capabilities and to enhance the
performance of common communication tasks, e.g., beam prediction and blockage
prediction.

Simulation results over different vehicular mobility scenarios using realistic
mmWave radar and communication ray-tracing data and vehicular traffic show
that the proposed method achieves significant T2U association performance,
matching the detected radar targets to the respective communication users with
a probability of correct association increasing with the antenna array size at
the BS—highlighting the respective increase of the separability of the VEs in
the beamspace. Moreover, we show that the modified YOLO architecture can
perform both beam prediction and radar target detection, with similar
performance in mean average precision on the latter over different antenna
array sizes. This allows us to effectively predict both target positional
information (in terms of bounding boxes in the radar image) and
classification, and beam prediction starting from the observation of the whole
radar image and, therefore, jointly considering the presence of multiple radar
targets in the environment. As a future work, we plan to investigate the
integration of radar multi-target tracking by keeping information on the
identity of the detected vehicular targets over consecutive time steps, thus
reducing the T2U association frequency and increasing the efficiency of the
association workflow.

## Acknowledgment

The research has been carried out in the framework of the Joint Lab between
Huawei and Politecnico di Milano.

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