Radial line slot antenna array

Abstract

In some examples, a method for generating a set of slot activation configurations for a holographic radial line slot antenna array comprising a plurality of slots defining a preconfigured slot pattern, each slot activation configuration defining a beam pattern for a signal to be emitted by the antenna, the method comprises generating measurements for mutual coupling between the plurality of slots in the presence of a signal to be applied to the antenna, where the measurements comprise a set of scattering parameters defining a scattering matrix for the antenna, generating a set of impedance parameters for the array using the measurements for mutual coupling, controlling resonance of at least one of the plurality of slots by adjusting capacitance values ​​of variable capacitance devices provided at both ends of the slots, measuring a value for the antenna gain of the beam pattern associated with the capacitance values, selecting a final value of capacitance that results in the highest measured value of gain for the beam pattern, and selecting a slot activation configuration for the beam pattern based on the selected final value of capacitance.

Description

[Technical field]

[0001] The present invention relates to an antenna array. An embodiment relates to a radial slot line antenna array. [Background technology]

[0002] The size, weight, power consumption, and implementation cost of antennas or antenna arrays in a platform can be prohibitive, leading to suboptimal deployment, where, for example, certain desired functionality may be sacrificed in favor of lower cost or smaller alternatives. For example, active electronically scanned antenna arrays (AESA) and passive electronically scanned antenna arrays (PESA) are heavy, expensive, and require large amounts of power to operate and keep cool. Similarly, passive reflector-type antennas are large and not conducive to implementation on certain platforms, such as modern aircraft, where (at least) their size may interfere with the aerodynamic profile of the platform.

[0003] To reduce cost and size, some antenna structures use a single voltage source to drive the elements of the antenna, thereby reducing the physical size of the structure and its implementation costs. However, by using only a single source, the individual elements cannot be selectively controlled. This therefore limits their use with respect to emitted beams, for example, since the array cannot be scanned. Phase shifters can be used to provide some control over the emitted beam, but these are generally ferrite-based and therefore lossy, leading to inefficiencies. Conversely, a transmitter provided for each antenna element can provide full control of the phase and amplitude of the emitted beam, for example allowing scanning. However, such systems are expensive and generally large, for example as a result of the increased area required for the drive mechanism. Hence, there is often a trade-off between implementing an antenna that is expensive and / or large / heavy, but efficient and more controllable, and an antenna that is cheaper and / or smaller / lighter, but less efficient and less functionally useful. Summary of the Invention

[0004] According to a first aspect of the present disclosure, there is provided a method for generating a set of slot activation configurations for a holographic radial line slot antenna array comprising a plurality of slots defining a preconfigured slot pattern, each slot activation configuration defining a beam pattern for a signal to be emitted by the antenna, the method comprising: generating measurements of mutual coupling between the plurality of slots in the presence of a signal to be applied to the antenna, where the measurements comprise a set of scattering parameters defining a scattering matrix for the antenna, generating a set of impedance parameters for the array using the measurements of mutual coupling; controlling resonance of at least one of the plurality of slots by adjusting capacitance values ​​of variable capacitance devices provided at both ends of the slots; measuring a value for the antenna gain of the beam pattern associated with the capacitance values; selecting a final value of capacitance that results in the highest measured value of gain for the beam pattern; and selecting a slot activation configuration for the beam pattern based on the selected final value of capacitance.

[0005] In an implementation of the first aspect, a set of sub-wavelength slot elements distributed across the slot surface can be dynamically switched "on" or "off" to generate a reconfigurable antenna that is low cost, low weight, and low profile. In an example, a value for the radiated power of the antenna can be measured. A value for the power in the direction of the peak gain for the antenna can be measured. An updated measurement of the mutual coupling between multiple slots in the presence of a capacitance value can be generated.

[0006] The measurements for mutual coupling can be generated by calculating respective measurements of currents flowing through resistive elements logically arranged across the ports of the plurality of slots. Adjusting the capacitance values ​​of the variable capacitance devices can comprise adjusting respective values ​​of reactive capacitance for the plurality of slots. The set of impedance parameters for the array can be converted into updated measurements for mutual coupling between the slots when the capacitance values ​​are present. Respective measurements for excitation of the plurality of slots can be calculated. The resonance of at least one of the plurality of slots can be controlled or changed by adjusting or modifying the capacitance values ​​of the variable capacitance devices provided across the slot using one of a plurality of discrete values ​​for capacitive reactance.

[0007] According to a second aspect of the present disclosure, there is provided a non-transitory machine-readable storage medium encoded with instructions for generating a set of slot activation configurations for a holographic radial line slot antenna array comprising a plurality of slots defining a preconfigured slot pattern, each slot activation configuration defining a beam pattern for a signal to be emitted by the antenna, the instructions being executable by a processor of the machine to cause the machine to: generate an impedance matrix for the array using a set of scattering parameters for the array; tune resonant frequencies of the slots using capacitive reactances to thereby generate an updated impedance matrix for the array; calculate respective measurements of currents around the plurality of slots using the updated impedance matrix; calculate respective measurements of voltages across the plurality of slots using the current measurements and the impedance matrix; convert the updated impedance matrix to an updated set of scattering parameters; and calculate a radiation pattern for the antenna using the updated set of scattering parameters and the voltage measurements.

[0008] In an embodiment of the second aspect, the resonant frequency can be optimized using a plurality of different combinations of capacitive reactance to minimize the power reflected from the input port of the array. The resonant frequency can be optimized using a plurality of different combinations of capacitive reactance to minimize the power transmitted to the unloaded coaxial port of the array. The resonant frequency can be optimized using a plurality of different combinations of capacitive reactance to maximize the power radiated in a selected direction. In an example, a set of slot activation configurations can be generated, each slot activation configuration defining a capacitive reactance for each of a plurality of slots for a given beam pattern for the array. The resonant frequency of the slot can be tuned using one of a plurality of discrete values ​​for the capacitive reactance.

[0009] Embodiments of the present invention will now be described, by way of example only, with reference to the drawings in which: [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 is a schematic diagram of an RLSA array, according to an example. [Diagram 2] 1 is a flowchart of a method according to an example. [Diagram 3] FIG. 1 is a schematic diagram of a machine according to an example. [Figure 4] 1 is a flowchart of a method according to an example. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Illustrative embodiments are described below in sufficient detail to enable those skilled in the art to embody and implement the systems and processes described herein. It is important to understand that the embodiments may be provided in many alternative forms and should not be construed as being limited to the examples set forth herein.

[0012] Thus, while the embodiments can be modified in various ways and can take various alternative forms, specific embodiments thereof are shown in the drawings and will be described in detail below by way of example. There is no intention to be limited to the particular forms disclosed. On the contrary, all modifications, equivalents, and alternatives falling within the scope of the appended claims should be covered. Elements of the illustrative embodiments are consistently designated by the same reference numerals throughout the drawings and the detailed description, where appropriate.

[0013] The terminology used herein to describe the embodiments is not intended to be limiting in scope. The articles "a", "an" and "the" are singular in that they have a single referent, but the use of the singular in this document should not exclude the presence of more than one referent. In other words, an element referred to in the singular can have a number of one or more, unless the context clearly dictates otherwise. It is further understood that the terms "comprises", "comprising", "includes" and / or "including", as used herein, specify the presence of stated features, items, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, items, steps, operations, elements, components and / or groups thereof.

[0014] Unless otherwise defined, all terms used herein (including technical and scientific terms) should be interpreted as is conventional in the art. It should be further understood that terms in common usage should also be interpreted as is conventional in the relevant art, and should not be interpreted in an idealized or overly formal sense unless expressly defined as such herein.

[0015] A radial line slot antenna (RSLA) is a low-cost antenna structure that comprises a radiating element, a cavity, a background plate, and a feed for supplying a signal to the radiating element. The radiating element and the background plate typically comprise a pair of metal disks, such as aluminum, copper, or brass, separated by a cavity, thereby forming a parallel plate waveguide fed at the center by a feed, which can be, for example, a coaxial feed or a waveguide transition. The cavity between the parallel plates can be filled with a low-permittivity substrate, such as a dielectric material, or a slow-wave structure. This can help prevent the formation of grating lobes in the far-field pattern. In conjunction with the radiating element and the background plate, the cavity acts as a circular waveguide that guides the signal from the feed to propagate radially.

[0016] A RLSA typically comprises a number of through slots or apertures in a radiating element, conceptually arranged as a number of slot pairs, in which each pair effectively functions as an antenna element for the RLSA, such that all of the multiple slot pairs of a radiating element form an array antenna. The slot pairs are arranged in a predefined pattern arranged to generate a fixed beam at a given frequency in a given polarization, and the slots of a slot pair are typically arranged with respect to each other such that their major axes are orthogonal to each other. The orientation of the slots can be determined by analyzing the field vectors propagated by each slot in the array, and it is common to consider the slots of a slot pair as in-phase and out-of-phase, and then use a cumulative sum of these sets of slots to achieve the desired polarization.

[0017] In general, the interactions between antenna elements in an RLSA array as a result of mutual coupling between small slots make it very difficult to produce the correct amplitude and phase taper at both ends of the array for a given beam angle. Hence, RLSA arrays, in which the slots are fixed in defined locations and only the slot sizes and positions can be optimized to produce a specific beam shape in a given direction, are generally not considered to be practical candidates for tunable antenna arrays and are therefore optimized for one specific beam angle.

[0018] FIG. 1 is a schematic diagram of an RLSA array according to an example. The RLSA array comprises a radiating element 101, a cavity 105, a background plate 103, and a coaxial feed 107. A slot 109 is provided in the radiating element 101. The slot 109 forms a discontinuity in the radiating element. Hence, a signal from the feed 107 will generate a voltage at both ends of the slot. The wall 111 can be a conductive material or can be left open. There are numerous ways in which the slots can be positioned in the radiating element, and the methods described herein do not depend on the overall slot pattern. For example, a two-dimensional spiral slot array can be used.

[0019] According to an example, a method is provided for generating a set of slot activation configurations in a RLSA, thereby enabling a desired amplitude and phase taper across the array. Thus, a holographic antenna array in the form of a tunable RLSA can be implemented in which the beam position and operating frequency can be adjusted to any one of a number of predefined configurations.

[0020] To enable the RLSA to be scannable, the slots constituting a slot pair should be small and spaced apart from each other by a distance less than the dominant operating wavelength. For example, for an array having a diameter of 300 mm and an operating frequency of about 13 GHz, slots having dimensions of about 4×2 mm can be used. More specifically, slots having dimensions of about 4.3×1.5 mm can be used. More specifically, slots having dimensions of 4.35×1.625 mm can be used.

[0021] As a result of the slot size, there is scattering in and out of the antenna array. This results in distorted patterns, which means that the phase of the signal emitted from the antenna may not be as intended. Therefore, in general, it is difficult to predict what effect each slot will have.

[0022] An S-parameter matrix (S-matrix) can be generated that accounts for mutual coupling between all slots and all feed ports of the antenna array in order to create a beam pattern that incorporates all antenna parameters of interest such as directivity, sidelobe levels, input matched radiated power, etc. In an example, the generated S-matrix can be used to evaluate the array performance in various configurations where antenna elements (i.e., slot pairs) and / or individual slots are "on" or "off."

[0023] According to an example, measurements of the current across the resistive elements can be calculated, from which it is possible to calculate the voltage across the slots for a given input signal. The voltage measurements for the slots can be used to generate an s-matrix, from which a z-parameter matrix (z-matrix) can be generated that comprises the impedance parameters of the array and represents the input and output currents flowing through the ports associated with the slots. There will be a real and an imaginary component of the impedance for each slot. To maximize the energy radiated from the array, the imaginary component of the impedance for the slot should be zero. That is, to increase the power factor, the imaginary part of the load impedance should be as small as possible so that the impedance is real valued. In an example, when the slots are sub-wavelength, capacitance can be added across the ports of the slots to tune them so that they resonate. In an example, reactive capacitance can be used (and tuned) to determine the point at which the maximum radiated energy occurs. The z-matrix, which defines the impedance value for the array that provides such maximum radiated energy, can be converted back to an s-matrix to allow the power value for the array to be determined. This process can be repeated using various combinations of capacitance values ​​for the slots to determine a set of slot activation configurations that define values ​​for the capacitance of the slots that result in maximum radiated energy for a desired direction and polarization. In an example, a genetic algorithm can be used to effectively cycle between various combinations of capacitance values ​​to determine the slot activation configuration for a target beam pattern.

[0024] According to an example, given an optimal value for capacitance, the slots can be effectively turned on or off. That is, for a given beam pattern to be emitted from the array, a slot activation configuration can be determined, the slot activation configuration representing a set of capacitance values ​​for each slot of the array that results in maximum radiated energy in a desired direction and for a polarization. Deviations from these capacitance values ​​will reduce the radiated energy. Hence, a set of slot activation configurations can be determined, each of which defines a set of slot capacitance values ​​that allows a beam to be emitted from the array in a desired direction. From this, according to an example, a holographic array can be implemented in which the slot activation configuration allows the slots to be effectively turned on or off.

[0025] FIG. 2 is a flow chart of a method for generating a set of slot activation configurations for a holographic RLSA array according to an example. As described above, the RLSA array comprises a number of slots that define a preconfigured slot pattern, and each slot activation configuration defines a beam pattern in which a signal is to be emitted by the array. In block 201, measurements are generated for mutual coupling between a number of slots in the presence of a signal to be applied to the antenna. In an example, the measurements comprise a set of scattering parameters that define a scattering matrix (s-matrix) for the antenna. The scattering matrix can be calculated by considering all slots and ports on all feeds of the antenna with resistive elements, such as 50 ohm resistors. The current passing through the resistive elements can be calculated to obtain s-parameters for the array, thereby enabling characterization of the coupling from each port to every other port in the array.

[0026] In block 203, the measurements of mutual coupling are used to calculate a set of impedance parameters for the array. The impedance matrix allows capacitance to be added to the geometry of the array, thereby allowing tuning of the resonant frequency of the slots. The z-parameters of the z-matrix are generally related to their s-parameters by the following equation:

[0027]

number

[0028] where 1 N is the identity matrix,

[0029]

number

[0030] is a diagonal matrix having the square root of the characteristic impedance at each port as its non-zero elements.

[0031] In block 205, the resonance of at least one of the plurality of slots is controlled or varied by adjusting or selecting a value of capacitance of a variable capacitance device, such as a varactor diode, provided across the slot. That is, the resonant frequency of the slot is tuned by varying the capacitance of the slot, measuring a value for the antenna gain for the beam pattern (block 207), and selecting a final value of capacitance that results in the highest measured value of gain for the beam pattern (block 209). Because the beam pattern for the array changes depending on the state of activity of the slots, different beam patterns can be generated by cycling through different combinations of capacitance for one or more slots to vary the degree to which one or more slots resonate.

[0032] In block 211, a slot activation configuration for the beam pattern is selected based on the final values ​​of the selected capacitances. That is, given a desired beam pattern for the array, the slot activation configuration defines a set of slots that should be switched on or off (or in a semi-active state of emission). The emission state of a slot is determined, in an example, by the capacitive reactance for that slot. Such a value can be selected to effectively prevent the slot from radiating, radiating at a maximum value, or anywhere between these extremes. Thus, in tuning the resonant frequency of the slots, the value for the antenna gain for a given combination of capacitance values ​​associated with the slots of the array gives rise to a beam pattern due to coupling between the slots in their various active states. By cycling through various combinations of capacitances for the slots of the array, for example using a genetic algorithm, a set of configurations can be constructed, each of which is mapped to a given beam pattern, some of which may be of interest and others of which may not. From this, by varying the capacitance of the slots to modify their state (e.g., on, off, semi-active, etc.), a picture can be constructed of configurations that result in desirable or desired beam patterns.

[0033] According to an example, the slots can be switched on or off or provided in a semi-active state by applying a capacitance selected from one of a plurality of values, which may be, for example, discrete values. Hence, a desired beam pattern to be emitted by the array may be associated with a slot activation configuration in which a certain percentage of the slots are radiating at a first level, a certain percentage of the slots are radiating at a second level, and so on. The first level may correspond to the slots being effectively off, while the second level may correspond to the slots being effectively on and radiating at or near resonance. In between these states, various other levels of slot activity, in which the slots are radiating below resonance but are not "off," may be provided depending on the prevailing value of the capacitance for one or more slots.

[0034] The present disclosure is described with reference to flowcharts and / or block diagrams of methods, devices, apparatus, and systems according to examples of the disclosure. Although the described flow diagrams may show a particular order of execution, the order of execution may differ from the order of execution depicted. Blocks described in connection with one flowchart may be combined with blocks of another flowchart. In some examples, some blocks of a flow diagram may not be required and / or additional blocks may be added. It should be understood that each flow and / or block in the flowchart and / or block diagram, and combinations of flows and / or diagrams in the flowchart and / or block diagram, may be implemented by machine-readable instructions.

[0035] The machine-readable instructions may be executed by a machine, such as a general-purpose computer, a processor of a smart device, e.g., a user equipment such as a smartphone, a dedicated computer, an embedded processor, or other programmable data processing device to realize the functions described in this description and the figures. In particular, a processor or processing device may execute machine-readable instructions. From this, a module of the device (e.g., a module implementing a converter for converting an s-matrix to a z-matrix and vice versa) may be implemented by a processor that executes machine-readable instructions stored in a memory, or a processor that operates according to instructions embedded in a logic circuit. The term "processor" should be interpreted broadly to include a CPU, a processing unit, an ASIC, a logic unit, or a set of programmable gates, etc. All the methods and modules may be executed by a single processor or may be divided among several processors.

[0036] Such machine-readable instructions may also be stored in a computer-readable storage device that can direct a computer or other programmable data processing device to operate in a particular mode. For example, the instructions may be provided on a non-transitory computer-readable storage medium encoded with instructions executable by a processor.

[0037] 3 is a schematic diagram of a machine according to an example. In the example of FIG. 3, the machine 301 comprises a processor 303 and a memory 305 for storing instructions 307 executable by the processor 303. A storage device 309 can be used to store data 311 representing any one or more of the slot activation configurations, s parameters and / or matrices, z parameters and / or matrices, and a set of capacitance values. The instructions 307 executable by the processor 303 can cause the machine to generate an impedance matrix for the array using a set of scattering parameters for the array, tune the resonant frequencies of the slots using the capacitive reactances to thereby generate an updated impedance matrix for the array, calculate respective measurements of currents around the plurality of slots using the updated impedance matrix, calculate respective measurements of voltages across the plurality of slots using the current measurements and the impedance matrix, convert the updated impedance matrix to an updated set of scattering parameters, and calculate a radiation pattern for the antenna using the updated set of scattering parameters and the voltage measurements.

[0038] By way of example, measurements of mutual coupling between slots of an array comprise an s-matrix that characterizes the geometry of the array. The s-matrix can be generated by applying a port to every point of the geometry of the array of interest, where the port can comprise a resistor at which voltage and current can be measured. The s-matrix calculated for the array can be converted to an impedance matrix (z-matrix) as described above. Given an impedance matrix [Z], a capacitive reactance can be applied to each slot to obtain a load impedance matrix [Z loaded ], so:

[0039]

number

[0040] where [C] is a 1D array of (capacitive) reactances given by:

[0041]

number

[0042] Therefore, there is a new impedance matrix with the capacitance added, so:

[0043]

number

[0044] New Z matrix ([Z loaded ]) to allow the S-parameters of the unloaded coaxial ports of the array to be examined, and / or the excitation [V excite ] can be converted to an S-parameter matrix to allow the calculation of [Z loaded ] can be used to calculate the current around each slot using Ohm's law, where [V] is a 1D array of applied voltages. In an example, 1V can be applied to the first element (representing the coaxial feed port) and all other voltages can be set to 0, i.e.:

[0045]

number

[0046] Therefore, loaded ] is then calculated as the voltage across the slot [V slot ] can be used to calculate:

[0047]

number

[0048] where [Z] is the original (no-load) impedance matrix. [V slot ] can be used to perform an array factor (AF) calculation to determine the antenna radiation pattern according to the following formula:

[0049]

number

[0050] Here, N is

[0051]

number

[0052] The array of emitters is located at a n is the complex-valued excitation coefficient,

[0053]

number

[0054] is the directional unit vector.

[0055] Thus, by way of example, the S-parameters of the unloaded feed port and the antenna radiation pattern can be calculated. These variables can be optimized using an optimization routine, such as a genetic algorithm. In an example, the optimization can aim to minimize the power reflected from the input port and / or the power transmitted to the second unloaded coaxial port (power losses are assumed to be radiated). The optimization can aim to maximize the power radiated in a given direction and also minimize the power radiated in all other directions. Other parameters related to the antenna pattern can be included, such as axial ratio, cross polarization, etc.

[0056] By way of example, the antenna pattern and s-parameters can be predicted using an initial estimate of the capacitance on the slot elements, followed by an optimization as described above, which can be repeated for several antenna beam pointing angles.

[0057] Hence, the machine can perform a method for generating a set of slot activation configurations for a holographic radial line slot antenna array comprising a plurality of slots defining preconfigured slot patterns, each slot activation configuration defining a beam pattern for a signal to be emitted by the antenna.

[0058] Such machine-readable instructions may also be loaded onto a computer or other programmable data processing device so that the computer or other programmable data processing device executes a sequence of operations to generate a computer-implemented process, such that the instructions executing on the computer or other programmable device provide operations for achieving the functions specified by the flow(s) in the flowcharts and / or the block(s) in the block diagrams.

[0059] Furthermore, the teachings herein may be implemented in the form of a computer or software product, such as a non-transitory machine-readable storage medium, the computer software or product comprising a plurality of instructions, e.g., machine-readable instructions, stored in the storage medium for causing a computing device to perform the methods described in the examples of this disclosure.

[0060] In some examples, some methods may be performed in a cloud computing or network-based environment. A cloud computing environment may provide various services and applications over the Internet. These cloud-based services (e.g., software as a service, platform as a service, infrastructure as a service, etc.) may be accessible through a web browser or other remote interface. Various functions described herein may be provided through a remote desktop environment or any other cloud-based computing environment.

[0061] FIG. 4 is a schematic diagram of a method according to an example. In block 401, for a given RLSA array geometry of interest, an s-matrix is ​​generated as described above. In block 403, the S-matrix from block 401 for the array in question is converted to a Z-matrix as described above, and in block 405, capacitances are applied into the slot ports to tune the slots of the array. As described above, the tuning can be arranged so that the slots operate on resonance, effectively off, or somewhat in between, depending on the value of the capacitance applied. For a given beam pattern under investigation, the slots can thus operate in any one of a number of regimes, thereby allowing complex beam patterns and beam steering to be provided. In block 407, a new S-matrix is ​​determined and reduced to include only the coaxial ports, as described above. That is, in the example, the loaded Z-matrix can be converted back into an S-parameter matrix, allowing investigation into what the S-parameters of the unloaded coaxial ports are. In block 409, the voltage on each slot is determined when an input voltage is applied to the first coaxial port of the array (i.e., to the feed of the array). In an example, this input voltage may be 1 V. In block 411, an array factor calculation may be performed to determine the antenna radiation pattern using the voltage on each slot as the excitation.

[0062] Although various embodiments are described and / or illustrated herein in the context of a fully functional computing system, one or more of these illustrative embodiments may be distributed as a program product in various forms, regardless of the particular type of computer-readable storage medium used to actually effect the distribution. The embodiments disclosed herein may also be implemented using software modules that perform certain tasks. These software modules may include scripts, batches, or other executable files that may be stored on a computer-readable storage medium or in a computing system. In some embodiments, these software modules may configure a computing system to execute one or more of the illustrative embodiments disclosed herein. In addition, one or more of the modules described herein may transform data, physical devices, and / or representations of physical devices from one form to another.

[0063] The preceding description is provided to enable those skilled in the art to best utilize various aspects of the exemplary embodiments disclosed herein. This exemplary description is not intended to be exhaustive or to be limited to any precise form disclosed. Many modifications and variations are possible without departing from the spirit and scope of the present disclosure. The embodiments disclosed herein should be considered in all respects as illustrative and not restrictive. In determining the scope of the present disclosure, reference should be made to the appended claims and their equivalents.

Claims

1. 1. A method for generating a set of slot activation configurations for a holographic radial line slot antenna array comprising a plurality of slots defining preconfigured slot patterns, each slot activation configuration defining a beam pattern for a signal to be emitted by the antenna, the method comprising: generating a measurement of mutual coupling between the plurality of slots in the presence of a signal to be applied to the antenna, wherein the measurement comprises a set of scattering parameters defining a scattering matrix for the antenna; generating a set of impedance parameters for the array using the measurements of mutual coupling; and controlling the resonance of at least one of the plurality of slots by adjusting a capacitance value of a variable capacitance device provided across the slot; measuring a value for an antenna gain of a beam pattern associated with said capacitance value; selecting a final value of capacitance that results in the highest measured gain for said beam pattern; selecting a slot activation configuration for the beam pattern based on the selected final capacitance value; A method comprising:

2. Measuring a value for the radiated power of said antenna. The method of claim 1 further comprising:

3. Measuring a value for power in a direction of peak gain for said antenna. The method of claim 1 or 2, further comprising:

4. generating an updated measurement of mutual coupling between the plurality of slots when the capacitance values ​​are present; The method of any one of claims 1 to 3, further comprising:

5. determining said measurements of mutual coupling by calculating respective measurements of current flowing through resistive elements logically disposed across ports of said plurality of slots; The method of any one of claims 1 to 4, further comprising:

6. The method of any one of claims 1 to 5, wherein adjusting the capacitance value of the variable capacitance device comprises adjusting respective values ​​of reactive capacitance for the plurality of slots.

7. converting the set of impedance parameters for the array into an updated measurement of mutual coupling between the slots when the capacitance values ​​are present; The method of any one of claims 1 to 6, further comprising:

8. calculating respective measurements for excitation of said plurality of slots; The method of claim 7 further comprising:

9. controlling resonance of at least one of the plurality of slots by adjusting a value of capacitance of a variable capacitance device provided across the slot using one of a plurality of discrete values ​​for capacitive reactance. The method of any one of claims 1 to 8, further comprising:

10. A non-transitory machine-readable storage medium encoded with instructions for generating a set of slot activation configurations for a holographic radial line slot antenna array comprising a plurality of slots defining preconfigured slot patterns, each slot activation configuration defining a beam pattern for a signal to be emitted by the antenna, the instructions being executable by a processor of a machine, thereby causing the machine to: generating an impedance matrix for the array using a set of scattering parameters for the array; tuning the resonant frequencies of the slots using capacitive reactance to thereby generate an updated impedance matrix for the array; calculating respective measurements of currents around the plurality of slots using the updated impedance matrix; calculating respective measurements of voltage across the plurality of slots using the current measurements and the impedance matrix; converting the updated impedance matrix into an updated set of scattering parameters; calculating a radiation pattern for the antenna using the updated set of scattering parameters and the voltage measurements; and A storage medium that causes the

11. The machine, 11. The storage medium of claim 10, further comprising instructions for optimizing the resonant frequency using a plurality of different combinations of capacitive reactances to minimize power reflected from an input port of the array.

12. The machine, 12. The storage medium of claim 10 or 11, further comprising instructions for optimizing the resonant frequency using a plurality of different combinations of capacitive reactances to minimize power transmitted to an unloaded coaxial port of the array.

13. The machine, 13. The storage medium of claim 10, further comprising instructions for optimizing the resonant frequency using a plurality of different combinations of capacitive reactances to maximize power radiated in a selected direction.

14. The machine, 14. The storage medium of claim 10, further comprising instructions for generating a set of slot activation configurations, each slot activation configuration defining a capacitive reactance for each of the plurality of slots for a given beam pattern for the array.

15. The machine, The storage medium of any one of claims 9 to 14, further comprising instructions for tuning the resonant frequency of a slot using one of a plurality of discrete values ​​for the capacitive reactance.

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