EP4208919A1

EP4208919A1 - Method and apparatus for designing a phased array antenna, phased array antenna and method for operating a phased array antenna

Info

Publication number: EP4208919A1
Application number: EP20768018.2A
Authority: EP
Inventors: Frank Mayer; Burak SAHINBAS; Christian Steinmetz; Hans Adel
Original assignee: Fraunhofer Gesellschaft zur Forderung der Angewandten Forschung eV
Current assignee: Fraunhofer Gesellschaft zur Forderung der Angewandten Forschung eV
Priority date: 2020-09-04
Filing date: 2020-09-04
Publication date: 2023-07-12
Also published as: WO2022048772A1

Abstract

A method for designing a phased array antenna comprises a step of determining, for at least one antenna element set which includes a plurality of antenna elements of the phased array antenna, a set of phase shift values to which switchable phase shifters for the antenna elements of the antenna element set are switchable, so that, during operation of the phased array antenna, the phased array antenna is steerable towards directions within a predetermined direction range by selecting, for each of the antenna elements of the antenna element set, one of the phase shift values out of the determined set of phase shift values. The determining of the set of phase shift values for a respective antenna element set comprises determining, for a plurality of candidate sets of phase shift values, each of the candidate sets comprising a number of phase shift values, respective antenna quality measures describing a quality of an operation of the phased array antenna using the respective candidate set of phase shift values as the set of phase shift values.

Description

Method and apparatus for designing a phased array antenna, phased array antenna and method for operating a phased array antenna

Description

Technical Field Embodiments of the present disclosure relate to a method for designing a phased array antenna. In particular, some embodiments relate to a method for determining respective sets of phase shift values for one or more antenna element sets of the phased array antenna. Further embodiments relate to an apparatus for designing a phased array antenna. Further embodiments of the present disclosure relate to a phased array antenna. Additional embodiments relate to a method for operating a phased array antenna. Further embodiments relate to computer programs for designing a phased array antenna or for operating a phased are antenna.

Some embodiments of the present disclosure relate to a sectored phased array antenna, for example, for use in Internet of Things (loT) satellite communication.

Background

A phased array antenna is steerable towards different directions by adjusting relative phase differences between signals transmitted or received by individual antenna elements of the phased array antenna. Phased array antennas are commonly applied for satellite communication, which may be used, among other applications, in Machine to Machine (M2M) or loT type applications, connecting fixed or mobile “terminals” via a satellite communication link to the internet or other infrastructure (e.g. servers, databases, “the cloud”). Communication may be uni-directional - typically from the terminals to the satellite, e.g. for reporting location or state information or sensor readings - or bi-directional, transmitting messages or data from and to the terminals.

M2M or loT type terminals may be deployed in larger quantities and thus are cost and resource constraint. Resource constraints include total energy budget (e.g. for battery powered devices), available or permitted peak transmit power, antenna gain and pointing performance (i.e. accuracy and resolution of selecting the pointing direction, and pointing errors introduced by the components and their arrangement), and overall size of the terminal and antenna.

M2M or loT type terminals may be operated within a geosynchronous (GSO) or non- geosynchronous (NGSO) satellite network. The latter case ranges from single (or limited number) of satellites in “scanning mode”, where communication takes place only during the limited duration the satellite is visible from the loT terminal’s location to “mega constellations”, where multiple NGSO satellites are available for communication at any given point in time. As design and deployment of a NGSO constellation is capital expensive and time consuming, use of existing GSO infrastructure, already built and deployed for use with standard VSAT terminals with frequencies in C-, Ku- or Ka-Band is an interesting alternative.

Different from standard VSAT terminals that use quite large and highly directive “parabolic dish” or “phased array” antennas, said M2M or loT type terminals are resource constraint and thus require a more compact and cost efficient antenna design, while still being compatible with the existing satellite infrastructure and regulatory constraints. For many common loT/M2M use cases, the terminal is mobile or portable. This requires adjustment of the antenna’s beam direction, to account for changes in terminal orientation and longitude/latitude location. While such beam steering may be accomplished by mechanical means, it is in general preferable to use electronic beam steering, to avoid mechanical wear and tear and to improve robustness.

For a typical antenna, directivity G is proportional to the antenna aperture area while beam width b_dia is indirectly proportional to the aperture size. E.g. the directivity and beam width of a parabolic dish reflector type antenna may be approximated by and , where d_refl is the reflector size (in meter), λ the wavelength of the signal

(in meter) and ε the antenna efficiency. G is the resulting peak directivity (linear power gain, usually converted to decibels) and b_dia is the resulting beam width (beam diameter measured with respect to the -3dB directivity contour) in degree. Thus, use of a compact antenna not only implies limited directivity, but also creates unwanted interference from or to other satellites or terrestrial sources. This limits spectral efficiency for loT/M2M terminals when receiving and constraints the amount of power (or power density) an loT/M2M terminal is allowed to transmit. Regarding the latter, the ITU (International Telecommunication Union) and local authorities (e.g. FCC, Federal Communication Commission, an United States government agency) have defined strict power spectral density (PSD) masks, constraining the equivalent isotopically radiated power (e.i.r.p.) density transmitted into the direction of other satellites or other systems, and thus, depending on beam width, pointing performance and main-to-side lobe ratio, these masks also indirectly constrain the peak power and PSD towards the satellite of interest.

Existing antenna designs used for VSAT terminals are generally characterized by providing a high-gain beam, with narrow beam width in both horizontal (azimuth) and vertical (elevation) direction (“pencil beam”).

For some use cases, for example an M2M/loT terminal on earth communicating with a GSO satellite, data throughput is low, and thus a system communicating at very low spectral efficiency may be acceptable. In exchange for increased demand in bandwidth, transmit power and terminal antenna gain can be traded in and reduced. As described in W02018/029220A1 or W02018/029302A1 , this does help in meeting the spectral power density (PSD) mask when dimensioning and operating the M2M/loT system.

Electronically steerable “phased array” antennas providing such beam characteristics are known from prior art; many of these designs focus on improving side-lobe performance, i.e. increasing the antenna gain into the wanted direction while minimizing radiation into unwanted directions. Such prior art includes:

DE2855623A1 discloses a phased array antenna, composed of a planar array of antenna elements arranged in a matrix of vertically stacked horizontal rows.

US5512906A discloses an array of antenna elements configured in a lattice-like layer, each element being similarly oriented such that the whole of the antenna elements form a homogeneous two-dimensional antenna aperture surface which can be planar or curved to conform to a desired shape.

EP2176923 B1 , Figure 2, discloses a phased array antenna configured in receive mode, and comprising a Direct Radiating Array (DRA) with aperture formed by a 2 dimensional array of NE antenna elements. The array is typically but not necessarily planar. The array comprises a regular geometry in terms of element centre locations (but not essentially), usually on a square, rectangular of hexagonal grid.

US6404404B discloses a hexagonally shaped array, with tapering as means for side-lobe reduction. US2019252774AA discloses tapering and irregularity, also for side-lobe reduction. Rectangular outline phased arrays are known for variation in pointing and side-lobe performance, depending on angular (azimuth) beam steering target. A natural way to overcome such variations is the use of a circular multi-ring arrangement of the antenna elements; this provides a direct mapping of elevation steering to the phase difference between rings and of azimuth steering to the phase difference between ring sectors. Such prior art includes:

EP0315689B1 discloses a concentric ring structure. US2003090433A discloses a plurality of concentric circle array antennas each having a different radius disposed on an identical plane, and a plurality of element antennas arranged circumferentially in each of the concentric circle array antennas. US4797682A discloses a concentric ring arrangement, with tapering. EP0523422A1 discloses yet another concentric ring arrangement, with a set of active and a set of passive (parasitic) element, to assist the directivity of the antenna.

When it comes to beam steering, some of the aforementioned concepts control the phase relation between individual antenna elements or of groups of antenna elements in order to obtain constructive signal aggregation in the direction of interest (US5872547A, US2004246191AA); this is also known from related prior art on phase arrays, e.g. as disclosed in US2016164174AA. Some concepts apply equal phase and amplitude to a selected group of elements, to generate a constant beam sector (US5241323A). Some concepts define groups of antenna elements and use a switching network to connect to the different groups depending on direction (US7522095BA, US3806932A); this may include beneficial use of inactive elements as parasitic elements (US6268828B).

Regular, circular, ring or sectored phased array arrangements are also widely known from the state of the art:

US3255450 describes a fixed multiple-beam beam-forming-network based on the use of so-called "Butler matrices". A Butler matrix is a multiport network having N inputs and N outputs, comprising of N/2*log2(N) 4-port devices (couplers), with a fixed phase difference at the 3rd and 4th port, allowing fixed value phase shifts in increments of 180/N degree.

EP1642357B1 (US2006208944A) relates to a phased array antenna system with adjustable electrical tilt. More specifically, the antenna of each sector is connected to a base station for radio communication with all of the mobile radios in that sector. EP1680834B1 discloses a system similar to that of EP1642357B1 .

US2010194629A relates to the simplification of reconfigurable beam-forming network processing within a phased array antenna for a telecommunications satellite, and further relates to a phased array antenna, formed as a plurality of overlapping sub-arrays, having an optimized formation of beams within a predefined geographical region, and a process for optimizing the beam-forming characteristics of such phase array antenna.

To summarize, prior art includes: beam-steerable phased array antennas, with various layouts, including rectangular, circular, concentric ring and arbitrary shaped outline of the array, with regular, irregular and tapered arrangement of the antenna elements on a planar or arbitrary surface (conformal array); use of circular (2-D ring or concentric rings and 3-D cylindrical shaped) antenna element layouts and their benefits for beam steering in elevation and azimuth direction; control of the phase relation between individual antenna elements and/or control of the amplitude of antenna elements for the purpose of beam steering; as well as methods for calculating the phase relation, considering the relative locations of the antenna elements (e.g. on regular or arbitrary surfaces).

Further, it is known that the number of phases can be reduced if the number of elements is sufficiently large, as the phase deviation in each of the individual elements may then be averaged out over the large number of elements in the array. Therefore, known implementations use hundreds to thousands of elements and thus are outside scope for size constraint applications like the loT/M2M terminal.

In view of the prior art, it is desirable to have a concept that provides for an improved tradeoff between an overall size, component count, component (e.g. phase shifter) complexity and control, energy consumption, transit power, antenna gain and directivity of the phased array antenna.

Summary

Embodiments of the invention rely on the idea, that a phased array antenna may provide a good trade-off between a low complexity, for example low cost and low size, and a high antenna quality, characterized for example by a high directivity and/or a high antenna gain, if respective phase shifts for antenna elements of the phased array antenna are limited to values of a fixed set of phase shift values. A particularly low complexity and/ or a small size of the phased array antenna may be achieved, if the number of antenna elements is low and/or if the set of phase shift values available for the antenna elements is small and/or identical for all antenna elements of an antenna element set, i.e. a subset of antenna elements, of the phased array antenna. The inventors realized, that despite the limited options of phase shift vales available for the individual antenna elements, an antenna quality of the phased array antenna may be good, if the set of phase shift values is determined specifically for the respective antenna element set according to the properties of the phased array antenna, e.g. according to a geometry of the antenna elements and their arrangement. For that purpose, determining the set of phase shift values may include a determination, for example a calculation, of an antenna quality measure for an operation of the phased array antenna using a candidate set of phase shift value. By determining the antenna quality measure for a plurality of candidate sets, the set of phase shift values to be used for the phased array antenna may be determined under consideration of a desired application and antenna characteristic, like directivity, side-lobe isolation and/or a direction range within which the antenna is to be steerable. Thus, a number of phases required by the array may be reduced, while still maintaining beam steering capability over azimuth and elevation range of interest. For example, the determination of the antenna quality measure may consider one or more or all of the resulting antenna characteristics as inputs and may combine these in into a quality measure value (e.g. a single numerical value per set). This antenna quality value may then be used to rank the individual candidate sets by achieved “quality”, for example, in order to decide if the candidate set meets a minimum criteria and/or select one or multiple candidate sets based on their quality value.

Therefore, embodiments of the invention provide a method for designing a phased array antenna, e.g. for determining phase shift values for a phased array antenna. The method comprises determining, for at least one antenna element set which includes a plurality of antenna elements of the phased array antenna, a set of phase shift values. For example, the phased array antenna includes one or more antenna element sets, which each include a plurality of antenna elements of the phased array antenna, i.e. each of the antenna element sets may include a subset of antenna elements of the phased array antenna. The set of phase shift values may be determined individually or specifically for one of the one or more antenna element sets. The set of phase shift values comprises phase shift values to which (or between which) switchable phase shifters for the antenna elements of the (e.g. the respective, the currently considered of the at least one) antenna element set are switchable, so that, during operation of the phased array antenna, the phased array antenna is steerable towards directions within a predetermined direction range by selecting, for each of the antenna elements of the antenna element set, one of the phase shift values out of the determined set of phase shift values, i.e. the set of phase shift values determined for the (respective, currently considered) antenna element set, i.e. the antenna element set which includes the respective antenna element. For example, the switchable phase shifters may be associated with, or connected to, respective antenna elements of the antenna element set, e.g. each antenna element may be connected to a respective switchable phase shifter. Each switchable phase shifter of the switchable phase shifters for the antenna elements of the antenna element set may be switchable to (or between) the phase shift values included in the set of phase shift values determined for the antenna element set. For example, that is, the antenna elements of one antenna element set may share a common basis of phase shift values to which respective switchable phase shifters of the antenna elements may be adjusted. Determining the set of phase shift values for a respective antenna element set (of the at least one antenna element set) comprises determining (e.g. calculating), for a plurality of candidate sets of phase shift values, each of the candidate sets comprising a number of phase shift values, respective antenna quality measures (e.g. antenna quality values), i.e. respective antenna quality measures for the individual candidate sets. For example, the number of phase shift values may be equal for all of the candidate sets or may be different between several of the candidate sets. The number of phase shift values may be one or higher. The antenna quality value may be determined individually for a respective candidate set. The antenna quality measure describes a quality of an operation of the phased array antenna using the respective candidate set of phase shift values as the set of phase shift values (e.g. from which, during operation, an actual phase shift is selected for each of the antenna elements of the antenna element set associated with the set of phase shift values). For example, the antenna quality measure may describe a quality, for example a maximum quality, of a directivity pattern which is achievable when using the respective candidate set, that is, when selecting, for each of the antenna elements of the antenna element set of phase shift value from the respective candidate set.

Determining one set of phase shift values for all antenna elements of one antenna element set allows for a cost efficient and/or space-efficient implementation of the phased array antenna. Further, determining the antenna quality measure for a plurality of candidate sets allows for determining the set of phase shift values so that the set of phase shift values enables a good, in terms of the antenna quality measure, operation of the phased array antenna. As the determined antenna quality measure describes the quality of the operation of the specific phased array antenna, for example characterized by a geometry and an arrangement of the antenna elements of the phased array antenna, the set of phase shift values may be determined specifically for the phased array antenna and/or specifically in view of a specific kind of the antenna quality measure. Therefore, the method allows for an adaption, e.g. an optimization, of the set of phase shift values to the geometry and to an application of the phased array antenna. Consequently, the method allows for designing the phased array antenna so that a good trade-off between a high antenna quality and a low number of phase shift values available for individual antenna elements may be achieved.

According to embodiments, the method comprises determining respective sets of phase shift values (e.g. separate or individual sets of phase shift values) for a plurality of antenna element sets, the antenna element sets including respective pluralities of antenna elements of the phased array antenna. By determining sets of phase shift values for a plurality of antenna element sets, different phase shift values are available for antenna elements of different antenna element sets, thus providing a high flexibility of adapting the phase shift values to the phased array antenna. That is, the sets of phase shift values may be adapted to their respective antenna element sets, which may result in a better antenna quality measure or a lower number of phase values per phase shift value set.

According to embodiments, determining the set of phase shift values for a respective antenna element set further comprises determining the set of phase shift values based on the candidate sets under consideration of the respective determined antenna quality measures. For example, the set of phase shift values may be determined by selecting one of the candidate sets as the set of phase shift values, for example according to the antenna quality measures determined for the candidate sets.

According to embodiments, for each antenna element of the at least one antenna element set, the switchable phase shifter for the respective antenna element is switchable to each of the phase shift values of the set of phase shift values of the respective antenna element set. As each of the switchable phase shift is switchable to each of the phase shift values, the phased array antenna is steerable accurately.

According to embodiments, determining the set of phase shift values for the respective antenna element set comprises determining at least one selected candidate set of phase shift values. Determining the at least one selected candidate set comprises obtaining a set of candidate sets of phase shift values. The set of candidate sets is selected based on a symmetry property of an arrangement of the plurality of antenna elements of the phased array antenna. Each candidate set of phase shift values comprises a number of phase shift values, e.g. all candidate sets may comprise the same number of phase shift values or several of the candidate sets may comprise different numbers of phase shift values. The number of phase shift values may be one or higher. Determining the at least one selected candidate set further comprises determining, for each of the candidate sets, the antenna quality measure, and selecting, from the set of candidate sets, at least one of the candidate sets as the at least one selected candidate set on the basis of the antenna quality measures determined for the candidate sets. For example, the one or more candidate sets yielding the best antenna quality measure, e.g. the highest or lowest antenna quality measure value, beyond the antenna quality measures determined for the candidate sets may be selected, or candidate sets, for which the antenna quality measure exceeds a predetermined threshold, maybe selected as the at least one selected candidate set. Determining the at least one selected candidate set further comprises using one of the at least one selected candidate sets as the set of phase shift values. For example, the candidate set with the best antenna quality measure may be used as the set of phase shift values.

As the set of candidate sets is selected based on a symmetry property of the arrangement of the plurality of antenna elements, the number of candidate sets in the set of candidate sets may be small, and at the same time, the set of candidate sets may cover a large number of possibilities, or a dense set of phase shift values. Having a dense set of phase shift values allows determining the set of phase shift values so that a high antenna quality is achieved, while having a small number of candidate sets provides for a low computational effort.

According to embodiments, determining the selected candidate set further comprises redefining the set of candidate sets based on the at least one selected candidate set. Further, determining the selected candidate set may comprise determining, for each of the candidate sets (of the redefined set of candidate sets) the antenna quality measure, and selecting, from the (redefined) set of candidate sets, at least one of the candidate sets as the at least one selected candidate set on the basis of the antenna quality measures determined for the candidate sets. That is, the candidate set may be recursively or iteratively adapted, for example until the antenna quality measure of the at least one selected candidate set fulfils a predetermined criterion (e.g. exceeds a predetermined threshold) or until a maximum number of recursions or iterations is reached. Thus, redefining the set of candidate sets based on the at least one selected candidate set may, provide for an accurate determination of the set of phase shift values, while keeping the number of candidate sets, for which the antenna quality measure is to be obtained, small. Thus, the set of phase shift values may be determined accurately with a limited computational effort.

According to embodiments, the antenna elements of the respective antenna element set are arranged in a pattern which is rotationally symmetric with respect to discrete rotation angles. For example, the discrete rotation angles may multiples of 360°/(n+1), n being a positive integer. A rotationally symmetric arrangement of the antenna elements of the respective antenna element set allows for using a smaller number of phase shift values in the set of phase shift values, for example without a loss in an antenna quality. Therefore, the rotationally symmetric arrangement allows to have a small number of phase shift value, even though the set of phase shift values is equal for all antenna elements of the respective antenna element set. Furthermore, a rotationally symmetric arrangement of the antenna elements facilitates a computationally efficient determination of the antenna quality measure and/or of reference phase shift values, as the rotational symmetry may be exploited in the determination.

According to embodiments, the antenna elements of a respective antenna element set are arranged in a pattern which is symmetric with respect to one or more mirror axes, and each of the candidate sets for the respective antenna element set comprises, or may even consist of, one or more pairs of opposite phase shift values. That is, e.g., the phase shift values are opposite to each other with respect to a phase value of a reference antenna signal of the phased array antenna. For example, they may be opposite with respect to 0°, that is they may form pairs of a positive and a negative of the same number. Consequently, the mirror symmetry has the advantage that after determining a phase shift value for an antenna element are assigning of phase shift value to an antenna element, the opposite value of the determined phase shift value may be attributed to the opposite antenna element without further calculation. Thus, the mirror symmetry facilitates an efficient determination of the phase shift values.

According to embodiments, the antenna elements of the phased array antenna are arranged in an antenna element pattern which is rotationally symmetric with respect to discrete rotation angles. A rotationally symmetric antenna element pattern allows to determine the antenna quality measure particularly efficient, as the rotational symmetry may be exploited, so that it may be sufficient to perform some or all calculations for determining the antenna quality measure only for a predetermined azimuthal sector having a central angle equal to the rotation angle of the rotational symmetry. For example, the antenna quality measure may be evaluated only within the predetermined azimuthal sector, e.g. only for sector test steering directions within the predetermined azimuthal sector.

According to embodiments, determining the antenna quality measure for a respective candidate set comprises, for at least one test steering direction, determining, for the antenna elements of the at least one antenna element set (e.g. for each of the antenna elements or for each of a subset of the antenna elements of the phased array antenna), (respective) reference phase shift values for directing the phased array antenna towards the respective test steering direction. For example, respective phase shift values may be determined for each of the antenna elements of the at least one antenna element set, or may be determined for each of a subset of, the antenna elements of the at least one antenna element set. The reference phase shift values may be determined without constraints, that is, the reference phase shift values may take arbitrary values within the accuracy of the calculation. Thus, a resolution of a set of values from which the reference phase shift values are determined is higher than a distance between phase shift values of the respective candidate set. Thus, the reference phase shift values may serve as target values or may be regarded as optimal values for the respective phase shift values of the antenna elements. Determining the antenna quality measure for the respective candidate set further comprises, for the at least one test steering direction, associating (or mapping) each of the antenna elements to one of the phase shift values of the respective candidate set under consideration of the reference phase shift values (determined for the antenna elements), and determining (or calculating) a directivity pattern of the phased array antenna for an operation of the phased array antenna using, for each of the antenna elements, the respective associated phase shift value. Determining the antenna quality measure for the respective candidate set further comprises determining the antenna quality measure based on the at least one directivity pattern determined for the at least one test steering direction. Determining the reference phase shift values, and using the reference phase shift values for attributing respective phase shift values of the candidate set to each of the antenna elements allows for a classification or measurement of the antenna quality which may be achieved using the respective candidate set. Thus, this determination of the antenna quality measure allows to select the set of phase shift values so that a high antenna quality may be achieved. Further, the at least one test steering direction may be chosen within a particular region of interest, e.g. the predetermined range. Thus, the determination of the set of phase shift values may be adapted to the predetermined range by selecting the at least one test steering direction accordingly, thus providing the possibility to flexibly adapt the phased array antenna to a particular application, and to achieve a good trade-off between accuracy or directivity and the size of the predetermined range.

According to embodiments, the associating of the antenna elements to one of the phase shift values comprises associating each of the antenna elements to the phase shift values of the respective candidate set which is closest to the reference phase shift value determined for the respective antenna element, e.g. having the smallest distance to the reference phase shift value. This selection rule for associating the antenna elements to the phase shift values may be performed efficiently in terms of computation power.

According to embodiments, determining the antenna quality measure for the respective candidate set comprises determining, for each of a plurality of test steering directions, a respective directivity pattern. The determining of the respective antenna quality measure further comprises selecting, for a plurality of probe directions within the predetermined direction range, respective selected test steering directions based on at least one of a directivity and a side-lobe isolation of the directivity patterns determined for the test steering directions. For example, the test steering direction, the directivity pattern of which fulfills a predetermined criterion may be selected. The predetermined criterion may, for example, be the maximum or minimum directivity or side-lobe isolation beyond all test steering directions with respect to the currently considered direction. Thus, the determination of the phase shift values may be based on a desired evaluation criterion, the directivity and/or the side-lobe isolation, allowing for an optimization or enhancement of the phased array antenna regarding specific desired antenna characteristics.

According to embodiments, the antenna elements of the phased array antenna are arranged in an antenna element pattern which is rotationally symmetric with respect to discrete rotation symmetry angle. Further, determining the antenna quality measure for the respective candidate set comprises determining, for each of a plurality of test steering directions, a respective directivity pattern, wherein respective azimuthal coordinates of the plurality of test steering directions are within a predetermined azimuthal sector, the central angle of the predetermined azimuthal sector being equal to the rotation symmetry angle. Furthermore, the antenna quality measure is determined based on an evaluation of the directivity patterns determined for the plurality of test steering directions within the predetermined azimuthal sector. Thus, by exploiting the rotational symmetry for the determination of the antenna quality measure, the antenna quality measure may be determined accurately, while keeping the number of test steering directions low. Thereby, computational power is saved.

According to embodiments, the antenna elements of the respective antenna element set are arranged in a pattern which is symmetric with respect to a mirror axis. Further, the candidate sets comprise one or more opposite pairs of phase shift values (e.g. the individual candidate sets respectively comprise one or more opposite pairs of phase shift values). Associating the antenna elements to the phase shift values comprises assigning opposite phase shift values to antenna elements which are opposite with respect to the mirror axis. Thus, the symmetry of the arrangement of the antenna elements may be exploited for associating the phase shift values to the antenna elements, so that the determination of the set of phase shift values is particularly efficient. Further embodiments of the invention provide an apparatus for designing a phased array antenna. The apparatus is configured for determining, for at least one antenna element set which includes a plurality of antenna elements of the phased array antenna, a set of phase shift values to which switchable phase shifters for the antenna elements of the antenna element set are switchable, so that, during operation of the phased array antenna, the phased array antenna is steerable towards directions within a predetermined direction range by selecting, for each of the antenna elements of the antenna element set, one of the phase shift values out of the determined set of phase shift values. Determining the set of phase shift values for a respective antenna element set comprises determining, for a plurality of candidate sets of phase shift values, each of the candidate sets comprising a number of phase shift values, respective antenna quality measures describing a quality of an operation of the phased array antenna using the respective candidate set of phase shift values as the set of phase shift values.

The apparatus relies on the same ideas as the method described above, providing equal or equivalent functionalities and advantages. The apparatus may optionally be combined with (or supplemented by) any of the features, functionalities and details described herein with respect to the corresponding method for designing a phased array antenna. The apparatus may optionally be combined with the mentioned features, functionalities and details both individually or in any combination of them.

Further embodiments of the invention provide a phased array antenna comprising a plurality of antenna elements. At least one antenna element set, which is part of the phased array antenna, includes a set of antenna elements of the plurality of antenna elements. The antenna elements of the (respective, the currently considered of the at least one) antenna element set are connected (directly or indirectly) to switchable phase shifters. For example, each antenna element is connected to a respective switchable phase shifter. The phase shifters are switchable to (or between) a set of phase shift values. The switchable phase shifters may shift an antenna signal of the antenna element connected to a respective switchable phase shifter with respect to a reference phase by the phase shift value selected for the respective switchable phase shifter. The set of phase shift values is determined by the above described method for designing a phased array antenna.

As the set of phase shift values is determined by the above described method, a number of phase shift values in the set of phase shift values may be small, but the phased array antenna may nevertheless provide a high antenna quality (e.g. in terms of directivity and/or side-lobe isolation). Due to the small number of phase shift values, the switchable phase shifters may be implemented particularly space- and cost-efficiently.

Further embodiments of the invention provide a phased array antenna comprising a plurality of antenna elements. At least one antenna element set, which is part of the phased array antenna, includes a set of antenna elements of the plurality of antenna elements. The antenna elements of the (respective, the currently considered of the at least one) antenna element set are connected to switchable phase shifters. For example, each antenna element is connected to a respective switchable phase shifter. The phase shifters are switchable to (or between) a set of phase shift values. The switchable phase shifters may shift an antenna signal of the antenna element connected to a respective switchable phase shifter with respect to a reference phase by the phase shift value selected for the respective switchable phase shifter. The set of phase shift values differs from a set of equidistant values. For example, one or more of the phase shift values differ from the set of equidistant values by at least 2% or 5% or 10% or by at least ±2°, ±5° or ±10°. As the set of phase shift values differs from a set of equidistant values, the phase shift values are particularly well adapted to a geometry and/or a desired application/characteristic of the phased array antenna. Therefore, the phased array antenna may have a good performance in terms of side-lobe isolation and/or directivity and nevertheless a number of phase shift values of set of phase shift values may be low, that is, the switchable phase shifters may be switchable to only a limited number of phase shift values, so that they may be implemented by a limited number of fixed phase shifters. Therefore, the phased array antenna may be implemented very cost- and space-efficiently.

According to embodiments, the set of phase shift values differs from a set of equidistant integer (e.g. positive or negative integers) multiples of 360°/2ⁿ. Thus, the phase shift values may be well adapted to a geometry of the phased array antenna.

According to embodiments, a first set of phase shift values, to which the antenna elements of a first antenna element set are switchable, differs from a second set of phase shift values, to which the antenna elements of a second antenna element set are switchable. Thus, the respective sets of phase shift values of the first and the second antenna element sets may be adapted individually to a geometry and/or a desired application/characteristic of the phased array antenna. Consequently, respective numbers of phase shift values of the sets of phase shift values may be not unnecessarily large, but may be limited to a small number. In other words, the number of implemented phase shift values, implemented e.g. in terms of fixed phase shifters, may be efficiently exploited in terms of an adaption of the phase shift values regarding the desired characteristic of the phased array antenna.

According to embodiments, the plurality of antenna elements is arranged in an antenna array pattern which is symmetric with respect to a mirror axis, and the set of phase shift values comprises one or more pairs of opposite phase shift values. Thus, opposite phase shift values are available for opposite antenna elements, allowing for an accurate steering of the phased array antenna towards a desired direction.

According to embodiments, a shape of a patch of the antenna element is rotationally symmetric (e.g. with respect to the plane, within which the antenna element pattern is rotationally symmetric) to an order equal or higher than the order of the rotational symmetry of the antenna element pattern. The rotational symmetry of the patch of the antenna element provides for a good beam shaping characteristic of the phased array antenna, so that the phased array antenna may have a high directivity.

Further details, functionalities and advantages of the phased array antenna correspond to those described with respect to the method for designing a phased array antenna. The phased array antenna may optionally be combined with any of the features, functionalities and details described with respect to the phased array antenna as described with respect to the method for designing a phased array antenna.

Further embodiments of the invention provide a method for operating a phased array antenna. The method comprises selecting, for each of antenna elements of at least one antenna element set of the phased array antenna, one phase shift value out of a set of phase shift values available for the (e.g. each of) the antenna elements of the respective antenna element set, so that the phased array antenna is directed towards a selected direction. The set of phase shift values differs from a set of equidistant values. Alternatively, the set of phase shift values is determined by any of the methods for designing a phased array antenna described above.

The method for operating a phased array antenna relies on the same ideas as the phased array antenna described above, providing equal or equivalent functionalities and advantages. The method may optionally be combined with any of the features, functionalities and details described herein with respect to the corresponding phased array antenna, both individually or in any combination of them. Further embodiments of the invention provide a computer program for implementing any of the methods for designing a phased array antenna or for operating a phased array antenna as described above.

Brief description of the figures:

Advantageous implementations of the present invention are described in more detail below with respect to the figures, among which:

Fig. 1 illustrates an antenna element pattern according to an embodiment,

Fig. 2 illustrates a phased array antenna according to an embodiment,

Fig. 3 illustrates a phased array antenna according to another embodiment,

Fig. 4 shows a flowchart of a method for designing a phased array antenna according to an embodiment,

Fig. 5 shows a flowchart for determining a set of phase shift values according to an embodiment,

Fig. 6 shows a flowchart for determining an antenna quality measure according to an embodiment,

Fig. 7 illustrates symmetry properties and phase relations between antenna elements of an antenna element set according to an embodiment,

Fig. 8 shows plots of directivity patterns for reference phase shift values and for a first steering direction according to an embodiment,

Fig. 9 shows plots of directivity patterns for reference phase shift values and for a second steering direction according to an embodiment,

Fig. 10 shows plots of directivity patterns for reference phase shift values and for a third steering direction according to an embodiment,

Fig. 11 shows a plot of a directivity pattern for reference phase shift values for another steering direction according to an embodiment,

Fig. 12 shows a plot of an aggregated directivity for reference phase shift values according to an embodiment, Fig. 13 illustrates a selection pattern for the aggregated of Fig. 12,

Fig. 14 shows Table 4, comprising an assignment of phase shift values to antenna elements according to an embodiment,

Fig. 15 shows a plot of a directivity pattern for assigned phase shift values for a test steering direction according to an embodiment,

Fig. 16 shows a plot of an aggregated directivity for assigned phase shift values according to an embodiment,

Fig. 17 illustrates a selection pattern for the aggregated directivity of Fig. 16,

Fig. 18 shows a plot of an aggregated directivity for assigned phase shift values using individual sets of phase shift values according to an embodiment,

Fig. 19 illustrates a selection pattern for the aggregated directivity of Fig. 18,

Fig. 20 shows a plot of an aggregated directivity for assigned phase shift values according to another embodiment,

Fig. 21 illustrates a selection pattern for the aggregated directivity of Fig. 20,

Fig. 22 shows a plot of an aggregated directivity according to another embodiment,

Fig. 23 shows plots of directivity patterns for circular antenna elements according to an embodiment,

Fig. 24 shows plots of directivity patterns for circular antenna elements according to another embodiment,

Fig. 25 illustrates an apparatus for designing a phased array antenna according to an embodiment, and

Fig. 26 shows a flowchart of a method for operating a phased array antenna according to an embodiment.

Detailed description of illustrative embodiments

In the following, embodiments are discussed in detail, however, it should be appreciated that the embodiments provide many applicable concepts that can be embodied in the context of phased array antennas. The specific embodiments discussed are merely illustrative of specific ways to implement and use the present concept, and do not limit the scope of the embodiments. In the following description, a plurality of details is set forth to provide a more thorough explanation of embodiments of the disclosure. However, it will be apparent to one skilled in the art that other embodiments may be practiced without these specific details. In other instances, well-known structures and devices are shown in form of a block diagram rather than in detail in order to avoid obscuring examples described herein. In addition, features of the different embodiments described herein may be combined with each other, unless specifically noted otherwise.

In the following description of embodiments, the same or similar elements or elements that have the same functionality are provided with the same reference sign or are identified with the same name, and a repeated description of elements provided with the same reference number or being identified with the same name is typically omitted. Hence, descriptions provided for elements having the same or similar reference numbers or being identified with the same names are mutually exchangeable or may be applied to one another in the different embodiments.

Fig. 1 illustrates a plurality of antenna elements #1 to #25 of a phased array antenna according to an exemplary embodiment, the plurality of the antenna elements comprising the exemplary number of 25 antenna elements. The antenna elements are arranged in an antenna element pattern 10. The plurality of antenna elements comprises a first antenna element set 12 and a second antenna element set 14. The first antenna element set 12 comprises antenna elements #2 - #9, the second antenna element set 14 comprises antenna elements #10 - #25. The plurality of antenna elements further comprises a central antenna element #1. In the shown example, the antenna elements of the first and the second antenna element sets are arranged in respective concentric rings around the central antenna element #1. Further examples of the antenna element pattern do not comprise a central antenna element. Furthermore, some examples of the antenna element pattern 10 comprise only one antenna element set, while other examples comprise more than two antenna element sets.

In the example shown in Fig. 1 , the radii of the respective concentric rings of the antenna element sets are evenly distributed with respect to the center of the concentric rings, that is, the radius of the second antenna element set 14 is twice the radius of the first antenna element set 12. According to other examples, the radii of the antenna element sets may be distributed unevenly. The antenna element pattern 10 is rotationally symmetric regarding rotations by multiples of 45°, and consequently inhibits a mirror symmetry regarding several axes through the center of the concentric rings, the axes pairwise enclosing an angle of 45°. The symmetry properties of the antenna element pattern 10 are discussed in more detail with respect to Fig. 7.

Fig. 2 illustrates a phased array antenna 90 according to an embodiment. The phased array antenna 90 comprises an antenna signal transceiver 20 configured for providing (or receiving) an antenna signal 22 to (or from) each of a plurality of switchable phase shifters 30a-f. The plurality of switchable phase shifters 30 comprises switchable phase shifters 30a to 30f. Each of the switchable phase shifters 30a-f is connected to a respective antenna element 11a-f of antenna elements 11. Each of the switchable phase shifters 30a-f is configured to shift the phase of the antenna signal 22 by a phase shift value to which the respective switchable phase shifter is adjusted.

For example, each of the switchable phase shifters includes a number of fixed value phase shifters which may be selected for the respective switchable phase shifter, so that the respective switchable phase shifter shifts the phase of the antenna signal 22 by the fixed value of the selected fixed value phase shifter. That is, each fixed value phase shifter provides a specific phase shift value to which the switchable phase shifter is switchable. Thus, each of the switchable phase shifters 30a-f is switchable to a respective set of phase shift values which may depend on the implementation of the respective switchable phase shifter 30a-f.

The antenna signal 22, when provided by the antenna signal receiver 20, may excite the antenna elements 11 , so that each of the antenna elements 11 transmits an electromagnetic signal contribution. The superposition of the electromagnetic signal contributions transmitted by antenna element 11 results in a beam or electromagnetic signal emitted by the phased array antenna 90. An electromagnetic signal or beam that is incidental to the phased array antenna may excite each of the antenna elements, which transform the electromagnetic signal into electronic signals, provided via the respective switchable phase shifters to the antenna signal transceiver 20, which may receive a superposition of the respective electronic signals. By adjusting the phase relation between the antenna elements by means of the switchable phase shifters, the phased array antenna may be directed towards a desired direction. That is, the electromagnetic signal or beam transmitted by the phased array antenna has its maximum directivity in the desired direction or a sensitivity of the phased array antenna for receiving electromagnetic radiation is maximum with respect to the desired direction.

The respective phase shift values which have to be assigned to the individual antenna elements for directing the phased array antenna towards the desired direction may be determined so that the contributions of the individual antenna elements combine to form a plane wave propagating in the desired direction according to well-known models for phased array antennas.

In other words, the phased array antenna 90 provides an example, in which the number of phase values is limited to a very low number, e.g. between 2 and 4, e.g. 3. This allows using a limited set of fixed phase value phase shifters that are switched as required into the signal path feeding each antenna element. Fig. 2 may represent an example of one of such signal paths, exemplarily comprising 3 phase values and 6 antenna elements. The fixed value phase shifters may, e.g. make use of fixed length delay lines and pairs of RF switches for selecting the required phase shift value.

The plurality of antenna elements may optionally comprise a first antenna element set and a second antenna element set. For example, the antenna elements 11a-c are part of the first antenna element set, and the antenna elements 11 d-f are part of the second antenna element set. The switchable phase shifters 30a-c which are connected to the antenna elements of the first antenna element set may be implemented equally with respect to each other, so that they share a first common set of phase shift values. Equivalently, the switchable phase shifters 30d-f may share a second common set of phase shift values.

Fig. 3 illustrates a phased array antenna 300 according to an embodiment. The phased array antenna 300 comprises a plurality of antenna elements 311 . The plurality of antenna elements comprises at least one antenna element set 312 which includes a set of antenna elements of the plurality of antenna elements 311. The antenna elements of the antenna element set 312 are connected to switchable phase shifters 330 which are switchable to a set of phase shift values 332. As illustrated in Fig. 3, each of the antenna elements of the antenna element set 312 may be connected to switchable phase shifter 330 being switchable to the same set of phase shift values 332.

For example, the switchable phase shifters 330 shift a phase of their respective input signals so that phases of their respective output signals, which are provided to their respective connected antenna elements 311 , are shifted with respect to a phase of an antenna reference signal by the respective phase shift values which are selected for the switchable phase shifters. For example, the phase shifters 330 receive the antenna reference signal as an input signal. The phase of the antenna reference signal may be 0°, or any other value. The antenna signal 22 of Fig. 2 may be an example for the antenna reference signal.

The phased array antenna 90 may be an example of the phased array antenna 300, the antenna element set 12, 14 may be an example of the antenna element set 312, the antenna element 11 a-f may be examples of the antenna elements 311 , and the switchable phase shifters 30 may be examples of the switchable phase shifters 330.

According to embodiments, the set of phase shift values 332 is determined by the method 400 for designing a phased array antenna as described below with respect to Fig. 4.

According to embodiments, the set of phase shift values 332 differs from a set of equidistant values. Differing may mean, in this context, that, if assigning each of the phase shift values of set of phase shift values to one of the values of the set of equidistant values, at least one of the phase shift values differs from its assigned value by at least 10% or 5% or 2% or at least ±10°, ±5° or ±2°. For example, the set of phase shift values 332 may be determined by the method 400.

As the phase shift values are determined by the method 400 or as they differ from a set of equally spaced values, they may be adapted to the properties of the antenna array pattern. As a consequence, the number of phase shift values, to which the switchable phase shifters of switchable may be small. This reduces component complexity: the switchable phase shifters may for example be implemented using the fixed value phase shifters. Each fixed- value phase shifter may be composed of only a few basic components, compared to continues-values phase shifters that require use of more sophisticated integrated circuits. This implementation may also reduce component cost: the cost for the RF switch pair used in a fixed-values phase shifter is low and the phase shift may be realized as fixed-length delay line on the same printed circuit board as the antenna, while the prices for a continues- values phase shifter are much higher, depending on frequency and resolution. The implementation may also reduce signalling complexity and increases beam-steering speed: e.g. selecting one out of an exemplary number of four fixed phases, requires only a 2-bit control signal per phase shifter, compared to 4 to 8 bit for each continuous-phase phase shifter. Phase change are communicated 2 or 4 times faster if the signalling is done sequentially.

According to embodiments, the antenna elements are not necessarily arranged in N concentric rings and M identical circular sectors, that is, the antenna elements are not necessary arranged in a rotationally symmetric antenna element pattern, but the antenna element pattern may still provide symmetry properties which may be exploited for obtaining the set of candidate sets, determining the reference phase shift values, and/or determining the antenna quality measure.

According to embodiments, the set of phase shift values differs from a set of equidistant integer multiples of 360°/2ⁿ.

The plurality of antenna elements 311 may comprise a plurality of antenna element sets 312. The switchable phase shifters 330 of a respective antenna element set may be switchable to a respective set of phase shift values.

Accordingly, according to embodiments, a first set of phase shift values, to which the antenna elements of a first antenna element set are switchable, differs from a second set of phase shift values, to which the antenna elements of a second antenna element set are switchable. Switching the antenna elements may refer to a switching of the respective switchable phase shifters of the antenna elements.

For example, the antenna elements of the first antenna element set 12 of the exemplary antenna element pattern 10 of Fig. 1 may be switchable to a first set of phase shift values and the second antenna element set 14 may be switchable to a second set of phase shift values.

According to embodiments, the plurality of antenna elements 311 is arranged in an antenna element pattern which is symmetric with respect to a mirror axis, and the set of phase shift values 332 comprises one or more pairs of opposite phase shift values.

The respective differences between two opposite phase shift values and a predetermined phase Y may be negated values. That is, a pair of opposite phase shift values may comprise the values Y+X and Y-X with respect to the predetermined phase Y. E.g., the predetermined phase may be the phase of the reference antenna signal 22. In the non-limiting examples described below, Y is assumed to be 0°, so that a pair of opposite phase shift values may be represented as X and -X.

For example, the antenna elements 311 may be arranged in the antenna element pattern 10, without limitations to the number of the antenna elements, the number of concentric rings, the radii of the concentric rings and the number of antenna elements per concentric ring. The antenna element 311 may alternatively be arranged in different antenna element patterns with mirror symmetry. According to embodiments, the antenna elements are implemented as patch antennas.

According to embodiments, a shape of patches of the antenna elements is rotationally symmetric to an order equal or higher than the order of the rotational symmetry of the antenna element pattern.

A rotationally symmetric shape of the patches of the antenna elements is particularly beneficial in combination with a rotationally symmetric or antenna element pattern. The rotationally symmetric shape of patches may increase the quality of the beam shaping characteristics of the phased array antenna. An example for an antenna quality for the phased array antenna with rotationally symmetric patches is given in Fig. 23.

According to embodiments, the phased array antenna is for use in communication, for example satellite communication, or other applications, such as radar, RFID reader, RF scanner, RF ranging. Communication may be uni-directional, e.g. Machine-to-Machine (M2M) or “Internet of Things” (loT) type applications, with many terminals transmitting data towards a satellite (or any other receiver, including terrestrial). Communication may further be Bi-directional, e.g. Machine to Machine (M2M) or “Internet of Things” (loT) type applications, with many terminals transmitting data towards a satellite and the same terminals also capable of receiving data from the satellite (or any other receiver, including terrestrial).

Fig. 4 shows a flowchart of a method 400 for designing a phased array antenna, e.g. the phased array antenna 300, according to an embodiment. The method 400 comprises a step of determining 401 , for the at least one antenna element set 312 which includes a plurality of antenna elements 311 of the phased array antenna 300, the set of phase shift values 332, to which the switchable phase shifters 334 of the antenna elements of the antenna element set 312 are switchable so that, during operation of the phased array antenna, the phased array antenna is steerable towards directions within a predetermined direction range by selecting, for each of the antenna elements of the antenna element set 312, one of the phase shift values out of the determined set of phase shift values 332. The determining 401 comprises a step 402 of determining, for a plurality of candidate sets 462 of phase shift values, respective antenna quality measures 474 describing a quality of an operation of the phased array antenna 300 using the respective candidate set of phase shift values as the set of phase shift values 332. Each of the candidate sets comprises a number of phase shift values. According to embodiments, the method 400 comprises separately determining respective sets of phase shift values for a plurality of antenna element sets which include respective pluralities of antenna elements of the phased array antenna 300.

For example, with respect to the antenna element pattern 10 of Fig. 1 , the method 400 may comprise determining 401 a first set of phase shift values for the first antenna element set 12, and determining 401 a second set of phase shift values for the second antenna element set 14.

For example, explained with respect to Fig. 2, the antenna elements 11a-c may be part of the first antenna element set 12, and the antenna elements 11 d-f may be part of the second antenna element set 14. Each of the switchable phase shifters 30a-c connected to the antenna elements 11a-c may be switchable to phase shift values of the first set of phase shift values. Accordingly, each of the switchable phase shifters 30d-f connected to the antenna elements 11 d-f may be switchable to phase shift values of the second set of phase shift values.

In the case of more than one antenna element set 312, the respective sets of phase shift values for the antenna element sets may be determined separately from each other. For example, the set of phase shift values for the respective antenna element set may be determined under the assumption of predetermined phase shift values or determined (e.g. regarded optimum) reference phase shift values for the antenna elements of other antenna element sets. Alternatively, the set of phase shift values 332 for the respective antenna element set 312 may be determined under consideration of the determination of the set of phase shift values for another antenna element set of the plurality of antenna element sets. For example, a plurality of combinations of respective candidate sets for the plurality of antenna element sets may be considered or tested for determining the respective sets of phase shift values for the plurality of antenna element sets.

To continue to the description of Fig. 4, the set of phase shift values 332 may be universal for the antenna element set 312, i.e. all antenna elements of the antenna element set 312, for which the set of phase shift values 332 is determined.

Consequently, according to embodiments, for each antenna element of the at least one antenna element set 312, the switchable phase shifter 30 for the respective antenna element 311 is switchable to each of the phase shift values of the set of phase shift values 332 of the respective antenna element set 312. According to embodiments, the determining 401 further comprises an additional step of determining the set of phase shift values 332 based on the candidate sets 462 under consideration of the respective antenna quality measures 474 determined for the candidate sets 462.The determining of the set of phase shift values 332 based on the candidate sets 462 may be performed after step 402 of Fig. 4.

Thus, the antenna quality measure determined for a respective candidate set may be evaluated with respect to a predetermined criterion or may be compared to the antenna quality measures determined for the one or more others of the plurality of candidate sets.

The antenna quality measure determined for a respective candidate set may thus give an estimate for an antenna quality which is to be expected, if the phased array antenna is operated using the respective candidate set, that is, that the switchable phase shifters for the antenna elements of the antenna element set 312, for which the candidate set is evaluated, are switchable to the phase shift values of the respective candidate set. For example, determining the antenna quality measure for a respective candidate set may refer to an evaluation of a cost function for an (simulated or hypothetic) operation of the phased array antenna. For example, the antenna quality measure may be determined by calculating or determining a cost function from an aggregated directivity.

The determining 402 of the antenna quality measure for the plurality of candidate sets 462 may aim for selecting or approximating or determining the set of phase shift values 332 so that the determined set of phase shift values fulfils a predetermined criterion, like yielding the best antenna quality measure beyond a selection of candidate sets or exceeding a predetermined threshold for the antenna quality measure. In the former case, the determining 402 may be performed for a predefined set of candidate sets, which optionally may be redefined or modified iteratively. In the latter case, the determining 401 may start with the determination 402 for a predetermined candidate set, which is subsequently iteratively or recursively adapted. That is, in examples, each of the plurality of candidate sets may be derived from a previous candidate set or from the predetermined candidate set.

In other words, considering for example the “N concentric rings” property of a general arrangement of antenna elements, the set of phase values may differ from ring to ring, however the same set is required for all antenna elements within a ring. The phase values in each set may be selected such as (approximate) beam steering within the full azimuth and elevation range with in a sector of interest is maintained, and beam widening and appearance of side-lobes is kept within design targets. Mathematically speaking, the values in the set may minimize a cost function.

According to embodiments, the antenna elements of the respective antenna element set is arranged in a symmetric pattern, and determining 401 the set of phase shift values is performed under consideration of the symmetry of the symmetric pattern.

For example, the symmetric antenna element pattern allows for exploiting the element arrangement properties of the array in order to minimize the number of phases (e.g. phase shift values) or number of fixed value phase shifters for steering the beam.

In the following, several embodiments for the step 401 of determining the set of phase shift values 332 are described.

Fig. 5 shows a flowchart for determining 501 the set of phase shift values 332 according to an embodiment. The determining 501 may correspond to the determining 401 . Determining 501 the set of phase shift values 332 for the respective antenna element set 312 comprises a step 551 of determining at least one selected candidate set 552 of phase shift values. The determining 551 comprises obtaining 561 a set of candidate sets 562 of phase shift values. The set of candidate sets 562 may be an example of the plurality of candidate sets 462. The set of candidate sets 562 is selected based on a symmetry property of an arrangement of the plurality of antenna elements 311 of the phased array antenna. Each candidate set of phase shift values comprises a number of phase shift values. Step 551 further comprises determining 563, for each of the candidate sets, the antenna quality measure. Furthermore, step 551 comprises a step 565 of selecting, from the set of candidate sets 562, at least one of the candidate sets as the at least one selected candidate 552 set on the basis of the antenna quality measures determined for the candidate sets 562. The step 551 of determining the set of phase shift values 332 further comprises a step 555 of using one of the at least one selected candidate sets as the set of phase shift values 332. The step 561 of obtaining the set of candidate sets 562 may include receiving or retrieving a predetermined set of candidate sets or may include determining the set of candidate sets 562.

For example, the candidate sets 562 may be selected in accordance with a desired phase resolution, and a desired number, or range, for the number of phase shift values of the respective candidate sets 562. The phase resolution may for example be chosen as 360°/2ⁿ, with n being an integer number, e.g. between 4 and 8. Such a choice provides a good compromise between a limited number of possible candidate sets and a good phase resolution.

The step 563 may be an example of step 402 of Fig. 4. Step 653 may be performed as step 663 as described with respect to Fig. 6.

According to embodiments, step 551 of determining the selected candidate set comprises a further step 567 of redefining the set of candidate sets 562 based on the at least one selected candidate set 552. Step 551 then comprises determining the antenna quality measure for each of the candidate sets of the redefined set of candidate sets 562, and selecting from the redefined set of candidate sets 562, the at least one selected candidate sets on the basis of the antenna quality measures determined for the candidate sets.

Accordingly, step 551 may be performed recursively or iteratively, redefining the set of candidate sets after each recursion or iteration. The recursive adaption of the set of candidate sets 562 for example allows to start with a low phase resolution of the candidate sets 562, so that the number of candidate sets may be low. For example, the phase shift values of a first set of candidate sets may be values out of a set of values having a first resolution. For example, the first set of candidate sets may be predetermined and may be used for starting a recursive adaption in step 551 . After determining the at least one selected candidate sets, the sets of candidate sets may be adapted so that the phase shift values of the candidate sets take values out of a second set of values having a higher resolution than the first set of values, but only considering values within a predetermined range around the phase shift values of the at least one selected candidate sets. The recursion may be continued until the resolution of the set of values, out of which the phase shift values for the candidate sets are selected, reaches or exceeds a predetermined threshold. Alternatively, the recursion may be continued until at least one of the antenna quality measures determined in step 563 reaches or exceeds a predetermined threshold.

In the above described case that the phased array antenna comprises a plurality of antenna element sets, the respective sets of phase shift values for the antenna element sets may be determined separately or independently from each other, or each of them may be determined under consideration of the set of phase shift values selected for one or more further antenna element sets. For example, step 561 may include to obtain respective sets of candidate sets for each of the antenna element sets. In step 563, the antenna quality measure may be determined for each combination of candidate sets for the individual antenna element sets. Alternatively, step 563 may be performed for a set of combinations of candidate sets for the individual antenna element sets. In the latter case, step 567 may include to recursively adapted the set of combinations. In other words, the set of candidate sets 562 may comprise respective subsets of candidate sets for the individual antenna element sets.

According to an embodiment, the number of phase shift values of the respective candidate sets is recursively adapted. For example, a number of phase shift values per candidate set may be increased, until a desired antenna quality measure is achieved.

The consideration of symmetry properties of the antenna element pattern for the selection of the set of candidate sets 562 may reduce the number of candidate sets, which are to be considered for a desired phase resolution of the candidate sets and a desired number of phase shift values per candidate set. The extent, to which the number of candidate sets may be reduced, may depend on the symmetry properties of the pattern of the respective antenna element set 312.

In other words, embodiments of the method 400 may use properties of the proposed antenna element arrangement to derive corresponding symmetry properties in the phase assignment for the elements for the purpose of beam steering. Considering these symmetry properties significantly reduces the number of phase options that have to be considered when limiting the number of fixed value phase shifters and optimizing their values.

According to embodiments, the antenna elements 311 of the respective antenna element set 312 are arranged in a pattern which is rotationally symmetric with respect to discrete rotation angles. This is, for example, the case for the antenna element pattern 10, as will be described with respect to Fig. 7.

According to further embodiments, the antenna elements 311 of the respective antenna element set 312 are arranged in a pattern which is symmetric with respect to one or more mirror axes, and each of the candidate sets 562 for the respective antenna element set 312 comprises one or more pairs of opposite phase shift values.

As a consequence, assuming a given phase resolution and a given number of phase shift values per candidate set, the number of candidate sets for which the antenna quality measure is to be determined may be reduced to candidate sets with opposite phase shift values.

An example of how rotational and mirror symmetry may be exploited for determining the set of phase shift values 332 will be given below with respect to Fig. 7 by means of the rotationally symmetric antenna element pattern 10, which comprises both rotational symmetry and mirror symmetry. Nevertheless, similar considerations are valid for different antenna element patterns.

Fig. 6 shows a flowchart of a determination 663 of an antenna quality measure 674 for a respective candidate set of the candidate sets 562. The antenna quality measure 674 may correspond to the antenna quality measure 474. The determination 663 may correspond to the determination of the antenna quality measure as performed, for each of the candidate sets in step 563 of Fig. 5. The determination 663 comprises a step 671 of determining, for at least one test steering direction, a directivity pattern 686 of the phased array antenna. The determination 671 of the directivity pattern comprises determining 681, for the antenna elements of the at least one antenna element set 312, reference phase shift values 682 for directing the phased array antenna towards the respective test steering direction. Step 671 further comprises associating 683 each of the antenna elements to one of the phase shift values of the respective candidate set under consideration of the reference phase shift values. Step 671 further comprises a step 685 of determining the directivity pattern 686 of the phased array antenna for an (simulated or hypothetic) operation of the phased array antenna using, for each of the antenna elements, the respective associated phase shift value. Step 663 further comprises determining 673 the antenna quality measure based on the at least one directivity pattern 686 determined for the at least one test steering direction.

For example, 663 may comprise defining a set of test steering directions and determining, for each of the test steering directions a respective directivity pattern 686 according to step 671. For example, the set of test steering directions may include test steering directions covering the predetermined direction range, which may correspond to a desired direction range within which the phased array antenna is desired to be specified or to be operated.

In some embodiments, the test steering directions may follow a regular grid within the predetermined direction range. In other embodiments, the test steering directions may be distributed under consideration of typical beam width, and/or may seek for an approximately homogeneous distributions of the test steering directions (or beam steering targets) over the predetermined direction range (a region of interest or sector of interest).

The step 681 of determining the reference phase shift values 682 and/or the definition of the test steering directions, may be based on the geometry of the phased array antenna and may make use of geometric considerations or of a computational model aiming for a generation of the plane wave propagating in the direction of using the respective test steering direction. The determination of the reference phase shift values may be particularly efficiently, if symmetry properties of the antenna element pattern of the phased array antenna are considered.

According to embodiments, the antenna elements of the phased array antenna 300 are arranged in an antenna element pattern which is rotationally symmetric with respect to discrete rotation angles.

In case of a rotationally symmetric antenna element pattern, it may be sufficient to determine respective directivity patterns for test steering directions within a predetermined azimuthal sector of the antenna element pattern, so that computational effort may be saved. Accordingly, the test steering directions may be distributed within a sector of interest.

Accordingly, according to embodiments in which the antenna elements are chosen to be arranged in a rotationally symmetric antenna element pattern, the step 663 comprises determining, for each of a plurality of test steering directions, a respective directivity pattern, wherein respective azimuthal coordinates of the plurality of test steering directions are within a predetermined azimuthal sector, the central angle of the predetermined azimuthal sector being equal to the rotation symmetry angle. Step 673 may in this case comprise determining the antenna quality measure 674 based on an evaluation of the directivity patterns 686 determined for the plurality of test steering directions within the predetermined azimuthal sector. The predetermined azimuthal sector may be chosen so that the central angle of the predetermined azimuthal sector equals the rotation symmetry angle of the rotational symmetry of the antenna element pattern.

According to some embodiments, the antenna elements of the respective antenna element set are arranged in a pattern which is symmetric with respect to a mirror axis, and the candidate sets (682) comprise one or more opposite pairs of phase shift values. In this case, in step 683 opposite phase shift values may be associated to to antenna elements which are opposite with respect to the mirror axis (opposite value with respect to the phase value of the antenna reference signal).

An example, of how the test steering directions, and the reference phase shift values 682 may be derived for a mirror symmetric antenna element pattern (discrete rotation symmetry angles of 3607(n+1)), as it may be made use of in step 681 , is described with respect to Fig. 7.

According to embodiments, the step 683 of associating each of the antenna elements 311 to one of the phase shift values of the respective candidate set comprises selecting from the respective candidate set, for each of the antenna elements 311 , the phase shift value which is closest to the reference phase shift value determined for the respective antenna element, so as to associate each of the antenna elements with the phase shift value selected for the respective antenna element.

For determining 685 the directivity pattern 686, a plurality of probe directions (or test points or probe points) within the predetermined directivity range may be defined. Similar to the definition of the test steering directions, the symmetry properties of the antenna element pattern may be exploited. For example, in case of a rotationally symmetric antenna element pattern, a region of interest, within which the plurality of probe directions is defined may be limited to one azimuthal sector, for example the predetermined azimuthal sector within which the test steering directions are selected. It should be noted, that the probe directions may be selected independently from the test steering direction. In particular, the number of probe directions may be independent from the number of test steering directions. According to embodiments, the number of probe directions is larger, for example by at least one or two orders of magnitude, than the number of test steering directions. The probe directions may for example be located in a regular grid (regular with respect to azimuth/elevation or with respect to a 3D grid) within the region of interest. An example for a region of interest is given by the region of interest 98 in Fig. 11 to Fig. 22.

The determination of the directivity pattern 686 for the respective test steering direction may comprise, determining, for each of the test points, the directivity to the direction of the respective test point, for example, by summing up the complex (or amplitude/phase) signal vectors from each antenna element to the test point, assuming for each of the antenna elements the phase shift value associated to the respective antenna element in step 683and considering or calculating the resulting amplitude and phase of an electromagnetic signal transmitted by the individual antenna elements in the direction of the test point.

The step 671 may be performed for a plurality of test steering directions, yielding a respective plurality of directivity patterns.

Accordingly, according to embodiments, the step 663 of determining the antenna quality measure for the respective candidate set comprises determining, for each of the plurality of test steering directions, a respective directivity pattern. According to this embodiment, the step 673 of determining the antenna quality measure based on the directivity patterns 686 may comprise selecting, for a plurality of probe directions within the predetermined direction range, respective selected test steering directions based on at least one of the directivity and a side-lobe isolation of the directivity patterns determined for the test steering directions. The plurality of probe directions may be equivalent to, or may be different from the plurality of probe directions used for determining the directivity pattern 686 in step 685. Thus, the plurality of probe directions may be distributed within the predetermined direction range or may be distributed within a region of interest, which may form a part of the predetermined direction range, for example one azimuthal sector in case of a rotationally symmetric antenna element pattern.

This step 673 of determining the antenna quality measure may comprise to determine an aggregated directivity based on the directivity patterns 686 determined for the plurality of test steering directions. From the aggregated directivity, the antenna quality measure may be determined by evaluating a cost function of the aggregated directivity. Thus, a result of the cost function may represent the antenna quality measure.

For example, for each of the plurality of probe directions, the plurality of directivity patterns 686 may be evaluated regarding a predetermined criterion by applying the predetermined criterion on the directivity and/or a side-lobe isolation in the respective probe direction of the directivity patterns 686. For example, for each of the probe directions, the directivity pattern having the best directivity or side-lobe isolation or weighted combination of both maybe selected as the selected test steering direction. An aggregated directivity pattern or composed directivity pattern may indicate, for each of the probe directions, the directivity of the phased array antenna for the selected test steering direction. Optionally, a selection pattern may be determined, which may indicate the selected test steering direction for each of the probe directions. Examples for aggregated directivity patterns (or aggregated directivities) and the selection pattern will be described with respect to Fig. 12, Fig. 13, Fig. 16, Fig. 17, Fig. 20, Fig. 21 and Fig. 22.

For example, the aggregated directivity G_a may be calculated according to G_a = G_a(az,el) = where G_b denotes the directivity patterns 686 for the respective test steering directions, and b indexes the test steering directions.

Examples of cost functions for determining the antenna quality measure from the aggregated directivity include (but are not limited to):

• average aggregated directivity, i.e.

® worst case (minimum) aggregated directivity, i.e. C₂ = min(G_a)

• best case (minimum) aggregated directivity ripple, i.e. C₃ = max(G_a) - min(G_a) • worst case (minimum) aggregated side-lobe isolation, i.e. C₃ = min(S_a)

Assume G_b(az, el) is the directivity at a point (az, el) within the sector of interest when steering the beam to the b-th target, then is the aggregated directivity over the area and is the aggregated side-lobe isolation, with G_b being the peak directivity of the first (highest directivity) side-lobe anywhere within the field of view.

For example, the cost function may be evaluated within a sector of interest or region of interest, which may differ or may be equal to the sector of interest of the region of interest within which the test steering directions and/or the plurality of probe directions may be distributed.

In other words, such a cost function may be calculated over a number B of beam steering targets (test steering directions) and over the area of a sector of interest. Calculating the cost function may requires steering the beam to B target locations, and calculating the directivity for a number of T “test” or “probe” points at (az_t, el_t) within the sector of interest. Thus, the complexity of calculating the cost function may be

The cost function may be evaluated for each candidate set of phases, selecting one phase value for each antenna element from the candidate set. In the general case, if there are P phases in the set and A antenna elements, there are P^A possible phase assignments to the elements of the array. Even for rather small number for P (e.g. P = 4) and A (e.g. A = 25) the number of combinations P^A = 4²⁵ = 1.126 • 10¹⁵ may be prohibitively large for a full search. The number of options to be evaluated can be reduced to only 1 by first calculating the optimum phase assignment for a given target location, and then mapping the optimum phase value to the closest value from the set and using this “approximate” phase for the respective antenna element. However, even with this reduction, the cost function has to be calculated for each candidate set.

Fig. 7 illustrates symmetry properties and an assignment of phase shift values for the example of the antenna element pattern 10 according to an embodiment. The example of the antenna elements 10 is composed of 25 radiating elements (or antenna elements or elements). Further examples of the antenna element pattern may have a different number of antenna elements, for example smaller or larger. The antenna elements may be arranged planar, and may have the shape of micro-strip line circular patch antenna elements. The exemplary antenna element pattern 10 is composed of 1 central element, and 2 concentric element rings, spaced at a radius of λ/2. As indicated in the right panel Fig. 7, the first ring has 8 elements, #2 to #9, spaced 360°/8 = 45° in azimuth; the second ring has 16 elements, #10 to #25, spaced 360°/16 = 22.5° in azimuth. Consequently, all 45° sectors in antenna element pattern 10 are identical. If the antenna element pattern 10 is rotated by multiples of 45°, this results in the same arrangement of the elements (regarding the positions of the antenna elements position), and a permutation of element indices depending on the ring:

• Central element is always #1

• Elements in the first ring permute by 1 for each multiple of 45°, i.e. #2 → #3, #3 → #4, ... #8 → #9, #9 → #2 for each +45° rotation.

• Element in the second ring permute by 2 for each multiple of 45°, i.e. #10 → #12,

#11 #13, #12 -» #14, #23 → #25, #24 #10, #25 #11 for each +45° rotation

For the example, the predetermined direction range is chosen to be 360° in azimuth and 15° to 90° in elevation, due to the symmetry properties, the consideration of the beam steering may (e.g. for simplicity) be limited to the azimuth sector of +/- 22.5° and over the required elevation range (e.g. 15° to 90°), which may be referred to a region of interest are a sector of interest. Same may be applied for the calculation of the corresponding phase assignment (e.g. the reference phase shift values 682) for each antenna element. This is without loss of generality, as steering to any other angular sector may use the phase assignment calculated for the +/- 22.5° case on the permuted set of antenna elements.

Phase shift values for steering the phased array antenna towards a desired direction may, for example, be calculated according to the following scheme:

• set element #1 as “reference” and assign a constant phase of 0°, although any other value may be used as a reference phase without limitation.

• use element #2 for up-down steering (elevation) and assume a phase P₁ as required for steering to the wanted elevation angle (within the range of e.g. 15° to 90°)

• use element #4 for rotational steering (azimuth) and assume a phase P₂ as required for steering to the wanted azimuth angle (with the range of e.g. -22.5° to +22.5°)

Given the geometrical arrangement of the antenna elements of the exemplary antenna element pattern 10 and the requirement to have an equal-distance (modulo wavelength λ) path from each antenna element to the far field point S (= GSO or NGSO satellite location) for constructive combining of the antenna element signals at S, the phase assignments (reference phase shift values 682) for all other elements are dependent only on P1 and P 2 and can be derived as follows:

Fig. 7 (left) illustrates the phase assignments while Fig. 7 (right) indicates the geometry properties used in deriving the equations. According to an embodiment, (e.g. the antenna element pattern 10, but also more general patterns) the arrangement of antenna elements is characterised as follows:

• N concentric rings, each with a different radius r_i

• M identical angular sectors, each spanning 360 °/M

• all elements are arranged in a single plane (planar array) In the example of Fig. 1, N = 3, with r_i = , for ring i (where i = 0 is the central element) and M = 8. Various other examples with equal or non-equal radius spacing and regular or irregular element arrangement within each sector are possible.

In this more general case, we again assume two phases, P_el and P_az as variable and calculate the phase for each element j of the array as P_j = r_i(j)· P_el · cos (δ(j)) + r_i(j)·

P_az · sin(δ(j)), where r_i(j) is the radius of the ring r_i the element ; is on, and δ(j) is the angle between the x-axis and the line from centre to the element j. Varying P_el and P_az allows steering the beam in any direction within the sector and to the extend supported by the underlying antenna array and the individual element directivity pattern. Vice versa, if a target (satellite) location is given by azimuth angle az and elevation angle el, perfect constructive combining of the 3 “unit signal paths” from (0; 0), (λ/2; 0) and (0; λ/2) is achieved when

• P_el = -180° • cos(el) • cos(az)

• P_az = —180° • cos(el) • sin(az)

Using these relations, it should be noted that the points (0; 0), (λ/2; 0) and (0;λ/2) in the array are “virtual” (for calculation only) and may or may not coincide with actual element locations; for the specific example above, (0; 0) corresponds to the central element #1 , (λ/2; 0) corresponds to element #2 to and (0; λ/2) to element #4.

Thus, using the above equations, the reference phase shift values 682 may be calculated from the test steering direction, which may be defined by defining P_el and P_az.

Table 1 lists that phase values (e.g. reference phase shift values 682) calculated from the above equations for 3 beam steering examples (e.g. examples for the test steering direction); note that all calculations are modulo 360, and the phases are exemplary mapped to the range -180° to +180°.

Table 1

Fig. 8, Fig. 9 and Fig. 10 illustrate examples of the beam directivity corresponding to the exemplary steering directions of Table 1 , namely beam steering to azimuth = 0°, elevation = 15°, beam steering to to azimuth = 0°, elevation = 90°, and beam steering to azimuth = 15°, elevation = 40°, respectively, each shown in a 2D polar view 892, 992, 1092 and a 3D view 894, 994, 1094. The plots assume antenna elements with isotropic radiation pattern. The beam directivities are calculated for an operation of the phased array antenna using the reference phase shift values 682. Thus, the directivity patterns shown in Fig. 8, Fig. 9 and Fig. 10 may represent reference directivity patterns, which may serve as target directivity patterns or may be regarded as optimum directivity patterns. The calculations assume half-sphere isotopically directivity for the antenna elements with 50% efficiency (thus, 0 dBi effective directivity into the upper half sphere).

In the following, it is further demonstrated by means of the non-limiting example of the antenna element pattern 10 described with respect to Fig. 7, how a symmetric arrangement of the antenna elements of the at least one antenna element set may limit the number of candidate sets 562, e.g. even while keeping a number of phase shift values per candidate set and a phase resolution for the phase shift values of the candidate sets constant. Without considering symmetry, (i.e. an un-symmetric antenna element pattern, e.g. an arrangement not composed of N rings and M identical sectors), a large number of candidate sets will have to be evaluated. In the present example, the number of phase shift values per candidate set is assumed to be identical, however, similar considerations hold for different examples. Considering a rather small number P of phase shift values (e.g. P = 4) and a rather coarse phase resolution (e.g. 22.5°, providing R = 17 phase options in the range ] - 180: 180]), there may be = 2380 phase sets to be evaluated, e.g. as candidate sets. For a specific element arrangement composed of N rings and M identical sectors, the optimum phase assignment has certain regularities as described below with respect to Fig. 7.

• Element values come in pairs, with same absolute value but negated sign (that is, opposite pairs with respect to a phase value of 0°, which is assumed for a reference antenna signal), e.g. P1 and -P1 , P2 and -P2, P12 and -P12, P12* and -P12* in the inner ring and 2P1 and -2P1 , 2P2 and -2P2, P3 and -P3, P4 and -P4, P5 and -P5, P3* and -P3*, P4* and -P4*, P5* and -P5* in the outer ring

• Element values may not cross rings, that is, the phase shift values for the two concentric rings are independent from each other. Nevertheless, there may be instances of identical values in the inner and outer ring for a given beam steering target, however these values will not be identical for all possible variation of the beam steering target. E.g. P1 , P2, P12 and P12* (and their negatives) are only on the inner ring and 2P1 , 2P2, P3, P4, P5 are only on the outer ring. Using these properties allows reducing the phase options for each ring independently and also reduces the number of phase sets to only the ones containing “negated sign pairs". In the example of the N = 3 ring array with M = 8 identical sectors, and with P = 4 and R = 17, there are only P/2 = 2 independent phases per set, while the other P/2 phases should be the negated sign pair counter parts. Further, the range of the P/2 = 2 independent phases is limited to the range [0: 180], while the range [-180: -0] is reserved for the negated sign pair counter parts. Thus, in this example, there may only be phase sets to be evaluated. 15 of these combinations may be further excluded (see Table 3) as they are not truly composed of 4 different phase values when phase ambiguities are considered, and thus only 21 unique phase sets remain.

Further, as the element values do not cross rings, each ring may be optimized using an independent set of phases. As the optimum phase assignment in the rings scales with ring radius, such use of independent sets is generally beneficial and improves beam steering performance. Considering the 21 phase sets per ring, the total number of combinations for optimizing the inner and outer ring independently is 21² = 441 and results in a total of 8 phases (4 in the inner and 4 in the outer ring) being provided.

In comparison, optimizing for the same total number of phases in the general case, without taking advantage of the properties of the “N rings and M identical sectors” arrangement requires the evaluation of phase sets.

In the following, an exemplary embodiment of the method 400 is described using the example of the antenna element pattern 10 of Fig. 1 , with the elevation angle range of e.g. 15° to 90° and the azimuth angle range of e.g. -22.5° to +22.5° for the sector of interest. Implementations of the individual steps may be implemented in the method 400 of Fig. 4 individually or in combination.

For example, the plurality of probe directions within the sector of interest, as described with respect to step 685, may be defined by sub-dividing the area of interest into a regular grid of points spaced 1° in azimuth and elevation. This provides T=45-76=3420 test (probe) points (or probe directions). The grid may be regular in the azimuth/elevation domain, but not necessarily in any other projection, e.g. in a 3D Cartesian view. Defining the plurality of test directions may be referred to as a step 1. Table 2 shows an example for a definition of test steering directions, as it may be implemented in step 663 of Fig. 6, for an example of 45° rotational symmetry of the antenna element pattern, for example the antenna element pattern 10, as described with respect to Fig. 7. The shown example comprises number of 28 beam steering directions. Defining the test steering directions or beam steering targets may be referred to as a step 2.

Table 2

Due to the rotational symmetry, the test steering directions may be defined within a predetermined azimuthal sector, which in the present example may have a central angle of 45°, corresponding to the central angle of one circular sector of the antenna element pattern 10 of Fig. 7.

For example, the method may comprise a step 3 of calculating the directivity G_b(az, el) for each steering target beam B1 to B28 using the respective reference phase shift values 682, as may for example be implemented in step 681 .

Fig. 11 shows a plot of a directivity pattern 1192 for one steering target, e.g. B11 , according to an embodiment. The directivity pattern 1192 may have been calculated using reference phase shift values for the respective test steering direction. The triangular highlighted region shows an example for a region of interest 98 or sector of interest, defined by the (az, el) range.

In a step 4, the method may further comprise to calculate the aggregated directivity over B1 to B28, for example, by using the reference phase shift values 682. The aggregated directivity determined by using the reference phase shift values may provide a reference antenna quality, to which the antenna quality measure may be compared.

In the case of rotational symmetry, as in the present example, the azimuthal range of the region of interest 98 may correspond to the predetermined azimuthal sector within which the test steering directions are located. Thus, due to the rotational symmetry, information about the (aggregated) directivity for the entire azimuthal range (360°) may be concluded from the (aggregated) directivity for the predetermined azimuthal sector.

Fig. 12 shows a plot of an example of an aggregated directivity 1296, which may have been obtained from the directivity patterns for the reference phase shift values, for example the directivity pattern 1192.

Fig. 13 illustrates a selection pattern 1397, which indicates the regions of the aggregated directivity 1296 where each of the beams B1 to B28 “is best”, i.e. match the criteria.

The method may further comprise a step 5 of calculating the cost function (the antenna quality measure) from the aggregated directivity pattern 1296, that is to calculate the cost function for the reference phase shift values which may be regarded as the optimum phase assignment. For example, the cost function C1 , average (in dB) aggregated directivity over the area of interest, as explained with respect to Fig. 6, may be used. For the example of the aggregated directivity 1296 shown in Fig. 12, that is, for an optimum phase assignment with unconstrained values, the cost function may calculate as C1 = 13.78 dB.

Calculating the directivity using the reference phase shift values may be part of step 501. For example, if the step 551 of determining the at least one selected candidate set comprises a recursive redefinition 567 of the set of candidate sets, the directivities are calculated for the test steering directions using the reference phase shift values 682 may serve for defining a stop condition for the recursive redefinition of the set of candidate sets 562. For example, the recursive redefinition 567 may be stopped, if a difference between the cost function determined for the at least one selected candidate set and the cost function determined for the reference phase shift values is below a predetermined threshold. Additionally or alternatively, the aggregated directivity determined from the reference phase shift values may be used for selecting the respective test steering directions to be used for each of the plurality of probe directions for the determination of the aggregated directivity in step 673.

In other words, besides directivity G_b(az, el) for each steering target, a step of calculating the directivity for each steering target beam also provides the optimum phase assignment for each steering target beam B1 to B28.

In a step 6, a number of phase shift values for each candidate set and a phase resolution for the candidate sets is selected to constrain the possible phase shift values. Step 6 may be part of step 561. In the following illustrative example, a number of P = 4 phase shift values per candidate set and a phase resolution of R = 17 is used, that is the resolution is chosen to be 3607(17-1). Table 3 lists the unique phase sets, i.e. all unique combination of P = 4 phase values forming two negated sign pairs (or opposite pairs), with values in 22.5° increments.

Table 3

Table 3 may represent an example of how to obtain the set of candidate sets 562 and the consideration of symmetry properties of the antenna element pattern. As the antenna element pattern 10 is mirror symmetric, only candidate sets with opposite pairs are considered.

Looping over the 21 unique phase sets, each unconstraint phase value of the optimum phase assignment (e.g. the reference phase shift values 682) for each steering target beam B1 to B28 (e.g. the plurality of test steering directions) to the nearest value in the phase set, as it may be implemented in step 683 of Fig. 6.

Fig. 14 comprises Table 4, which shows an example, with the unconstraint values 682 of the optimum phase assignment for steering target beam B11 mapped to the phase values available in Phase Set 5, which is an example for one of the candidate sets 562. In the shown example, the same set of phase shift values is used for the inner ring 12 (the first antenna element set) and the outer ring 14 (the second antenna element set) of the antenna element pattern 10. Table 4 further indicates the association of each of the candidate sets to one of associated phase shift values 1485 of the phase set 5. As described with respect to step 551 of determining the at least one selected candidate set, some embodiments include to recursively adapted 567 the set of candidate sets 562. For example, adapting the set of candidate sets may be implemented by “successive approximation” to derive solution candidates. For example, the 21 candidate sets listed in Table 3 provide the seed solution (first set of candidate sets or start set) and the resolution of the individual phase values, that is the phase shift values of the candidate sets, is increased in multiple iterations. In each iteration, the cost function may be evaluated for each of the phase sets. All phase sets, the cost function of which does not meet or exceed a given criterion are dropped and only the remaining subset may be kept for the next iteration. Before going into this next iteration, the interval distance may be decreased, for example halved, and the candidate set may be expanded by adding additional phase sets which are within a +/- interval distance. For example: The first iteration considers the 21 “Phase Sets” listed in Table 3 (ignoring the ones labelled as “not used”). Now assume that only Phase Set #1 , i.e. {+22.5°,;+45.0°; -45.0°; -22.5°} and Phase Set #6 {+22.5°;+157.5°; -157.5°; -22.5°} meet the minimum cost criteria, e.g. are selected as the at least one selected candidate sets 552. Thus the second iteration considers the subset {+22.5°;+45.0°; -45.0°; -22.5°} and {+22.5°, ;+157.5°; -157.5°; -22.5°} and adds

{+22.5°-5.75°;+45.0°-5.75; -(45.0°-5.75°); -(22.5°-5.75°)}

{+22.5°-5.75°;+45.0°; -45°; -(22.5°-5.75°)}

{+22.5°-5.75°;+45.0°+5.75; -(45.0°+5.75°); -(22.5°-5.75°)}

{+22.5°;+45.0°-5.75; -(45.0°-5.75°); -22.5°}

{+22.5°;+45.0°+5.75; -(45.0°+5.75°); -22.5°}

{+22.5°+5.75°;+45.0°-5.75; -(45.0°-5.75°); -(22.5°+5.75°)}

{+22.5°+5.75°;+45.0°; -45.0°; -(22.5° +5.75°)}

{+22.5°+5.75°;+45.0°+5.75; -(45.0°+5.75°); -(22.5°+5.75°)} as expansion for the Phase Set #1 and

{+22.5°-5.75°;+157.5°-5.75; -(157.5°-5.75°); -(22.5° -5.75°)}

{+22.5°-5.75°;+157.5°; -(157.5°); -(22.5°-5.75°)}

{+22.5°-5.75°;+157.5°+5.75; -(157.5°+5.75°); -(22.5°-5.75°)} {+22.5°;+157.5°-5.75; -(157.5°-5.75°); -22.5°}

{+22.5°;+157.5°+5.75; -(157.5°+5.75°); -22.5°}

{+22.5°+5.75°;+157.5°-5.75; -(157.5°-5.75°); -(22.5°+5.75°)}

{+22.5° +5.75° ;+157.5° ; -157.5°; -(22.5° +5.75°)}

{+22.5°+5.75°;+157.5°+5.75; -(157.5°+5.75°); -(22.5° +5.15°)} as expansion for the Phase Set #6.

Note that the third and fourth phase value in each pair are dependent on the first and second value, thus, in this example, each new iteration produces only 8 new combinations per surviving phase set. In contrast to the approach to apply “successive approximation” to the general problem (see below), where each surviving set would be expanded by new combinations, the here described recursive adaption may make beneficial use of the antenna properties, such decreasing the number of new combinations.

Fig. 15 shows a plot of a directivity pattern 1592 according to an embodiment. The directivity pattern 1519 represents the directivity for steering target B11. Compared to the “optimum” unconstraint phase assignment used for Figure 11 , the beam has shifted a few degrees towards higher elevation and two prominent side-lobes have appeared.

Fig. 16 shows a plot of an aggregated directivity 1696 according to an embodiment. The aggregated directivity 1696 is derived from the directivity patterns for the steering directions B1 to B28 using the assigned phase shift values.

Fig. 17 illustrates a selection pattern 1797 according to an embodiment. The selection pattern 1797 indicates, which of the test steering directions is selected for the respective probe directions for the aggregated directivity 1696. In other words, the selection pattern 1797 indicates the regions where each of the beams B1 to B28 “may be best”. Compared to the optimum unconstraint phase assignment used for Fig. 12 and Fig. 13, aggregated directivity may have been degraded towards lower elevations, and the cost function drops by approx. 3 dB to C1 = 10.78 dB when using Phase Set 5.

The directivity pattern 1592, and the aggregated directivity 1696 may have been determined using identical phase sets for the inner ring 12 in the outer ring 14 of the antenna element pattern 10. According to embodiments, the set of phase values for the first antenna element set 12 and the set of phase values for the second antenna element set 14 or determined individually, that is they may differ from each other.

Alternatively, the individual sets of phase shift values for the first and the second antenna element sets 12, 14 may be determined, as described with respect to step 551 of Fig. 5. In the presently described example, looping over all 21 unique phase sets independently for the elements of the inner and outer ring identifies the phase set {45.0; 135.0; -135.0; -45.0} as best option for the inner ring and the phase set {45.0; 157.5; -157.5; -45.0} as best option for the outer ring.

Fig. 18 shows a plot of an aggregated directivity 1896 according to an embodiment. The aggregated directivity 1896 is obtained using individual sets of phase shift values for the respective antenna element sets. Compared to the optimum unconstraint phase assignment used for Fig. 12 in Fig. 13, the aggregated directivity 1896 may have degraded towards lower elevations, and the cost function is C1 = 11 .62 dB. Thus, determining individual sets of phase shift values for the respective antenna element sets may yield a higher antenna quality.

Fig. 19 illustrates a selection pattern 1997 for the aggregated directivity 1896 according to an embodiment. The selection pattern 1997 indicates, which of the test steering directions is selected for the respective directions of the aggregated directivity 1896.

Fig. 20 shows a plot of an aggregated directivity 2096 according to an embodiment. For obtaining the aggregated directivity 2096, in comparison to the aggregated directivity 1896, a higher phase resolution for the phase shift value was selected. The phase resolution for the aggregated directivity 2096 is 5.625°, corresponding to a number of possible phase shift values of R = 65. As this significantly increases the number of combinations, e.g. to 465 for P = 4 and R = 65, the phase refinement may be limited to the range around the previously found best option. For example, a recursive adaption of the candidate sets, as described with respect to step 567, may be performed. Such a refinement identifies the phase set {39.375; 123.750; -123.750; -39.375} as best option for the inner ring and the phase set {56.250; 168.750; -168.750; -56.250} as best option for the outer ring. Compared to the optimum unconstraint phase assignment used for Fig. 12 in Fig. 13, aggregated directivity is still degraded towards lower elevations, but the cost function has improved to C1=11 .90 dB, indicating the average performance of the complexity and cost optimized antenna may be just 1 .9 dB worse than an antenna with optimum and error-free phase assignments. Fig. 19 also shows, that a high phase resolution may improve the antenna quality. Fig. 21 illustrates a selection pattern 2197 for the aggregated directivity 2096 according to an embodiment. The selection pattern 2097 indicates, which of the test steering directions is selected for the respective directions of the aggregated directivity 2096.

Fig. 22 shows a plot of an aggregated directivity 2296 obtained according to another embodiment. The antenna element pattern to which the aggregated directivity 2296 refers comprises a central element, eight elements in the first (inner) ring and 16 elements in the second (outer) ring, resulting in 45° sectors for the rotational symmetry. The analysis is chosen to be limited to one sector of interest, which may for example be defined as -22.5° to +22.5° azimuth, and 15° to 90° elevation. For the example of Fig. 22, the number of beam steering target locations is 36, in contrast to the 28 beam steering target locations of 28 used for the examples of figures 15 to 21. The 36 beam steering target locations may include steering targets for low elevation, for example towards the horizon.

In this example the evaluation of the cost function of the antenna quality measure may be limited to a region of interest, for example an elevation range of 30° to 90°, for determining or optimizing the average directivity or aggregated directivity. As low elevation ranges may be rarely used, determining the result, e.g. the choice of number of phase shift values, for the higher ranges may improve an overall operation performance of the phased array antenna.

For example, initial beam steering target locations are obtained by selecting P_al from the interval [-60:15:60] and P_el from the interval [-180:30:0], that is selecting a value for P_al from -60° to 60° with a phase resolution of 15° (9 possible values) and selecting a value for P_el from -180° to 0° with a phase resolution of 30° (7 possible values). For each of the 63 P_al, P_el pairs, i.e. the plurality of test steering directions or beam steering targets, reference phase shift values for all antenna elements are derived, using the given geometrical arrangement of the antenna elements (see Fig. 7). The directivity pattern 2296 illustrated in Fig. 22 represents the directivity patterns aggregated over all these initial 63 beam steering target locations. As several of these initial beam steering targets are outside the region of interest 98, only those 36 beam steering targets that result in a beam steering target within the region of interest 98 may be kept and used when evaluating the quality measure.

According to examples, the antenna quality measure may be evaluated regarding different numbers of phase shift values of the sets of phase shift values 332. For example, 7 cases may be considered that differ in the number of phase values in the set of phase values for the first and second ring: • Case “2I + 2O”: 2 phase values for the first ring, 2 phase values for the second ring

• Case “3I + 2O”: 3 phase values for the first ring, 2 phase values for the second ring

• Case “2I + 3O”: 2 phase values for the first ring, 3 phase values for the second ring

• Case “3I + 3O”: 3 phase values for the first ring, 3 phase values for the second ring

• Case “4I + 3O”: 4 phase values for the first ring, 3 phase values for the second ring

• Case “3I + 4O”: 3 phase values for the first ring, 4 phase values for the second ring

• Case “4I + 4O”: 4 phase values for the first ring, 4 phase values for the second ring

Method 400 may be applied independently to each of these 7 case, starting with an initial phase resolution of 45° and considering only sets with the required number of elements (2, 3 or 4), containing negated pairs and considering phase ambiguities.

• For the “2I + 2O” case, both the first and second set of candidate sets for this initial phase resolution may be {-45; 45}; {-90; 90}; {-135; 135}, {-180; 180}

• For the “3I + 2O” case, the first set of candidate sets for this initial phase resolution may be {-45; 0; 45}, {-45; 90; 45}; {-45; 135; 45}; {-45; 180; 45}, {-90; 0; 90}; {-90; 45; 90}; {-90; 135; 90}; {-90; 180; 90}; ... while the second set of candidate sets may be again {-45; 45}; {-90; 90}; {-135; 135}, {-180; 180}

• First and second set of candidate sets for the other cases may be constructed following the same pattern.

Step 501 may also be applied independently for each of the 7 cases, selecting in 565 at least one of the candidate set on the basis of antenna quality measure, and optionally redefining, in step 567, the set of candidate sets by halving the phase resolution and constructing new candidate sets using the at least one selected candidate set plus one or more sets derived from the selected candidate set (e.g. by varying the candidate set phase shift values by +/- the new phase resolution). Note that while the method may start with identical first and second candidate sets, 565 may perform a different down selection for first and second candidate set and 567 may perform a different redefining of the first and second candidate set. This may lead to the set for the first and second ring converging to different values, and 555 producing different sets of phase shift values 332 In the following, results for the cost function for embodiments with different numbers of phase shift values of the sets of phase shift values are compared, for the example of a number of phase shift values between 2 and 4, chosen independently for the inner and outer ring. Results for this modified set of optimization constraints are summarized in Table 5. Considering the number of phase options and their respective values traded-off against the resulting average directivity, the “3I + 3O” variant with 3 phase option for the inner and 3 phase options for the outer ring represents a preferred embodiment. This variant requires a total of 5 different phase shifters, with one 180° phase shifter used in both the inner and outer ring, plus a +/-56° phase shifter pair in the inner ring and a +/-64° phase shifter pair in the outer ring. Despite the reduced set of phase options, the average directivity is only 0.79 dB less than the in the “Reference Case” (using unconstraint, infinitely precise phases). This limited loss indicates little extra potential for increasing the number of phase options (e.g. gaining only 0.3 dB extra when using 8 different phase shifter values in the “4I + 4O” variant)

Table 5

According to embodiments, the set of phase shift values 332 may not be optimized or maybe optimized or approximated using one of the following methods.

According to embodiments, the step 401 may be implemented alternatively. Alternative implementations of the step 401 of determining the set of phase shift values may include optimisation and search techniques like successive approximation using interval split, “simulated annealing” or execution of random experiments. Such methods may provide only an approximate or “best local” solution, however without having to consider all options and thus not having to reduce the number of option upfront by considering symmetry or regularity properties in the array and phase assignment.

For example, successive approximation methods may be used, which use variation of the “Newton-Raphson” method and considers a first (“seed”) solution and a first interval width. The seed solution and first interval may e.g. be set manually or obtained from a coarse extensive search (e.g. in 180° or 90° phase steps) through the design space. This first solution is refined in subsequent steps, by considering the seed value for each of the phase shifter, plus the 2 new values at +/- interval distance. The cost function is then calculated for all 3 phase values at each of the phase shifters. Once the value of the cost function is obtained for all these combinations, the phase values for each phase shifter corresponding to the best solution are identified. Only those values are kept as seed for the next iteration, and the interval is halved.

Further example using simulated annealing, may also start with a first (“seed”) solution and generates variation of this solution using a probabilistic approach. Depending the how aggressive the initial solution is varied in subsequent steps, the algorithm may converge towards a local optimum (similar to successive approximation) or a global optimum.

Further example using random experiments may generate a set of possible solution, by assigning a random phase value to each element, assessing the cost function for each solution and repeating as long as no “acceptable” solution (i.e. where the cost function exceeds a given threshold) is found. The random process assigning the phase to each element may be unconstraint (i.e. using a uniform distribution over the range [-180° to +180°]), constraint to a given sub-range per element or biased using a non-uniform distribution function.

Such a cost function is calculated over a number B of beam steering targets and over the area of the sector of interest. Assume G_b(az, el) is the directivity at a point az, el) within the sector of interest when steering the beam to the b-th target, then is the aggregated directivity over the area and is the aggregated side-lobe isolation, with G_b being the peak directivity of the first (highest directivity) side-lobe anywhere within the field of view.

Fig. 23 and Fig. 24 show plots of respective directivity patterns for antenna elements of a circular patches according to an embodiment. Fig. 23 shows a 2-D polar plots 2392 and a 3D plot 2394 for a steering direction of 0° azimuth and 15° elevation. Fig. 24 shows a 2-D polar plots 2492 and a 3D plot 2494 four steering direction of 15° azimuth and 40° elevation. The predominantly “upwards” (zenith) facing directivity of the circular patch causes the peak directivity point to shift towards higher elevations (zenith). For example, when steering to 15° elevation, the actual directivity peak is at approx. 37°; when steering to 40° elevation, the actual peak is at approx. 48° elevation. The antenna elements 311 may be implemented as circular patches independently from other features of the herein described embodiments.

According to embodiments, a bias to the target elevation may be applied, steering the beam to a lower elevation in order to have the peak directivity point positioned at the wanted elevation. However, this biasing may be limited to a minimum elevation target of 0°, and, depending on the directivity characteristics of the antenna elements, the resulting peak directivity point may not be steerable below a certain elevation limit. Note that the steering bias and the range limitations is only related to the directivity characteristics of the antenna elements and the planar nature of the array, and may not relate to the element phase assignments based on the method and equations described above. Thus, biasing the elevation may be included in all embodiments described above, independently from the implementation of the specific embodiment.

Fig. 25 illustrates an apparatus 2500 for designing a phased array antenna 300 according to an embodiment. The apparatus 2500 comprises a phase shift value determination module 2501. The module 2501 is configured for determining, for at least one antenna element set 312 which includes a plurality of antenna elements 311 of the phased array antenna 300, a set of phase shift values 332 to which switchable phase shifters 330 for the antenna elements 311 of the antenna element set 312 are switchable, so that, during operation of the phased array antenna 300, the phased array antenna is steerable towards directions within a predetermined direction range by selecting, for each of the antenna elements of the antenna element set 312, one of the phase shift values out of the determined set of phase shift values 332. The module 2501 comprises a candidate set a variation module 2502. Module 2502 is configured for determining 402, for a plurality of candidate sets 462 of phase shift values, each of the candidate sets comprising a number of phase shift values, respective antenna quality measures 474 describing a quality of an operation of the phased array antenna 300 using the respective candidate set of phase shift values as the set of phase shift values.

For example, module 2501 may be configured to perform the step 401 , and module 2502 may be configured to perform step 402. Fig. 26 illustrates a method 2600 for operating a phased array antenna 300. The method 2600 comprises a step 2601 of selecting, for each of antenna elements 311 of at least one antenna element set 312 of the phased array antenna 300, one phase shift value out of a set of phase shift values 332 available for the antenna elements 311 of the respective antenna element set 312, so that the phased array antenna is directed towards a selected direction. The set of phase shift values 332 differs from a set of equidistant values.

In the following, further details, features and advantages of the phased array antenna 300 and the method 400 are described, which may be combined with the phased array antenna 300 and/or the method 400 individually or in combination.

In order to realize a small size of the phased array antenna, it may be favourable to have a low number of antenna elements. However, for steering a phased array antenna with a low number of antenna elements towards a specific direction, it may be necessary, to achieve the best possible result, to adjust the phase shift value for the individual antenna elements very accurately, as demonstrated, for example, by Table 1 for the above described example of the antenna element pattern 10.

Despite being derived from only 2 phase values P_el and P_az, Table 1 indicates that a huge number of different phase values (to which the switchable phase shifters are switchable) may be required to target the 3 sample steering positions. An actual implementation of the phased array antenna would likely have to use continuously steerable phase shifter at each element (except #1), in order to precisely steer to each target location within the azimuth sector of interest.

Method 400 may provide for a possibility to determine the set of phase shift values so that the phased array antenna may achieve a high directivity towards directions within the predetermined range, while holding the number of phase shift values low. Accordingly, determining the set of phase shift values with a method 400 allows for designing a phased array antenna, for example the phased array antenna 300, being easy to build and to control and having low component cost in contrast to a phased array antenna with continuously steerable phase shifters. Accordingly, the phased array antenna 300 with a set of phase shift values 322 may meet the objective of a low complexity and low-cost antenna.

Although, the set of phase shift values does not necessarily correspond to the reference phase shift values, e.g. those of table 1. Variations in the element phase may result in reduced “beam steering performance” (which may, e.g., be represented by the antenna quality measure), i.e. - a movement of the beam in elevation and/or azimuth (if all signal paths still constructively combine in a single point); or

- a widening of the beam (if signal the paths only approximately constructively combine); or in the appearance of “side-lobes” (if one set of paths constructively combines in one point, and other sets of paths constructively combine in secondary points)

However, the inventors realized, that smaller variations in the phase values (resulting in only limited variation in beam location or shape) may be in general acceptable and often unavoidable, e.g. due to the finite number of phases supported by an actual phase shifter device or due to random phase errors introduced by physical effects. The method 400 may provide for a concept to determine the set of phase shift values vote that the variation in beam location or shape, compared to the usage of the reference phase shift values, is particularly low.

According to embodiments, the phased array antenna 300 provides a beam-steerable antenna, tailored for use by low-throughput M2M/loT type terminals, communicating with a satellite in GSO orbit or with one or more satellites in NGSO, with the primary objective of reducing form factor, complexity and cost of such an antenna. The antenna may be based on the well-known principles of the phased array, using a regular arrangement of the individual antenna elements.

In some embodiments, the beam-steerable (phased array) antenna 90 covers the full hemispherical range, i.e. 360° in azimuth and 0° to 90° (zenith) in elevation; this allows communication with the satellite independent of the relative location of M2M/loT terminal and satellite. However, as the distance between M2M/loT terminal on Earth and the satellite extends for low elevation angles and is impaired by atmosphere and ground reflections, communication between M2M/loT terminal and satellite at low elevation may be operationally problematic. Thus, in some embodiments, the operational elevation range for the antenna may be limited to e.g. 15° or 20° to 90° (zenith), which allows the use of a planar antenna arrangement, despite the directivity deficits at low elevation angles known for planar elements and arrangements.

Some embodiments provide a method to design a steerable antenna for communication between a terrestrial loT/M2M terminal and satellite infrastructure in GSO or NGSO orbit, based on the well-known principles of phased array antennas, and considering the resource and size constraints of the loT/M2M terminal. Some embodiments provide a corresponding antenna. The number of radiating elements in this phased array may be limited (e.g. less than 100 elements) and the radiating elements are preferably arranged in a regular and symmetrical pattern. The regularity and symmetry properties of this arrangement are exploited to minimize the number of fixed phase values required for steering the antenna, while optimizing directivity towards the satellite of interest (the “wanted beam”) and minimizing directivity into other directions (the “unwanted side-lobes”). This includes a method for deriving element phase relations from the arrangement, calculating the set of phase pattern needed at each element for steering, mapping this set of phase pattern to a bound set of element phases and assessing the directivity properties (“wanted beam” peak directivity and beam width, directivity variation over coverage, relative “unwanted side-lobe” directivity) of the phased array when only using the fixed phase values. Geometrically properties of the arrangement are used to significantly reduce the number of options that have to be considered in the optimisation process, allowing faster convergence.

Further, the inventors realized, that for some applications, for example for the above mentioned M2M or loT satellite communication, the amount of data transmitted by a single terminal may be very small and transmissions may occur infrequently while the amount of spectrum designated to the system may be comparable large (few to several MHz of bandwidth). The inventors concluded, that this allows operating the communication link at low spectral efficiency and/or assigning only a small fraction of the designated satellite link bandwidth and capacity to an individual terminal. For the exemplary use case of an M2M/loT terminal on earth communicating with a GSO satellite, data throughput may be low, and thus as system communicating at very low spectral efficiency may be acceptable. In exchange for increased demand in bandwidth, transmit power and terminal antenna gain can be traded in and reduced. This allows compromising on antenna gain, beam width and side lobe performance. The inventive idea allows for implementing a low complex phased array antenna, for example a phased array antenna having a comparably low number of antenna elements and/or a comparably low number of phase shift values available for the antenna elements.

According to embodiments, symmetry properties may be considered to offset or to consider the distance of (and thus delay and phase between) the geometrical positions of the antenna elements in the array.

Although some aspects have been described as features in the context of an apparatus it is clear that such a description may also be regarded as a description of corresponding features of a method. Although some aspects have been described as features in the context of a method, it is clear that such a description may also be regarded as a description of corresponding features concerning the functionality of an apparatus.

Some or all of the method steps may be executed by (or using) a hardware apparatus, like for example, a microprocessor, a programmable computer or an electronic circuit. In some embodiments, one or more of the most important method steps may be executed by such an apparatus.

Depending on certain implementation requirements, embodiments of the invention can be implemented in hardware or in software or at least partially in hardware or at least partially in software. The implementation can be performed using a digital storage medium, for example a floppy disk, a DVD, a Blu-Ray, a CD, a ROM, a PROM, an EPROM, an EEPROM or a FLASH memory, having electronically readable control signals stored thereon, which cooperate (or are capable of cooperating) with a programmable computer system such that the respective method is performed. Therefore, the digital storage medium may be computer readable.

Some embodiments according to the invention comprise a data carrier having electronically readable control signals, which are capable of cooperating with a programmable computer system, such that one of the methods described herein is performed.

Generally, embodiments of the present invention can be implemented as a computer program product with a program code, the program code being operative for performing one of the methods when the computer program product runs on a computer. The program code may for example be stored on a machine readable carrier.

Other embodiments comprise the computer program for performing one of the methods described herein, stored on a machine readable carrier.

In other words, an embodiment of the inventive method is, therefore, a computer program having a program code for performing one of the methods described herein, when the computer program runs on a computer.

Another embodiment of the inventive methods is, therefore, a data carrier (or a digital storage medium, or a computer-readable medium) comprising, recorded thereon, the computer program for performing one of the methods described herein. The data carrier, the digital storage medium or the recorded medium are typically tangible and/or non- transitory. A further embodiment of the inventive method is, therefore, a data stream or a sequence of signals representing the computer program for performing one of the methods described herein. The data stream or the sequence of signals may for example be configured to be transferred via a data communication connection, for example via the Internet.

A further embodiment comprises a processing means, for example a computer, or a programmable logic device, configured to or adapted to perform one of the methods described herein.

A further embodiment comprises a computer having installed thereon the computer program for performing one of the methods described herein.

A further embodiment according to the invention comprises an apparatus or a system configured to transfer (for example, electronically or optically) a computer program for performing one of the methods described herein to a receiver. The receiver may, for example, be a computer, a mobile device, a memory device or the like. The apparatus or system may, for example, comprise a file server for transferring the computer program to the receiver.

In some embodiments, a programmable logic device (for example a field programmable gate array) may be used to perform some or all of the functionalities of the methods described herein. In some embodiments, a field programmable gate array may cooperate with a microprocessor in order to perform one of the methods described herein. Generally, the methods are preferably performed by any hardware apparatus.

The apparatus described herein may be implemented using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer.

The methods described herein may be performed using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer.

In the foregoing Detailed Description, it can be seen that various features are grouped together in examples for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed examples require more features than are expressly recited in each claim. Rather, as the following claims reflect, subject matter may lie in less than all features of a single disclosed example. Thus the following claims are hereby incorporated into the Detailed Description, where each claim may stand on its own as a separate example. While each claim may stand on its own as a separate example, it is to be noted that, although a dependent claim may refer in the claims to a specific combination with one or more other claims, other examples may also include a combination of the dependent claim with the subject matter of each other dependent claim or a combination of each feature with other dependent or independent claims. Such combinations are proposed herein unless it is stated that a specific combination is not intended. Furthermore, it is intended to include also features of a claim to any other independent claim even if this claim is not directly made dependent to the independent claim.

The above described embodiments are merely illustrative for the principles of the present disclosure. It is understood that modifications and variations of the arrangements and the details described herein will be apparent to others skilled in the art. It is the intent, therefore, to be limited only by the scope of the pending patent claims and not by the specific details presented by way of description and explanation of the embodiments herein.

Claims

1 . Method (400) for designing a phased array antenna (300), comprising: determining (401 , 501), for at least one antenna element set (312) which includes a plurality of antenna elements (311 ) of the phased array antenna (300), a set of phase shift values (332) to which switchable phase shifters (330) for the antenna elements of the antenna element set (312) are switchable, so that, during operation of the phased array antenna, the phased array antenna is steerable towards directions within a predetermined direction range by selecting, for each of the antenna elements of the antenna element set (312), one of the phase shift values out of the determined set of phase shift values (332), wherein determining (401 , 501) the set of phase shift values (332) for a respective antenna element set (312) comprises determining (402, 563, 663), for a plurality of candidate sets (462, 562) of phase shift values, each of the candidate sets comprising a number of phase shift values, respective antenna quality measures (474, 674) describing a quality of an operation of the phased array antenna using the respective candidate set of phase shift values as the set of phase shift values (332).

2. The method of claim 1 , wherein the method comprises determining (402, 563) respective sets of phase shift values (332) for a plurality of antenna element sets (312) which include respective pluralities of antenna elements (311) of the phased array antenna (300).

3. The method of claim 1 or 2, wherein determining (401) the set of phase shift values (332) for the respective antenna element set (312) further comprises determining the set of phase shift values based on the candidate sets under consideration of the respective determined antenna quality measures.

4. The method of any of the claims 1 to 3, wherein for each antenna element (311) of the at least one antenna element set (312), the switchable phase shifter (330) for the respective antenna element is switchable to each of the phase shift values of the set of phase shift values (332) of the respective antenna element set.

5. The method of any of claims 1 to 4, wherein determining (501) the set of phase shift values for the respective antenna element set (312) comprises: 57 determining (551) at least one selected candidate set (552) of phase shift values, wherein determining the at least one selected candidate set comprises obtaining (561) a set of candidate sets (562) of phase shift values, wherein the set of candidate sets (562) is selected based on a symmetry property of an arrangement (10) of the plurality of antenna elements (11 , 311) of the phased array antenna, and wherein each candidate set of phase shift values comprises a number of phase shift values, determining (563), for each of the candidate sets, the antenna quality measure, and selecting (565), from the set of candidate sets (562), at least one of the candidate sets as the at least one selected candidate set (552) on the basis of the antenna quality measures determined for the candidate sets (562), using (555) one of the at least one selected candidate sets as the set of phase shift values.

6. The method of claim 5, wherein determining (501 ) the selected candidate set further comprises redefining (567) the set of candidate sets (562) based on the at least one selected candidate set (552), determining (563), for each of the candidate sets (562), the antenna quality measure, selecting (565), from the set of candidate sets (562), at least one of the candidate sets as the at least one selected candidate set (552) on the basis of the antenna quality measures determined for the candidate sets (562).

7. The method of any of the claims 5 or 6, wherein the antenna elements of the respective antenna element set are arranged in a pattern which is rotationally symmetric with respect to discrete rotation angles.

8. The method of any of the claims 5 to 7, wherein the antenna elements of the respective antenna element set are arranged in a pattern which is symmetric with respect to one or more mirror axes, and 58 wherein each of the candidate sets (462, 562) for the respective antenna element set comprises one or more pairs of opposite phase shift values.

9. The method of any of the claims 5 to 8, wherein the antenna elements of the phased array antenna are arranged in an antenna element pattern which is rotationally symmetric with respect to discrete rotation angles.

10. The method of any of claims 1 to 9, wherein determining (663) the antenna quality measure (674) for a respective candidate set comprises: for at least one test steering direction, determining (681), for the antenna elements of the at least one antenna element set, reference phase shift values (682) for directing the phased array antenna towards the respective test steering direction, associating (683) each of the antenna elements to one of the phase shift values of the respective candidate set under consideration of the reference phase shift values, determining (685) a directivity pattern (686) of the phased array antenna for an operation of the phased array antenna using, for each of the antenna elements, the respective associated phase shift value, determining (673) the antenna quality measure (674) based on the at least one directivity pattern (686) determined for the at least one test steering direction.

11. The method of claim 10, wherein the associating (683) of the antenna elements (311) to one of the phase shift values comprises associating each of the antenna elements to the phase shift value of the respective candidate set which is closest to the reference phase shift value determined for the respective antenna element.

12. The method of any of the claims 10 or 11 , wherein determining (663) the antenna quality measure for the respective candidate set comprises: determining, for each of a plurality of test steering directions, a respective directivity pattern, and selecting, for a plurality of probe directions within the predetermined direction range, respective selected test steering directions based on at least one of a 59 directivity and a side-lobe isolation of the directivity patterns determined for the test steering directions. The method of any of the claims 10 to 12, wherein the antenna elements of the phased array antenna are arranged in an antenna element pattern which is rotationally symmetric with respect to a discrete rotation symmetry angle, and wherein determining (663) the antenna quality measure for the respective candidate set comprises determining, for each of a plurality of test steering directions, a respective directivity pattern, wherein respective azimuthal coordinates of the plurality of test steering directions are within a predetermined azimuthal sector, the central angle of the predetermined azimuthal sector being equal to the rotation symmetry angle, and determining (673) the antenna quality measure (674) based on an evaluation of the directivity patterns (686) determined for the plurality of test steering directions within the predetermined azimuthal sector. The method of any of claims 10 to 13, wherein the antenna elements of the respective antenna element set (312) are arranged in a pattern which is symmetric with respect to a mirror axis, wherein the candidate sets comprise one or more opposite pairs of phase shift values, and wherein associating (683) the antenna elements to the phase shift values comprises assigning opposite phase shift values to antenna elements which are opposite with respect to the mirror axis. Apparatus (2500) for designing a phased array antenna (300), configured for determining (401), for at least one antenna element set (312) which includes a plurality of antenna elements (311) of the phased array antenna (300), a set of phase shift values (332) to which switchable phase shifters (330) for the antenna elements (311 ) of the antenna element set (312) are switchable, so that, during operation of the phased array antenna (300), the phased array antenna is steerable towards directions within a predetermined direction range by selecting, for each of the 60 antenna elements of the antenna element set (312), one of the phase shift values out of the determined set of phase shift values (332), wherein determining (401) the set of phase shift values for a respective antenna element set comprises determining (402), for a plurality of candidate sets (462) of phase shift values, each of the candidate sets comprising a number of phase shift values, respective antenna quality measures (474) describing a quality of an operation of the phased array antenna (300) using the respective candidate set of phase shift values as the set of phase shift values.

16. Phased array antenna (90, 300), comprising a plurality of antenna elements (311), wherein at least one antenna element set (12, 14, 312) includes a set of antenna elements of the plurality of antenna elements (11 , 311), wherein the antenna elements of the antenna element set (12, 14, 312) are connected to switchable phase shifters (30, 330) which are switchable to a set of phase shift values (332), wherein the set of phase shift values (332) is determined by the method of any of the claims 1 to 14.

17. Phased array antenna (90, 300), comprising a plurality of antenna elements, wherein at least one antenna element set (12, 14, 312) includes a set of antenna elements of the plurality of antenna elements (11 , 311), wherein the antenna elements of the antenna element set (12, 14, 312) are connected to switchable phase shifters (30, 330) which are switchable to a set of phase shift values (332), wherein the set of phase shift values (332) differs from a set of equidistant values.

18. Phased array antenna (90, 300), according to claim 17, wherein the set of phase shift values differs from a set of equidistant integer multiples of 360°/2ⁿ.

19. Phased array antenna (90, 300) according to any of the claims 17 or 18, wherein a first set of phase shift values, to which the antenna elements of a first antenna element set are switchable, differs from a second set of phase shift values, to which the antenna elements of a second antenna element set are switchable.

20. Phased array antenna (90, 300) according to any of the claims 17 to 19, wherein the plurality of antenna elements is arranged in an antenna element pattern which is symmetric with respect to a mirror axis, and wherein the set of phase shift values comprises one or more pairs of opposite phase shift values. 21 . Phased array antenna (90, 300) according to claim 20, wherein a shape of patches of the antenna elements is rotationally symmetric to an order equal or higher than the order of the rotational symmetry of the antenna element pattern.

22. Method (2600) for operating a phased array antenna (300), comprising selecting (2601 ), for each of antenna elements (311) of at least one antenna element set (312) of the phased array antenna, one phase shift value out of a set of phase shift values (332) available for the antenna elements (312) of the respective antenna elements set, so that the phased array antenna is directed towards a selected direction, wherein the set of phase shift values (332) differs from a set of equidistant values.

23. Computer program for implementing the method of any of claims 1 to 14 or 22 when being executed on a computer or signal processor.