High Gain Fan-Beam Pattern Antenna Based on the Utilization of Diffracted Fields From Dielectric Slabs Edges for IoT and Sensing Applications

A high gain, low-cost antenna structure is designed for a smart car parking system. The antenna uses Printed Ridge Gap Waveguide (PRGW) technology, which is fully shielded, and suppresses any parasitic radiation from the feed, and minimizes back-lobe radiation. The proposed antenna uses a single MSL feed point, which eliminates the need for any complex feeding network design, and allows the antenna to be integrated easily with PCB transceiver circuitry. A novel technique for the design procedure is proposed, the technique provides a generalization of using either electric or magnetic excitations with dielectric or magnetic rectangular slabs. A unique physical insight accompanied with a thorough analysis of the propagation mechanism is provided. The technique has a significant impact on reducing the complexity of the feeding network. The realized structure is compact, low profile, and low cost. The beam pattern of the antenna is a Fan-Beam (Elliptical) pattern which is well suited for various sensing and Internet of Things (IoT) applications.


I. INTRODUCTION
W IRELESS connectivity is among the most essential services of the current age. Recently, the advancement in wireless connectivity led to the invention of several IoT technologies. The Internet of Things adopts a plethora of applications. A transmitting/receiving antenna is an integral component of any IoT communicating entity. The performance of these antennas is a determining factor for the whole system performance. Several interesting antenna works have been proposed in the Industrial Electronics [1], [2], [3], [4], [5], [6], [7], IoT and Sensors literature [8], [9], [10], [11], [12], [13], [14], [15]. In [16] a patch antenna with a fence-strip resonator was designed for smart homes IoT applications. For such application the antenna pattern needs to be Omni-directional. In [17] an innovative and novel glasses frame antenna for IoT applications was implemented.
In [18] a programmable beam scanning antenna without phase shifters operating in the X-band was designed for IoT relay communication. In [19] a shark-fin antenna was designed and implemented, the antenna is suitable for future railway communication systems. In [20] a multiband printed smartwatch antenna was presented, the proposed antenna aimed to increase the number of frequency bands and Omnidirectivity. In [21] a patch antenna was employed in a new structural health monitoring (SHM) system using spectrum sensing and radio-frequency identification technology to measure structural strain. In [22] an electronically steerable parasitic array radiator (ESPAR) was utilized to be used in a dense wireless sensor network operating in a harsh environment (Industrial Internet of Things "IIoT" applications). Moreover, the modelling of these antennas is pretty essential in the antenna design process, for example in [23], since the existing antenna equivalent models are inflexible because they assume rectangular antenna contour, a hybrid-equivalent surface-edge current model was proposed to overcome the limitation of the existing models, these models are pretty useful for vehicle to everything (V2X) communication [23]. One growing necessity is having an intelligent car parking system, especially in modern smart cities, these systems depend heavily on radar technologies to sense vehicles presence [24], [25], [26], [27]. Fig. 1 illustrates a typical car parking system architecture. The sensing antennas detects the reflection from the cars located underneath, and based on the reflected energy from the cars, the system can be calibrated in the digital domain to indicate the location of the empty spots, and guide new coming cars to them. Accordingly, the quality of the sensing antenna in such a system is a critical factor in determining the performance quality of the whole system. In this work we propose a low-cost, printed, fully packaged, high gain antenna that can be employed effectively in car parking systems and several radar sensing applications. The antenna possesses a fan beam type of pattern, where the beam is narrow in one plane (i.e., E-plane) and wide in the other plane (i.e., H-plane). Such beam pattern is necessary for such application due to the complexity of the vehicle chassis structure [28], where the scattering and reflections of the waves can occur at several angles and not necessarily in the direction of the main narrow beam. Therefore the fan beam pattern can detect a wide range of angles in the wide beam plane, at the same time it can provide the high boost in the gain to compensate for the high path loss at higher frequencies. In addition, having a fan beam antenna is mandatory for several radar and sensing systems [29], [30], [31], [32], [33], [34], [35], [36], [37], [38]. As high gain antennas are essential in compensating the path loss in wireless communication links [39], [40], [41], [42], [43], especially at higher frequencies [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], there are many different types of structures and varieties of techniques that can provide high gain. For example, reflector antennas are well known for their high directivity, and recently reflect/transmit-arrays have been used as well [54], [55], [56]. Lenses can focus the radiation in the intended direction, and hence possess a high-gain performance [57]. These structures can achieve high performance metrics, but on the other hand, they are well known for being bulky and not suitable for highly integrated systems. On the counterpart, planar antenna arrays are very well suited for integration and are compact in size. By doubling the number of elements in an array, an extra 3-dB can be obtained. As the size of the array (i.e., number of elements) increases, the size of the associated feeding network increases in a proportional manner [58], [59]. This increase in size not only increases the complexity of the design, but also increases the number of discontinuities and junctions in the feeding structure, consequently, the losses incorporated in such a feeding network increases [60], [61], [62]. Therefore, it is very valuable to figure out new techniques to minimize the size of the feeding network. In this work,  we propose a unique design perspective to reduce the size of the feeding network, where a single slot antenna excitation can provide a gain of 16 dBi. The proposed antenna is fully packaged using Electromagnetic Band Gap (EBG) technology, such packaging maintains a high radiation efficiency at higher frequencies, and it eliminates any back-lobe radiation. The antenna possesses a fan-beam pattern that is well suited for sensing and IoT applications. The antenna is extremely low in cost and has a relatively low profile. Fig. 2 shows the main building block of the proposed structure. Part (a) shows the electric case where an infinitesimal electric delta excitation is located between two dielectric slabs with a relative permittivity (ε r ). Part (b) shows the dual case of an infinitesimal magnetic delta excitation between two magnetic slabs with a relative permeability (μ r ). In [48], it was shown that inserting a dipole in between two metallic sheets can increase the gain of the structure significantly. The concept was analyzed theoretically using the Uniform Theory of Diffraction (UTD) [63], and was verified numerically using the Method of Moments (MOM) and the Finite Element Method (FEM) (i.e., full-wave solution), it was also shown how diffracted fields could act as secondary sources, and by controlling their phases, the radiation characteristics of the structure can be controlled. In [50], it was shown that this concept could be extended to the E-and H-plane by inserting the dipole in a metallic rectangular ring rather than just having it between two sheets. The concept was detailed and different possibilities to replace the electric source with a magnetic source, and the metallic ring with a dielectric material were shown. The dielectric material reflectivity can be maximized if the dielectric thickness is an odd integer multiple of a quarter wavelength (Appendix A). In this work, we show that rather than utilizing the dielectric slabs to operate as reflectors, the dielectric slabs can still be used when their transmission coefficient is increased instead. In such case, the transmitted waves from the slabs can be utilized to excite another pair of slabs and generate diffracted fields that act as secondary sources, and boost the radiation in the boresight direction. Electric current sources are usually realized by electric dipole antennas, and magnetic current sources are usually realized by narrow slot antennas. To illustrate the concept, we realize the structure in Fig. 2-(a) using an electric dipole antenna between two dielectric slabs. The dielectric constant of the used slabs is 10.2, the dipole antenna length is 6.7 mm, and the center frequency of operation is 20 GHz. Table 1 shows the dimensions of the rectangular dielectric slabs and the separation distance from the dipole antenna. Two cases are studied, case (a) when the thickness of the slab is chosen to maximize reflectivity, and case (b) when the thickness of the slab is chosen to maximize transmission. The obtained directivities in each case are: D a = 8.5218 dBi (Reflection), and D b = 8.3634 dBi (Transmission). Fig. 3 shows the electric field heat map in each case; as can be noticed in the transmission case, the wave propagates in the slab, and it gets detached at the other interface of the slab. Thus, the radiation is increased in the end-fire direction (i.e., transverse to the boresight direction, θ =90 • ).

II. SINGLE PAIR (INFINITESIMAL EXCITATION BETWEEN TWO SLABS)
In the reflection case, the wave reflection is maximized from the slab, and the radiation in the end-fire direction is  minimized. Fig. 4 shows the radiation patterns in the principal planes. The radiation is strong at the 90-degree angle in the H-plane for the transmission case, while it is minimal for the reflection case as expected. The radiation pattern in the E-plane is not affected as the slabs are only located in the H-plane of the dipole. It is also worth noting that the dielectric slab has a finite size in the z-axis, and therefore the effective dielectric constant has to be used instead of the absolute dielectric constant value. The effective dielectric constant can be obtained using a full-wave solver. It is also important to note that the effective dielectric constant value can vary depending on the wave-front, polarization, and the distance from the source. The absolute dielectric constant calculations give a good initial condition to set the slab dimensions and converge to the effective dielectric constant value with the aid of a full-wave simulator (HFSS).

III. MULTIPLE PAIRS (INFINITESIMAL EXCITATION IN BETWEEN MULTIPLE PAIR OF SLABS)
Fig . 5 shows the extended version of the proposed configuration in Fig. 2-(a). To illustrate the concept, the electrical current excitation, which is usually realized by a dipole antenna, radiates in an Omni-directional fashion in the H-plane, the radiated wave impinges on the interface of the first dielectric slab (located at both the right and left sides of the dipole). By designing the thickness of this slab along

FIGURE 7. H-plane (top) and E-plane (bottom) for multiple dielectric slabs (different number of pairs of dielectric slabs is used), transmission case.
the x-axis, the slab reflectivity can be minimized, and hence the wave can propagate through the dielectric slab, and then it gets reradiated at the other side to impinge on the next adjacent dielectric slab. Due to the finite size of the dielectric slab in the z-axis, edge diffracted fields are generated; those diffracted fields can be seen as secondary generated sources.
By controlling the distance between the slabs and the source, the phases of these secondary sources can be controlled, in such a way the phases are set to be equal, so that those secondary sources radiate in phase in the boresight direction. Fig. 6 shows the electric field heat map of the proposed structure. In the xz-plane, the diffracted fields can be noticed at the edges of the slabs. In the xy-plane, it can be noticed that the field intensity is reduced by moving away from the source, as in each slab a portion of the energy is diffracted from the edges and reradiated; this sequence continues until the wave energy is completely vanished. This mechanism has a tremendous advantage in tapering  the diffracted secondary sources' power level to reduce the side-lobe level. It is important to notice that the effective dielectric constant of the slab is less than the actual dielectric constant of the material due to its finite size in the z-axis. The depicted understanding in Fig. 5, along with a full-wave solver can be used to optimize such structure to maximize the gain performance. Table 2 shows the distances between the adjacent slabs; the dipole and slab dimensions are the same as for Fig. 2a structure. Fig. 7 shows the radiation patterns in principle planes for a different number of pairs of dielectric slabs. As can be seen, the beam width in the H-plane is reduced by increasing the number of pairs, and the side lobes at 90 degrees are reduced with each extra pair. From the E-plane, it is easier to see the gradual increase in the directivity for each extra pair. In Fig. 7, zero pair refers to the dipole directivity (i.e., without dielectric slabs). Fig. 8 shows the maximum directivity for each number of pairs, as can be noticed, after the 4 th pair, the directivity increment saturates to almost 13 dBi; this is expected as the energy is lost gradually in each pair in the form of diffracted fields. At a certain point, the structure might be seen as an antenna exciting several DRAs parasitically. Some works, as in [64], [65], [66], [67], [68], [69], a DRA excited several adjacent parasitic DRAs. However, in those works, the distance between the elements is very small electrically, where the elements couple strongly through the near field, and sometimes the DRAs together can be seen as one large DRA element with air gaps. Those gaps can be equivalently perceived as lumped element phase shifters. In such a case, the aperture is enlarged which enhances the gain, and the coupling to the source alters the input impedance. However, in this work the distance from the source is increased so that it can go up to 0.4λ o , and the distance between the dielectrics can go up to 0.55λ o . This distance allows the wave detaching from the source to spread spherically in space before reaching the adjacent element. In addition, such distance from the source reduces the effect of the adjacent dielectric slabs on the input impedance of the source. This technique, therefore, can have a higher gain performance by maximizing the aperture of the antenna.

IV. PRACTICAL REALIZATION CONSIDERATIONS
Electric dipoles require differential feeding. This usually can be done with a Balun circuit. Therefore, realizing electric dipoles is more complex to achieve than realizing magnetic sources, which can be easily realized by a narrow slot. Perfect Magnetic Conductor (PMC) reflectors do not exist in nature, and they require periodic structures to emulate them [70]. Dielectric slabs are ubiquitous and more affordable than magnetic slabs. Therefore, a hybrid configuration is proposed in Fig. 9, where it uses a magnetic source (slot antenna), and the dielectric slabs, and a Perfect Electric Conductor (PEC) as a half-plane. In such case, the dielectric material thickness should be modified to attain the required equal phase shifts of the diffracted fields and allow the wave to propagate through them and get transmitted to the next adjacent slab. Fig. 10 shows the 3D HFSS model of the proposed structure in Fig. 9 with the following slab dimensions: width = 3.75 mm, length = 16 mm, and height = 1.5 mm. The slot length is 6.7 mm, and its width is 0.5 mm. The spacing between the slabs is given in Table 3. Fig. 11 shows the magnetic field heat map and the 3D radiation pattern, as noticed, the radiation pattern is a fan-beam (elliptical) type of pattern. Fig. 12 shows the radiation patterns in the principal planes achieving a 16.5 dBi directivity.

V. ANTENNA ARRAY CONFIGURATION
The proposed element in the previous section is electrically large (i.e., 5.2λ o wide), which raises the question of whether the element can be further expanded in a larger linear array without generating grating lobes? The answer is simply yes, where the element can be viewed as a sub-array (i.e., subarray of diffracted fields or secondary sources). This subarray can be overlapped, as shown in Fig. 13 by another sub-array. In such case, the entire array can be viewed as a superposition of the two arrays, the first is the one shown in red, referring to real sources (slots), and the second is shown in yellow, referring to induced fields (diffracted fields). The two linear arrays are separated by the height of the slab (i.e., 1.5 mm); in such case, the height can be neglected, and the whole two linear arrays can be considered as one linear array. As explained in previous sections, tapering of the diffracted fields also plays a role in further suppressing the grating lobes. Fig. 13 shows the HFSS 3D model of the antenna array configuration. Fig. 15 shows the magnetic field heat map. The slab dimensions are: width = 3.75mm, length = 16 mm, height = 1.5mm. The dielectric constant is 10.2, the loss tangent is 0.0023.
The slot length is 6.7 mm, and its width is 0.5 mm. The distance between the slots is 78.25 mm (5.2 λ o ). The spacing between the slabs is shown in Table 4. Fig. 16 shows the radiation patterns in principle planes, a directivity of 18.9 dBi is obtained. Fig. 17 shows the directivity for both one slot and two slot excitations, the difference is almost 2.4 dB, and this is due to sharing the elements in between the slots rather than just doubling the whole single slot structure, which can make it less than the expected 3 dB difference. Sharing the elements is essential to maintain suppressed side-lobes. The increase of the directivity of the antenna is always associated with increasing the antenna electrical aperture size, which is proportional to the physical aperture. The ratio of the effective electrical aperture to the physical aperture is known as the aperture efficiency, which is 17.8% for the single slot excitation, and 20.3% for the two slots. Even though the distance between the slots has increased, it still has eliminated the need for a complicated feeding by just feeding two elements. This implies that only one power divider is needed. This significantly reduces the complexity of the feeding network and the associated losses with discontinuities and junctions. This technique becomes more suitable for higher frequencies, as in mm-wave applications, where the physical distance becomes very small and antennas turn to be more efficient. In addition, a narrow relative bandwidth can translate to a large absolute bandwidth at mmwave frequencies. Table 5 shows a comparison illustrating the number of feed points needed for each element type ("ME Dipole" stands for a "Magneto Electric Dipole"); the number of feed points is reduced by the increase of element gain. As can be seen, this method provides a considerable reduction in the number of feed points.

VI. REALIZATION OF THE PROPOSED ANTENNA STRUCTURE
To realize the antenna structure, the slot antenna was fed by a packaged microstrip line, such method has a great advantage in suppressing any back-lobe radiation from the slot, and it maintains neat radiation characteristics. A mushroom cell periodic structure is used to realize the electromagnetic bandgap (Appendix B). Fig. 18 shows the realization of the proposed structure. As shown in the transparent view, the location of the microstrip T-stub termination with respect to the mushroom cells is crucial in introducing resonances with proper quality factors to match the slot antenna to 50 ohms. Table 6 shows the corresponding dimensions of the structure; the spacing between the dielectric slabs is the same as in Fig. 11, and Table 3. It is worth noting that the matching bandwidth is 10%, however as explained before, the antenna is a narrow band in terms of pattern stability; the pattern is stable within 3% of the center frequency. Due to the change of the phases at the edges with the frequency, the side lobes level will start increasing gradually as the frequency shifts from the center frequency. Fig. 19 shows the radiation pattern of the antenna at different frequencies within its 3% bandwidth. It is also worth noting that the long feed line exists to connect the antenna to the connector; such a long line can be eliminated in an integrated system by having the transceiver output close to the feed point. The long line and connector losses can be de-embedded in such case. Figs. 20-22 show the prototyping results, the pattern was characterized in an anechoic chamber; a standard gain horn comparison method was used for the gain measurement. An acceptable agreement with simulated results is achieved. Fig. 23 demonstrates the relation between the source phase and diffracted field phases; the source field can be fairly  approximated to a spherical source as given in (1). The phases of each edge consequently can be calculated as given by (2)- (6). An additional phase shift is introduced by the material (θ m ). In this case, it is approximated by (π + π /4), which is only important for the first element as other element phases become relative, the π is due to the fact that high permittivity materials act close to the metallic surface looking from outside, and the π /4 comes from the diffraction coefficients term [71].
Even though this approach is not rigorous, it is still very effective in understanding the radiation mechanism and converging to the desired design. The wavenumbers in free space and the dielectric slab are calculated as in (7) and (8), respectively. The dielectric constant used is the effective dielectric constant (ε r−eff = 6.65); it is worth mentioning that the  polarization of the source affects the effective dielectric constant. As can be seen, the wave propagates in two mediums (i.e., free space and dielectric material). The dielectric material reflectivity can be maximized if the dielectric thickness is an odd integer multiple of a quarter guided wavelength, and it can be minimized (i.e., the transmission is maximized) if the dielectric thickness is a multiple of a half-guided wavelength. For this mode of operation, maximizing the transmission coefficient is desired. Table 7 shows the dimensions obtained from calculations and from the full-wave simulation; as can be noticed, the difference is small. Fig. 24 shows the calculated phases for 5 pairs of dielectric slabs. It can be seen that by increasing the diffracted sources, the slope of the edge element becomes larger, which means that the bandwidth of this method is narrow (3%). A lower number of slabs can be used to enlarge the bandwidth at the expense of the gain value. Due to the symmetry of the structure, the antenna does not steer by frequency. However, the side-lobes increase as the left and right sides start steering in opposite directions. The impedance bandwidth independently depends on the source type only. This suggests that this method is more suitable for high-frequency narrowband applications. According to the spatial distribution of the diffracted elements and the main source, the array factor can be calculated as in (9) [60], [61], [62]. Assuming  an equal phase and equal amplitude for each source (i.e., I n = 1, and δ n = 0), we obtain the array factor as given in Fig. 25. As can be seen, in the case of taking the center to center spacing between the dielectric slabs, the grating lobes peaks between 60-90 degrees.
I n e −jkd n sin(θ)+δ n (9) Table 8 indicates the center to center spacing. Taking the sub-element spacing between the diffracted sources further reduce the side lobes, note that the transmitting aperture generates diffracted fields which are embedded within the transmitting faces aperture radiation, as such the sub-element spacing counts for the radiating aperture diffracted sources. The element factor and the power tapering of the diffracted sources compensate such side lobes and further reduce them below −10 dB. As shown in Fig. 6, the diffracted sources scatter inward toward the boresight, and also their strengths are tapered as well, which eventually gives the total pattern obtained by the full-wave simulation in Fig. 7 with suppressed side-lobes. Nonetheless, it is not trivial to predict the pattern factor of the diffracted sources, as each source is excited and interacts with the diffracted elements.   Fig. 26 shows the calculated radiation efficiency of the proposed structure, as can be seen the radiation efficiency goes up to 89%. A 16 dBi gain is achieved with just a single feed point, and this has a positive impact on maintaining a high radiation efficiency by avoiding the losses that would rise from the use of a power divider feeding network. In addition, the solution is fully printed and does not require any bulky waveguide feed or transitions, the long feed line exists only for characterization purposes, in an integrated solution, the long line can be eliminated by having the transceiver chipset near the antenna. Table 9 shows the calculated aperture efficiency. As can be noticed, the radiation efficiency is constant regardless of the number of dielectric slabs due to the use of a single feed point in all cases. On the other hand, the aperture efficiency peaks when one pair of dielectric slabs is used and drops gradually with the increase of number of slabs. This suggests that this technique is more suitable for higher frequencies such as mm-wave frequencies. At mm-Wave frequencies the radiation efficiency is more of a concern compared to the aperture efficiency (i.e., size is not an issue, as the size of the antenna is very small at such frequency). In addition, a narrow relative bandwidth can translate to a large absolute bandwidth at mm-wave frequencies. The aperture efficiency is calculated using (10)- (11).
where, λ is the free space wavelength, D o is the maximum directivity, A em is the maximum effective, A p is the physical area, and η ap is the aperture efficiency. A detailed quantitative analysis along with a semi analytical model using the Uniform Theory of Diffraction (UTD) was derived in [71]. The unique aspect is that UTD along with the diffracted sources perspective give clear explanation and analysis of the behavior of such structure. It is noted in Table 9 that the directivity increment is not consistent as in Fig. 8, especially for pairs three and four. This is due to the finite size of the ground plane, which will produce edge-diffracted fields from the end-fire radiation coming from the transmitting face of the slab. Those edge-diffracted fields can affect the boresight peak directivity. In addition, Table 9 shows the directivity values based on the spacing between the slabs that is determined by the final optimized structure with five slabs. Where the spacing values were optimized together to obtain a better SLL performance for the whole structure (also note that the realized EBG slot is not as ideal as the dipole case). In [72] it was shown that the beam pattern can be further focused to a pencil-beam type of pattern by conforming the shape of the dielectric slabs with the wave-front of the radiating element. A pencil-beam pattern is required for point to point line of sight communication systems. Further analysis reveals the relation with Fresnel zones. As such the qualitative, UTD, and Fresnel zones approaches coincide with each other to conclude the characteristics of the antenna, these approaches are very powerful in obtaining a very straightforward and fast design procedure. Table 10 shows a comparison of the antenna performance metrics with other works in the literature, the proposed antenna has a good merit in terms of its gain performance and boresight beam direction when compared to other works. It is worth noting that these antennas are travelling wave antennas, where their radiation characteristics changes rapidly with frequency sweep, even though their impedance bandwidth can be significantly larger, the stable bandwidth of operation is limited to 3% around the operating frequency.

VII. CONCLUSION
This paper has proposed a unique design perspective to reduce the size of the feeding network. A low profile and a compact size antenna with a single feed point has been realized, the antenna has achieved a peak gain of 16 dBi, and an average gain of 14 dBi over a 3% fractional bandwidth, the side lobes have been adequately suppressed with a level less than −10 dB. This technique had a significant impact on reducing the complexity of the design of the feeding network. As the antenna has a narrow bandwidth and turns to be more efficient at higher frequencies, employing the antenna in a larger number of element array with a triangular lattice at mm-wave frequencies can be very useful for various mm-wave applications. Potential future work would be studying the power tapering quantitatively to implement any distribution like Chebyshev and others. For example, in [73], a series fed patch antenna array produces a 10 dBi gain with reduced side lobes; however, it uses a power divider feeding network, the feeding network can be eliminated by applying the proposed concept in this work.   shows the calculated reflection coefficient magnitude versus the slab thickness; as can be seen, maximum reflection and minimum transmission can be achieved when the slab thickness is multiple odd integers of a quarter guided wavelength. The dielectric constant of the slab is 10.2. Fig. A.3 shows the reflection coefficient for a quarter guided wavelength slab for all the angles of incidence [74], [75].  [79], [80], [81], [82].