Phased array beam shaping for beam squint loss mitigation in an RF beamforming architecture

Abstract

A method for controlling beam squint in a radio frequency beamforming architecture comprises: forming a beam based on a desired steering angle and a desired bandwidth, the beam having a cross-sectiona

Description

FIELD OF THE INVENTION The invention relates to phased array antenna systems and methods of operating phased array antenna systems. In particular, but not exclusively, the invention relates to phased array antenna systems and methods of operating phased array antenna systems with reduced beam squint loss. BACKGROUND According to basic array theory, a plane wave arriving from a direction not equal to boresight reaches some elements within a phased array before reaching other elements in the phased array. In order to account for this difference such that the output of all of the elements in the phased array add up / combine in phase, the relative time delay in the waveform received at all of the elements in the phased array can be accounted for. This can be done by adding time delays to the signals for different elements in the phased array, where the element which received the plane wave first is provided with the longest time delay. Beam squint is a known phenomenon that arises in phased array antennas when phase delays are used instead of true time delays. In an antenna array that uses phase delay to enable the output of all of the elements in the phased array to add up / combine, the required time delay is implemented at each element using a phase delay component, whereby the required phase delay and time delays are related such that do = 2ir*f*dt (where do is the phase delay, f is the frequency of electromagnetic radiation and dt is the time delay). The time delay associated with a given phase delay setting is dependent on the frequency: dt = 1 / (27t*f)*dO. Since the angular direction of the phased array’s main beam is defined by the relative time delay between elements, it then follows that, as the instantaneous frequency changes for a given relative phase delay (where the relative phase delay is calculated for a given ‘synthesis frequency’), the time delays will change and the direction of the main beam will also change. In a pure time delay based system, this frequency dependence does not exist. The main beam generated by the phased array remains in the same angular direction as the frequency varies - there is no beam squint. Beam squint then is fundamental to an array beamforming system which relies on relative phase differences, and this applies to any stage of a beamformer (the combining or splitting can be done in stages). Given that there is a need to align the main beam direction to a target (whether this be for communications, Radar, or anything else), the degradation caused by beam squint can be quantified by the amount of antenna gain loss introduced by the main beam misalignment. Figure 1 shows a computer simulated example of beam squint loss in a phased array antenna array with an angle to the target of 70°. At Figure 1, there is a graph 100 showing Directivity, measured in dBi, on the y-axis 104, versus Azimuth Angle, measured in degrees, on the x-axis 102. There is shown a first plot 106 at a synthesis frequency of 11.7 GHz for a target steering angle of 70°. The synthesis frequency may be the central frequency in a range of frequencies over which communication is performed, such that the central frequency is the frequency halfway between a lower frequency and an upper frequency, where the difference between the lower and upper frequencies defines the communication bandwidth for a given system. The effect of the beam squint loss is shown when comparing the first plot 106 at 11.7 GHz with a second plot 108 at a different frequency of 11.85 GHz, where conditions for simulation are otherwise the same. The second plot 108 may represent the directivity at one frequency within the communication bandwidth for the phased array antenna array, which, in an example, is a frequency within the bandwidth of the simulated system. For the second plot 108, the peak Directivity as a function of Azimuth Angle is offset from the peak Directivity as a function of Azimuth Angle compared with the first plot 106. In this case, the change in frequency from 11.7 GHz to 11.85 GHz results in a shift along the x-axis 102 with a Beam Squint Angle (BSA) of -1.8°. The overall effect is that for the desired steering angle of 70° (as determined for the phased array antenna at a synthesis frequency of 11.7 GHz), the change in frequency causes a relative drop in Directivity for the same Azimuth Angle. In the case shown at Figure 1, at the desired steering angle of 70° there is a Beam Squint Loss (BSL) of 1.29 dB between the two frequencies. Therefore, it can be seen how directing a phased array antenna array to a target source can result in a variation in gain for variations in communication frequencies with the target source. There are many advantages to a phased array antenna array that implements phase delay to provide the required time delay. Therefore, it would be beneficial to address beam squint loss in order to improve overall system performance in a phased array antenna array. SUMMARY OF INVENTION In order to mitigate for at least some of the above-described problems, there is provided: a method for controlling beam squint in a radio frequency beamforming architecture, the method comprising: forming a beam based on a desired steering angle and a desired bandwidth, wherein the beam has a cross-sectional area in a plane perpendicular to the radial direction of the desired steering angle comprising a first dimension perpendicular to the radial direction and a second dimension perpendicular to the radial direction and the first dimension; and altering the formed beam in response to a change in the desired steering angle such that the first dimension is greater than the second dimension and has a magnitude based on the change in the desired steering angle, thereby dynamically controlling beam squint. Advantageously, beam squint mitigation ensures overall array peak directivity / gain is reduced by the minimum amount possible whilst also reducing the beam squint loss. The antenna gain is a scaling of directivity, so the method of the present invention is intended to optimize both parameters. Beneficially, the formed beam is altered in response to a change in the desired steering angle thereby dynamically to provide improved system performance. Altering the formed beam may further comprise determining a change in the desired bandwidth. Beneficially, by altering the formed beam based on a change in the desired bandwidth means that the overall performance is optimized across the range of frequencies of communication. Altering the beam may comprise changing the first dimension in a plane perpendicular to the radial direction and parallel to the component of the radial direction in a plane defined by a plurality of elements of the radio frequency beamforming architecture. The ratio of the first dimension to the second dimension may be based on a minimization of gain loss across the desired bandwidth for the change in the desired steering angle. Advantageously, changing the first dimension in the plane perpendicular to the radial direction and parallel to the component of the radial direction in the plane defined by the plurality of elements of the radio frequency beamforming architecture provides a way to account for variations in communication frequencies to ensure optimal gain across the range of frequencies. Forming the beam may comprise selectively controlling the amplitude and / or phase of signals applied to each antenna of a plurality of antenna elements of a phased array antenna of the radio frequency beamforming architecture. Advantageously, the plurality of elements of a phased array antenna can be independently manipulated in order to provide an optimal beam dependent on the steering direction and bandwidth. Altering the formed beam may comprise altering the amplitude applied to one or more antenna elements of the plurality of antenna elements. Beneficially, as a communication target changes position relative to the phased array antenna, the formed beam changes, dynamically to provide optimal gain as a function of steering angle and / or bandwidth. The amplitude may be determined based on a comparison of the gain across the desired bandwidth for the application of a first distribution of amplitudes for the plurality of antenna elements with the gain across the desired bandwidth for the application of a second distribution of amplitudes for the plurality of antenna elements, thereby to reduce the rate of change in gain as a function of frequency across the desired bandwidth. Advantageously, optimal conditions for a particular phased array antenna are determined based on a comparison of practical implementations. Determining the desired steering angle may comprise determining a location of a target and wherein determining a change in the desired steering angle is based on at least one of monitoring changes in the location of the target and accessing data relating to the target stored in a database. Beneficially, the method is adapted for changes in location of the target such that temporal losses due changes in steering angle and / or bandwidth are reduced. The magnitude may be based on correlating at least one of the desired steering angle and the desired bandwidth with data stored in a database. Advantageously, the use of stored data means that optimal beams can be applied without performing calculations dynamically and centrally stored data can be applied to multiple phased array antennae. The cross-sectional area may be determined at a fraction of the maximum gain of the beam in the radial direction for a central frequency of the desired bandwidth. Beneficially, the fraction of the maximum gain of the beam in the radial direction for a central frequency of the desired bandwidth provides a comparable reference point for determining changes in the formed beam for different desired steering angles and / or bandwidths. There is also provided a phased array antenna system comprising: a plurality of independently controllable antenna elements, wherein the phased array antenna system is configured to apply phase delay and / or amplitude factors to one or more of the plurality of antenna elements in order to form a beam, wherein the phased array antenna system is further configured to perform the method described herein. Further aspects of the invention will be apparent from the description and the appended claims. BRIEF DESCRIPTION OF THE FIGURES The invention is further and more particularly described, by way of example only, and with reference to the accompanying drawings, in which: Figure 1 shows an example of the effects of beam squint loss; Figure 2 shows a phased array antenna system; Figure 3 shows a method of operating a phased array antenna system; Figures 4A and 4B show uniform element amplitude weighting and a corresponding formed beam, respectively; Figures 5A and 5B show a non-uniform element amplitude weighting and a corresponding formed beam, respectively; Figure 6 shows spatial plots of gain for beams with different steering angles; and Figure 7 shows spatial plots of gain for beams with different steering angles with a beam squint mitigation technique applied. DETAILED DESCRIPTION OF FIGURES As described above, the beam squint angle is a fundamental effect in a phased array antenna and cannot be avoided without resorting to a true-time delay beamformer. However, given that it is not always desirable to use a true-time delay beamformer, it would be beneficial to mitigate for the losses in a phased array antenna. A beam squint loss mitigation technique is described herein, which can be implemented at a phased array antenna such that the beamwidth of the main beam that is formed is extended, but in a way that introduces minimal array gain degradation. Figure 2 shows a phased array antenna system 200. There is shown a phased array antenna 202 comprising a plurality of antenna elements 204. The phased array antenna 202 is a flat panel array that is shown to extend in an x-y plane defined by the x-axis 208 and the y-axis 210, the x-axis 208 and the y-axis 210 being perpendicular to one another and mutually perpendicular to the z-axis 212. Whilst a defined number of antenna elements 204 are shown as part of the phased array antenna 202, in further examples any appropriate number of antenna elements in any particular pattern are provided. The ellipses 206 illustrate how, in further examples, the phased array antenna 202 may be extended in either, or both, of the x and y directions. In further examples, the phased array antenna 202 has fewer antenna elements 204 than shown in Figure 2. Whilst the phased array antenna 202 is a flat panel array, in further examples the phased array antenna 202 is provided with any suitable surface morphology and arrangement of antenna elements 204 in order to implement the functionality described herein. The phased array antenna 202 comprises circuitry enabling independent control of the antenna elements 204. The phased array antenna 202 is in communication with a computing device 216 that comprises a memory 218, a processor 220 and an interface 222. The phased array antenna 202 is in communication with the computing device 216 via communication path 214 between a communication interface of the phased array antenna 202 and a communication interface of the computing device 216. The interface 222 is a user interface that provides visual, audio and / or any other data type of data to a user and / or allows for one or more user inputs. In further examples, the interface 222 provides an input and / or output to one or more computing systems such that information is transferred to and / or received from one or more communication sources via the phased array antenna 202, such as one or more satellites. The computing device 216 is in communication with a network 226, via a further communication path 224. The network 226 comprises one or more further computing and / or data storage devices, enabling data to be transmitted and / or received by the antenna elements 204 of the phased array antenna 202 and processed by the one or more further computing and / or data storage devices of the network 226. The communication paths 214, 224 are wired and / or wireless communication paths. In further examples, the communication paths 214, 224 comprise one or more intermediate devices and the communication paths via the one or more intermediate devices are formed to provide any appropriate combination of wired and / or wireless communication protocols. Whilst the computing device 216 is shown as a single component that is distinct from the phased array antenna 202, in further examples the functionality of the computing device 216 is implemented in any appropriate combination of separated and / or integrated components. The phased array antenna 202 is used to form a beam for operation with one or more targets, such as one or more satellites, one or more Radars and / or other communication targets. A beam is formed by selectively controlling the amplitude and / or phase of signals applied to each antenna element of the plurality of antenna elements 204. The signals applied to each antenna element are controlled by the computing device 216. In further example, the signals are applied and / or controlled by any appropriate computing device and / or controller in order to implement the functionality described herein. Control of the plurality of antenna elements may be performed by the implementation of any appropriate combination of local and remote commands. Whilst the phased array antenna system 200 shows one phased array antenna 202, in further examples the phased array antenna system 200 comprises any number of phased array antennae which can be operated separately, or in combination. Figure 3 shows a process flow S300 describing a method for operating a phased array antenna system, such as the phased array antenna system 200 described with reference to Figure 2. In further examples, the process flow S300 is implemented in any appropriate system to provide the functionality described herein. The process S300 starts at step S302, where the process S300 is initiated. The process S300 is initiated in response to a command. The command is initiated by a user through a user interface, such as the interface 222 of the phased array antenna 202 of Figure 2, or by further input means forming part of the computing device 216 and / or part of the network 226. In further examples, the command is a response to reaching a step in a process, or in response to any appropriate signal, such as a signal indicating a beam is to be formed based on a particular steering angle and / or frequency range of communication and / or any other appropriate parameter. Once the process S300 has been initiated at step S302, the process S300 moves to step S304 where a beam to form is determined based on a desired steering angle and / or desired bandwidth. The desired steering angle and / or desired bandwidth are any steering angle and / or range of frequencies of electromagnetic radiation to enable communication (including transmission and / or reception) between the phased array antenna 202 and one or more further communication sources (not shown in Figure 2), such as communication satellites. The desired steering angle is an angle formed between a target, such as a satellite, and the planar face of a flat panel phased array antenna, such as the x-y plane described with respect to Figure 2. The steering angle can be defined in any appropriate co-ordinate system, such as a polar co-ordinate system, where the steering angle is in a radial direction, r, which can be defined in terms of angular components: 0, the polar angle and ¢, the azimuthal angle. The desired bandwidth is a range of frequencies around a central frequency, for which communication is enabled. The desired bandwidth may be dependent on the type of communication and the type of equipment being used. The desired steering angle and / or desired bandwidth are based on facilitating communication between the phased array antenna 202 and a communication source. Therefore, the desired steering angle and / or desired bandwidth may be determined based on identifying a location of the communication source and / or operating frequency of communication with the communication source. The parameters for controlling the plurality of antenna elements 204 of the phased array antenna 202 in order to form a beam are determined based on identifying input parameters and referencing a look up table, such as a look up table stored in the memory 218 of the computing device 216. In an example, the parameters for forming the beam may be determined based on a default set of input parameters stored in the memory 218. In further examples, any additional and / or alternative steps to determine a beam are used. In an example, the input parameters for different steering angles and bandwidths are predetermined by computer simulation. Input parameters are determined based on the correlation of the desired steering angle and the desired bandwidth with data stored in a database, such as the memory 218 of the computing device. In further examples, the input parameters are additionally or alternatively predetermined based on experimental results. In an example, the input parameters are determined for the phased array antenna 202 based on the number and distribution of antenna elements 204. In further examples, additionally or alternatively, input parameters are determined based on the application of data derived for one or more phased array antennae with a different number and / or distribution of antenna elements. Once the input parameters for forming the beam have been determined, the process moves to step S306 where the beam is formed. The beam is formed through the application of signals to the plurality of antenna elements 204 in the phased array antenna 202 such that the amplitude and / or phase of the signals applied to the plurality of antenna elements 204 results in constructive interference of radiation received and / or transmitted by the phased array antenna 202 in a direction based on the steering angle. As described above, in a phased array antenna, the application of signals to the antenna elements such that a beam is directed to a target with a desired steering angle is conventionally determined for a central frequency of a communication bandwidth, however, beam squint, as a frequency-dependent phenomenon, results in misalignment with respect to the desired steering angle for all other frequencies. The beam that is determined and formed at steps S304 and S306 of process S300 is formed in accordance with a beam squint loss mitigation technique described herein. The main beam formed in this manner can be defined in respect of a cross-sectional area in a plane perpendicular to the radial direction of the desired steering angle, where the cross-sectional area has a shape comprising a first dimension and a second dimension, where the first and second dimensions are perpendicular to the radial direction and perpendicular to one another. In an example, relative changes (for example, changes as a function of the desired steering angle and / or desired bandwidth) in the cross-sectional area of the main beam are determined at a fraction of the maximum power of the main beam in the radial direction, for example at half the maximum power of the main beam in the radial direction. Compared with conventional beamforming techniques, the beamwidth of the main beam is extended in a way that introduces minimal array peak gain degradation. Since beam squint appears in a direction parallel to the phase gradient across the array face (radial direction of the desired steering angle), the beamwidth is widened in this plane only. This ensures that the overall array directivity / gain is reduced by the minimum amount possible while still reducing the beam squint loss. The amount that the beam is widened is a function of the desired steering angle, as the beam squint angle increases with the magnitude of the steering angle from boresight. Differences between the conventional application of signals in a phased array antenna and the application of the beam squint mitigation technique are shown at Figures 4A to 5B. Figures 4A and 4B show uniform element amplitude weighting and a corresponding formed main beam, respectively. Figure 4A shows a view 400B of a phased array antenna 402 comprising a plurality of antenna elements 404 and a plot of element amplitude weighting 406. The phased array antenna 402 is an exemplary implementation of the phased array antenna 202 of Figure 2. The phased array antenna 402 is a flat panel array that is shown to extend in an x-y plane defined by the x-axis 208 and the y-axis 210, the x-axis 208 and the y-axis 210 being perpendicular to one another and mutually perpendicular to the z-axis 212. Plotted along the z-axis 212 is a representation of element amplitude weighting 406 for the plurality of antenna elements 404. The element amplitude weighting 406 is uniformly applied in signals at each antenna element of the plurality of antenna elements 404. Such an element amplitude weighting results in a conventional beam formed as described with reference to Figure 4B. Figure 4B shows a view 400B of the phased array antenna 402 of Figure 4A and a corresponding beam formed based on the element amplitude weighting 406 of Figure 4A. There is shown a beam 412 having a cross-sectional area 414 with a first dimension 416 and a second dimension 418. The beam 412 is directed in a radial direction 406, r, which can be defined in terms of angular components: 0, the polar angle 410 and ¢, the azimuthal angle 408. The beam 412 has a cross-sectional area in a plane perpendicular to the radial direction 406 of the steering angle, where the first dimension 416 is perpendicular to the radial direction 406 and where the second dimension 418 is perpendicular to the radial direction 406 and to the first dimension 416. The first dimension 416 is in a plane with a constant azimuthal component value equal to the azimuthal component of the steering angle. The beam 412 is representative of a beam formed for a central frequency of a desired bandwidth. With the application of signals such that there is a uniform amplitude weighting distribution at the antenna elements of the phased array antenna 402 as seen in Figure 4A, the first dimension 416 and the second dimension 418 are dependent on the array aperture dimensions and the antenna element pattern / distribution. Uniform amplitude weighting results in a nominal, or unmodified condition. As an approximation, the cross-sectional area 414 in the unmodified condition is circular such that the first dimension 416 and the second dimension 418 have similar magnitudes. In the conventional system described with respect to Figures 4A and 4B, there are significant beam squint losses, as described further with reference to Figure 6, below. In contrast to Figures 4A and 4B, Figures 5A and 5B show the application of signals at the antenna elements of a phased array such that there is a non-uniform element amplitude weighting and a corresponding formed beam, respectively, for the same phased array antenna 402 described with reference to Figures 4A and 4B. Figure 5A shows a view 500B of a phased array antenna 502 comprising a plurality of antenna elements 404 and a plot of element amplitude weighting 505. The phased array antenna 402 is an exemplary implementation of the phased array antenna 202 of Figure 2 and described with respect to Figures 4A and 4B. The phased array antenna 402 is a flat panel array that is shown to extend in an x-y plane defined by the x-axis 208 and the y-axis 210, the x-axis 208 and the y-axis 210 being perpendicular to one another and mutually perpendicular to the z-axis 212. Plotted along the z-axis 212 is a representation of element amplitude weighting 505 for the plurality of antenna elements 404. The element amplitude weighting 505 is non-uniformly applied in signals at each antenna element of the plurality of antenna elements 404 to provide a weighting distribution that is different from the weighting distribution described with respect to Figure 4A. Such an element amplitude weighting results in beam formed as described with reference to Figure 5B. The variation in amplitude weighting distribution across the phased array antenna 402 is such that it varies in the direction of component of the radial direction in the x-y plane defined by the x-axis 208 and the y-axis 210. Whilst a particular variation in amplitude weighting distribution applied to the antenna elements of the phased array antenna 402 is shown, in further examples the distribution is of any particular variation shape to provide the functionality described herein. The variation in the distribution of amplitude weighting affects the magnitude of the first dimension 416 of a beam formed by the application of signals to the plurality of elements 404 of the phased array antenna 402, as described with respect to Figure 4B. Figure 5B shows a view 500B of the phased array antenna 402 of Figure 5A and a corresponding beam formed based on the element amplitude weighting 505 of Figure 5A. There is shown a beam 512 having a cross-sectional area 514 with a first dimension 516 and a second dimension 518. The beam 512 is directed in a radial direction 506, r, which can be defined in terms of angular components: 0, the polar angle 510 and ¢, the azimuthal angle 508. The beam 512 has a cross-sectional area in a plane perpendicular to the radial direction 506 of the steering angle, where the first dimension 516 is perpendicular to the radial direction 506 and where the second dimension 518 is perpendicular to the radial direction 506 and to the first dimension 516. The first dimension 516 is in a plane with a constant azimuthal component value equal to the azimuthal component of the steering angle. The beam 512 is representative of a beam formed for a desired steering angle and a central frequency of a desired bandwidth in accordance with the process S300 described with reference to Figure 3. In the application of a uniform amplitude weighting distribution at the antenna elements of the phased array antenna 402 as seen in Figure 4A, the first dimension 416 and the second dimension 418 are dependent on the array aperture dimensions and the antenna element pattern / distribution. Uniform amplitude weighting results in a nominal, or unmodified condition. In contrast, as shown at Figures 5A and 5B, the application of a different weighting is used to alter the first dimension 516 of Figure 5B compared with the first dimension 416 of Figure 4B. In particular, the first dimension 516 of the beam 512 is greater than the second dimension 518 of the beam at all steering angles away from boresight. The magnitude of the first dimension 516 depends on the desired steering angle and the desired bandwidth. The magnitude of the first dimension 516 is based on the range of frequencies, i.e., the desired bandwidth, used for communication. The magnitude of the first dimension 516 also depends on the desired steering angle such that the first dimension 516 is altered in a plane perpendicular to the radial direction and parallel to the component of the radial direction in a plane defined by the plurality of elements of the radio frequency beamforming architecture, in cases where the phased array antenna is a flat phased array antenna. Accordingly, a comparison of the first dimension 516 of the beam 512 at an equivalent fraction of the maximum power for a given frequency is different compared to the first dimension 416 of the unmodified beam 412 at the equivalent fraction of the maximum power for the given frequency. By varying the magnitude of the first dimension 516 as a function of the desired steering angle and desired bandwidth, the rate of change of gain as a function of frequency across the desired bandwidth can be reduced as a function of steering angle compared with a phased array antenna that does not implement the technique described herein. Accordingly whilst there is some loss in the peak gain associated with a particular steering angle compared with conventional techniques, there is a relatively less severe change in gain loss as a function of frequency deviating from the central frequency of the desired bandwidth for which the beam 512 is formed. The magnitude of the first dimension 516 compared to the second dimension 514 may be determined by referencing a look up table of data based on previously collected experimental and / or simulated data. In an example, the ratio of the first dimension 516 to the second dimension 514 is based on a minimization of gain loss across the desired bandwidth for the change in the desired steering angle. In order to show an example of how gain loss might be minimized, Figures 6 and 7 show plots of gain with and without the beam squint loss mitigation technique applied. Figure 6 shows spatial plots of gain for beams, formed by a phased array antenna, with different steering angles without the beam squint mitigation technique applied and Figure 7 shows spatial plots of gain for beams with different steering angles with a beam squint mitigation technique applied. In an example, Figure 6 relates to the uniform application of signals at antenna elements 404 across a phased array antenna 402, as described with reference to Figures 4A and 4B. The spatial plot 600A of Figure 6 shows a plane defined by a first axis 602, u, and a second axis 604, v. The first axis 602 and second axis 604 represent directions in space and may correspond to a plane parallel to and coinciding with a plane defining a flat panel phased array antenna. The spatial plot 600A shows representations of two beams 610, 612 with two different radial direction components, r1, r2 in the u-v plane, along a radial steering r, shown by the arrow 606. The first beam representation 610 is for a beam with a component, r1, in the u-v plane along a radial steering direction 606. The second beam representation 612 is for a beam with a different component, r2, in the u-v plane along a radial steering direction 606. Further detail is illustrated in a plot 600B of Gain, in dB, along an axis 608 versus the radial steering direction 606. The plot 600B shows a cross-sectional representation of the first beam representation 610 and the second beam representation 612. The first beam representation 610 has a plot 616 representing gain for a main beam at a synthesis frequency (where the peak of the plot 616 corresponds to the synthesis frequency, which may be the central frequency of a desired bandwidth) and a plot 618 representing gain for the main beam at an instantaneous frequency (where the peak of the plot 618 corresponds to the instantaneous frequency). The change in frequency results in a beam squint angle 617, BSA1, and a relative drop in gain at the synthesis frequency, illustrated by the beam squint loss 619, BSL1a. The second beam representation 612 has a plot 620 representing gain for a main beam at the synthesis frequency (where the peak of the plot 620 corresponds to the synthesis frequency, where the synthesis frequency is the same as for the plot 616 with the component r1 in the u-v plane in the radial direction) and a plot 622 representing gain for the main beam at the instantaneous frequency (where the peak of the plot 622 corresponds to the instantaneous frequency, where the synthesis frequency is the same as for the plot 618 with the component r2 in the u-v plane in the radial direction). The change in frequency results in a beam squint angle 621, BSA2, and a relative drop in gain at the synthesis frequency, illustrated by the beam squint loss 623, BSL2a. In contrast to Figure 6, Figure 7 illustrates the application of the beam squint mitigation technique described herein, for example as described in reference to process S300 of Figure 3. In an example, Figure 7 relates to the non-uniform application of signals at antenna elements 504 across a phased array antenna 502, as described with reference to Figures 5A and 5B. The spatial plot 700A of Figure 7 shows a plane defined by a first axis 702, u, and a second axis 704, v. The first axis 702 and second axis 704 represent directions in space and may correspond to a plane parallel to and coinciding with a plane defining a flat panel phased array antenna. The first axis 702 corresponds to the first axis 602 described with reference to Figure 6. The second axis 704 corresponds to the second axis 604 described with reference to Figure 6. The spatial plot 700A shows representations of two beams 710, 712 with two different radial direction components, r1, r2 in the u-v plane, along a radial steering r, shown by the arrow 706. The two beams 710, 712 correspond to the two beams 610, 612 with the two different radial direction components, r1, r2 in the u-v plane, as described with reference to Figure 6. In contrast to the beams 610, 612 of Figure 6, the beams 710, 712 show the application of the beam squint mitigation technique, where the beams 710, 712 are widened as a function of the steering angle (and hence component of the radial steering direction in the u-v plane) in a direction parallel to the phase gradient across the array face (radial direction of the steering angle). The first beam representation 710 is for a beam with a component, r1, in the u-v plane along a radial steering direction 706. The second beam representation 712 is for a beam with a different component, r2, in the u-v plane along a radial steering direction 706. Further detail is illustrated in a plot 700B of Gain, in dB, along an axis 708 versus the radial steering direction 706. The plot 700B shows a cross-sectional representation of the first beam representation 710 and the second beam representation 712. The first beam representation 710 has a plot 716 representing gain for a main beam at a synthesis frequency (where the centre of the flat portion of the peak of the plot 716 corresponds to the synthesis frequency, where the synthesis frequency is the same as for the plot 616 with the component r1 in the u-v plane in the radial direction) and a plot 718 representing gain for the main beam at an instantaneous frequency (where the centre of the flat portion of the peak of the plot 718 corresponds to the instantaneous frequency, where the synthesis frequency is the same as for the plot 618 with the component r2 in the u-v plane in the radial direction). The flat portions at the peaks of the plots 716, 718 correspond to the widening of the beam that is formed. The change in frequency results in a beam squint angle 717, BSA1. The beam squint angle 717, BSA1 of Figure 7 is the same as the beam squint angle 617, BSA1 of Figure 6. In contrast to plots 616, 618 of Figure 6, whilst there is a relative drop in gain at the synthesis frequency, illustrated by the beam squint loss 719, BSL1b, the relative drop is considerably less than the relative drop when the beam squint mitigation technique is not applied. The second beam representation 712 has a plot 720 representing gain for a main beam at the synthesis frequency (where the centre of the flat portion of the peak of the plot 720 corresponds to the synthesis frequency, where the synthesis frequency is the same as for the plot 716 with the component r1 in the u-v plane in the radial direction) and a plot 722 representing gain for the main beam at the instantaneous frequency (where the centre of the flat portion of the peak of the plot 722 corresponds to the instantaneous frequency, where the synthesis frequency is the same as for the plot 718 with the component r2 in the u-v plane in the radial direction). The flat portions at the peaks of the plots 720, 722 correspond to the widening of the beam that is formed. The change in frequency results in a beam squint angle 721, BSA2. The beam squint angle 721, BSA1 of Figure 7 is the same as the beam squint angle 621, BSA1 of Figure 6. In contrast to plots 620, 622 of Figure 6, whilst there is a relative drop in gain at the synthesis frequency, illustrated by the beam squint loss 723, BSL1b, the relative drop is considerably less than the relative drop when the beam squint mitigation technique is not applied. In an example, the beam 710 with the component r1 in the u-v plane in the radial direction is formed at step S306 of process S300. In such a case, the formed beam is based on a desired steering angle and a desired bandwidth, wherein the beam has a cross-sectional area in a plane perpendicular to the radial direction of the desired steering angle comprising a first dimension perpendicular to the radial direction and a second dimension perpendicular to the radial direction and the first dimension, and the first dimension is greater than the second dimension. In response to determining a change in the desired steering angle to a desired steering angle with a component r2 in the u-v plane in the radial direction, as described with reference to the beam 712 in Figure 7, the beam is altered such that the magnitude of the dimension perpendicular to the radial direction changes, as shown at Figure 7. The width of the beams 710, 712 with beam squint mitigation are wider in the radial direction at an equivalent fraction of the maximum power compared with the beams 610, 612 without beam squint mitigation. The width of the beams 710, 712 in a direction perpendicular to the radial steering direction, r, is the same at corresponding points of the beams 710, 712 with beam squint mitigation compared with beams 610, 612 without beam squint mitigation. Whilst the beams 710, 712 are described in respect of widening in a direction parallel to the phase gradient across the array face, it will be understood that changes in steering angle and bandwidth can result in a relative narrowing of the beam width, e.g., when the steering angle varies from one with the radial component r2 in the direction of the radial component r1. Whilst the width of the beams 710, 712 perpendicular to the radial steering direction, r, are not changed with respect to an unmodified condition in order to provide beam squint mitigation, in further examples the width of the beams 710, 712 perpendicular to the radial steering direction, r, may be varied with respect to the unmodified condition whilst still providing improvements. The main beam peak gain 714 for the plot 716 at the synthesis frequency for the component r1 in the radial direction 706 is sacrificed slightly compared with the main beam peak gain 614 for the plot 616 at the synthesis frequency for the component r1 in the radial direction 606, due to the widening of the beam. However, this counterintuitive sacrifice provides significant benefits in the relative loss of gain as a function of frequency. It can be seen that, depending on the range of frequencies used for communication, a beam can be widened in a direction (for example, the direction 516, described with reference to Figure 5), such that the amount of gain loss accepted in order to accommodate beam squint variation as a function of frequency can be determined for different steering angles in order to provide a best overall performance. Once the beam has been formed at step S306, the process moves to step S308, where a step of determining whether any changes in the beam are required. Changes in the beam are required when, for example, a phased array antenna is communicating with a satellite, such as a Low Earth Orbit (LEO) satellite that is a moving target. Accordingly, as the target moves across the sky, the desired steering angle changes. Changes in the desired steering angle are made by monitoring changes in the location of the target and accessing data relating to the target stored in a database. Alternatively or additionally, changes in the desired steering angle are determined based on stored data, for example, data relating to a known trajectory of a target. Additionally or alternatively, it is determined if there are any changes in the desired bandwidth. If there are changes in the desired steering angle and / or desired bandwidth, the process moves to step S310 where an altered beam is determined. Such a determination is based on referencing data stored in a database. For example, the amplitude applied to one or more antenna elements 204 of the phased array antenna 202 is controlled by the computing device 216 in order to alter the formed beam in response to a change in the desired steering angle and / or desired bandwidth. In an example, a known distribution of amplitudes is applied to the one or more antenna elements 204 in order to provide a beam for a particular desired steering angle and / or desired bandwidth. In response to a change in the desired steering angle and / or desired bandwidth, a different known distribution of amplitudes is applied to the one or more antenna elements 204. Once the determination has been made, the process moves to step S306 and the updated beam is formed. The process continues to step S308. If it is determined at step S308 that no changes are to be implemented, the process moves to step S312, where it is determined if the process has ended. If not, the process moves back to step S306 and the beam is maintained until such a time that there is a change, or it is determined at step S312 that the process S300 has finished, in which case the process S300 moves to step S314, where it ends. The beam formed by the phased array antenna 204 is altered as frequently as required to maintain communication needs and the process S300 continues as long as required in order to provide communication. Whilst process flow S300 shows a defined number of steps in a particular order, in further examples the process flow S300 comprises additional and / or alternative steps in any appropriate order, such that the functionality described herein is implemented. Advantageously, the methods and systems described herein enable improved communication within phased array antenna systems, and in particular within dynamically changing phased array antenna systems, where the efficient and effective application of signals to phased array antenna elements is performed in such a way that provides overall system improvements. Various further aspects and embodiments of the present invention will be apparent to those skilled in the art in view of the present disclosure. “and / or” where used herein is to be taken as specific disclosure of each of the two specified features or components with or without the other. For example “A and / or B” is to be taken as specific disclosure of each of (i) A, (ii) B and (iii) A and B, just as if each is set out individually herein. Unless context dictates otherwise, the descriptions and definitions of the features set out above are not limited to any particular aspect or embodiment of the invention and apply equally to all aspects and embodiments which are described. It will further be appreciated by those skilled in the art that although the invention has been described by way of example with reference to several embodiments. It is not limited to the disclosed embodiments and that alternative embodiments could be constructed without departing from the scope of the invention as defined in the appended claims.

Claims

1. A method for controlling beam squint in a radio frequency beamforming architecture, the method comprising:forming a beam based on a desired steering angle and a desired bandwidth, wherein the beam has a cross-sectional area in a plane perpendicular to the radial direction of the desired steering angle comprising a first dimension perpendicular to the radial direction and a second dimension perpendicular to the radial direction and the first dimension; andaltering the formed beam in response to a change in the desired steering angle such that the first dimension is greater than the second dimension and has a magnitude based on the change in the desired steering angle, thereby dynamically controlling beam squint.

2. The method according to claim 1, wherein altering the formed beam further comprises determining a change in the desired bandwidth.

3. The method according to any preceding claim, wherein altering the beam comprises changing the first dimension in a plane perpendicular to the radial direction and parallel to the component of the radial direction in a plane defined by a plurality of antenna elements of the radio frequency beamforming architecture.

4. The method according to any preceding claim wherein the ratio of the first dimension to the second dimension is based on a minimization of gain loss across the desired bandwidth for the change in the desired steering angle.

5. The method according to any preceding claim, wherein forming the beam comprises selectively controlling the amplitude and / or phase of signals applied to each antenna element of a plurality of antenna elements of a phased array antenna of the radio frequency beamforming architecture.

6. The method according to claim 5, wherein altering the formed beam comprises altering the amplitude applied to one or more antenna elements of the plurality of antenna elements.

7. The method according to claim 6, wherein the amplitude is determined based on a comparison of the gain across the desired bandwidth for the application of a firstdistribution of amplitudes for the plurality of antenna elements with the gain across the desired bandwidth for the application of a second distribution of amplitudes for the plurality of antenna elements, thereby to reduce the rate of change in gain as a function of frequency across the desired bandwidth.

8. The method according to any preceding claim, wherein determining the desired steering angle comprises determining a location of a target and wherein determining a change in the desired steering angle is based on at least one of monitoring changes in the location of the target and accessing data relating to the target stored in a database.

9. The method according to any preceding claim, wherein the magnitude is based on correlating at least one of the desired steering angle and the desired bandwidth with data stored in a database.

10. The method according to any preceding claim, wherein the cross-sectional area is determined at a fraction of the maximum power of the beam in the radial direction for a central frequency of the desired bandwidth.

11. A phased array antenna system comprising:a plurality of independently controllable antenna elements, wherein the phased array antenna system is configured to apply phase delay and / or amplitude factors to one or more of the plurality of antenna elements in order to form a beam, wherein the phased array antenna system is further configured to perform the method according to any of claims 1 to 10.

12. A computer readable medium comprising instructions which, when executed by a computer, cause the computer to perform the steps of any of claims 1 to 10.

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