Steerable microwave antenna and method thereof

Abstract

The present document discloses a steerable-beam microwave antenna, arranged for steering a beam relative to a longitudinal axis of the antenna, comprising: a discrete transmitarray comprising a plurality of sub-wavelength phase-shifting unit-cells, rotatably mounted for rotating about said longitudinal axis, having an aperture orthogonal to said longitudinal axis; a feeder for emitting and / or receiving a microwave signal to and / or from the discrete transmitarray, comprising at least one rotatable feeding part; wherein the unit-cell layout of the discrete transmitarray has a phase distribution which superimposes a phase gradient along a transversal axis orthogonal to said longitudinal axis and a rotationally-symmetric phase correction centred on said longitudinal axis. It is also disclosed a method for operating and a method of manufacturing said steerable-beam microwave antenna.

Description

D E S C R I P T I O N STEERABLE MICROWAVE ANTENNA AND METHOD THEREOF TECHNICAL FIELD

[0001] The present disclosure relates to a steerable microwave antenna and method thereof, in particular microwave Risley prisms based on transmit-arrays (TAs). BACKGROUND

[0002] Wide angle beam steering is a fundamental requisite for millimeter-wave communication systems. Mechanical scanning using two transmit-arrays (TAs) with independent axial rotation movements - known as the Risley prism approach – is considered as a potential enabling technology for many cost-driven applications. There is an ongoing research effort to improve this solution, however, grating lobes are still a main limitation for the operation of these antennas.

[0003] Over recent years, there has been numerous developments on broadband satellite communication (SATCOM) user terminals, as this is a key technology that is expected to drive market acceptance of internet through satellite services [1], [2]. Specifically, for satellite-on- the-move (SOTM) applications and fixed satellite connectivity with low and medium earth orbit (LEO / MEO) satellites, steerable antenna solutions are required. Electronically steerable phased array antennas are an obvious candidate thanks to their high flexibility and scalability [3]. However, their high cost and power consumption are still major limitations for mass market applications, despite the interesting synergies with millimeter-wave terrestrial technologies [4].

[0004] Mechanically steered antennas are considered a viable solution for low-cost user terminals. However, they are generally quite bulky, which typically limits their use to fixed and satellite-on-the-pause (SOTP) services or slow-moving platforms (e.g. cruise chips). The concept of passive transmit-array (TA), also referred to in some works as phase shifting surface (PSS) or metasurface, has gained a lot of interest over the last decade. Some early developments considered the combination of translation and rotation [5], or two independent rotations [6] to achieve two-dimensional (2D) beam steering using low-cost multi-layer PCBtechnology. The second concept is an adaptation of the well-known Risley prism. The original idea of combining two dielectric wedges or prisms to deflect a beam is attributed to John Herschel (1792-1871), who used prisms in his astronomical work to measure the spectra of stars. It was later popularized by Samuel Risley (1845-1920) who developed a convenient rotary mechanism for use in ophthalmology [7].

[0005] Adapting the Risley prism concept to the microwave domain, taking full advantage of the benefits of TA technology and specifically its wide-band or dual-band characteristics [8], has led to several promising developments and is a topic attracting a lot of attention from researchers. The first development [6] used a centralized feeding point (i.e., horn antenna), resulting in a rather high profile. A similar approach was recently implemented in [9]. The high profile was mitigated in

[0010] using a partially reflecting surface (PRS) to lower the height of the feeding section. A dual-polarized continuous transverse slot (CTS) array design was used in

[0011] for the same purposes.

[0006] Interestingly, the work in [6] considered the possibility to combine the focusing PSS together with the first prism to reduce the number PSS required from 3 to 2. A similar idea can be implemented in array-fed Risley prisms combining the array and the first prism functionality into a single array design with a deflected beam. This concept was recently reported in

[0012] ,

[0013] . These solutions all suffer from a same limitation, as radiation patterns exhibit high side lobes in some planes. These high side lobes are found to be a consequence of the phase wrapping implemented in TAs to reduce the phase range required for a given unit cell design, resulting in a pattern with a large period. This is a major problem in user terminal applications, as antenna patterns need to comply with stringent mask regulations to avoid inter- and intra-system interference.

[0007] These facts are disclosed in order to illustrate the technical problem addressed by the present disclosure. GENERAL DESCRIPTION

[0008] It is an aim of the present invention to provide a solution to mitigate high side lobes in microwave Risley prisms based on TAs. This design limitation is equivalent to grating lobes in phased array theory, so the same terminology is employed herein.

[0009] It is disclosed a steerable-beam antenna for microwave frequencies, or a steerable- beam microwave antenna, arranged for steering a beam relative to a longitudinal axis of the antenna, comprising: a discrete transmitarray comprising a plurality of sub-wavelength phase- shifting unit-cells, rotatably mounted for rotating about said longitudinal axis, having an aperture orthogonal to said longitudinal axis; a feeder, in particular a rotatable feeder, for emitting and / or receiving, i.e., feeding, a microwave signal to, and / or from the discrete transmitarray, in particular comprising at least one rotatable feeding part, i.e., an active part; wherein the unit-cell layout of the discrete transmitarray has a phase distribution, which superimposes of a phase gradient, of an additive phase gradient along a transversal axis orthogonal to said longitudinal axis and of a rotationally-symmetric phase correction centred on said longitudinal axis.

[0010] Alternatively, it is also disclosed a steerable-beam microwave antenna comprising a feeding structure having at least one part mounted for rotation about a longitudinal axis of the antenna, and a discrete transmitarray composed of sub-wavelength unit-cells mounted for rotation about said longitudinal axis, with its aperture orthogonal to said longitudinal axis, wherein the discrete transmitarray unit-cell layout follows a phase distribution adding a phase gradient along a transversal axis, orthogonal to said longitudinal axis, and a rotationally symmetric phase correction, defined around said longitudinal axis, for side lobe level reduction.

[0011] In an embodiment, the discrete transmitarray is a first discrete transmitarray, and wherein said feeder comprises: a fixed antenna, e.g., a low-gain antenna, for emitting and / or receiving a microwave signal; a second discrete transmitarray comprising a plurality of sub- wavelength phase-shift unit-cells, rotatably mounted for rotating about said longitudinal axis, having an aperture orthogonal to said longitudinal axis; a fixed microwave lens for changing a spherical wave emitted and / or received by the fixed antenna into a plane-wave for feeding the second discrete transmitarray; wherein the unit-cell layout of the second discrete transmitarray has a phase distribution which superimposes a phase gradient along a transversal axis orthogonal to said longitudinal axis and a rotationally-symmetric phase correction centred on said longitudinal axis compensating, in part or in full, the rotationally- symmetric phase correction of the first discrete transmitarray for side lobe level reduction.

[0012] In an embodiment, the unit-cell layout of the second discrete transmitarray has a phase distribution which superimposes a phase gradient along a transversal axis orthogonal to said longitudinal axis and a rotationally-symmetric phase correction centred on said longitudinal axis cancelling the rotationally-symmetric phase correction of the first discrete transmitarray for side lobe level reduction.

[0013] In an embodiment, a feeding structure comprises a fixed antenna, preferably a fixed low-gain antenna or a fixed small antenna, such as a horn antenna or a patch antenna, a second discrete transmitarray composed of sub-wavelength unit-cells mounted for rotation about said longitudinal axis of the antenna, with its aperture orthogonal to said longitudinal axis, and a fixed third discrete transmitarray comprising sub-wavelength unit-cells with its aperture orthogonal to said longitudinal axis, wherein the second discrete transmitarray unit- cell layout follows a phase distribution adding a phase gradient along a second transversal axis, orthogonal to said longitudinal axis, and a rotationally symmetric phase correction, defined around said longitudinal axis and compensating the rotationally symmetric phase correction of the first discrete transmitarray, for side lobe level reduction, and wherein the third discrete transmitarray unit-cell layout follows a phase distribution changing the spherical wave produced by the fixed small antenna into a plane-wave along said longitudinal axis.

[0014] In an embodiment, the feeding structure comprises: a fixed small antenna, such as a horn antenna or a patch antenna, and a second discrete transmitarray composed of sub- wavelength unit-cells mounted for rotation about said longitudinal axis of the antenna, with its aperture orthogonal to said longitudinal axis, wherein the second discrete transmitarray unit-cell layout follows a phase distribution adding a phase gradient along a second transversal axis, orthogonal to said longitudinal axis, and a rotationally symmetric phase correction, defined around said longitudinal axis and cancelling the rotationally symmetric phase correction of the first discrete transmitarray, for side lobe level reduction, and a further phase correction changing the spherical wave of the fixed small antenna into a plane-wave along said longitudinal axis.

[0015] In an embodiment, the feeding structure is an array with a phase distribution adding a phase gradient along a second transversal axis, orthogonal to said longitudinal axis, and a rotationally symmetric phase correction, defined around said longitudinal axis and cancellingthe rotationally symmetric phase correction of the first discrete transmitarray, for side lobe level reduction.

[0016] In an embodiment, the rotationally symmetric phase correction, defined around said longitudinal axis, for side lobe reduction, produces a spherical wave with a virtual focal point located below the plane collocated with the aperture of the feeding structure, on the opposite side of the at least one transmitarray.

[0017] In an embodiment, the rotationally symmetric phase correction, defined around said longitudinal axis, for side lobe reduction, produces a spherical wave with a virtual focal point located above the plane collocated with the aperture of the feeding structure, on the side of the at least one transmitarray.

[0018] In an embodiment, at least one of the transmitarrays is composed of sub-wavelength unit-cells formed on a dielectric medium.

[0019] In an embodiment, at least one of the transmitarrays is composed of sub-wavelength unit-cells obtained as perforations in a dielectric medium.

[0020] In an embodiment, at least one of the transmitarrays is composed of sub-wavelength unit-cells formed of metallic inserts in a dielectric medium.

[0021] In an embodiment, at least one of the transmitarrays is composed of sub-wavelength unit-cells formed as a stack of printed circuit boards comprising metallic inserts on dielectric slabs.

[0022] In an embodiment, the feeding structure is a corporate array with a parallel signal distribution in the aperture controlling both the amplitude and the phase for further side lobe reduction.

[0023] In an embodiment, the feeding structure, or the feeder, is a radial line slot array or a continuous transversal slot array with a serial signal distribution in the aperture controlling both the amplitude and the phase for further side lobe reduction.

[0001] In an embodiment, wherein one or more rotatable parts are arranged to be mechanically actuated, in particular by a motor.

[0002] In an embodiment, the Steerable-beam microwave antenna comprises a data processor, i.e. a microcontroller unit, configured for actuating an actuator or motor forrotating one or more of said transmitarrays by adjusting a relative angle between the transversal axis of the first discrete transmitarray and the transversal axis of the second discrete transmitarray, for primarily elevation beam steering.

[0003] In an embodiment, the steerable-beam microwave antenna comprises a data processor, i.e. a microcontroller unit, configured for actuating an actuator or motor for rotating one or more of said transmitarrays by adjusting a sum angle of the transversal axis of the first discrete transmitarray with the transversal axis of the second discrete transmitarray, for azimuth beam steering.

[0024] It is further disclosed a user terminal comprising the steerable beam antenna wherein the at least two rotating parts are mechanically actuated and the relative angle between said first and second transversal axes produces primarily elevation beam steering while the combined rotation of all rotating parts produces azimuth beam steering.

[0025] It is also disclosed a method for operating the steerable-beam microwave antenna, the method comprising actuating an actuator or motor for rotating one or more of said transmitarrays by adjusting a relative angle between the transversal axis of the first discrete transmitarray and the transversal axis of the second discrete transmitarray, for elevation beam steering.

[0026] It is further disclosed a manufacturing method for obtaining a steerable-beam microwave antenna, arranged for steering a beam relative to a longitudinal axis of the antenna, comprising: providing a discrete transmitarray comprising a plurality of sub- wavelength phase-shifting unit-cells, rotatably mounted for rotating about said longitudinal axis, having an aperture orthogonal to said longitudinal axis; providing a rotatable feeder for emitting and feeding a microwave to the discrete transmitarray; wherein the unit-cell layout of the discrete transmitarray has a phase distribution of an additive phase gradient along a transversal axis orthogonal to said longitudinal axis and of a rotationally-symmetric phase correction centred on said longitudinal axis.

[0027] The co-design of the phase correction of the two rotating surfaces contributes to reducing the high side lobes in standard Risley prims implemented using transmitarrays.

[0028] Experimental results herein disclosed confirm that the predicted grating lobes of the conventional design are mitigated, corresponding to a significant reduction of the side lobelevel (SLL) in the complete scanning range of operation. For the given full-dielectric Ka-band design example, it is possible to scan up to 55 degrees with SLL < -8.3 dB and scan loss of -3.6 dB, whereas, with the conventional approach, the same scan implies SLL < -4.4 dB and a scan loss of -6.1 dB. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The following figures provide preferred embodiments for illustrating the disclosure and should not be seen as limiting the scope of the invention.

[0030] Figure 1: Schematic representation of a microwave Risley prism TA configuration with a centralized feeding point using (a) a separate collimating lens and (b) combining the collimating lens with the first deflecting TA prism, including the definition of the TA rotation angles ^^1and ^^2, and associated beam pointing direction ( ^^^^, ^^^^).

[0031] Figure 2: Schematic representation of the phase variation profile example of the two TAs of a conventional Risley prism configuration with design parameter values ^^0= 25° , ^^ = 30 ^^ ^^ ^^, ^^ = 140 mm, ^^ = 100 mm.

[0032] Figure 3: Schematic representation of geometric locus using orthographic projection coordinates of the position of the grating lobes caused when using a conventional Risley prism TA configuration.

[0033] Figure 4: Phase variation profile example of the two TAs of the Risley prim configuration according to the present invention.

[0034] Figure 5: Amplitude and phase transmission response of the full-dielectric unit cells at the design frequency (30 GHz).

[0035] Figure 6: Dielectric Risley prism TA implementations and associated design parameters.

[0036] Figures 6A, 6B: (a) antenna configuration used for implementing both dielectric Risley prism concepts and (b) a representation of the amplitude and phase of the co-polarized electric field component after passing thought each TA for the conventional and generalized approaches

[0037] Figure 7: Radiation patterns at 30 GHz of the conventional Risley prism for ^^1= − ^^2= {90°, 75°, 60°, 45°, 30°, 0°}.

[0038] Figure 8: Normalized radiation patterns at 30 GHz of the conventional approach, considering different beam directions corresponding to ^^1= − ^^2= {90°, 30°, 0°}, corresponding to (a), (b) and (c) respectively.

[0039] Figure 9: Dielectric implementation of the two TAs for (a) the conventional and (b) the generalized Risley prism design approaches, following Eq. (10) and (11) and Eq. (18) and (19), respectively.

[0040] Figure 10: Radiation patterns at 30 GHz of the generalized Risley prism design approach, according to the present invention, for ^^1= − ^^2= {90°, 75°, 60°, 45°, 30°, 0°}.

[0041] Figure 11: Normalized radiation patterns at 30 GHz of the generalized Risley prism design approach for ^^1= − ^^2= {90°, 30°, 0°}, corresponding to (a), (b) and (c) respectively.

[0042] Figure 12: Pair of 3D-printed PLA TAs for (a) the conventional and (b) the generalized implementations of the Risley prism concept and (c) the measuring setup.

[0043] Figure 13: Measured and simulated normalized radiation patterns at 30 GHz for the plane ^^ = 90° and ^^1= − ^^2= 90° (boresight) of the conventional (dashed lines) and generalized (solid lines) approaches.

[0044] Figure 14: Measured and simulated normalized radiation patterns at 30 GHz for the plane ^^ = 0° and ^^1= ^^2= 0° (maximum scanning position) of the conventional (dashed lines) and generalized (solid lines) approaches.

[0045] Figure 15: Measured normalized radiation patterns at 30 GHz for ^^1= − ^^2= 30° along the planes ^^ = 90° (solid line) and ^^ = 0° (dashed line) for the conventional (dashed lines) and generalized (solid lines) approaches. DETAILED DESCRIPTION

[0046] The Risley prism TA configuration stems from the optical counterpart implementation, that considers an incident plane wave (paraxial ray approximation) passing through a cascade of two 1D tilting surfaces (“prims”) with independent axial rotation angles ^^1and ^^2used for steering the beam in zenith, ^^^^, and azimuth, ^^^^. In microwave antenna designs, a thirdsurface is required to focus the beam to a centralized feeding element, typically a horn antenna, as schematically represented in Fig.1a.

[0047] Figure 1 shows schematic representations of a microwave Risley prism TA configuration with centralized feeding point using (a) a separate collimating lens and (b) combining the collimating lens with the first deflecting TA prism, including the definition of the TA rotation angles ^^1and ^^2, and associated beam pointing direction ( ^^^^, ^^^^), wherein 101 represents a lens and 102 represents a horn.

[0048] In an embodiment, the collimating lens and the first deflecting layer are combined into a single surface (see Fig.1b).

[0049] In another embodiment, an array feeder can be adapted to the generalized formulation described herein, replacing the collimating lens and horn.

[0050] Let us consider the stationary frame ( ^^, ^^, ^^) placed at the horn aperture (101). The axial rotating angles ^^1and ^^2are measured relative to the local coordinate systems ( ^^^^, ^^^^, ^^) solidary with the corresponding aperture, according to

[0051] For an arbitrary phase ^^^^ ^^impinging the first TA, the intended outgoing wave phase ^^^^ ^^ ^^for the conventional Risley prism operation is

[0052] where ^^0is the free-space wave vector, ^^0is the deflecting angle (same for both surfaces) of the TA prisms in the ^^ ^^1and z ^^2planes, according to desired antenna beam pointing direction ( ^^^^, ^^^^).

[0053] Considering that the transmitted electric field by the antenna in a rectangular aperture of area ^^ = ^^ × ^^ parallel to TA2 can be described by (ideal phase shift correction) ^^^^ ^^= | ^^^^ ^^| ^^− ^^ ^^ ^^ ^^ ^^ (3)

[0054] if follows from the usual Physical Optics geometric optics (PO-GO) framework

[0014] the corresponding far field

[0055] where, ^^ is the observation distance and ^^ = cos ^^ sin ^^, ^^ = sin ^^ sin ^^ are the orthographic projection coordinates. The beam pointing direction ( ^^^^, ^^^^) can be estimated imposing that the argument of the integral (4) adds in phase, which according to (1)-(3) impliesor explicitly in spherical coordinates gives

[0015]

[0056] Introducing the auxiliary angles ^^ = ( ^^^^− ^^^^) / ^^ and ^^ = ( ^^^^+ ^^^^) / ^^ leads to the simplified expressions [6] { sin

[0057] The maximum scanning range in zenith angle is then given by ^^^^^^ ^^ ^^= sin−1(2 sin ^^0) (9)

[0058] In a conventional approach, the first TA converts the incident wavefront, originated by a spherical source placed at focal distance ^^, into a collimated offset beam with zenith angle ^^0measured in the ^^1z plane, corresponding to the phase correction

[0059] The second aperture, placed with small vertical separation ^^ above the first TA, tilts the incoming beam by ^^0measured in the ^^2z plane, according to the phase correction

[0060] Each aperture is then assembled as a collection of unit cells that locally impose the discretized wrapped phase values of (9) and (10) (priorly calculated using periodic boundary assumption). The unit cell period ^^ imposes a spatial discretization of the aperture ^^ (“pixelization”), which verifies the condition ^^ < 2 to ensure that only the two fundamental TE / TM Floquet modes are above cutoff, and thus avoiding grating lobes. The corresponding 360-degree phase profiles of both TAs are show in Fig.2.

[0061] Figure 2 shows a schematic representation of the phase variation profile example of the two TAs of a conventional Risley prism configuration with design parameter values ^^0= 25°, ^^ = 30 ^^ ^^ ^^, ^^ = 140 mm, ^^ = 100 mm. Nearly macro periodicity with size ^^^^2implicit on TA2.

[0062] The inset of this figure, highlights the macro-cell pattern along the tilt direction of TA2that results from the phase wrapping (201), i.e.

[0063] Using this phase wrapping into the periodic structure composed by macro-cells of size ^^^^2× ^^ one can infer the high order Floquet modes that can propagate in the TA2. Under this assumption the aperture fields are invariant under the transformation ^^2′= ^^2+ ^^^^2therefore, it can be expressed in terms of its harmonicswhere ^^^^are the corresponding Fourier coefficients:

[0064] The relative amplitude of these coefficients will depend on the interplay between a wide variety of complex effects that correlates with the unit cell reflections and coupling fields between the two apertures. Hence, there is no general analytical formulation that allow calculating a priori (14). On the other hand, the far-field of each harmonic, ^^^^^^^^, can be estimated by including in (4) the additional harmonic terms expressed in (13)

[0065] Replacing (1) in the previous equation one can estimate the expected direction for the local maximum associated to each harmonic (grating lobe) by imposing a constructive interference analogous to (5) (cos ^^1+ ( ^^ + 1) cos ^^2) (16)(sin ^^1+ ( ^^ + 1) sin ^^2)where ^^ = 0 reduce to (5) corresponding to the main lobe direction. The other values for ^^ will give the possible directions for the high order grating lobes associated with TA2. The geometric locus of these local maximums are equally space points in the orthographic projection plane by sin( ^^0) along the line (Fig.3) ^^^^^^− ^^^0^ = tan ^^2(^^^^^^− ^^^0^) (17)

[0066] Figure 3 shows a schematic representation of geometric locus using orthographic projection coordinates of the position of the grating lobes caused when using conventional transmit-arrays configuration.

[0067] The grating lobes are in general scattered along the ( ^^, ^^) scanning plane. They appear in the main plane (xz or yz), where most 1D radiation patterns in the literature are reported, e.g. [6]

[0010] , only for specific rotation angles ( ^^2={0°, 180°}, ( ^^2={−90°, 90°}respectively. Moreover, it is not mandatory that all harmonics in TA2 are excited for all beam scanning positions. Working with the orthographic projection coordinates provide a simple way of identifying the reported grating lobe pattern otherwise more obscure in the ( ^^, ^^) plane.

[0068] The phase law for TA1 given by (10) is the same type used in [5] for beam scanning using translation movement. It has been demonstrated that high gain (30 dBi) and low SLL in all planes (better than -20 dB) can be achieved with this phase profile. Therefore, by modifying the phase correction of TA2 to obtain a wrapped phase layout like in the conventional TA1, one breaks the macro-scale periodicity and thus improves the SLL.

[0069] Equations (9) and (10) can thus be generalized, according to the present invention, by adding and subtracting an arbitrary function that is invariant under an axial rotation Ψ(^^, ^^)which will result in the same outgoing phase (2), i.e.

[0070] The fact that the two apertures are distanced by ^^ can be compensated in the phase correction. However, usually ^^ ≪ ^^ and therefore it has little influence, and the perturbationcan be disregarded. The function Ψ( ^^, ^^) can be used to implement the virtual focus approach introduced in [5].

[0071] The TA1prism is designed to convert a spherical incident wave at the focal distance ^^ into an ongoing spherical wave front at the distance ^^2, i.e.

[0072] The parameter ^^2is set a priori in such a way that the macro-cell periodicity of the conventional approach (Fig.2) is avoided in both TAs (Fig.6). This formulation is equivalent to splitting the collimating function across the two TAs, rather than implementing it on the first deflecting layer only.

[0073] Figure 4 shows a phase variation profile example of the two TAs of the Risley prim configuration according to the present invention, referred to as the generalized Risley prism configuration, with design parameter values ^^0= 25°, ^^ = 30 ^^ ^^ ^^, ^^ = 140 mm, ^^ = 100 mm, ^^2= 150 mm.

[0074] The full-wave assessment of perforated dielectric slabs as TAs becomes much more accessible than the case of stacked patch-based TA case, e.g. [5]. In fact, modelling electrically large apertures composed of fine subwavelength details, as is the case of stacked patch type of unit cells, requires large amount of memory, barely available in most high-end workstations, leading to time-consuming full-wave simulations. Moreover, the manufacturing of the dielectric counterparts can be done through the fast and low-cost process of FDM 3D printing

[0016] . But on the downside, the dielectric unit cells are thicker, have higher losses and free-space mismatch.

[0075] In an embodiment, a fully dielectric version of a Risley prism beam-steering microwave antenna uses flat perforated slabs as TAs.

[0076] In an embodiment, the TA unit cell is a hollow square prism with 14-mm height and 2.5-mm side ( ^^⁄ 4 @ 30 ^^ ^^ ^^), made of polylactic acid (PLA) ( ^^^^= 2.98 and tan ^^ = 0.0148 ).

[0077] In an embodiment, PLA unit cells are advantageously designed to be 14-mm thick to ensure a 304º phase delay span at 30 GHz (design frequency). Both the dielectric losses andthe contrast to free space sets a limit to the maximum transmission of the unit cells, which is always above -1.7 dB.

[0078] Figure 5 shows the amplitude and phase transmission performance / response of the full-dielectric unit cells at the design frequency (30 GHz).

[0079] To compare both design approaches for the Risley prism microwave antenna, a set of design parameters were pre-defined.

[0080] In an embodiment, ^^0= 25° which provides a maximum scanning of ^^^^^^ ^^ ^^= 57.6° for Ψ = 0° (according to (9)). Although theoretically wider beam scanning could be achieved if higher ^^0values were considered, the physical limitation of the effective aperture variation with the cosine of the steering angle limits the 3 dB scanning range up to 60 degrees.

[0081] In an embodiment, the focal distance and aperture dimensions are ^^ = 100 mm and ^^ = 140 mm, respectively, which allow using a standard 14.5 dBi gain horn antenna at 30 GHz to illuminate the aperture (TA1) with a proper edge taper (12 dB) (see Fig.6 a).

[0082] Figure 6 shows two dielectric Risley prism TA implementations and associated design parameters.

[0083] Figures 6A, 6B show (a) an antenna configuration used for implementing both dielectric Risley prism concepts (conventional and generalized) and (b) a representation of the amplitude and phase of the co-pol field component after passing thought each TA for the conventional and generalized approaches with ^^1= − ^^2= 90°.

[0084] The considered virtual focal distance is ^^2= 150 mm, Eq. (20), as discussed previously. The distance between the two apertures is ^^ = 1 mm, which still provides a margin for contactless mechanical rotation of the two TAs. The full-wave numerical results are obtained using the FDTD solver of CST Microwave Studio. In Fig. 6 b), the near-field co- polarized electric field component after passing through each TA is represented in amplitude and phase for boresight collimation (corresponding to ^^1= − ^^2= 90). The phase representation after the first TA illustrates well the difference of both approaches. This representation after the second TA also shows that the combined effect of both TAs produces roughly the same desired output. The advantage of using the generalized approach, according to the present invention, is evident only in the far-field (where the radiation lobes are formed).The cross-polarized electric field component levels in the radiation patterns of both approaches are always below -30 dB, and therefore will not be shown herein.

[0085] Figure 7 shows the radiation patterns at 30 GHz of the conventional Risley prism for

[0086] Figure 8 shows the normalized radiation patterns at 30 GHz of the conventional approach considering different beam directions corresponding to ^^1= − ^^2= {90°, 30°, 0°}, reported in (a), (b) and (c) respectively.

[0087] Apart from the most tilted beam ( ^^1= ^^2= 0°), the scanning performance of this antenna seems interesting with SLL in the scanning plane below ‒13.2 dB, scan loss of 3.4 dB for scanning up to 47° and maximum gain of 26.4 dBi at 30 GHz. However, as shown in Fig.8, the grating lobes appear outside the ^^ ^^ plane and are indeed dominant for the SLL calculation. The actual SLL of the scanning antenna up to 47º is -8 dB instead, where the secondary lobes are widely separated from the main lobe. This is particularly problematic for SATCOM applications such as SOTM and SOTP connectivity, which typically impose very restrictive SLL masks far from the main beam pointing direction. These grating lobes will thus constitute a major limitation in operation as they will require significant power back-off with degraded link budget in transmit and possibly higher interferences in receive. It is also interesting to confirm that the grating lobes appear in the positions predicted, which confirms the interpretation of these side lobes, and allows to distinguish them from other SLL sources (Table I).

[0088] Table I - Confirmation of harmonics representation of grating lobes applied for the conventional configuration. ^^^^^^ ( ^^ , ^^ )(°) H^^1 2armonic, n Theory CST Theory CST 0 0 0 0 0 (90, −90) 1 0 0 -0.42 -0.43 ^^0= 25° -1 0 0 0.42 0.43 -2 0 0 0.84 0.82 0 0.73 0.73 0 0 (30, −30) -1 0.36 0.37 0.21 0.22 ^^0 = 25°-2 0 0 0.42 0.41 -3 -0.36 -0.36 0.63 0.63 (0,0)0 0.84 0.84 0 0^^0= 25° -1 0.42 0.43 0 0 -2 0 0 0 0 -3 -0.42 -0.43 0 0 -4 -0.84 -0.83 0 0

[0089] Figure 9 shows a dielectric implementation of the two TAs for (a) the conventional and (b) the generalized Risley prism design approach, Eq. (10) and (11) and Eqs. (18) and (19), respectively. The layout of the two dielectric TAs is herein shown, for the case where ^^2= − ^^1which, according to (6) and (7), provides elevation scanning along the ^^ ^^ plane between [0, 57°].

[0090] The scanning performance obtained using full-wave simulation in CST at 30 GHz for ^^1= {90°, 75°, 60°, 45°, 30°, 0°} are shown in Fig.7 for the conventional Risley prism design approach.

[0091] Figure 10 shows the radiation patterns at 30 GHz of the generalized Risley prism design approach

[0092] The two dielectric TAs are designed using the generalized approach, according to the present invention, resulting in the layouts shown in Fig.9 b). The axial rotation angles ^^1= {90°, 75°, 60°, 45°, 30°, 0°} resulting in Fig. 10, which compares directly with Fig. 7 (conventional approach).

[0093] Figure 11 shows the normalized radiation patterns at 30 GHz of the generalized Risley prism design approach for ^^1= − ^^2= {90°, 30°, 0°}, reported in (a), (b) and (c) respectively.

[0094] A significant improvement in SLL is obtained for all beam positions when considering the complete 2D scanning plane, Fig.11 versus Fig.8. Surprisingly, this is more evident for the most tilted case ( ^^1= ^^2= 0°). For this rotation angle the generalized design according to the present invention provides a SLL of -9.7 dB and 22.8 dBi Gain @ 30GHz, which compares with -3.5 dB and 21.8 dBi @ 30GHz of the conventional case. It is also confirmed that the enhancement of the performance of the generalized approach is verified across all the operating bandwidth of the TA, as shown in TABLE II and III.

[0095] Table II - Comparison of the bandwidth performance of the conventional and generalized Risley prism implementations for = − ^^2= 0°^^ = 0° Conventional Generalized Freq. Gain (dBi) SLL (dBi) ^^^^ ^^ ^^^^^^ ^^ ^^(GHz)(°)Gain (dBi) SLL (dBi) (°)28.0 18.9 -1.8 65 20.4 -4.1 60 28.5 19.4 -2.1 64 21.3 -5.8 59 29.0 20.2 -2.5 60 22.0 -7.1 58 29.5 20.8 -3.1 58 22.3 -8.3 55 30.0 21.3 -3.5 57 22.8 -9.7 54 30.5 21.7 -3.6 56 23.6 -11.8 53 31.0 21.8 -3.9 54 23.7 -12.7 52 31.5 21.7 -3.9 52 23.7 -12.3 51 32.0 22.0 -3.5 51 23.8 -12.0 50

[0096] Table III - Comparison of the bandwidth performance of the conventional and generalized Risley prism implementations for= − ^^2= 90° ^^ = 90° Conventional Generalized Gain Freq. (GHz) SLL (dBi) ^^^^ ^^ ^^Gain (dBi) ^^^^ ^^ ^^(dBi)(°)SLL (dBi) (°)28.0 22.4 -6.5 1 23.3 -6.2 -2 28.5 23.1 -7.2 1 23.8 -7.6 -2 29.0 24.1 -8.1 1 24.6 -9.8 -2 29.5 24.7 -8.5 0 25.0 -11.1 -2 30.0 25.3 -8.4 0 25.5 -13.3 -2 30.5 25.7 -8.4 0 25.9 -14.9 -2 31.0 25.7 -8.1 0 25.9 -15.8 -2 31.5 25.7 -7.9 0 26.0 -15.8 -2 32.0 26.1 -8.2 0 26.4 -16.0 -2

[0097] Figure 12 shows a pair of 3D-printed PLA TAs for (a) the conventional and (b) the generalized implementations of the Risley prism concept and (c) the measuring setup.

[0098] The prototypes were fabricated using 3D-printing, including the supporting structure, all in PLA material. The layouts of the two lenses for both approaches and of the complete antenna under test in an anechoic chamber are shown in Fig.12 a), b) and c), respectively.

[0099] Figure 13 shows the measured and simulated normalized radiation patterns at 30 GHz for the plane ^^ = 90° and ^^1= − ^^2= 90° (boresight) of the conventional (dashed lines) and generalized (solid lines) approaches. The grey scale used in the inset of the figure is the same as in Fig.11.

[0100] Figure 14 shows the measured and simulated normalized radiation patterns at 30 GHz for the plane ^^ = 0° and ^^1= ^^2= 0° (maximum scanning position) of the conventional (dashed lines) and generalized (solid lines) approaches. The grey scale used in the inset of the figure is the same as in Fig.11.

[0101] Figure 15 shows the measured normalized radiation patterns at 30 GHz for ^^1= − ^^2= 30° along the planes ^^ = 90° (solid line) and ^^ = 0° (dashed line) for the conventional (dashed lines) and generalized (solid lines) approaches. The grey scale used in the inset of the figure is the same as in Fig.11.

[0102] The measured normalized radiation pattern cuts along the main planes, i.e. ^^ = {0°, 90°}, are presented in Fig.13, Fig.14 and Fig.15. For all the considered scanning positions ( ^^1= − ^^2= {0°, 30°, 90°}) a significant suppression of grating lobes (each identified in the inset of these figures by the corresponding harmonic order ^^) was verified experimentally. This is particularly visible for the maximum scanning position ^^1= ^^2= 0° (corresponding to ^^^^^^ ^^ ^^= 55°) where all the grating lobes are aligned with the plane ^^ = 0°. The generalized design approach, according to the present invention, allows improving the antenna gain by a factor of 2.2 dB and SLL from -4.4 to -8.3. It is also worth highlighting the good agreement between simulations and measurements shown in Fig.14 and Fig.15. Minor discrepancies are resulting from manufacturing and assembly tolerances.

[0103] Herein, a generalized Risley prism design approach is presented using TAs that allows wide beam scanning with a reduced SLL when compared to the conventional design approach. It is verified that the grating lobes in the conventional design are caused by the inherent periodicity of a tilting TA phase correction (as is usually considered), which limits the SLL performance of the antenna. Full-dielectric TAs were used to demonstrate the effectiveness of the proposed formulation. The developed framework is applicable to any type of Tas and to any frequency of operation within the microwave range.

[0104] In an embodiment, more general arbitrary phase perturbation functions Ψ(^^, ^^)(see Equations 18 and 19), can be considered for fine tuning optimizations.

[0105] The solution herein presented extends the potential of TAs thus achieving low-cost, high-performance, wide angle beam steering.

[0106] The term "comprising" whenever used in this document is intended to indicate the presence of stated features, integers, steps, components, but not to preclude the presence or addition of one or more other features, integers, steps, components, or groups thereof.

[0107] The disclosure should not be seen in any way restricted to the embodiments described and a person with ordinary skill in the art will foresee many possibilities to modifications thereof. The above-described embodiments are combinable.

[0108] The following claims further set out particular embodiments of the disclosure.

[0109] References [1] R. Correia et al., “User Terminal Segments for Low-Earth Orbit Satellite Constellations: Commercial Systems and Innovative Research Ideas,” IEEE Microw. Mag., vol.23, no.10, pp.47-58, Oct.2022. [2] G. Amendola et al., “Antennas and RF front-end technologies for the Ku and Ka-band LEO user segment,” IEEE Microw. Mag., early access. [3] T. Chaloun et al., “Electronically steerable antennas for future heterogeneous communication networks: review and perspectives,” IEEE J. Microwaves, vol.2, no.4, pp.545-581, Oct.2022. [4] W. Hong et al., “The Role of Millimeter-Wave Technologies in 5G / 6G Wireless Communications,” IEEE J. Microwaves, vol.1, no.1, pp.101-122, Jan.2021. [5] E. B. Lima et al., “Circularly polarized wide-angle beam steering at Ka-band by in-plane translation of a plate lens antenna,” IEEE Trans. Antennas Propag., vol.63, no.12, pp.5443-5455, Dec.2015. [6] N. Gagnon and A. Petosa, "Using Rotatable Planar Phase Shifting Surfaces to Steer a High-Gain Beam," IEEE Trans. Antennas Propag., vol.61, no.6, pp.3086-3092, June 2013. [7] S. D. Risley, “A new rotary prism,” Trans. Am. Ophthalmol. Soc., vol.5, 1889, pp.412-413. [8] S. A. Matos et al., "High Gain Dual-Band Beam-Steering Transmit Array for Satcom Terminals at Ka- Band," IEEE Trans. Antennas Propag., vol.65, no.7, pp.3528-3539, July 2017. [9] F. Ahmed et al., "A Near-Field Meta-Steering Antenna System with Fully Metallic Metasurfaces," IEEE Trans. Antennas Propag., early access.

[0010] M. U. Afzal and K. P. Esselle, “Steering the beam of medium-to-high gain antennas using near-field phase transformation,” IEEE Trans. Antennas. Propag., vol.65, no.4, pp.1680–1690, Apr.2017.

[0011] T. Lou et al., “Compact dual-polarized continuous transverse stub array with 2-D beam scanning," IEEE Trans. Antennas Propag., vol.67, no.5, pp.3000-3010, May 2019.

[0012] Z. Zhang et al., "A Low-Profile, Risley-Prism-Based, Beam-Steerable Antenna Employing a Single Flat Prism," IEEE Trans. Antennas Propag., vol.70, no.8, pp.6646-6658, Aug.2022.

[0013] J. Wang and Y. Rahmat-Samii, "A Simplified Configuration of Beam-Steerable Risley Prism Antennas: Principles and Validation," IEEE Antennas Wirel. Propag. Lett., vol.21, no.11, pp.2288-2292, Nov.2022.

[0014] S. J. Orfanidis, (2002) Electromagnetic Waves and Antennas [Online]. Available: www.ece.rutgers.edu / ~orfanidi / ewa, pp.808.

[0015] J. Wang and Y. Ramhat-Samii, "Phase Method: A More Precise Beam Steering Model For Phase- Delay Metasurface based Risley Antenna," 2019 URSI Int. Symp. Electromag. Theory (EMTS), San Diego, CA, USA, May 2019, pp.1-4.

[0016] S. A. Matos et al., "3-D-Printed Transmit-Array Antenna for Broadband Backhaul 5G Links at V- Band," in IEEE Antennas and Wireless Propagation Letters, vol.19, no.6, pp.977-981, June 2020.

Claims

C L A I M S 1. Steerable-beam microwave antenna, arranged for steering a beam relative to a longitudinal axis of the antenna, comprising: a discrete transmitarray comprising a plurality of sub-wavelength phase-shifting unit-cells, rotatably mounted for rotating about said longitudinal axis, having an aperture orthogonal to said longitudinal axis; a feeder for emitting and / or receiving a microwave signal to and / or from the discrete transmitarray, comprising at least one rotatable feeding part; wherein the unit-cell layout of the discrete transmitarray has a phase distribution which superimposes a phase gradient along a transversal axis orthogonal to said longitudinal axis and a rotationally-symmetric phase correction centred on said longitudinal axis.

2. Steerable-beam microwave antenna according to the previous claim, wherein said discrete transmitarray is a first discrete transmitarray, and wherein said feeder comprises: a fixed antenna for emitting and / or receiving a microwave signal; a second discrete transmitarray comprising a plurality of sub-wavelength phase-shift unit-cells, rotatably mounted for rotating about said longitudinal axis, having an aperture orthogonal to said longitudinal axis; a fixed microwave lens for changing a spherical wave emitted and / or received by the fixed antenna into a plane-wave for feeding the second discrete transmitarray; wherein the unit-cell layout of the second discrete transmitarray has a phase distribution which superimposes a phase gradient along a transversal axis orthogonal to said longitudinal axis and a rotationally-symmetric phase correction centred on said longitudinal axis compensating, in part or in full, the rotationally-symmetric phase correction of the first discrete transmitarray for side lobe level reduction.

3. Steerable-beam microwave antenna according to claim 2, wherein the fixed microwave lens is a fixed third transmitarray comprising a plurality of sub-wavelength phase-shift unit-cells, having an aperture orthogonal to said longitudinal axis, and wherein the unit-cell layout of the fixed third transmitarray has a phase distribution changing a spherical wave produced by the fixed antenna into a plane-wave for feeding the second discrete transmitarray.

4. Steerable-beam microwave antenna according to claim 2, wherein the fixed microwave lens is part of the second discrete transmitarray wherein the unit-cell layout of the second discretetransmitarray has a phase distribution which superimposes a phase gradient along a transversal axis orthogonal to said longitudinal axis and a rotationally-symmetric phase correction centred on said longitudinal axis compensating, in part or in full, the rotationally-symmetric phase correction of the first discrete transmitarray for side lobe level reduction, and a further phase correction for changing the spherical wave emitted and / or received by the fixed antenna into a plane-wave.

5. Steerable-beam microwave according to any of the previous claims, wherein the phase correction is configured to produce a spherical wave with a virtual focal point located below a plane collocated with the aperture of the fixed antenna on the opposite side of the transmitarray, or above a plane collocated with the aperture of the feeder on the side of the transmitarray.

6. Steerable-beam microwave antenna according to any of the previous claims wherein the fixed low-gain antenna is a horn antenna or a patch antenna.

7. Steerable-beam microwave antenna according to any of the previous claims wherein one or more of said transmitarrays is composed of sub-wavelength unit-cells formed on a dielectric medium.

8. Steerable-beam microwave antenna according to the previous claim, wherein the sub-wavelength unit-cells are perforations in the dielectric medium or metallic inserts in the dielectric medium.

9. Steerable-beam microwave antenna according to any of the previous claims wherein one or more of said transmitarrays is composed of sub-wavelength unit-cells formed as a stack of printed circuit boards comprising metallic inserts on dielectric slabs.

10. Steerable-beam microwave antenna according to any of the previous claims wherein the feeder is a corporate array with a parallel signal distribution in the aperture for controlling both amplitude and phase for further side lobe reduction.

11. Steerable-beam microwave antenna according to any of the previous claims wherein the feeder is a radial line slot array or a continuous transversal slot array with a serial signal distribution in the aperture for controlling both the amplitude and the phase for further side lobe reduction.

12. Steerable-beam microwave antenna according to any of the previous claims wherein one or more rotatable parts are arranged to be mechanically actuated, in particular by a motor.

13. Steerable-beam microwave antenna according to any of the previous claims further comprising a microcontroller unit configured for actuating an actuator or motor for rotating one or more of said transmitarrays by adjusting a relative angle between the transversal axis of the first discrete transmitarray and the transversal axis of the second discrete transmitarray, for primarily elevation beam steering.

14. Steerable-beam microwave antenna according to any of the previous claims further comprising a microcontroller unit configured for actuating an actuator or motor for rotating one or more of said transmitarrays by adjusting a sum angle of the transversal axis of the first discrete transmitarray with the transversal axis of the second discrete transmitarray, for azimuth beam steering.

15. Method for operating a steerable-beam microwave antenna of any of the previous claims, the method comprising actuating an actuator or motor for rotating one or more of said transmitarrays by adjusting a relative angle between the transversal axis of the first discrete transmitarray and the transversal axis of the second discrete transmitarray, for elevation beam steering.

16. Method for operating a steerable-beam microwave antenna of any of the previous claims, the method comprising actuating an actuator or motor for rotating one or more of said transmitarrays by adjusting a sum angle of the transversal axis of the first discrete transmitarray with the transversal axis of the second discrete transmitarray, for azimuth beam steering.

17. Manufacturing method for obtaining a steerable-beam microwave antenna, arranged for steering a beam relative to a longitudinal axis of the antenna, comprising: providing a discrete transmitarray comprising a plurality of sub-wavelength phase-shifting unit- cells, rotatably mounted for rotating about said longitudinal axis, having an aperture orthogonal to said longitudinal axis; providing a feeder for emitting and / or receiving a microwave signal to and / or from the discrete transmitarray; wherein the unit-cell layout of the discrete transmitarray has a phase distribution which superimposes a phase gradient along a transversal axis orthogonal to said longitudinal axis and a rotationally-symmetric phase correction centred on said longitudinal axis.

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