# Conformal Wide-Angle Scanning Leaky-Wave Antenna for V-Band On-Body
Applications

Pratik Vadher, Zvonimir Šipuš, Anja K. Skrivervik, Qihang Zeng, Ronan Sauleau,
John S. Ho, Giulia Sacco, and Denys Nikolayev Manuscript received July XX,
2024, revised XX X, 2024.This project has received funding from the French
Agence Nationale de la Recherche (ANR) through the Project MedWave under Grant
ANR-21-CE19-0045; and by the European Union’s Horizon Europe research and
innovation program through the Marie Skłodowska-Curie IN-SIGHT project
N∘101063966\. (Corresponding authors: Denys Nikolayev,
<EMAIL_ADDRESS>Giulia Sacco, giulia.sacco@univ-rennes1.fr)This
work is supported by the European Union through European Regional Development
Fund (ERDF), Ministry of Higher Education and Research, CNRS, Brittany region,
Conseils Départementaux d’Ille-et-Vilaine and Côtes d’Armor, Rennes Métropole,
and Lannion Trégor Communauté, through the CPER Project CyMoCod.P. Vadher, R.
Sauleau, G. Sacco, and D. Nikolayev are with the IETR – UMR 6164, CNRS / Univ
Rennes, FR-35000 Rennes, France.Z. Šipuš is with the Faculty of Electrical
Engineering and Computing, University of Zagreb, 10000 Zagreb, CroatiaA. K.
Skrivervik is with the Microwave and Antenna Group, Ecole Polytechnique
Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.Q. Zeng, and J. S. Ho are
with the Department of Electrical and Computer Engineering, the Institute for
Health Innovation and Technology, and the N.1 Institute, National University
of Singapore, Singapore 117583

###### Abstract

Wearable on-body millimeter-wave (mmWave) radars can provide obstacle
detection and guidance for visually impaired people. However, their everyday
performance is hindered by the rigid form factor and limited scanning range.
In this article, we propose a low-profile, fast-scanning leaky-wave antenna
(LWA) operating in the unlicensed V-band ($5764\text{\,}\mathrm{GHz}$) to be
integrated for on-body applications such as lightweight portable frequency-
modulated continuous wave (FMCW) radars. The proposed LWA consists of
meandering microstrips that can conform to the human body curvatures while
maintaining beam-forming and beam-scanning properties. Experimental results
demonstrate that the planar LWA achieves a realized gain above
$10\text{\,}\mathrm{dB}$ with a fan-beam steering range in the H-plane from
$-40\text{\,}\mathrm{\SIUnitSymbolDegree}$ to
$43\text{\,}\mathrm{\SIUnitSymbolDegree}$ over the operating frequency band
while the half power beam-width (HPBW) is within
$20\text{\,}\mathrm{\SIUnitSymbolDegree}$. Since for the foreseen application
the antenna is supposed to conform to the user’s body, the performance is also
analyzed for a bent condition. The beam steering range changes to
$-32\text{\,}\mathrm{\SIUnitSymbolDegree}$ to
$50\text{\,}\mathrm{\SIUnitSymbolDegree}$ when placed on the knee
(corresponding to $80\text{\,}\mathrm{mm}$ radius). Under bending conditions,
the LWA exhibits a maximum degradation of $1.75\text{\,}\mathrm{dB}$, while
the HPBW increases to $25\text{\,}\mathrm{\SIUnitSymbolDegree}$. This shows
that due to the small size of the antenna, the impact of bending is low and
the beam-forming and beam-scanning property of the designed LWA remain intact.
Furthermore, we enable 2-D spatial scanning by employing an array of twelve
LWAs with phased excitation, extending the scanning range in the E-plane from
$-40\text{\,}\mathrm{\SIUnitSymbolDegree}$ to
$40\text{\,}\mathrm{\SIUnitSymbolDegree}$, while the HPBW remains below
$20\text{\,}\mathrm{\SIUnitSymbolDegree}$ across the operational frequency
range.

###### Index Terms:

leaky-wave antenna (LWA), wearable radars, V-band, higher spatial order,
meandering microstrip antenna, conformal antenna.

##  I Introduction

Enhancing navigation aids for visually impaired people is essential for
improving their mobility and independence. Recent advancements in mobile
technology have led to an increased interest in developing wearable devices as
assistive tools for individuals with visual impairments [1, 2, 3, 4]. Of the
various sensing modalities, millimeter-wave (mmWave) radars offer a cost-
effective, lightweight, and robust sensing solution, since they do not depend
on the ambient light conditions and do not affect the user’s privacy. In
particular, short range frequency-modulated continuous wave (FMCW) radars can
be implemented in a compact electronic system due to their low power
consumption and low profile [5, 1]. Traditionally these sensors have been
placed on rigid objects (e.g., white canes and engineered glasses) which can
burden the user [1, 6]. An improved solution consists in placing the radar on
the user’s body in a way that does not hamper their movements, and that is
comfortable to be worn [7].

To facilitate radar-based sensing within a wearable form factor, unlicensed
V-band extending from $57\text{\,}\mathrm{GHz}64\text{\,}\mathrm{GHz}$ is a
promising solution for radar applications, since it provides a high range
resolution, while being less susceptible to the interference from nearby
devices [8]. A compact radar can be implemented with a low profile unobtrusive
conformal antenna. When positioning the antenna on the user’s body, the
compact size of the conformal antenna at these frequencies, reduces the impact
of body curvature (radius ranging from
$40\text{\,}\mathrm{mm}240\text{\,}\mathrm{mm}$ [9]) by limiting the bending-
related distortions.

Figure 1: An on-body FMCW V-band radar for sensing and detecting obstacles in
the outdoor environment. (a) Array of 12 LWAs. The scan in the Y–Z plane is
due to frequency scanning, while the scanning in X–Z plane is due to
electronic scanning. (b) A single LWA and radiated fan-beam in the Y–Z plane.
(c) Possible antenna placements and corresponding curvature radii.

Leaky-wave antennas (LWAs) can be fed very easily and provide main-beam
steering capability with frequency due to the dispersive nature of the guiding
media [10, 11, 12]. Since the antenna is to be placed conformally on the
user’s body, it is of paramount importance that the antenna is flexible [13,
14]. To improve flexibility and reduce manufacturing costs, microstrip-based
LWAs [15, 16, 17, 18] are preferable to substrate integrated waveguide (SIW)
based LWAs [19, 20, 21] given the absence of via holes. Additionally, periodic
meandering microstrips LWAs provide a good control over the path taken by the
electromagnetic (EM) wave in the guiding medium, since the microstrip
intervals between the corners—corresponding to the radiating discontinuities
in this type of LWA—can be tailored to ensure optimal polarization and
scanning range of the main fan-beam [15, 22, 23].

For radar applications where localization is required, it is advisable to have
large angular coverage [5, 24]. To fulfill this purpose, the use of LWA in
combination with FMCW radars represents a promising solution to limit the
number of channels and the use of complex phase shifters [25, 26]. LWAs
proposed earlier for such applications in V-band [16, 24] can have large
scanning range, but are characterized by a low rate of change of the main beam
pointing direction with frequency, i.e., a low beam steering rate
($S_{\textrm{m}}$). To limit the spectral resources for a given scanning range
[11, 27, 28], a faster $S_{\textrm{m}}$ is required.

Here we propose and demonstrate a conformal LWA that can be fabricated using a
single printed layer and provides wide-scanning angle from
$-40\text{\,}\mathrm{\SIUnitSymbolDegree}$ to
$43\text{\,}\mathrm{\SIUnitSymbolDegree}$ and
$-32\text{\,}\mathrm{\SIUnitSymbolDegree}$ to
$50\text{\,}\mathrm{\SIUnitSymbolDegree}$ when deformed on a curved surface
over the operating range. The unit cell is composed of 4 meanders. The
microstrip-based design of the LWA provides an effective control over the size
of unit cell and hence over $S_{\textrm{m}}$. The length of the microstrip
intervals between the mitred corners (radiating discontinuities) are tailored
to improve cross-polarization discrimination (XPD) ratio over a wide operation
band $57\text{\,}\mathrm{GHz}64\text{\,}\mathrm{GHz}$.

The paper is structured as follows. Section II describes the proposed antenna
system and conformal wearable implementations. Section III explains the leaky-
wave theory of the proposed antenna followed by the construction of a
meandered guiding medium resulting in a slow wave structure (SWS). A technique
to modify the SWS to obtain a radiation, while eliminating the open stopband
(OSB) is subsequently explained. Section IV describes the design of feeding
structure and the measurements of the designed prototype in planar and
conformal environments. Section V contains the comparison with state-of-the-
art followed by conclusions.

##  II Operational Principle and Antenna Requirements

A lightweight wearable on-body radar should be able to detect and warn users
of obstacles, as well as create a map of their surroundings to aid their
navigation [Fig. 1 (a,b)]. The proposed antenna system is designed to be used
in combination with an FMCW radar. To enable the 2-D scanning, an array of
twelve LWAs is used as shown in Fig. 1(a). The scanning in the Y–Z plane is
ensured by the leaky-wave phenomenon, while the beamforming in the X–Z plane
is obtained electronically, by modifying the excitation of the different LWAs
[29, 30]. Furthermore, the antenna can be positioned conformally to the body
surface, as shown in the Fig. 1(b). Some possible locations along with the
typical curvature radii[9] are shown in Fig. 1(c). The LWA is backed by a
ground plane to limit the radiation towards the user [16].

##  III Leaky-Wave theory for the Proposed Antenna

Figure 2:  Conductor backed periodic meandering microstrip LWA.

Figure 3: Brillouin diagram of the proposed leaky-wave meandering microstrip
structure.

Fig. 2 shows the design of the proposed periodic meandering microstrip based
LWA. A $0.254\text{\,}\mathrm{mm}$-thick layer of Rogers 3003
($\varepsilon_{r}~{}=~{}$3.0, $\tan\delta~{}=~{}0.0010$) is utilised as
substrate. The structure leaks energy due to the mitred corners which act as
radiating discontinuities. The leaky radiation due to a periodic structure can
be analyzed by the Bloch–Floquet theorem with the use of spatial harmonics
[31, 32]. The phase constant corresponding to the $n^{\mathrm{th}}$ space
harmonic $\beta_{n}$ satisfies

$\beta_{n}p=\beta_{0}p+2n\pi\,,$ (1)

where $n$ ranges from $-\infty$ to $+\infty$. Here $\beta_{0}$ is the zeroth
order spatial harmonic of a periodic LWA.

The spatial harmonics that satisfy the condition $|\beta_{n}|p<|k_{0}|p$
contribute to the leaky-wave radiation. A guiding medium with periodic
radiating discontinuities can scan the main beam from backward to forward
direction.

If most of the power from the structure is radiated, the direction of maximum
radiation $\theta_{max,n}$ corresponding to the $n^{\mathrm{th}}$ spatial
harmonic is given by [32, 33, 34, 35]

$\theta_{max,n}=\sin^{-1}(\beta_{-n}p/k_{0}p)\,,$ (2)

where $k_{0}$ is the free space wave number.

For the proposed structure, the $n=-2$ spatial harmonic, as shown in the
Brillouin diagram in Fig. 3, is responsible for radiation in desired operating
range ($57\text{\,}\mathrm{GHz}64\text{\,}\mathrm{GHz}$) .

Consequently, according to equation (2), when the phase difference across the
unit cell ($\beta_{-n}p$) is zero, the direction of the main beam associated
to the $n^{\mathrm{th}}$ spatial harmonic is broadside. Since the spatial
harmonic $n=-2$ is responsible for radiation in the desired band, the phase
difference across the unit cell with a period $p$ from equation (1)
corresponds to:

$\beta_{-2}p|_{f=f_{\mathrm{d}}}=0\rightarrow\beta_{0}p|_{f=f_{\mathrm{d}}}=4\pi\,,$
(3)

where $f_{\mathrm{d}}$ is the desired frequency corresponding to the broadside
radiation for $n=-2$. Equation (3) further implies that
$\beta_{\mathrm{0,tem}}|_{f=f_{\mathrm{d}}}\times l=4\pi$ [15, 22]. Here,
$\beta_{\mathrm{0,tem}}$ is the phase constant of the microstrip media, $l$
denotes the total pathlength of the meandering microstrips. The pathlength of
the microstrip is calculated based on the model proposed by [23].

###  III-A Non-radiating Guiding Medium with Dispersion Control

A meandering microstrip structure with equal meanders is shown in Fig. 4
(depicted as solid boundary line). The phase contributions corresponding to
the horizontal and vertical intervals of the meander are listed in Table I. A
guiding medium based on meandering microstrip allows to finely control the
path of the travelling wave by altering the length of the intervals between
the corners of the meander [36].

The proposed SWS is designed such that a single meander results in a phase
difference of $\pi$ at $f_{\text{d}}$. The rate of change of the phase
constant ($\beta$) with frequency (i.e., the dispersion rate) can be increased
by decreasing the period $p_{0}$ of the single meander. The period $p_{0}$ can
be reduced—while maintaining the same electrical length of the meander—by
decreasing the horizontal interval and increasing the vertical interval of the
meander by the same amount. Consequently, the impact of the variation of the
horizontal segment (denoted by $\zeta$) on $\beta$ is shown in Fig.5(a)
indicating a high control over the dispersion rate of the meandering
microstrip guiding medium.

In the desired operating range of 57 to $64\text{\,}\mathrm{GHz}$, the
dispersion constant of the structure lies outside the light cone, resulting in
a confined surface wave within the guiding medium without any leaky radiation.
This is illustrated in Fig. 5(b), which shows the magnitude of the E-field
obtained from the full-wave simulation of 72 cascaded meanders (equivalent to
the final length of the LWA), all having equal lengths with $\zeta=\pi/15$ and
$\Delta\psi=0$ at $f_{\text{d}}$.

Figure 4:  Meandered microstrip guiding medium with equal meanders (shown as solid line) behaving as non-radiating slow-wave structure; and unit cell formed by 4 modulated meanders (shown in grey) for constructive radiation leading to leaky-wave behaviour. TABLE I: Geometrical parameters (Fig. 4) and corresponding phase differences at the design frequency $f_{\text{d}}$. Segment | Denoted by | Phase diff. at $f_{\text{d}}$ | Prototyped Dimensions
---|---|---|---
|  |  | (rad) | (mm)
Horizontal length of meander | $\mathrm{d}$ | $\zeta$ |  $\pi/$15 | 0.11
Vertical length of meander | $\mathrm{s}$ | $\pi/2-\zeta$ |  $\pi/2-\pi/$15 | 0.868
Change in vertical length of meander | $\Delta{x}$ | $\Delta\psi$ | 0.3 | 0.158

(a)

(b)

(c)

Figure 5: (a) Phase constant vs frequency for a structure with equal meanders (b) Distribution of the absolute value of the $\bm{E}$ field in the H-Plane (Y–Z Plane). Confined surface waves at $f_{\text{d}}$ for a structure with equal meanders ($\Delta\psi=0$) and leaky-wave radiation for the case $\Delta\psi=0.3$ as the wave travels down the meandering microstrips, (c) Changes in the directivity of the proposed structure at $f_{\text{d}}$ (in the broadside radiation) for two cases of $\Delta\psi$ (for $\zeta=\pi/15$). TABLE II: Phase shifts of $\bm{E}$ at the mitred corners corresponding to $\mathrm{R}_{i,1}$ and $\mathrm{R^{a}}_{i,1}$ at $f_{\text{d}}$ induced by the pathlength. Corner |  $\mathrm{R^{a}}_{1,1}$ |  $\mathrm{R}_{1,1}$ |  $\mathrm{R^{a}}_{2,1}$ |  $\mathrm{R}_{2,1}$ |  $\mathrm{R^{a}}_{3,1}$ |  $\mathrm{R}_{3,1}$ |  $\mathrm{R^{a}}_{4,1}$ |  $\mathrm{R}_{4,1}$
---|---|---|---|---|---|---|---|---
Spatial Vector Direction |  $\mathrm{(\hat{x}+\hat{y})}$ |  $\mathrm{(-\hat{x}-\hat{y})}$ |  $\mathrm{(\hat{x}+\hat{y})}$ |  $\mathrm{(-\hat{x}-\hat{y})}$ |  $\mathrm{(\hat{x}+\hat{y})}$ |  $\mathrm{(-\hat{x}-\hat{y})}$ |  $\mathrm{(\hat{x}+\hat{y})}$ |  $\mathrm{(-\hat{x}-\hat{y})}$
Phase at $f_{\text{d}}$ |  $\frac{\pi}{2}+\frac{\zeta}{2}-\Delta\psi$ |  $\pi-\frac{\zeta}{2}-+2\Delta\psi$ |  $\frac{3\pi}{2}+\frac{\zeta}{2}-+\Delta\psi$ |  $2\pi-\frac{\zeta}{2}$ |  $\frac{5\pi}{2}+\frac{\zeta}{2}++\Delta\psi$ |  $3\pi-\frac{\zeta}{2}++2\Delta\psi$ |  $\frac{7\pi}{2}+\frac{\zeta}{2}++\Delta\psi$ |  $4\pi-\frac{\zeta}{2}$
TABLE III: Phase shifts of $\bm{E}$ at the mitred corners corresponding to $\mathrm{L}_{i,1}$ and $\mathrm{L^{a}}_{i,1}$ at $f_{\text{d}}$ induced by the pathlength. Corner |  $\mathrm{L^{a}}_{1,1}$ |  $\mathrm{L}_{1,1}$ |  $\mathrm{L^{a}}_{2,1}$ |  $\mathrm{L}_{2,1}$ |  $\mathrm{L^{a}}_{3,1}$ |  $\mathrm{L}_{3,1}$ |  $\mathrm{L^{a}}_{4,1}$ |  $\mathrm{L}_{4,1}$
---|---|---|---|---|---|---|---|---
Spatial Vector Direction |  $\mathrm{(-\hat{x}+\hat{y})}$ |  $\mathrm{(\hat{x}-\hat{y})}$ |  $\mathrm{(-\hat{x}+\hat{y})}$ |  $\mathrm{(\hat{x}-\hat{y})}$ |  $\mathrm{(-\hat{x}+\hat{y})}$ |  $\mathrm{(\hat{x}-\hat{y})}$ |  $\mathrm{(-\hat{x}+\hat{y})}$ |  $\mathrm{(\hat{x}-\hat{y})}$
Phase at $f_{\text{d}}$ |  $\frac{\pi}{2}-\frac{\zeta}{2}-\Delta\psi$ |  $\frac{\zeta}{2}$ |  $\frac{3\pi}{2}-\frac{\zeta}{2}-+\Delta\psi$ |  $\pi+\frac{\zeta}{2}-+2\Delta\psi$ |  $\frac{5\pi}{2}-\frac{\zeta}{2}++\Delta\psi$ |  $2\pi+\frac{\zeta}{2}$ |  $\frac{7\pi}{2}-\frac{\zeta}{2}++\Delta\psi$ |  $3\pi+\frac{\zeta}{2}++2\Delta\psi$

###  III-B Meandered LWA

The radiation resulting from a microstrip based LWA can be analysed in terms
of residual magnetic current densities (${{\mathcal{J}_{\mathrm{m}}}}$) at the
corners [22, 37]. The residual currents at each corner are shown in Fig. 4. To
achieve constructive addition of the electric fields from the residual
currents, the vertical length of the meanders can be periodically varied.

To obtain a periodic unit cell, four meanders designed in the previous section
are cascaded in series [Fig.4]. It is possible to modify the vertical length
of the meanders without changing the total pathlength of the unit cell ($4\pi$
for four meanders at $f_{\text{d}}$) to obtain a radiation in the far-field at
$f_{\text{d}}$. This is achieved by decreasing the vertical length of the
first meander by ${\Delta x}$, and increasing the length of the second meander
by the same quantity. A length ${\Delta x}$ results in a phase delay of
$\Delta\psi$ at $f_{\text{d}}$ (Table I). The third and fourth meanders are
modified accordingly to obtain a symmetric unit cell. The resultant unit cell
is depicted as grey in the Fig.4

For the proposed unit cell, the corners are denominated by
$\mathrm{L}_{{{i,n}}}$, $\mathrm{L^{\text{a}}}_{{{i,n}}}$,
$\mathrm{R^{\text{a}}}_{{{i,n}}}$, and $\mathrm{R}_{{{i,n}}}$, where $i$ $\in$
([$1,\mathrm{4}$]) indicates the $i^{\mathrm{th}}$ meander within the unit
cell, and $n\in[1,\mathrm{N}]$ corresponds to the $n^{\mathrm{th}}$ unit cell,
$\mathrm{N}$ being the total number of unit cells (Fig.4).

The microstrip line intervals result in a phase delay between the corners. The
phases corresponding to the corners of the first unit cell are indicated in
Table II and Table III.

Since equation (3) is satisfied at $f_{\text{d}}$—the radiation occurs in the
broadside direction. Subsequently, the ratio of the total electric field
generated by N such unit cells is obtained as the summation of the electric
fields for the unit cell [38] shown in Fig.4 generated by the
${{\mathcal{J}_{\mathrm{m}}}}$ oriented towards the direction
$\mathrm{(+\hat{x}+\hat{y})}$ is:

$\frac{E^{\text{tot}}_{\mathrm{{R^{a}}}_{2,n}|f=f_{\mathrm{d}}}}{E^{\text{tot}}_{\mathrm{{R^{a}}}_{1,n}|f=f_{\mathrm{d}}}}=\frac{\sum_{{n}=1}^{\mathrm{N}}e^{-j({\frac{3\pi}{2}+\frac{\zeta}{2}-\Delta\psi}+4(n-1)\pi)}}{\sum_{{n}=1}^{\mathrm{N}}e^{-j({{\frac{\pi}{2}+\frac{\zeta}{2}-\Delta\psi}}+4(n-1)\pi)}}=-1$
(4)

$\frac{E^{\text{tot}}_{\mathrm{{R^{a}}}_{4,n}|f=f_{\mathrm{d}}}}{E^{\text{tot}}_{\mathrm{{R^{a}}}_{3,n}|f=f_{\mathrm{d}}}}=\frac{\sum_{{n}=1}^{\mathrm{N}}e^{-j({\frac{7\pi}{2}+\frac{\zeta}{2}+\Delta\psi}+4(n-1)\pi)}}{\sum_{{n}=1}^{\mathrm{N}}e^{-j({{\frac{5\pi}{2}+\frac{\zeta}{2}+\Delta\psi}}+4(n-1)\pi)}}=-1$
(5)

The ratio of the total electric field generated by the summation of the
contributions ${{\mathcal{J}_{\mathrm{m}}}}$ oriented towards the direction
$\mathrm{(-\hat{x}-\hat{y})}$ at $f_{\text{d}}$ corresponds to:

$\frac{E^{\text{tot}}_{\mathrm{{R}}_{2,n}|f=f_{\text{d}}}}{E^{\text{tot}}_{\mathrm{{R}}_{1,n}|f=f_{\text{d}}}}=\frac{\sum_{{n}=1}^{\mathrm{N}}e^{-j({2\pi-\frac{\zeta}{2}}+4(n-1)\pi)}}{\sum_{{n}=1}^{\mathrm{N}}e^{-j({{\pi-\frac{\zeta}{2}-2\Delta\psi}+4(n-1)\pi})}}=-e^{-2j\Delta\psi}$
(6)

$\frac{E^{\text{tot}}_{\mathrm{{R}}_{4,n}|f=f_{\mathrm{d}}}}{E^{\text{tot}}_{\mathrm{{R}}_{3,n}|f=f_{\mathrm{d}}}}=\frac{\sum_{{n}=1}^{\mathrm{N}}e^{-j({4\pi-\frac{\zeta}{2}}+4(n-1)\pi)}}{\sum_{{n}=1}^{\mathrm{N}}e^{-j({{3\pi-\frac{\zeta}{2}+2\Delta\psi}}+4(n-1)\pi)}}=-e^{2j\Delta\psi}$
(7)

Equations (4) and (5) show that the electric fields at the corners
$\mathrm{R^{a}}_{i,n}$ are opposite to each other, while the electric field
vectors at $\mathrm{R}_{i,n}$ ($i\in[1,4]$) contribute to the far-field. By
repeating the same analysis for the corners $\mathrm{L}_{i,n}$ and
$\mathrm{L^{\text{a}}}_{i,n}$ (the phase at these are indicated in Table III)
it is possible to derive the same conclusion.

Note that if $\Delta\psi=0$, the resultant electric field is zero, reducing
the structure to the non-radiating SWS shown in Fig. 4 (equal meanders,
depicted as solid line).

An analytical model based on the equations is created to verify the
effectiveness and the results are compared with full-wave-simulations as shown
in Fig. 5(c) at $f_{\text{d}}$. As can be observed, when $\Delta\psi=0$, all
the meanders are of equal size leading to no radiation, when the meanders
become unequal with $\Delta\psi=$ 0.3, there is radiation. The above model
adopts simplifying assumptions, treating radiation sources as magnetic line
currents at the corners, as proposed by [23, 39]. Additionally, it assumes
that the attenuation of the traveling wave down the line is minimal and that
the bends are matched, resulting in no reflections. Although this approach
[40] loses information about mutual coupling, the effect of OSB and substrate
surface waves, it offers closed-form design solutions to guide the design of
the proposed meandering-microstrip LWA for the desirable radiation
characteristics at the frequency of broadside radiation.

###  III-C OSB Mitigation

A periodic structure has stop-bands, that result in a very low transmission of
the wave through the structure and in high energy being reflected back to the
source in this band of frequencies [31]. OSB occurring inside the radiation
zone limits the scanning near the the broadside direction [31, 41] and needs
to be mitigated.

The Bloch impedance $Z_{\mathrm{s}}$ can be used to characterize the presence
of OSB [42]. The $Z_{\mathrm{s}}$ can be calculated from the ABCD-parameters
obtained from the S-parameters computed in full-wave simulations [43]:

$Z_{\mathrm{s}}=\frac{-2\times\mathrm{B}}{(\mathrm{A}-\mathrm{D}-\sqrt{(\mathrm{A}+\mathrm{D})^{2}-4})}\,.$
(8)

Fig. 6(a) indicates that there is a resonance in the band around
$f_{\mathrm{d}}$ contributing to OSB. The impact of OSB on the antenna
performance in terms of realized gain of the LWA is shown in Fig. 6(b). There
is a severe reduction in gain in the broadside direction if OSB is not
mitigated.

Asymmetry can be introduced in the unit cell to mitigate OSB as shown in [44,
15] and [45]. Changing the angles of corners of the final two meanders as
shown in the Fig.6(c) introduces a small phase shift between the first couple
and the second couple meanders to avoid strong resonance and large reflection
in the band around $f_{\mathrm{d}}$. OSB mitigation can be observed from the
Bloch impedance $Z_{\mathrm{s}}$ plot with frequency [see Fig. 6(a)]. For
$\zeta=\pi/$15 and $\Delta\psi~{}=~{}$0.3, a value of $\delta q$ equal to
$0.05\text{\,}\mathrm{mm}$ is selected. The increase in the realized gain can
be observed at the broadside direction in Fig. 6(a). Additionally, it can be
noted that, since at $f_{\mathrm{d}}$ the contribution to the far-field is not
provided by the corners $\mathrm{L^{\text{a}}}_{{{i,n}}}$ and
$\mathrm{R^{\text{a}}}_{{{i,n}}}$, the change in the angle of these corners
will not affect the fields radiated from the contributing corners
$\mathrm{L}_{{{i,n}}}$ and $\mathrm{R}_{{{i,n}}}$.

Following the mitigation of OSB, the maximum realized gain obtained at the
broadside frequency as a function of $\Delta\psi$ is depicted in Fig.7 with
$\mathrm{N}=$ 30 unit cells for $\zeta=\pi/$15.

(a)

(b)

(c)

Figure 6: (a) Bloch impedance $Z_{\mathrm{s}}$ vs frequency, (b) Impact on the
realized gain before and after removal of OSB at the frequency $f_{\text{d}}$
in the broadside direction. Here, $f_{1}=f_{\mathrm{d}}-$
$1\text{\,}\mathrm{GHz}$ and $f_{1}=f_{\mathrm{d}}+$ $1\text{\,}\mathrm{GHz}$.
(c) Removal of OSB by changing the angle of mitred corner for the third and
fourth meander of the unit cell.

Figure 7: Realized gain at $f_{\text{d}}$ (in the broadside radiation) as a
function of $\Delta\psi$ (for $\zeta=\pi/15$).

###  III-D Impact of $\Delta\psi$ in the Operating Band

Full-wave simulations with $\mathrm{N}=$ 30 unit cells have been performed to
quantify the impact of $\Delta\psi$ on the LWA far-field in the band of
operation ($5764\text{\,}\mathrm{GHz}$) after the mitigation of OSB.

Fig.8(a) shows the change in realized gain for different values of
$\Delta\psi$ with $\zeta=\pi/$15\. Figures 7 and 8(a) show that the realized
gain initially increases with an increase in $\Delta\psi$, but then levels off
after certain value of $\Delta\psi$ ($=$ 0.3 in the current case). This
indicates that the unit cell becomes a more effective radiator as $\Delta\psi$
increases up to this point. As the radiation from each unit cell increases,
the effective aperture of the LWA reduces, resulting in larger 3-$\mathrm{dB}$
beamwidth as indicated in the Fig.8(b).

As indicated earlier, for a frequency scanning antenna of an FMCW radar, the
three parameters scanning rate, realized gain and 3$-\mathrm{dB}$ beamwidth
are important [11, 46]. In the proposed LWA, $\zeta$ can be varied to control
the scanning rate and hence the angular scanning of the antenna. $\Delta\psi$
can be then be increased to obtain desired realized gain and beamwidth values.
For the current prototype, the chosen parameters are listed in Table I which
result in realized gain of $10\text{\,}\mathrm{dB}$ and angular scanning of
$80\text{\,}\mathrm{\SIUnitSymbolDegree}$ symmetrically through broadside and
across the operating band.

(a)

(b)

(c)

Figure 8: (a) Maximum realized gain following the removal of the OSB in the
H-plane ($\phi=\pi/2$) for different $\Delta\psi$ as a function of the beam
pointing direction, (b) 3-$\mathrm{d}\mathrm{B}$ beamwidth of scanning beam vs
frequency for different values of $\Delta\psi$ at $f_{\text{d}}$. (c) Maximum
broadside realized gain at $f_{\text{d}}$ as a function of the number of unit
cells for $\Delta\psi=$ 0.3 and $\zeta=\pi$/15.

###  III-E Impact of the Number of Unit Cells

To maximise the radiation efficiency and radiate most of the energy from the
leaky-wave structure, while keeping it compact, determining the number of unit
cells to be included in the final design is of the utmost importance. Fig.
8(c) shows the change in gain with the increase in the number of unit cells.
After $\textrm{N}=$ 18 unit cells, the change in gain is minimal.

Further increasing the number of unit cells would result in a reduction of the
radiation efficiency as well as in an increase of the antenna dimensions. It
is worth noticing that the performance of a longer antenna is more likely to
be impacted by the bending. Hence $\textrm{N}=$ 18 unit cells is set as the
optimal length.

##  IV Prototype and Measurments for the Proposed Antenna

TABLE IV: Dimensions of the feed and the terminating patch. Dimensions |  Physical dim. (mm)
---|---
$\mathrm{Co_{SL}}$ |  2.8
$\mathrm{Co_{T}}$ |  1.5
$\mathrm{Co_{G}}$ |  2.47
$\mathrm{Co_{L}}$ |  1.75
$\mathrm{t_{50}}$ |  0.69
$\mathrm{Tx}$ |  2.5
$\mathrm{W_{patch}}$ |  2.55
$\mathrm{L_{patch}}$ |  1.23

###  IV-A Design of the Feed

(a)

(b)

(c)

Figure 9: (a) Design of the antenna feed. (b) Design of the patch to terminate
the LWA. (c) Fabricated prototype of the LWA.

Figure 10: CATR measurement setup for the prototype.

Figure 11: (a) Simulated and Measured S parameters for the planar condition.
Co-polar realized gain in the H-plane for frequencies $f=$ (b)
$57\text{\,}\mathrm{GHz}$ (c) $60\text{\,}\mathrm{GHz}$ (d)
$62\text{\,}\mathrm{GHz}$ (e) $64\text{\,}\mathrm{GHz}$ (f) Simulated and
measured realized gain and beamwidth for planar conditions.

Figure 12: (a) Simulated and measured S parameters for the bent condition with
radius of curvature ${R}=$ $80\text{\,}\mathrm{mm}$. Co-polar realized gain in
the H-plane for frequencies $f=$ (b) $57\text{\,}\mathrm{GHz}$ (c)
$60\text{\,}\mathrm{GHz}$ (d) $63\text{\,}\mathrm{GHz}$ (e)
$64\text{\,}\mathrm{GHz}$ (f) Simulated and measured realized gain and
beamwidth for convex conditions.

(a)

(b)

(c)

Figure 13: Variation of the realized gain as a function of frequency for (a)
planar, and (b) convex bent condition obtained from measurements. The dotted
line indicates the 3-$\text{\,}\mathrm{dB}$ beamwidth. (c) Radiation and total
efficiency of the proposed antenna.

Figure 14: (a) Array of 12 LWAs for pencil beam scanning. (b) U–V plane of the
normalized realized gain showing the scanning in 2-D.

The designed LWA based on a conductor-backed meandering microstrip is fed via
a $1.85\text{\,}\mathrm{mm}$ end-launch Southwest connector. The feed is
designed to avoid the use of vias in the transition from connector (coaxial)
to microstrip. Hence a conductor-backed co-planar waveguide transition is used
as shown in the Fig. 9(a). This is done to avoid the spurious radiation
occurring during the transition from co-axial feed to the microstrip. The feed
is designed to provide optimal performance in the antenna operating range
($57\text{\,}\mathrm{GHz}64\text{\,}\mathrm{GHz}$). The dimensions are listed
in the Table IV.

###  IV-B Design of the Patch to Terminate the LWA

Since, only one port of the LWA is used for scanning the space, the second
port of the LWA is terminated with a matched patch to avoid the use of second
connector, that would increase the dimension of the antenna and increase the
complexity of the measurement setup in the anechoic chamber (inset figure in
Fig. 10). The dimensions for the patch are listed in the Table IV. The
S-parameters for the patch are shown in the Fig. 9(b).

###  IV-C Performance of the Designed Prototype

####  IV-C1 In Planar conditions

The designed antenna is prototyped and the compact antenna test range (CATR)
measurements are performed at the CAMILLE facilities of IETR. A photo of the
prototyped LWA and the measurement setup are shown in Fig. 9(c) and Fig. 10
respectively. The length of the prototyped LWA is 5.77$\lambda_{\mathrm{d}}$
($\lambda_{\mathrm{d}}$ is wavelength in free space at $f_{\mathrm{d}}$). The
$\mathrm{S}_{11}$ is shown in Fig.11 (a) indicating that the antenna with the
feed remains well matched in the band of operation. As mentioned earlier, the
LWA is designed to be linearly polarized. This can be observed in the
radiation pattern in Fig.11(b–e). The LWA scans from
$-40\text{\,}\mathrm{\SIUnitSymbolDegree}$ to
$43\text{\,}\mathrm{\SIUnitSymbolDegree}$ in the range
$5764\text{\,}\mathrm{GHz}$. The 3-$\mathrm{dB}$ beamwidth throughout the
operational band remains below $20\text{\,}\mathrm{\SIUnitSymbolDegree}$. The
maximum side-lobe level remains below $10\text{\,}\mathrm{dB}$ throughout the
operational band.

The scanning rate ($S_{\mathrm{m}}$) of the LWA is
$12.1\text{\,}\mathrm{\SIUnitSymbolDegree}\text{/}\mathrm{GHz}$. The realized
gain of the antenna stays above $10\text{\,}\mathrm{dB}$ across the
operational range as shown in the Fig. 11(f).

####  IV-C2 In Conformal Conditions

The performance of the antenna in the bent condition is investigated
corresponding to the conformal placement on the knee (for $R=$
$80\text{\,}\mathrm{mm}$) as shown in the Fig. 1 (b). The corresponding
$|\mathrm{S}_{11}|$ is plotted in Fig. 12 (a) indicating the antenna remains
well matched. The normalized realized gain is reported in Fig. 12(b–e). The
beam-forming operation remains intact throughout the operational band for a
radius of curvature $R>$ $80\text{\,}\mathrm{mm}$ (lower radii are not
investigated currently). The realized gain decreases up to
$1.5\text{\,}\mathrm{dB}$ when the $R=$ $80\text{\,}\mathrm{mm}$ as shown in
Fig.12 (f).

The 3-$\text{\,}\mathrm{dB}$ beamwidth varies from
$15\text{\,}\mathrm{\SIUnitSymbolDegree}$ to
$23\text{\,}\mathrm{\SIUnitSymbolDegree}$ as depicted in Fig. 12 (f).
Additionally, there is a shift in the angular scanning domain in bent
condition of the LWA when compared to the planar condition [47] as shown in
the Fig. 13 (a–b). The change is less than
$8\text{\,}\mathrm{\SIUnitSymbolDegree}$ across the band of operation.

The radiation and total efficiency of the proposed LWA are shown in Fig. 13(c)
varying from $-3.3\text{\,}\mathrm{dB}$ to $-2\text{\,}\mathrm{dB}$.

###  IV-D Enabling 2-D Scanning using Array of LWAs

An LWA, as shown in Fig. 1(b), radiates a beam enabling scanning in the X–Z
plane. If 2-D scanning with a pencil beam is required [Fig.1 (a)], an array of
LWAs using beam-forming phased excitation can be employed.

Fig.14 (a) shows the design of an array of 12 LWAs which can be implemented on
a printed circuit board (PCB). This arrangement enables a pencil-beam scanning
in the X–Z and Y–Z planes as shown in Fig.14 (b). The arrangement starts by
creating a pair of LWA; mirrored and excited with a phase difference of $\pi$.
Six repetitions of such a configuration are placed at a distance
$d_{\text{{ant}}}=$ $3\text{\,}\mathrm{mm}$. The phase difference between each
pair can be varied to obtain beamforming in the X–Y plane.

The realized gain radiation pattern for different frequencies and phase
excitations is plotted in the Fig. 14 (b) projected in the U–V plane
($\mathrm{U}=\sin\theta\cos\phi$, $\mathrm{V}=\sin\theta\sin\phi$).

Additional analysis such as the relative distance between the LWAs and phased
excitation between the subsequent LWAs for planar or conformal conditions can
be performed as carried out in [48].

###  IV-E Comparison with Other LWA Designs in V-band

In [49, 50, 51], the authors propose a frequency scanning LWA based on SIW
technology. However, the $S_{\mathrm{m}}$ is limited to
$2.15\text{\,}\mathrm{\SIUnitSymbolDegree}\text{/}\mathrm{GHz}$,
$4.45\text{\,}\mathrm{\SIUnitSymbolDegree}\text{/}\mathrm{GHz}$ and
$8.77\text{\,}\mathrm{\SIUnitSymbolDegree}\text{/}\mathrm{GHz}$ respectively.
LWAs proposed in the works [52, 53] demonstrate higher or comparable scanning
rate than the one proposed in this work, however, these antennas do not offer
control over the scanning rate and the realized gain at the same time. A
guiding medium created using the meander shaped SIW is proposed in [24, 5] to
provide additional control over scanning rate, however the angular coverage is
limited to $65\text{\,}\mathrm{\SIUnitSymbolDegree}$ over the
$5764\text{\,}\mathrm{GHz}$. Conformal analysis has been performed in the work
[54] but the scanning occurs over a large frequency range spanning
$2862\text{\,}\mathrm{GHz}$. Additionally, these LWAs utilize SIW or multi-
layer guiding structures, increasing the fabrication complexity.

##  V Conclusion

A single-layer low-profile V-band LWA is designed and prototyped for on-body
radar applications. To allow for bending, the antenna is designed on a
flexible substrate (Rogers 3003). The proposed meandering microstrip structure
allows for an accurate control the of scanning rate and realized gain. The
meandering microstrip design is fast scanning and avoids the use of vias to
increase the flexibility and reduce manufacturing defects and costs.
Investigation of the performance of the antenna is carried out for different
conformal environments. The results suggest that the beam-forming operation of
the LWA remains intact even when placed on conformal surfaces although the
peak realized gain reduces by $1.5\text{\,}\mathrm{dB}$. Furthermore, the
antenna design based on meandering microstrip can easily be integrated with a
PCB. Future work involves the integration of the designed antenna with the
commercially available hardware to realize an on-body radar.

## Acknowledgment

The authors would like to express gratitude to Christos Monochristou for his
technical insights into leaky-wave antennas and periodic structures, which
contributed significantly to the research.

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