In recent years, major technical innovations such as signal digitization and the introduction of fiber optics have had a major impact on the development of telecommunications. The modern high-speed telecommunications systems of today are in great demand in the microwave frequency band. At the same time, the millimeter band has become very attractive for the emergence of wireless applications [1] [2] . Recent advances in microwave circuit and device design mean that all these services can now be accessed on a single terminal, at the expense of increasingly drastic trade-offs between cost and complexity [1] - [4] .

We are witnessing far-reaching changes in the field of telecommunications, whether in mobile telephony, wireless networks, satellite networks, satellite television, radar applications (civil or military), etc. This considerable expansion has created enormous needs and has led to very rapid development of the electronic systems associated with these applications.

In electronics systems, in addition to all the functions required for digital transmission and modulation, there are also antennas for transmitting and receiving these signals. In these systems, antennae are components that require special study. To adapt antennas to the latest applications, their performance must be constantly improved. The antenna must also meet the constraints of frequency band multiplication and integration into terminal architecture [3] [4] .

These antennas are of various types, in terms of bandwidth, resonant frequency and power losses, to ensure smooth signal transmission [3] . Antennas are components in their own right in communication systems, requiring special design. As well as seeking to improve an antenna’s performance, it must be adapted to the latest applications. They must also meet the constraints of frequency band multiplication, broadband and integration. Last but not least, the characteristics of antennas must not be easily influenced by the environment.

The fields of remote sensing and target location use circular antennas such as horn or parabolic dishes [4] . However, these antennas are widely criticized on the market for their weight, high power losses and very small coverage area [5] . In addition, these antennas are narrow-band antennas, with low efficiency and poor signal-to-noise ratio. Existing antennas in this field are therefore unable to provide transmission while guaranteeing good signal quality.

In view of these counter-performances, the antennas used in radars for remote sensing are the subject of a great deal of research [6] . The demand for high-precision radars for military applications (detection and location) has led to a significant need for less complex, high-performance, low-cost electronically scanned systems. These devices overcome the mechanical drawbacks of classic systems, which are expensive and have a scanning rate that is too slow for most applications.

The current trend is to have radar systems that can detect obstacles at a certain depth and in liquid media. New antenna prototypes are being envisaged to cover a wide range of frequencies with angular scanning [5] - [15] .

Davide Comite et al. 2018 in [16] have proposed A low-cost compact planar leaky-wave antenna (LWA) offering directive broadside radiation over a significantly wide bandwidth. its design is based on an annular metallic strip grating (MSG) configuration, placed on top of a dual-layer grounded dielectric substrate. To design antenna, a method-of-moments dispersion analysis has been developed to characterize the relevant TM and TE modes of the perturbed guiding structure. this antenna is applied in radar and satellite communications at microwave and millimeter-wave frequencies as well as future 5G communication devices and wireless power transmission.

Jianfeng Chen et al. in 2020 [17] have proposed hybrid dispersion compensation method to design wideband fixed-beam leaky-wave antennas (LWAs), with the tilting angle customizable in both forward and backward quadrants.

A triangular dispersive prism constituted by metallic pins was presented to compensate for the dispersion of traditional LWAs and achieve a squint-free radiation in a relative bandwidth of 20%. However, that design suffered from the drawbacks of large geometry and limited angular range. To overcome these limitations, here a broadband gradient metasurface based on geometric phase theory is loaded in front of the prism to customize the radiation angle and reduce the total prism size.

HE Yejun et al in 2020 [18] have examined latest research progress of LWAs for 5G/B5G mobile communication systems. They showed that, the conventional classification and design methods of LWAs are introduced and the effects of the phase constant and attenuation constant on the radiation characteristics are discussed. Then two types of new LWAs for 5G/B5G mobile communication systems including broadband fixed-beam LWAs and frequency fixed beam-scanning LWAs have been summarised. The challenges and future research directions of LWAs for 5G/B5G mobile communication systems were presented.

Utkarsh Pandey et al. in 2023 [19] have presented a new thin substrate-integrated waveguide with twisted integrated–digitated capacitor-based corrugations that offers a transmission loss <0.55 dB. The presented waveguide operates at TE10 mode and is used to present a wideband beam-scanning leaky-wave antenna with an array of dumbbell-shaped slots. The antenna is shown to operate at a frequency band of 25 - 37 GHz and offers a gain >13 dBi throughout the frequency band. The proposed antenna being thin is extremely conformal and is suitable for applications in millimetre-wave off-body communication.

In this article, we propose a new microstrip leaky-wave antenna structure for radar systems. This antenna is designed using electromagnetic simulation software based on an integral formulation solved using the HFSS (High Frequency System Simulator) finite element method. Today, this finite element method (FEM) plays a fundamental role in the analysis of electromagnetic problems. The advantages of this method lie in its ability to adapt to structures with relatively complex geometrical shapes. Our structure’s excitation source ensures a periodic distribution of the excitation field over the patches.

Let’s consider a rectangular coordinate system (Ox, Oy, Oz), in which the (xOy) plane forms the separating surface between two media of different indices. Leaky-waves supported by this interface are characterised by the loss of energy by radiation as they propagate.

If the same wave can be guided along the 3 axes, in a medium where the wave number, in the case of free plane wave propagation, is K₀. It can be demonstrated that we must have:

$k_x^2+k_y^2+k_z^2=k_o^2$

where (k_x, k_y, k_z) are the propagation constants along the three respective directions (Ox, Oy, Oz). $k_o=\frac{2\pi }{{\lambda }_o}$ is the free-space wave number and λ₀ the free-space wavelength.

If the structure is infinite along (Ox) then k_x = 0 and suppose that propagation occurs along (Oy):

$k_y={\beta }_y-j{\alpha }_y$

$k_z={\beta }_z-j{\alpha }_z$

Let’s now consider the propagating structure made of a rectangular waveguide with metal patches regularly distributed along the Oz axis on one of the faces, with a periodicity p shown in Figure 1 . The phase constant of the structure is obtained by applying the Bloch-Floquet theorem [20] - [22] .

where $k_{zn}$ is the wave number of n^th mode of Floquet is given by

$k_{zn}=k_z+\frac{2\pi n}{p}=\left({\beta }_z-j{\alpha }_z\right)+\frac{2\pi n}{p}={\beta }_{zn}-j{\alpha }_z$ (1)

With ${\beta }_{zn}={\beta }_o+\frac{2\pi n}{p}$, is the phase constant of the n^th harmonic;

β_zn can take an infinity of values, β_o is the phase constant of the fundamental mode (n = 0); α_z is the attenuation constant in z direction, α_z ~ 0, almost all values of k_zn are real. However, for some negative values of n, the term β_zn may be less than k_o so k_zn is real.

In this case, the total field is fast, except for n = 0, because the fundamental mode is slow according to Ghomi [8] .

The excited modes in this case are Bloch-Floquet modes. The electric field of the wave is expressed using Boch-Floquet theorem as an infinite sum of non-uniform plane waves [20] [21] :

$E\left(x,y,z\right)={\displaystyle \sum a_n\left(x,y\right){\text{e}}^{-j{k}_{zn}z}}$ (2)

In practice, to avoid spurious lobes, it is advisable to work with only one fast harmonic [4] ; the n = −1 mode is then chosen to be the radiating mode.

The radiation harmonic n = −1 in the free space has an angle ${\theta }_{-1}$ who is given by:

${\theta }_{-1}={\sin }^{-1}\left(\frac{{\beta }_{z-1}}{k_o}\right)$ (3)

$k_o=\frac{2\pi }{{\lambda }_o}$ is the wave number and λ_o is the length of the wave in free space.

The sign ${\theta }_{-1}$ determines whether the resulting radiation is forward or backward. We can immediately see that the radiation condition is given by the following equation:

$-1<\frac{{\beta }_{zn}}{k_o}<1$ (4)

Thus to design an LWA, the following formulas are used to determine the dimensions of the antenna [18] [19] [22] [23] :

$\{\begin{array}{ll}\frac{{\lambda }_o}{\frac{\beta }{k_o}+1}\le l\le \frac{{\lambda }_o}{\frac{\beta }{k_o}-1}\hfill & \text{if}\frac{\beta }{k_o}>3\hfill \\ \frac{{\lambda }_o}{\frac{\beta }{k_o}+1}\le l\le \frac{2{\lambda }_o}{\frac{\beta }{k_o}+1}\hfill & \text{if}\frac{\beta }{k_o}<3\hfill \end{array}$ (5)

$0.2{\lambda }_o\le l\le 0.4{\lambda }_o$ (6)

$b<\frac{{\lambda }_o}{{\left({\epsilon }_{eff}-1\right)}^2}$ (7)

In this article, we have used software for an integral formulation solved using HFSS finite elements. Using a finite element calculation code. However, finite element codes have to convert partial differential equations into a system of linear equations whose coefficients depend on the type of problem and the media; an infinite space will lead to a system of infinite dimension whose numerical resolution will not be possible. This difficulty can be overcome by creating a problem approximated by an equivalent structure in a bounded volume, with boundary conditions chosen to approximate reality as closely as possible.

As an application, we propose to design an LWA meeting the following specifications:

The LWA is a microstrip antenna with a perfectly conducting ground plane ( Figure 2 ). on the top face of the substrate, metallic patches of inverted Τ shape were placed periodically with a period p to cause leakage wave radiation.

The adaptation level is excellent, comparable to structures found in the literature [24] [25] . Furthermore, analysis of the same figure illustrates −24.96 dB as the reflection coefficient level for the proposed antenna configuration. This reflects good isolation and therefore a low level of coupling between the radiating elements making up the antenna structure. This value is well below −10 dB, which means that the radiation power is sufficient.

The work in this article focuses on developing and improving the performance of new leaky-wave antenna configurations that can be adapted for use in radar systems. The study focused on the W-band, where we demonstrated the possibility of modifying resonant frequencies and reducing the number of patches required. The antenna we designed enabled us to observe the influence of the number of patches on the radiation pattern, and also to achieve low levels of minor’s lobes and good directivity at the operating frequency.

This work was carried out with the aid of a grant from UNESCO-TWAS and the Swedish International Development Cooperation Agency (Sida). The views expressed herein do not necessarily represent those of UNESCO-TWAS, Sida or kitsch Broard of Governors.