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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, XXX 2021 1
Millimeter-Wave Radar Scheme with Passive
Reflector for Uncontrolled Blind Urban Intersection
Dmitrii Solomitckii, Carlos Baquero Barneto, Matias Turunen, Markus All´
en, George Zhabko, Sergey Zavjalov,
Sergey Volvenko, and Mikko Valkama
Abstract—Modern millimeter-wave automotive radars are em-
ployed to keep a safe distance between vehicles and reduce
the collision risk when driving. Meanwhile, an on-board radar
module is supposed to operate in the line-of-sight condition, which
limits its sensing capabilities in intersections with obstructed vis-
ibility. Therefore, this paper investigates the scheme with passive
reflector, enabling the automotive radar to detect an approaching
vehicle in the non-line-of-sight (blind) urban intersection. First,
extensive radar measurements of the backscattering power are
carried out with the in-house assembled millimeter-wave radar
equipment. Next, the measured data is employed to calibrate an
accurate analytical model, deduced and described in this paper.
Finally, the analytical models are deployed to define the optimal
parameters of the radar scheme in the particular geometry of
the selected intersection scenario. Specifically, it is found that
the optimal angular orientation of the reflector is 43.5 °, while
the 20 m curvature radius shows better performance compared
to a flat reflector. Specifically, the curved convex shape increases
scattering power by 20 dB in the shadow region and, thus,
improves the detection probability of the vehicle, approaching
the blind intersection.
Index Terms—Automotive radars, collision risk, Kirchhoff
approximation, millimeter-wave radar, passive reflector, radar
measurement, vehicular systems
I. INT ROD UC TI ON
Recently, millimeter-wave (mmWave) automotive radars
have started to be actively deployed in both premium as well
as lower-budget commercial vehicles [1], in order to improve
the safety of pedestrians and drivers. This trend is motivated by
new traffic requirements, leading to the reduction of accidents
on the road. For example, the European New Car Assessment
Programme (NCAP) that started already in 2016, demands to
install at least one Advanced driver-assistance system (ADAS)
[2] on the vehicle to receive a five-star safety rating. Among
them, Adaptive cruise control, Automatic Emergency Braking,
Forward Collision-Avoidance Assist, Intersection Assistant,
and Automotive Night Vision are among the most common
radar-based ADAS elements deployed in vehicles. Addition-
ally, in the longer term perspective, the automotive radars
Manuscript received January 10, 2021; revised April 27, 2021. This article
contains measurement data openly available at [35].
Copyright (c) 2015 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
D. Solomitckii, C. Baquero Barneto, M. Turunen, M. All´
en, and M.
Valkama are with Electrical Engineering Unit, Tampere University, Finland
e-mail:(name.surname@tuni.fi)
G. Zhabko, S. Zavjalov, S. Volvenko, are with Dept. of Communi-
cation, Peter the Great St. Petersburg Polytechnic University, Russia e-
mail:(zhabko gp@spbstu.ru, zavyalov sv@spbstu.ru, volk@cee.spbstu.ru)
and other sensing instruments will assist also self-driving or
autonomous vehicles [3].
Nevertheless, automotive radars operate in the line-of-sight
(LOS) mode, which limits the ability to recognise an ap-
proaching vehicle behind a building in an uncontrolled blind
urban intersection. As a result, such unawareness about the
approaching vehicle leads to the collision risk, even though
an ADAS is on-board. This paper extends the research of the
radar scheme aided with a passive reflector in [4] and [5],
seeking to enable and facilitate detecting a car around the
corner. Specifically, in [4], the concept of the radar scheme
with passive reflector was originally proposed, including also
preliminary measurements. Further, in [5], the variant of
the scheme with a raised reflector, mitigating the blockage
effect, was suggested. In this paper, we develop and assess
the concept further, with notable contributions that can be
summarized as follows:
1) We carry out, report, and analyze an extensive set of
radar measurements in a practical and realistic vehicular
environment.
2) We derive an accurate electromagnetic model, building
on the measurement data, which can characterize and
predict the functionality of the proposed radar scheme.
3) We use the derived analytical model to define the
optimal parameters of the proposed radar scheme for the
geometry of the considered environment. Methodology-
wise, this can be extended in a straightforward manner
to any other practical environment as well.
The rest of the paper is organized as follows. Review of
the relevant technologies for the non-line-of-sight (NLOS)
radar detection is provided in Section II. Next, Section III
explains the measurement equipment and the considered de-
ployment scenario. Section IV introduces the methods for
analytical calculations and electromagnetic (EM) modelling.
Measurement-based and modeling-based results are described
in Sections V and VI, respectively. Finally, conclusions are
drawn in Section VII, while an example derivation of the
analytical formulas is given in Appendix A.
II. OVE RVIEW OF RELEVANT TECH NO LO GI ES
Around-the-corner detection and NLOS radars, which the
paper is focusing on, have already been addressed to some
extent in the existing literature. For example, in [6] and [7]
authors successfully recognized a human, standing in a NLOS
tunnel and T-shaped room, by performing 2.5–3.5 GHz and
24 GHz radar measurements. A similar study is reported in [8],
where a mobile human being, hidden behind a concrete wall,
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was identified by radar. In these studies, the illuminating
signal that is used for target detection is propagating without
employing additional artificial reflectors. Nevertheless, such
implementation is topology and scenario dependent and may
not work in some other deployments. Specifically, the results
in [4] show that NLOS detection is very challenging in
practical urban blind intersections, where the signal cannot find
a low-loss way to the around-the-corner region. Therefore, an
intriguing research prospect is to consider artificial features or
added material constructions to assist the NLOS around-the-
corner detection.
An alternative approach to the proposed passive reflector
considered in this work is to install and consider road-side
units (RSU) on the buildings, discussed, e.g. in [9]–[12],
to warn the vehicles about the potential collision risk. This
solution fits the vision of the 3rd Generation Partnership
Project (3GPP), where all vehicles are eventually going to
be connected to the infrastructure (vehicle-to-infrastructure
communication, i.e. V2X) network. However, the realization
of this idea in dense mobile urban conditions might be
challenging due to possible problems with finding a sufficient
amount of sites for deploying active RSUs as well as with
the resource allocation. Furthermore, this solution is still
primarily limited to lab prototypes, while the radars are already
commercially available and thoroughly spread and deployed.
Finally, following the standardization timeline, it is still likely
to take many years before the RSUs may find their way to
large scale deployments at the urban crossroads. We also note
that the Global Positioning System (GPS) or other relevant
satellite-based positioning systems such as Glonass, Galileo,
Beidou, etc., can be also taken into consideration for avoiding
collisions at intersections. For example, authors in [13] pro-
pose to exploit GPS communication specifically for collision
avoidance. However, typical urban scenarios may experience
significant positioning errors [14], especially in cities with
high-rise buildings, which degrade the overall reliability of
satellite positioning based methods.
Alternatively to the radio frequency (RF) based solutions,
optical systems may also be considered and engaged for the
NLOS detection. For example, promising results in [15]–[17]
proof the ability to detect objects behind an opaque wall
by the joint operation of laser and ultra-fast camera. Such
cooperative action has some conceptual similarities to the
proposed NLOS radar scheme, where the camera and laser
act as receiver and transmitter, respectively. Moreover, some
of the literature sources such as [18] offer to embed this idea
in the LIDAR functionality. However, the operation of the
NLOS laser-based method in harsh outdoor conditions with
finely dispersed particles – say fog, rain, dirt, etc. – can easily
be challenging. Specifically, the natural limitation of the light
associated with scattering and attenuation effects may crucially
reduce the reliability of the laser-based solutions [19]. For the
same reasons, the performance of image processing of video
cameras [20] can also be clearly limited. On the contrary, due
to larger wavelengths even at the mmWave bands compared to
the optical frequencies, the proposed RF-based radar scheme is
less affected by the harsh environmental conditions compared
to the optical solutions.
(a)
(b)
Fig. 1. (a) Photography illustration of the measured deployment
scenario with a blind intersection at the Hervanta Campus of Tampere
University, Finland. (b) Simplified two-dimensional representation of
the deployment scenario for analytical calculations and modeling.
In general, passive reflecting surfaces play an essential role
in radar testing. The most popular of these is the corner
reflector, returning the signal precisely to the source point. To
this end, smart surfaces are currently being actively studied
and considered, for example, in the context of 6G systems
[21], [22]. Recent advances in metamaterials offer the prospect
of deploying smart surfaces, or intelligent reflecting surfaces
(IRS), that can manipulate EM channels. For example, the
so-called programmable channel concepts in the context of
multi-user multiple-input and multiple-output (MU-MIMO)
transmission and beamforming are studied in [23]. In [24], IRS
technologies are emerging as an important paradigm for the
realisation of smart radio environments, where large numbers
of small, low-cost and passive elements reflect the incident
signal with an adjustable phase shift. In [25], the use of passive
reflectors for improving signal coverage in NLOS indoor areas
is investigated. Importantly, however, it is noted that all these
smart surface technologies are associated with relatively high
cost while also requiring a power supply. Oppositely, this paper
focuses on the deployment of a lower-cost and technologically
more simple purely passive reflector solution. While being
more likely to allow for large-scale deployments, because of
the reduced costs and ability to operate without an active
power source, the absence of any structural and functional
elements in the construction of the passive reflector may also
increase the reliability of the proposed scheme in typical harsh
outdoor environments.
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TABLE I
BAS IC PARA ME TER S OF T HE CON SI DER ED DE PLOY ME NT SCENARIO
Dimension Value/Range Definition
L1, m 6.5 Radar vehicle road width
L2, m 6.5 Detectable vehicle road width
∆1, m 5 Radar veh. trajectory shift
∆2, m 2.25, 3.25, 4.25 Detect. veh. trajectory shift
D1, m 10 Static distance of setup
D2, m 50–0Driving distance
A, m 1.2 x 1.6 Reflector’s area
φ,◦39.5, 43.5, 47.5 Reflector’s orientation angle
Rr, m ∞Reflector’s curvature radius
III. DEP LOY ME NT SC ENA RI O AN D MEA SU RE ME NT
EQUIPMENT
The topology of interest is an urban blind intersection
where buildings obstruct the LOS visibility between the two
approaching vehicles, driving along the perpendicular roads.
The considered example deployment scenario at the Hervanta
Campus of Tampere University, Finland, is illustrated in Fig.
1a within which the mmWave radar measurements are carried
out. The detectable car, Kia Ceed, drives along the road,
surrounded by two buildings. The car’s speed does not exceed
20 km/hfor safety reasons in the university campus area. The
walls of the surrounding buildings are covered with corrugated
metal sheets, and metal pipes are located next to them.
Such surrounding metallic surfaces may potentially contribute
to the formation of additional multipath components. This
statement will be studied more accurately in Section VI-B.
A constructional metallized foam-based insulator is employed
forming the 1.2x1.8 m planar reflector shown on the right
side of Fig. 1a. It is rigidly fixed to a heavy trolley to en-
able convenient transportation and reliable spatial orientation.
The metallized insulator reflects the signal, emitted from the
static mmWave radar setup, located at a certain distance. The
measuring radar equipment mimics the on-board automotive
radar module installed in the near-bumper zone. The top
view simplified representation of the measured deployment
scenario, illustrating also the exact dimensions, is shown in
Fig. 1b and further tabulated in Table I. In general, all the
listed parameters match the actual topology. We also note
that the angles were chosen experimentally to demonstrate
the impact of the reflector’s orientation in the most concrete
and explicit manner. In particular, after trial measurements, it
was determined that a reference angle of 43.5° yields the best
performance. To allow for accurate setting of the associated
angles, the measurements were carried out with a laser pointer
rigidly attached to the reflector.
In this paper, radar measurements are executed by in-house
assembled mmWave radar setup, operating at 28 GHz whose
detailed description can be found in [26]. The transmitting
(TX) and receiving (RX) antennas of this equipment are
located at 0.3 m above the ground, which fits the typical height
of the radar antenna for vehicle applications [27]. The core part
of the measurement setup is a vector signal transceiver (VST),
implementing the TX and RX functionalities at an intermediate
frequency (IF) of 3.5 GHz. This value perfectly meets the
characteristics of filters employed in the setup. Next, two
signal generators act as local oscillators to up/down-convert
the IF signal to/from the actual carrier frequency of 28 GHz.
The modulated orthogonal frequency-division multiplexing
(OFDM) signal is fed to horn TX antenna PE9851A-20 from
Pasternack with a gain of 20 dBi. The half-power beamwidths
(HPBWs) of the antenna, in vertical and horizontals planes,
are 17°. The backscattering power is captured by an identical
RX horn antenna. In the measurements, OFDM signal with
channel bandwidth of 200 MHz and 60 kHz subcarrier spacing
is utilized, inline with the 3GPP 5G New Radio specifications
at the mmWave bands [28]. The utilization of an actual data
modulated OFDM waveform is deliberately pursued, instead
of a dedicated radar waveform, in the spirit of RF conver-
gence [22], [29], [30]. For each of the analyzed deployment
configurations listed in Table I, the radar processing and the
corresponding radar image construction are carried out 20
times along the route of the vehicle illustrated in Fig. 1.
For the radar processing, the subcarrier-domain algorithms,
similar to [31], are applied to obtain the backscattering power
from all surrounding objects. However, in this paper, only the
backscattering power from the driving vehicle is of interest.
IV. ELE CT ROMAG NE TI C MOD EL IN G
A. Simplified Deployment Model
For the purpose of analytical EM modeling, Fig. 1b rep-
resents a simplified 2D version of the real-world measured
scenario illustrated in Fig. 1a. The dimensionality reduction
from 3D to 2D becomes feasible when the following sim-
plifying assumptions are applied. First, the orientation of the
reflector is strictly perpendicular to the road. Second, the
reflector shape remains constant along the y-axis. Finally, the
ground reflected multipath components are neglected, which
removes constructive and destructive interference at the RX
(for further details, refer to the 2-Ray model and corresponding
clarifications in [32]). The last simplification is justified by
the inability to accurately consider this phenomenon due
to the small wavelength (∼1 cm) and the high complexity
stemming from the non-uniform profile and roughness of the
road pavement.
Similarly to the measurements, the simplified modelling
deployment represents an intersection, where the LOS vis-
ibility is obstructed by a building, depicted by the thick
grey lines in Fig. 1b. The detectable (green) and the radar
(white) vehicles travel along the perpendicular roads with
a potential to collide at the point highlighted with the red
star. The driving trajectories (blue dash-dot lines) are shifted
by ∆1and ∆2relative to the blocking building walls. The
parameters L1and L2characterize the widths of the roads,
Adenotes the horizontal size of the passive reflector, while φ
refers to the rotation angle. Finally, distance D1is fixed and
defines the position of the radar equipment (radar vehicle in
practice), while D2changes along the whole driving path of
the green detectable vehicle. All these parameters are noted
and summarized in Table I.
B. Radar and Backscattering Power Calculations
According to ITU-R recommendations in [27], the radar
range equation (RRE) is a typical approach to calculate the
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backscattering power in the LOS conditions. In case of the
proposed NLOS radar scheme, the reflector acts as an ideal
lossless mirror only if D1and D2are significantly larger
(tens of meters) compared to the wavelength. Therefore, if
the reflecting point belongs to the reflector’s area, the power
backscattering at the RX can in principle be described through
the RRE as
Prre =P1G1G2λ2σ
(4π)3R4,(1)
where
R≈p(D1+L2)2+ (L1−∆1)2
+p(D2+L1)2+ (L2−∆2)2.(2)
In (1), λ=1 cm denotes the wavelength, G1and G2are TX
and RX antenna gains equal to 20 dBi,P1is the 10 dBm
transmit power, and finally, σis monostatic radar cross-section
(RCS) of the detectable vehicle (the green one in Fig.1b). The
total distance Ris expressed in (2), where dimensions D1,
D2,L1,L2,∆1,∆2are shown in Fig. 1b and parameterized
in Table I.
However, the expression in (1) is applicable only when the
detectable object is a ”point scatterer” [33], i.e., located in the
far-field region. In the considered deployment scenario, the
distance Rmay reach 23 m, at which the detectable vehicle
is too far from being a point scatterer. Additionally, the value
of the range D2may further substantiate the case, when the
reflecting point is out of the reflector area. Accordingly, a
more accurate physical model that takes into account all of
the above factors should be developed. This is pursued next.
Stemming from above reasoning, two expressions building
on the Kirchhoff theory [34] are introduced in this article
to calculate the backscattering power accurately. Specifically,
the backscattering power from the driving vehicle with flat
reflector (surface curvature Rr=∞m) is first expressed as
Pflat =P1G1G2z4
2σ
(4π)3
A
2
Z
−A
2
exp(−ik(R1+R2))
R2pR1R2(R1+R2)dx
4.(3)
On the other hand, the backscattering power from the de-
tectable vehicle in the radar scheme with curved reflector
(Rc6=∞m) can be calculated as
Pcurv. =P1G1G2R4
cσ
1024π3
β0
Z
−β0 exp(−ik(R1+R2))
R2pR1R2(R1+R2)!×
× (x−x1) sin β+ (z−z1) cos β
R1
+
+(x−x2) sin β+ (z−z2) cos β
R2!dβ
4
.
(4)
The parameters P1,G1,G2and σin equations (3) and (4)
have the same meaning as in (1). The radar-reflector distance
R1and the reflector-car distance R2as well as the locations
of the radar (x1,z1) and the detectable car (x2,z2) can, in
turn, be expressed as
R1=p(x−x1)2+ (z−z1)2,(5a)
R2=p(x−x2)2+ (z−z2)2,(5b)
x1=D1cos φ+ (L1−∆2)(cos φ−sin φ),(5c)
x2=−D2sin φ+ (L2−∆1)(cos φ−sin φ),(5d)
z1=D1sin φ+ (L1−∆2)(cos φ+ sin φ),(5e)
z2=D2cos φ+ (L2−∆1)(cos φ+ sin φ),(5f)
where L1,L2,∆1,∆2,D1and D2are listed in Table I, kis
the wavenumber magnitude, while φrefers to the orientation
angle illustrated in Fig. 1b. Finally, the scattering points of the
reflector with radius Rrin equation (4) can be calculated as
x=Rrsin β, (6a)
z=Rrcos β−Rr,(6b)
β0= arcsin(A/2Rr).(6c)
For readers’ convenience, the derivation details related to (3)
are presented in Appendix A, while (4) can be derived and
obtained in a very similar way. Furthermore, the numerical
results provided in Section VI will validate the correctness
and accuracy of the derived analytical model, when compared
against the basic RRE approach as well as against full EM
simulations in HFSS. We also note that an in-house numerical
tool, executable in Matlab Runtime environment, is available
in [35] for practical engineering calculations in the context of
the consider NLOS radar scheme and the associated modeling
equations.
Additionally, we also note that the Doppler shift or spread is
not included in (3) and (4). This is because with realistic values
of the velocity, the Doppler does not essentially affect the
backscattering power. In particular, additional calculations and
analysis show that even with an example velocity of 15 m/s,
the difference is commonly less than 0.1 dB when comparing
to the zero-velocity case.
Finally, we note that in (1), (3) and (4) the RCS of the
detectable vehicle σis unknown. Theoretically, it can be found
or expressed as [33]
σ= lim
r→∞ 4πr2|Escat |2/|Einc|2.(7)
The Einc in (7) denotes the amplitude of the incident plane
wave, and Escat indicates the scattered field, representing the
superposition of all surface currents. In the case of a perfect
electrical conductor (PEC), the flowing surface current does
not encounter any attenuation. Oppositely, if the surface is
resistive, then the surface current weakens proportionally to
the surface impedance η, that reads
η=sjωµ
σ0+jωη0.(8)
In (8), ωis angular frequency, µand are relative permeability
and permittivity, respectively, σ0is conductivity, and finally,
η0= 120πis free space impedance. Since the detectable car
has both PEC (body) and resistive (radiator grid, bumper)
elements, the expression in (8) can be applied in the EM
modelling. Additionally, RCS σis also a function of the
incidence angle φ0, expressed as
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(a) (b)
(c) (d) (e)
Fig. 2. (a) Radar image snapshot obtained with the mmWave mea-
surements at 28 GHz, where a backscattering power of −86 dBm
from the driving vehicle is detected at D2=16 m. (b) Another radar
image snapshot, with no observable backscattering power from the
driving vehicle, but showing spurious low-power target at D2=7 m.
(c)-(e) Three consecutive measurement attempts of the same scenario
with overlaid radar snapshots along the movement of the detectable
car.
φ0≈arctan L2−∆2
D2+L1.(9)
Substituting the numerical values to (9) gives the following
range of φ0=2.5–35.5° when considering the different values
of the involved variables listed in Table I.
V. MMWAVE RADA R MEA SU RE ME NT S
Comprehensive measurements of the backscattering power
in the scenario shown in Fig. 1a are next carried out by the
mmWave radar equipment described in Section III. The setup
is initially calibrated to Friis law in the free-space conditions,
where 9 dB loss is determined. Next, the radar setup is placed
at a location, specified by the distances D1and ∆1, while
the detectable car is initially located at max(D2). Then, by
the command of the radar equipment operator, the driver of
the detectable car starts driving from max(D2) to min(D2).
During this time that the vehicle is moving, multiple samples
of the backscattering power in the form of radar images are
captured by the radar setup and stored for further processing
and visualization. The measurement procedure is repeated
three times per scenario, each of which is characterized by
the particular combination of ∆2and φ(see Table I). The
total number of the unique scenarios being measured is thus
nine.
As an example, one captured radar image is shown in Fig.
2a, where the red spot at v=3.5 m/scorresponds to the
backscattering power from the detectable vehicle, located at
D2=16 m. It can be also observed that there are multiple spots
or ’targets’ at v=0 m/s, exposing the unwanted backscattering
power or clutter from the surrounding static environmental
objects. Therefore, in order to discard the less useful data or
focus on the essential area in the radar image, the rectangular
region of interest – outlined by dashed lines in Fig. 2a and
specified by velocity and distance ranges of v=2–5 m/sand
D2=3–50 m, respectively – is introduced. These values are
basically stemming from the overlaid radar observations in
Fig. 2c-2e. Then, inside this window of interest, the maxi-
mal backscattering power is always detected and stored as
a function of D2. It is also noted that such filtering does
not perform very well in some scenarios, due to spurious
power stemming most likely from some hardware artifacts that
are strictly speaking unknown to the authors. This effect is
explicitly illustrated in Fig. 2b, observable at v=2 m/sand
D2=7 m. Such spurious target, despite being relatively weak,
overestimates the power level in the rectangular area in such
cases where the actual backscattering power of the detectable
vehicle is absent (as in Fig. 2b). Accordingly, some additional
local windowing is applied to further improve the processed
data.
The backscattering peak, illustrated in Fig. 2a, moves syn-
chronously with the detectable car from max(D2) to min(D2).
This effect is depicted in Fig. 2c–2e, where multiple radar
images are overlaid in the same subfigure. The subfigures c)-e)
describe three measurement attempts in the same scenario with
∆2=2.25 m and φ=43.5°. It can be noticed that despite the
same scenario, the three pictures demonstrate slightly different
patterns of the backscattering power, stemming at least from
the following reasons. Firstly, the human driver cannot repeat
exactly the same velocity and acceleration profiles in different
measurement attempts. Moreover, the driver is not able to
keep the ideally constant dynamics of the car during driving
within an attempt. As an example, the red dashed line in Fig.
2d shows a velocity change by 0.6 m/safter some 20 m of
driving. Secondly, despite the presence of road markers, the
position of the car was varying up to roughly 0.20 m. Thirdly,
the radar operator is subject to uncertainty in the exact start
time of the recording, most likely up to 1 s, which undoubtedly
affect the interpretation of the individual measurement traces.
All the measured and stored backscattering powers for
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0 5 10 15 20 25 30 35 40 45 50
D2,m
-120
-100
-80
-60
Pbsc, dBm
Meas. @ =47.5 o,2 =3.25m Theor. @ =47.5 o,2 =3.25m
Spurious
Scattering
DD1
(a)
0 5 10 15 20 25 30 35 40 45 50
D2,m
-120
-100
-80
-60
Pbsc, dBm
Meas. @ =47.5 o,2 =4.25m Theor. @ =47.5 o,2 =4.25m
DD2
(b)
0 5 10 15 20 25 30 35 40 45 50
D2,m
-120
-100
-80
-60
Pbsc, dBm
Meas. @ =39.5 o,2 =3.25m Theor. @ =39.5 o,2 =3.25m
DD3
(c)
0 5 10 15 20 25 30 35 40 45 50
D2,m
-120
-100
-80
-60
Pbsc, dBm
Meas. @ =39.5 o,2 =4.25m Theor. @ =39.5 o,2 =4.25m
DD4
(d)
0 5 10 15 20 25 30 35 40 45 50
D2,m
-120
-100
-80
-60
Pbsc, dBm
Meas. @ =39.5 o,2 =2.25m Theor. @ =39.5 o,2 =2.25m
DD5
(e)
0 5 10 15 20 25 30 35 40 45 50
D2,m
-120
-100
-80
-60
Pbsc, dBm
Meas. @ =43.5 o,2 =3.25m Theor. @ =43.5 o,2 =3.25m
DD6
(f)
5 10 15 20 25 30 35 40 45 50
D2,m
-120
-100
-80
-60
Pbsc, dBm
Meas. @ =43.5 o,2 =4.25m Theor. @ =43.5 o,2 =4.25m
DD7
(g)
5 10 15 20 25 30 35 40 45 50
D2,m
-120
-100
-80
-60
Pbsc, dBm
Meas. @ =43.5 o,2 =2.25m Theor. @ =43.5 o,2 =2.25m
DD8
(h)
Fig. 3. Comparison between measured and analytical/simulated backscattering powers as functions of ∆2while considering different values
of φ. The following constant parameter values were utilized: A = 1.6 m,L1=6.5 m,D1=10 m, and ∆1=5 m. The value of the RCS
σ(φ0)varies from −7 dBsm to 10 dBsm according to Fig. 4b.
different measured scenarios are plotted with red circles in
Fig. 3. The analysis of the results and their comparison to
analytical models and EM simulations are provided in the next
section. The measurement data is openly available in [35] for
reproducible research and any potential follow-up work.
VI. FI NAL MO DE LI NG RE SU LTS A ND ANA LYSIS
A. EM Simulation of Radar Cross-Section
To supplement the evaluation of the analytical backscatter-
ing power expressions, the EM modelling of the RCS σis next
executed in Ansys HFSS, where the shooting and bouncing
ray (SBR+) method with the uniform theory of diffraction
(UTD) and physical optics (PO) are applied [36]. These
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(a)
-40 -30 -20 -10 0 10 20 30 40
', °
-10
-5
0
5
10
15
20
25
30
, dBsm
' = 0 °
Raw
Averaged
(b)
Fig. 4. (a) Illustration of the utilized 3D model of Kia Ceed with
assigned materials. (b) Multi-frequency raw (red circles) and averaged
(black) RCS values (σ) of Kia Ceed simulated in Ansys HFSS.
methods are the most accurate and computationally efficient
for electrically large objects compared to the alternative full-
wave methods. According to [36], SBR+ supports dielectric
materials and boundary conditions, which empowers to assign
different materials to the EM car model. Therefore, in this
paper, the impedance boundary condition is applied to all the
dielectric parts, while alternative boundary conditions – called
in HFSS as finite conductivity – are aimed for good conductors
[37]. All material are listed in Table II and highlighted through
different colors in Fig. 4a.
The computer-aided design (CAD) model of Kia Ceed [38]
is selected for HFSS simulation due to the list of fulfilled
requirements. First, the selected 3D CAD-model is seemingly
geometrically precise, that can be also inferred by the file
size of 30–50 MB. The rule-of-thumb range, showing a right
balance between computational time and the output accuracy,
is determined experimentally in [5]. Furthermore, the detailed
examination of the model shows sufficient density and good
quality of the facets. Specifically, they have the lowest aspect
ratio and do not produce sharp stitches. Secondly, the selected
3D CAD-model is an assembly (*.asm) of separate solid parts
(ring disks, glass parts, headlights), to which materials in
0 10 20 30 40 50
D2,m
-120
-110
-100
-90
-80
-70
-60
Pbsc,dBm
Theor.@Rr =20m, conv.
Theor.@Rr =100m, conv.
Theor.@Rr = m, flat
RRE
(a)
0 10 20 30 40 50
D2,m
-120
-110
-100
-90
-80
-70
-60
Pbsc,dBm
Theor.@Rr =20m, conc.
Theor.@Rr =100m, conc.
Theor.@Rr = m, flat
RRE
(b)
Fig. 5. Analytical calculation results of the backscattering power with
(a) convexly curved reflector, and (b) concavely curved reflector.
TABLE II
MATER IAL S UTI LIZ ED F OR SIM UL ATION I N HFSS
Part Material σ0, S/m tan δ η Ref.
Windshield Glass 6.4 0.1 0.011 150 [39]
Bumper Polymer 2.5 0.02 0.005 238 [39]
Radiator grid Polymer 2.5 0.02 0.005 238 [39]
Light beam Polymer 2.5 0.02 0.005 238 [39]
Body PEC 1 1030 0 0 HFSS DB
Table II can be assigned. The values for dielectric permittivity
, conductivity σ, and loss tangent tan δare taken from the
HFSS database and from [39], while impedance ηis calculated
with the expression in (8).
To shorten the computational time in HFSS, some prepro-
cessing of the 3D model is also utilized. First, the surfaces
or elements committing very low-level backscattering power
are removed. Such surfaces or elements are primarily charac-
terized by their small size, high surface impedance η, and/or
orientation of their normals perpendicular to the wave vector
of incident signal (roof, for instance) [5]. Additionally, interior
elements and rear parts of the car are removed (see Fig. 4a),
due to inability to model signal penetration into an object in
HFSS. Despite such simplifications, the calculation time on
the high-performance Lenovo Thinkpad P53 took more than
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20 hours.
The simulation of the monostatic σis performed in the
frequency range of 27.5–28.5 GHz with 0.1 GHz step, while
the plane wave sources/receivers are distributed around the
front part of the 3D model within the range of φ0varying from
−40.0° to 40.0° with respect to longitudinal central axis. The
direction of incidence at φ0=0° is strictly perpendicular to
the license plate and coincides with the longitudinal axis. The
results of the simulated RCS σare shown in Fig. 4b. Because
of the high variations of the simulated data (red circles), a
smoothing filter representing averaging over the frequency
range of 27.5–28.5 GHz with 0.1 GHz step is next applied,
yielding the smooth black dashed curve shown in the figure. It
can be seen that the maximum 10 dBsm scattering gain occurs
from the front bumper at φ0=0°, and decreases to −7 dBsm
already at φ0=12°. Based on (9), the angle φ0varies from
2.5° to 35.5° which corresponds to σrange from 10 dBsm
down to −7 dBsm. This obtained distribution or range for
the RCS σwill be substituted in expressions (3) and (4)
in order to evaluate the backscattering power characteristics,
while then also comparing to the corresponding measurement
based results. These are pursued next.
B. Assessment of the Backscattering Power
Next, the derived expressions in (3) and (4) are employed
to calculate the analytical backscattering power while com-
paring with the actual measured data from the mmWave radar
experiments. The input data is taken from the Table I. The
analytical results are shown as solid black lines in Fig. 3. It
can be observed that the analytical results predict well only
certain parts of the measured data. Oppositely, other groups
of measured samples, outlined with dashed ellipses, are also
observed in the measured data that are not directly disclosed
by the analytical expressions.
In order to explain the observed phenomenon, let us next
decompose the entire data into two subsets. One of them
is the low-order backscattering, where radiated and returned
radar signal interacts only with the reflector and the detectable
vehicle (brown dashed line M1in Fig. 1b). This paper focuses
in particular on this phenomenon, while the expressions in (3)
and (4) seek to describe it analytically. In Fig. 3c–3h, the
low-order backscattering flat-topped pulse appears closer to
min(D2)than the data in ellipses, due to the shortest propaga-
tion path. If the orientation angle φreduces (counterclockwise
rotation), the registered low-order backscattering pulse moves
to the shorter D2(compare Fig.3c and 3e). Oppositely, if φ
increases (clockwise rotation), then the reflector scatters the
signal almost along the road, which enables the detection
of the approaching vehicle at far distances meaning larger
values of D2. In Fig. 3a–3b, the backscattering flat-top pulse
embeds into the distribution, with the low-order part becoming
essentially non-distinguishable.
Stemming from the results, the angle value of φ=43.5°
is identified as optimal in the selected scenario and geometry
for the two reasons. First, the received backscattering power
at φ=43.5° is higher than at φ=39.5° and comparable with
φ=47.5°, which guarantees receiving the radar signal above
the noise floor. Another important criterion is the detection
distance denoted as DD in Fig. 3. Specifically, larger DD
provides more time to the radar vehicle to collect statistics
about the approaching car. For example, if the car speed
is 20 m/sand the radar image sampling rate of the radar
system is 0.1 s, then 10 samples with Pbsc ≥ −100 dBm can
be captured at DD6= 20 m in Fig. 3f while already less
than 5 samples at DD5= 10 m in Fig. 3e. Alternatively, the
longest DD might be considered in Fig. 3a or 3b for Pbsc ≤
−100 dBm. However, the power levels close to the noise floor
can be impractical. Therefore, results for the radar scheme
where the reflector is oriented at φ=43.5° can be considered
most reliable and representative for the selected deployment
scenario.
Another subset of the obtained data is the high-order
backscattering (measured data in dashed ellipses in Fig. 3),
where the radiated and returned radar signal interacts with the
detectable car, reflector, and the building wall elements (green
dashed line in Fig. 1b) and the additional metallic parts. This
data subset appears after the low-order backscattering as a
cluster (Fig. 3d) or tail (Fig. 3h). Due to the complexity of
the measured scenario, the classification, sorting and analytical
investigation of such high-order backscattering effects seems
highly challenging and requires more precise geometrical
measurements and advanced ray tracing simulations.
It should also be noted that in real-life scenarios, the
surrounding elements may create and obstruct the irradiated
and scattered signal. For example, the transmitted and received
signals can be blocked by people, vehicles, road infrastructure
elements, or trees on the sidewalk. Therefore, the proposed
radar scheme may have challenges to operate well in con-
ditions such as a wide avenue with heavy traffic, where the
blockage probability is high. Moreover, it is noted that the
utilization of the reflector reduces the capabilities to pursue
MIMO radar operation, stemming essentially from the keyhole
effect [40]. Specifically, because of the low spatial diversity
of the multipath components (dominant paths have the same
geometry), formed by canyon-like scenario and reflector acting
as a ”pinhole”, the spatial degrees of freedom are reduced.
Further analysis and developing potential means to address
these limitations form important topics for our future work
and research.
Lastly, we pursue an analytical investigation of the curved
reflector through the expression in (4), whose scattering ca-
pabilities are also preliminarily studied in [5]. In particular,
the EM modelling results showed that a convexly curved
surface exhibits a wider angular dispersion of the scattered
field compared to a flat surface. As a result, it may potentially
increase the width DD in Fig 3. The corresponding results of
the backscattering power in the proposed radar scheme with
curved and flat reflectors, respectively, are demonstrated in
Fig. 5a. Specifically, in this figure, three different radiuses Rr
of a convexly curved surface are compared to the flat reflector.
Both these shapes have similar area Alisted in Table I. It can
be seen that the smallest radius of 20 m (the solid red line in
Fig. 5a) prevents sharp decreasing of the backscattering flat-
top pulse and increases the DD as expected. Oppositely, the
maximal power level at Rr=20 m slightly drops relative to
the RRE (black dotted line). At the same time, in case of Rr
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=100 m, the shape of the backscattering pulse becomes com-
parable to a flat reflector (dashed blue line), having basically
infinitely large Rr. Alternatively, if the shape is concave (see
Fig. 5b), then DD reduces, and the observation becomes more
focused in the distance domain. The latter fact can be seen as
a narrow peak (the solid red line) of the backscattering power,
which is some 20 dB higher than the corresponding RRE based
curve. Based on Fig. 5a and 5b, the convex reflector with 20 m
curvature radius looks preferable for the practical applications
in the considered scenario type of deployments.
VII. CON CL US IO N
In this article, a radar scheme aided with a passive reflector
was studied and investigated, in order to allow for non-line-
of-sight vehicle detection and thereon to reduce the collision
probability in blind intersections. In the considered scheme,
the signal transmitted by the automotive radar propagates to
the detectable vehicle and back while interacting with the pas-
sive reflector. Therefore, the observable backscattering power
at the radar receiver is selected as the main metric of interest to
investigate the performance of the NLOS radar scheme. First,
practical mmWave measurements were carried out at 28 GHz,
considering an example vehicular deployment scenario at the
Hervanta Campus of Tampere University, Finland, with in-
house radar equipment. Then, analytical expressions were
derived and provided, stemming from the Kirchhoff theory,
to characterize and calculate the backscattering power while
calibrating the model with the measurement based results. The
obtained analytical curves fit the shape and position of the
measured data while providing also some additional informa-
tion. For example, visualizing, analyzing and comparing the
analytical and measured data discovered two clusters of the
received backscattering power created by propagation paths
interacting and non-interacting with the building walls and
metallic elements.
Additionally, in the considered deployment scenario context,
the optimal orientation angle of the reflector was determined
by the power level and duration of the low-order backscattering
pulse. Specifically, the probability of detecting the around-
corner vehicle rises proportionally to the received power
level and the duration of the low-order backscattering pulse.
Stemming from this, an orientation angle of φ=43.5° was
determined as the most appropriate one in the considered
deployment scenario. Finally, the convexly/concavely curved
and flat reflectors were also investigated analytically. As a
result, it was found that convex reflector with 20 m curvature
radius produces a wider pulse of the backscattering power.
Therefore, the utilization of reflectors with such shape can be
considered a promising approach, preferable to a flat reflector.
Our future work will focus on extending the modeling and
analysis of the NLOS radar scheme to MIMO radar context,
consisting of, e.g., the deployment of passive and active
surfaces while also addressing the potential limits in the spatial
degrees of freedom and their impact on the radar performance.
ACK NOW LE DG ME NT
This work was supported in part by the Academy of Finland
under the grants #319994, #328214, and #338224, in part by
Nokia Bell Labs, and in part by the Ministry of Science and
Higher Education of the Russian Federation as part of World-
class Research Center program: Advanced Digital Technolo-
gies (contract No. 075-15-2020-934 dated 17.11.2020).
APP EN DI X A
DER IVATIO N OF (3) F OR FL AT REFLECTOR
General expression for the electrical field Efrom the TX
point source at a distance Rcan first be written as
E=rP1G1η0
4π
exp(−ikR)
R=Dexp(−ikR)
R,(10)
where η0= 120πOhm is the free space impedance, P1is the
transmit power, G1is the transmit antenna gain, and kis the
magnitude of the wavenumber. Based on this, let us first find
the field E2, impinging on the detectable vehicle with RCS σ,
after being redirected by the reflector. Let us assume that E2
can be expressed in the form of E2=D·S(ρ1, ρ2), where
Sis an unknown coefficient. Then, the power flow density
can be written as p2=|E2|2/η0, and thereon the power flux
scattered by the car at a distance Rreads p3=p2σ/4πR2.
Therefore, E3is created by a point source and can be described
as |E3|=√p3η0. This expression can be rewritten with an
introduced phase as follows
E3=rp2ση0
4π
exp(−ikR)
R=|E2|rσ
4π
exp(−ikR)
R=
=D|S(ρ1, ρ2)|rσ
4π
exp(−ikR)
R=Fexp(−ikR)
R,
(11)
where
F=D|S(ρ1, ρ2)|rσ
4π.(12)
Next, we apply the principle of reciprocity. If the source
Dexp(−ikR)
Rat any abstract point 1 creates a field at any
other abstract point 2 such that |E2|=D|S|, then the source
Fexp(−ikR)
Rplaced at the point 2 gives the field at the point
1 that can be expressed
Erx =F|S|=D|S|2σ
4π=pP1G1ση0|S|2
4π.(13)
Therefore, the power flow near the RX antenna reads
prx =P1G1σ
(4π)2|S|4,(14)
while the backscattering power can be calculated as
P2=P1G1G2σλ2
(4π)3|S|4.(15)
Accordingly, the general problem for any type of reflector is
to find S(ρ1,ρ2) in (15). Below the problem is solved for the
case of flat reflector.
Let us reuse the points 1 and 2 in our application context.
To this end, let us assume that the radar vehicle is located
at the point 1 characterized by (x1,y1,z1), and r1is the
distance from point 1 to point (x,y,z) on the reflector’s
surface. Then, r2is the distance from the reflector to the point
2, located in position (x2,y2,z2). Then, the distances r1and
r2can be written as r1=p(x−x1)2+ (z−z1)2+y2and
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r2=p(x−x2)2+ (z−z2)2+y2. The E2(x2,z2) can be
calculated if the field, being re-reflected by the surface, at
the point (x,y,z) is known. The calculation of this can be
completed by the Kirchhoff formula (simplified, the Rayleigh
version, valid for flat objects), that states
E2(x2, z2) = 1
2πZS
E2(x, y, z)∂ψ(r2)
∂#»
ndS, (16)
where ψ(r2) = exp(−ikr2)
r2while #»
nrefers to the unit vector
normal to the surface. Integration is performed over the
reflector’s surface S. The derivative along the normal of the
function ψcan be calculated as ∂ψ/∂ #»
n=grad(ψ·#»
n).
Accordingly, a straightforward question of what E2is on
the surface Sarises. Based on the boundary conditions,
the tangential component of the total electric field on the
metal is zero, i.e. Dexp(−ikR)
R+E2(x, y, z) = 0. Thus, the
reflection coefficient Γ= –1. Therefore, E2should be negative.
Additionally, the following important issue is to be noted.
Integration in (16) is carried out only over the reflector surface
S. However, the perturbed field on the edges, contributing
to the formation of the scattered signal, is not considered.
Therefore, the expression in (16) should be considered only as
an approximation. Nevertheless, the Kirchhoff approximation
gives a small error for diffraction problems on large objects
(large when compared to the wavelength), and mainly in the
directions coinciding with the directions of the mirror plane
(especially in the shadow region).
The next step is to calculate S(ρ1,ρ2) for the considered flat
reflector. Incident field Dexp(−ik)√(x−x1)2+(z−z1)2+y2
√(x−x1)2+(z−z1)2+y2taken
with a minus sign can be expressed as
E2=−Dexp(−ik)p(x−x1)2+ (z−z1)2+y2
p(x−x1)2+ (z−z1)2+y2.(17)
Next, let us take the derivative of the function ψ, written as
∂ψ
∂n =∂ψ
∂z =−(ik +1
r2
)(exp(−ikr2)
r2
)(z−z2
r2
),(18)
which for the metallic surface and kr21can be rewritten
as
∂ψ
∂n (z= 0) = ikz2exp(−ikp(x−x2)2+z2
2+y2)
(x−x2)2+z2
2+y2.(19)
Finally, the expression for E2has the following form
E2(x2, z2) = −ikz2D
2πZS
exp(−ik(pR2
1+y2+pR2
2+y2))
pR2
1+y2(R2
2+y2)dS,
(20)
where the R1and R2are as given in (5a) and (5b). This
integral over the mirror surface is calculated from −A/2
to +A/2on the x-axis, and within the corresponding ver-
tical dimensions on the y-axis. For given distances and the
wavelength in Table II, the signal does not propagate beyond
the vertical reflector’s region. Therefore, the stationary phase
approximation method is employed to calculate the integral
over y, where the finite limits of integration are replaced by
infinite ones, yielding
I=
∞
Z
−∞
h(y)e−ikφ(y)dy =s−i2π
kφ(ys)h(ys) exp(−ikφ(y00
s)),(21)
where the stationary point (ys)is found through φ0(y)=0.
Specifically, in our case,
h(y) = −ikz2D
2π(R2
2+y2)}pR2
1+y2,(22a)
φ(y) = qR2
1+y2+qR2
2+y2,(22b)
φ0(y) = y
pR2
1+y2+y
pR2
2+y2,(22c)
φ00(y) = R2
1
(R2
1+y2)3
2
+R2
2
(R2
2+y2)3
2
.(22d)
Therefore, ys= 0. Then h(ys),φ(ys), and φ00(ys)can be
expressed as
h(ys) = −ikz2D
2πR1R2
2
,(23a)
φ(ys) = R1+R2,(23b)
φ00(ys) = R1+R2
R1R2
.(23c)
Substitution of these expressions into (21) yields the following
equation of the form
E2=exp(iπ
4)√kz2D
√2π
A
2
Z
−A
2
exp(−ik(R1+R2))
R2pR1R2(R1+R2)dx, (24)
where
S(ρ1, ρ2)
4=z4
2
λ2
A
2
Z
−A
2
exp(−ik(R1+R2))
R2pR1R2(R1+R2)dx
4.(25)
Finally, substitution of (25) in (15) provides the final expres-
sion of the backscattering power in the scheme with passive
flat reflector noted in (3).
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Dmitrii Solomitckii is a Postdoctoral research fel-
low at the Unit of Electrical Engineering at Tampere
University, Finland. He received his B.Sc. and M.Sc.
degrees in electronics and microelectronics from
St. Petersburg Electrotechnical University ”LETI” in
2006 and 2008, respectively. His research interests
are antennas, wave propagation, and PHY signal
processing in wireless communication and sensing.
He also has a broad practical experience in designing
of analogue, digital and mixed electronics for critical
applications.
Carlos Baquero Barneto is a doctoral candidate
at the Unit of Electrical Engineering at Tampere
University, Finland. He received his B.Sc. and M.Sc.
degrees in telecommunication engineering from Uni-
versidad Polit´
ecnica de Madrid, Spain, in 2017 and
2018, respectively. His research interest lies in the
area of joint communication and sensing systems’
design, with particular emphasis on 5G and beyond
mobile radio networks.
Matias Turunen is a research assistant at the De-
partment of Electrical Engineering at Tampere Uni-
versity (TAU), pursuing his M.Sc degree in electrical
engineering. His research interests include inband
full-duplex radios with an emphasis on analog RF
cancellation, OFDM radar, and 5G New Radio sys-
tems.
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2021.3093822, IEEE
Transactions on Vehicular Technology
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, XXX 2021 12
Markus All´
en received the B.Sc., M.Sc. and D.Sc.
degrees in communications engineering from Tam-
pere University of Technology, Finland, in 2008,
2010 and 2015, respectively. He is currently with
the Department of Electrical Engineering at Tampere
University as a University Instructor. His current
research interests include software-defined radios,
5G-related RF measurements and digital signal pro-
cessing for radio transceiver linearization.
George P. Zhabko was born in Leningrad, Russia,
in 1949. He graduated from Leningrad Polytechnic
Institute (now Peter the Great St. Petersburg Poly-
technic University (SPbPU)), Russia with a degree
in Radiophysics and Electronics in 1972. He is
currently a Senior Lecturer with the Higher School
of Applied Physics and Space Technologies, SPbPU.
His research interests include electromagnetic wave
propagation, antennas.
Sergey V. Zavjalov was born in Leningrad, Russia,
in 1988. He received the B.S., M.S., and Ph.D.
degrees from the Peter the Great St.Petersburg
Polytechnic University (SPbPU), Russia, in 2009,
2011, and 2015, respectively, all in communication
systems engineering. He is currently an Associate
Professor with the Higher School of Applied Physics
and Space Technologies, SPbPU. His research in-
terests include digital communications, spectrally
efficient signaling, UWB signals, and WiFi.
Sergey V. Volvenko was born in Temirtau, Kaza-
khstan, in 1971. He graduated from Tomsk State
University, Russia with a degree in Radiophysics and
Electronics in 1995. He is currently a Senior Re-
searcher with the Higher School of Applied Physics
and Space Technologies of Peter the Great St. Peters-
burg Polytechnic University (SPbPU). His current
research interests include signal processing, optimal
signals for wireless communications, meteor-burst
and UWB communication networks, Industrial In-
ternet of Things.
Mikko Valkama received his M.Sc. and D.Sc. de-
grees (both with honors) from Tampere University
of Technology in 2000 and 2001, respectively. Cur-
rently, he is a full professor and head of the Unit
of Electrical Engineering at Tampere University. His
general research interests include radio communi-
cations, radio localization, and radio-based sensing,
with particular emphasis on 5G and beyond mobile
radio networks.
