Patent Publication Number: US-2023155283-A1

Title: Beamforming via sparse activation of antenna elements connected to phase advance waveguides

Description:
If an Application Data Sheet (ADS) has been filed on the filing date of this application, it is incorporated by reference herein. Any applications claimed on the ADS for priority under 35 U.S.C. § § 119, 120, 121, or 365(c), and any and all parent, grandparent, great-grandparent, etc., applications of such applications are also incorporated by reference, including any priority claims made in those applications and any material incorporated by reference, to the extent such subject matter is not inconsistent herewith. 
     CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims the benefit of the earliest available effective filing date(s) from the following listed application(s) (the “Priority Applications”), if any, listed below (e.g., claims earliest available priority dates for other than provisional patent applications or claims benefits under 35 U.S.C. § 119(e) for provisional patent applications, and for any and all parent, grandparent, great-grandparent, etc., applications of the Priority Application(s)). In addition, the present application is related to the “Related Applications,” if any, listed below. 
     Priority Applications 
     This application is a continuation of U.S. Non-Provisional patent application Ser. No. 16/837,998, titled “Beamforming Via Sparse Activation of Antenna Elements Connected to Phase Advance Waveguides,” filed on Apr. 1, 2020 and issuing on Sep. 20, 2022 as U.S. Pat. No. 11,450,954 which is hereby incorporated by reference in its entirety. 
     Related Applications 
     If the listings of applications provided above are inconsistent with the listings provided via an ADS, it is the intent of the Applicant to claim priority to each application that appears in the Priority Applications section of the ADS and to each application that appears in the Priority Applications section of this application. 
     All subject matter of the Priority Applications and the Related Applications and of any and all parent, grandparent, great-grandparent, etc., applications of the Priority Applications and the Related Applications, including any priority claims, is incorporated herein by reference to the extent such subject matter is not inconsistent herewith. 
     TECHNICAL FIELD 
     This disclosure relates to reconfigurable antenna technology. Specifically, this disclosure relates to reconfigurable and tunable antennas with subwavelength antenna element spacings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    illustrates an example of an antenna pixel with four antenna elements connected to a waveguide. 
         FIG.  2 A  illustrates an example antenna pixel with four antenna elements extending from a waveguide in alternating directions. 
         FIG.  2 B  illustrates a simulation of the example antenna pixel of  FIG.  2 A  illustrating the relative phase advance of a signal along the waveguide and the relative field strength of each antenna element in greyscale. 
         FIG.  2 C  illustrates an example four-pixel antenna with one antenna element activated within each antenna pixel. 
         FIG.  2 D  illustrates an example graph of a beamform formed by the selective activation of one antenna element within each antenna pixel. 
         FIG.  3    illustrates an example of a reconfigurable antenna with one antenna element activated within each antenna pixel. 
         FIG.  4 A  illustrates a top view of an example antenna pixel with three antenna elements extending from a waveguide. 
         FIG.  4 B  illustrates a cross-sectional view of the example antenna pixel of  FIG.  4 A . 
         FIG.  4 C  illustrates an example antenna array using the antenna pixel illustrated in  FIG.  4 A  with a beamforming controller. 
         FIG.  5 A  illustrates a top view of an example antenna pixel with four offset antenna elements extending from a waveguide. 
         FIG.  5 B  illustrates an example cross-sectional view of a single antenna element of the antenna pixel of  FIG.  5 A . 
         FIG.  5 C  illustrates an example antenna array using the antenna pixel illustrated in  FIG.  5 A . 
         FIG.  6 A  illustrates a block diagram of a top view of an example cavity-based antenna element. 
         FIG.  6 B  illustrates a block diagram of a cross-sectional view of the example cavity-based antenna element. 
         FIG.  6 C  illustrates a graph of the phase control region of an example antenna element that is tunable between −45 degrees and +45 degrees. 
         FIG.  7 A  illustrates a portion of an example antenna with four parallel elongated waveguides with phase-adjustable antenna elements coupled thereto. 
         FIG.  7 B  illustrates a simulated activation and phase adjustment of one antenna element in each antenna pixel. 
         FIG.  8    illustrates a portion of an example antenna with four parallel elongated waveguides connected with meandering turns with phase-adjustable antenna elements coupled thereto. 
         FIG.  9    illustrates a flowchart of an example method of beamforming by activating one antenna element within each subwavelength antenna region. 
         FIG.  10    illustrates a flowchart of an example method of beamforming by selectively activating one antenna element within each one-half wavelength region of an array of subwavelength-spaced antenna elements. 
         FIG.  11 A  illustrates a simplified block diagram of four antenna pixels, each of which includes four antenna elements. 
         FIG.  11 B  illustrates a flowchart of an example method of beamforming by activating one antenna element within each antenna pixel, with reference to the antenna element locations shown in  FIG.  11 A . 
     
    
    
     DETAILED DESCRIPTION 
     This application is related to various metamaterial-surface antenna technology (MSAT) antennas and other antenna arrays utilizing antenna elements with subwavelength spacing. As an example, tunable leaky-wave MSAT or MSAT-like antenna architectures may utilize any number of antenna elements having subwavelength spacings. Phase characteristics and/or the magnitudes of the individual antenna elements may be selectively adjusted to generate a target beamform. At a high level of abstraction, the steering capabilities and/or the beam shaping characteristics of the antenna may be a function of the number and/or density of the individual antenna elements. 
     In some embodiments, individual antenna elements may have subwavelength interelement spacings. For example, individual antenna elements may have interelement spacings of less than one-half of the operational wavelength (λ/2). The interelement spacings may be, for example, one-fourth of the operational wavelength (λ/4), one-sixth of the operational wavelength (λ/6), one-tenth of the operational wavelength (λ/10), etc. Mathematical models and simulations may be utilized to determine the tuning characteristics (e.g., phase and amplitude) that should be applied to each subwavelength antenna element to achieve a given beamform. However, the activation and tuning of multiple antenna elements within a region having dimensions of less than one-half of an operational wavelength may result in significant cross-coupling between antenna elements. 
     The cross-coupling of closely spaced antenna elements can render mathematically calculated patterns (e.g., calculated naïve holograms), simulation results, and the like inaccurate. To address this, many subwavelength antenna element arrays utilize optimization techniques to improve beamforming accuracy and precision. For example, a controller may implement beamforming optimization in real-time during operation and/or prior to operation to create lookup tables or other databases associating various antenna element phase patterns with corresponding beamforms. 
     According to various embodiments of the presently described systems and methods, a reconfigurable antenna may include a plurality of antenna pixels that each include multiple phase-adjustable antenna elements coupled to a common waveguide. The waveguide (e.g., waveguide section) of each antenna pixel has a relative permittivity the provides a target phase advance across the length thereof. In various embodiments, each antenna pixel may comprise multiple discrete waveguides. For example, the antenna pixel may include a number of discrete waveguides corresponding to the number of unique antenna pixels. In other embodiments, the waveguide of each antenna pixel may be a waveguide section or portion of a common waveguide that is shared by multiple antenna pixels. 
     The phase advance characteristics of the waveguide of each antenna pixel and the interelement spacing of the antenna elements of each antenna pixel are configured to provide each of the antenna elements with a distinct phase advance value. As a specific example, the waveguide of each antenna pixel may provide a phase advance of 360 degrees along the length thereof with four antenna elements connected thereto. The antenna elements may be positioned along the waveguide with interelement spacings corresponding to incremental phase advance values of 90 degrees. For instance, the four antenna elements may be spaced to have phase advance values of 0 degrees, 90 degrees, 180 degrees, and 270 degrees. Alternatively, the four antenna elements may be evenly or unevenly spaced to have alternative phase advance values. Each of the antenna elements may have 90-degrees of phase adjustability. For instance, each of the antenna elements may be phase-adjustable between −45 degrees and +45 degrees. 
     A controller, such as a beamforming controller, may identify a target phase value for each antenna pixel in the reconfigurable antenna. The target phase values for each antenna pixel may be selected to generate a target beamform for transmitting and/or receiving electromagnetic radiation. As described above, each antenna element within a given antenna pixel is associated with a distinct phase advance relative to the other antenna elements. Accordingly, one of the antenna elements within each antenna pixel will be associated with a phase advance that approximates (e.g., closest to) the target phase value for the given antenna pixel. 
     The controller may activate the antenna element in each antenna pixel identified as having a phase advance closest to the target phase value of each respective antenna pixel. The phase advance associated with each activated antenna element of each antenna pixel may not exactly match the target phase value of each respective antenna pixel. Accordingly, the controller may adjust the phase of each of the activated (phase-adjustable) antenna elements to correspond to (e.g., be equal to, approximate, or more closely approximate) the identified target phase value for each respective antenna pixel. 
     In the specific example provided above, the waveguide of each antenna pixel provides a phase advance of 360 degrees along the length thereof with four antenna elements connected thereto. It is appreciated that alternative antenna designs may utilize a wide variety of phase advances and/or specific numbers of antenna elements. Antenna designs that utilize a number, N, of antenna elements that are associated with incremental phase advances and are each phase-adjustable with a range sufficient to allow for the antenna pixel to exhibit any target phase value (e.g., 0 degrees to 360 degrees). In other designs, one or more of the antenna pixels may not be fully adjustable between 0 degrees and 360 degrees. For example, each antenna pixel may only have a phase adjustability of 180 degrees, 270 degrees, 300 degrees, or other range less than a full 360 degrees. 
     In some embodiments, each antenna pixel may be described as having a length, L. The relative permittivity of the waveguide of each respective antenna pixel may be described as providing a phase advance of P degrees across the length L. A number of antenna elements N may be arranged along the length L of the waveguide. In some examples, the antenna elements may be evenly spaced along the length L of the waveguide such that the antenna pixels have interelement spacing corresponding to phase advances of P/N degrees. In other embodiments, the antenna elements may be unevenly spaced. For example, if the waveguide provides a phase advance of fewer than 360 degrees (e.g., 270 degrees), individual antenna elements may be spaced to provide the antenna pixel the broadest range of phase control given the phase-adjustability of the individual antenna elements. 
     For example, if the waveguide provides a phase advance of 270 degrees across the length L of an antenna pixel that includes three antenna elements, the antenna elements might be, for example, located positions corresponding to phase advance values of 80 degrees, 170 degrees, and 270 degrees. Assuming the antenna elements have a phase adjustability of −90 degrees and +90 degrees, the antenna pixel can be adjusted between 0 degrees and 360 degrees, with overlapping tunability between −10 degrees and 0 degrees. 
     Returning to the generalized example above, each of the N antenna elements in each respective antenna pixel is phase-adjustable between −(P/(2N) degrees and +(P/(2N) degrees. Antenna pixels with less phase-adjustability may provide for limited tunability and/or only allow for the approximation of a target phase value of each antenna pixel. 
     To provide another specific example, the waveguide of each antenna pixel may provide a phase advance of 270 degrees across a length thereof. Four antenna pixels may be positioned along the waveguide at positions corresponding to 0 degrees, 90 degrees, 180 degrees, and 270 degrees. The length (or another dimension) of the antenna pixel may correspond to one-half of an operational wavelength of the antenna system. The antenna pixel may be fully adjustable between 0 and 360 degrees through the use of antenna elements that are each phase adjustable between −45 degrees and +45 degrees. 
     In another embodiment, the waveguide of each antenna pixel may have a relative permittivity to provide a phase advance of 60 degrees between each antenna element. The antenna elements of each respective antenna pixel may be spaced equally along each respective waveguide and have a phase-adjustability of −30 degrees and 30 degrees. 
     Any of a wide variety of waveguides may be utilized to provide a target phase advance across each antenna pixel. In some examples, the waveguide may include a substrate, such as an RF-35 substrate or an RF-4 substrate. In some embodiments, an air-filled waveguide may be utilized. In some embodiments, the waveguide may comprise a stripline, such as a metal stripline, a doped semiconductor stripline, a low-loss stripline, or another conductor. 
     Each antenna pixel may include any number of antenna elements that may all be the same type of antenna element. In other embodiments, each antenna pixel may include a number of different types of antenna elements. Each antenna element may, for example, include a subwavelength cavity with an iris-coupled patch. Each antenna element may include a diode, such as a varactor diode or other type of diode. In such embodiments, a beamforming controller may selectively activate one antenna element and/or adjust the phase of the activated antenna element by selectively transmitting an electrical signal to a diode of such antenna element. For example, a voltage-controlled diode may selectively adjust the phase of the antenna element associated therewith. According to one example, each diode may be electrically connected to a controller (e.g., via traces or vias) to facilitate the application of a selectable voltage bias to the diode. For instance, one side of the diode may be connected to zero volts or ground, while the voltage applied to the other side is varied to attain a target phase response. 
     In some embodiments, each antenna element may include a microelectromechanical system (MEM) device that is voltage or current controlled to selectively activate and/or adjust the phase response of the antenna element. In some embodiments, each antenna element may include a liquid crystal tunable element that can be used to selectively activate and/or adjust the phase response of the associated antenna element. Combinations of antenna element types and features may be utilized for purposes of activating and/or tuning the phase and/or amplitude response of individual antenna elements. 
     In one embodiment, each antenna element may include a voltage-controlled element. A controller may selectively activate one of the antenna elements within an antenna pixel. The activated antenna element of each antenna pixel is associated with a phase advance most closely approximating a target phase value for each respective antenna pixel. Each antenna pixel may be associated with one or more tunable elements associated with the set of antenna elements in each respective antenna pixel. The controller may selectively adjust the phase of the activated antenna element via the one or more tunable elements associated with the set of antenna elements. 
     The antennas and antenna systems described herein may be configured with waveguides and antenna elements for operation within operational wavelengths suitable for and/or to facilitate wireless power transmission, data communication, imaging, radio frequency (RF) illumination, radar applications, and the like. For example, the various embodiments of the antennas and antenna systems described herein may be configured for operation within gigahertz frequencies, terahertz frequencies, or other electromagnetic frequency bands. In a specific example, the operational wavelength may be approximately 1.24 centimeters. The length of each respective waveguide or antenna pixel may be equal to one-half of the operational wavelength and include four antenna elements with interelement spacings of approximately 0.155 centimeters. A waveguide may have an electrical permittivity of 3.5 to provide a target phase advance to each sequential antenna element. 
     In some embodiments, a two-dimensional antenna may comprise an array of antenna pixels that each include N phase-adjustable antenna elements, where N is an integer greater than one. One or more waveguides may extend through one or more of the antenna pixels. Each waveguide may have a relative permittivity that provides a phase advance across each antenna pixel to provide antenna pixels connected thereto with distinct phase advance values. A beamforming controller may identify a target phase value for each antenna pixel that corresponds to a target beamform for the two-dimensional antenna. The controller may activate and adjust a phase response of one antenna element within each antenna pixel to selectively attain the target phase values. 
     The various antenna pixels may be square or elongated and may be equally or unequally spaced from one another. In some embodiments, the waveguides may be arranged as a plurality of parallel elongated waveguides. A set of phase-adjustable antenna elements may be coupled along the length of each of the elongated waveguides with interelement spacings to associate each antenna element with a distinct phase advance value. The parallel elongated waveguides may each be connected to one or more adjacent elongated waveguide with a phase advance component to provide a specific phase advance between adjacent parallel elongated waveguides. 
     Some of the infrastructure that can be used with embodiments disclosed herein is already available, such as general-purpose computers, computer programming tools and techniques, digital storage media, and communication links. Any of the systems, subsystems, modules, components, and the like that are described herein may be implemented as hardware, firmware, and/or software. Various systems, subsystems, modules, and components are described in terms of the function(s) they perform because such a wide variety of possible implementations exist. For example, it is appreciated that many existing programming languages, hardware devices, frequency bands, circuits, software platforms, networking infrastructures, and/or data stores may be utilized alone or in combination to implement a specific control function. 
     It is also appreciated that two or more of the elements, devices, systems, subsystems, components, modules, etc. that are described herein may be combined as a single element, device, system, subsystem, module, or component. Moreover, many of the elements, devices, systems, subsystems, components, and modules may be duplicated or further divided into discrete elements, devices, systems, subsystems, components, or modules to perform subtasks of those described herein. Any of the embodiments described herein may be combined with any combination of other embodiments described herein. The various permutations and combinations of embodiments are contemplated to the extent that they do not contradict one another. 
     As used herein, a computing device, system, subsystem, module, or controller may include a processor, such as a microprocessor, a microcontroller, logic circuitry, or the like. A processor may include one or more special-purpose processing devices, such as application-specific integrated circuits (ASICs), a programmable array logic (PAL), a programmable logic array (PLA), a programmable logic device (PLD), a field-programmable gate array (FPGA), or another customizable and/or programmable device. The computing device may also include a machine-readable storage device, such as non-volatile memory, static RAM, dynamic RAM, ROM, CD-ROM, disk, tape, magnetic, optical, flash memory, or another machine-readable storage medium. Various aspects of certain embodiments may be implemented using hardware, software, firmware, or a combination thereof. 
     The components of some of the disclosed embodiments are described and illustrated in the figures herein. Many portions thereof could be arranged and designed in a wide variety of different configurations. Furthermore, the features, structures, and operations associated with one embodiment may be applied to or combined with the features, structures, or operations described in conjunction with another embodiment. In many instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of this disclosure. The right to add any described embodiment or feature to any one of the figures and/or as a new figure is explicitly reserved. 
     The embodiments of the systems and methods provided within this disclosure are not intended to limit the scope of the disclosure but are merely representative of possible embodiments. In addition, the steps of a method do not necessarily need to be executed in any specific order, or even sequentially, nor do the steps need to be executed only once. As previously noted, descriptions and variations described in terms of transmitters are equally applicable to receivers, and vice versa. 
       FIG.  1    illustrates an example antenna pixel  100  with four antenna elements  121 ,  123 ,  125 , and  127  connected to a waveguide  110 . In the illustrated embodiment, the waveguide  110  of the antenna pixel  100  includes a stripline  111 . A signal  115  is directed to each of the antenna elements  121 ,  123 ,  125 , and  127  via the stripline  111  within the waveguide  110 . According to various embodiments, the electrical permittivity of the waveguide  110  and/or stripline  111  are selected to provide an incremental phase advance to each antenna element  121 ,  123 ,  125 , and  127 . In the illustrated embodiment, each of the antenna elements comprises a cavity with subwavelength dimensions, an iris  130 , a diode  140 , and a patch  150 . 
     In the illustrated embodiment, the antenna pixel  100  has a length dimension of approximately λ/2, where λ is an operational wavelength of an antenna system of which the antenna pixel  100  is a part. Each of the antenna elements  121 ,  123 ,  125 , and  127  has a dimension of approximately λ/8, such that four antenna elements are coupled to the waveguide  110 . A controller may be in communication with each of the antenna elements  121 ,  123 ,  125 , and  127 . Specifically, the controller may selectively transmit a control signal to one of the diodes  140  of one of the antenna elements  121 ,  123 ,  125  and  127  to selectively activate one of the antenna elements  121 ,  123 ,  125  and  127  and/or adjust a phase response thereof. 
     In some examples, the waveguide  110  may include a substrate, such as an RF-35 substrate with an electrical permittivity of approximately 3.5. The substrate may produce a phase advance in the stripline of −90 degrees across a distance of λ/8, such that each antenna element  121 ,  123 ,  125 , and  127  experiences incremental phase advances of −90 degrees. Each of the antenna pixels may allow for 90 degrees of phase control (e.g., −45 degrees to +45 degrees), such that, when combined with the phase advance experienced by each successive antenna element, the antenna pixel  100  can produce any phase response between 0 degrees and 360 degrees (a 2π phase range) by activating and adjusting one of the antenna elements  121 ,  123 ,  125 , and  127  while the others remain inactive. 
     As discussed above, an antenna may comprise a plurality of antenna pixels that each have a length less than λ/2 and enable a full 2π phase range. In alternative embodiments, an antenna system may include antenna pixels that have a length greater than λ/2 and/or enable a phase range of less than a full 2π. Such embodiments may provide reduced beamforming and/or steerability as compared to embodiments utilizing antenna elements with sub-λ/2 dimensions and/or reduced phase adjustability. 
       FIG.  2 A  illustrates an example antenna pixel  200  with four antenna elements  221 ,  223 ,  225 , and  227  extending from a waveguide  210  in alternating directions. The illustrated arrangement spatially separates the antenna elements  221 ,  223 ,  225 , and  227  to avoid or reduce cross-coupling therebetween. Each of the antenna elements  221 ,  223 ,  225 , and  227  includes a cavity connected to the waveguide  210 , an iris  230 , and a patch  250 . Each of the antenna elements  221 ,  223 ,  225 , and  227  may also include a diode. A controller may selectively activate one of the antenna elements  221 ,  223 ,  225 , and  227  by transmitting a control signal to the diode thereof. As described herein, the waveguide  210  may produce a phase advance across the length of the antenna pixel  200 , and each antenna element  221 ,  223 ,  225 , and  227  may be phase-adjustable by, for example, the controller varying the voltage applied to the diode thereof. 
       FIG.  2 B  illustrates a simulation of the example antenna pixel  200  of  FIG.  2 A  with a phase advance of 360 degrees across the entire antenna pixel  200 . The arrows illustrate the relative phase advance seen by each respective antenna element moving from left to right beginning with 0 degrees and ending at 270 degrees. The relative field strength of each antenna element  221 ,  223 ,  225 , and  227  is illustrated in greyscale. In the illustrated example, the waveguide produces a relative phase advance of 0 degrees at the first antenna element  221 , a relative phase advance of 90 degrees at the second antenna element  223 , a relative phase advance of 180 degrees at the third antenna element  225 , and a relative phase advance of 270 degrees at the fourth antenna element. As previously described, each of the antenna elements  221 ,  223 ,  225 , and  227  may provide 90 degrees of phase adjustability. In the illustrated simulation, the second antenna element  223  is activated and phase-adjusted to operate at the phase advance of 90 degrees, adjusted by 45 degrees in either direction (e.g., 45 degrees to 135 degrees). 
       FIG.  2 C  illustrates an example of an antenna  205  with four antenna pixels  201 ,  202 ,  203 , and  204 . One antenna element  261 ,  262 ,  263 , and  264  is activated in each antenna pixel  201 ,  202 ,  203 , and  204 , respectively, as shown by a white arrow. 
       FIG.  2 D  illustrates an example graph  275  of a simulated beamform  282  formed by the selective activation of the one antenna element  261 ,  262 ,  263 , and  264  within each antenna pixel  201 ,  202 ,  203 , and  204 . 
       FIG.  3    illustrates an example of a reconfigurable antenna  300  at a high level of abstraction. In the illustrated example, the reconfigurable antenna  300  includes  110  antenna pixels ( 11  antenna pixels wide and ten antenna pixels tall). Each antenna pixel is shown with four antenna elements (shown as boxes), one of which is activated (shown as a black box). A controller may determine a target pattern of phase values for the antenna pixels to generate a target beamform. The controller selectively activates one antenna element within each antenna pixel, to the exclusion of the others, and selectively adjusts (e.g., tunes) the phase of each activated antenna element to attain the target pattern of phase values. 
     In alternative embodiments, each antenna pixel may include only three antenna elements instead of four. In still other embodiments, each antenna pixel may include more than four antenna elements. In some embodiments, each antenna pixel may comprise a physically discrete component relative to each other antenna pixel. The discrete antenna pixels may be joined together and connected to a controller to form a functional antenna system. In other embodiments, an array of antenna elements may be conceptually divided up into a plurality of antenna pixels with dimensions of, for example, λ/2 or less. The controller may then selectively activate one of the antenna elements within each antenna pixel to generate a target beamform with reduced or eliminated cross-coupling between activated antenna elements. 
       FIG.  4 A  illustrates a top view of an example antenna pixel  400  with three antenna elements  425 ,  426 , and  427  extending from a waveguide stripline  410 ,  411 , and  412 . The antenna pixel  400  may have length and width dimensions of approximately λ/2. Each antenna element  425 ,  426 , and  427  may include an iris  430 , a diode  440 , and a patch  450 . In various embodiments, the waveguide stripline  410 ,  411 , and  412  may comprise a low-loss stripline, a substrate material, and/or an air-filled waveguide. 
     Each of the antenna elements  425 ,  426 , and  427  may be associated with a different phase advance and have limited or partial phase-adjustability. Collectively, however, the antenna pixel  400  may have a full 2π phase range even though each antenna element  425 ,  426 , and  427  has access to only a portion of the 2π phase range (e.g., 2/3π each). 
       FIG.  4 B  illustrates a cross-sectional view of the example antenna pixel  400  of  FIG.  4 A . Again, the antenna pixel  400  includes three antenna elements  425 ,  426 , and  427 . Each antenna element  425 ,  426 , and  427  includes a waveguide stripline  410 ,  411 , and  412  to excite the iris  430  and patch  450  of each respective antenna element  425 ,  426 , and  427  with different phase advances. A voltage-controlled diode  440  of each respective antenna element  425 ,  426 , and  427  can be adjusted to provide a target phase response. 
       FIG.  4 C  illustrates an example antenna system  405  with a two-dimensional antenna array of the antenna pixel illustrated in  FIG.  4 A  with a beamforming controller  490  connected thereto. The antenna array includes a 4×6 array of antenna pixels  400 , shown as a first column of antenna pixels  400   a - 400   d,  a second column of antenna pixels  400   e - h,  a third column of antenna pixels  400   i - l,  a fourth column of antenna pixels  400   m - p,  a fifth column of antenna pixels  400   q - t,  and a sixth column of antenna pixels  400   u - x.    
     The beamforming controller  490 , may identify a target phase value for each antenna pixel  400   a - x  in the antenna system  405 . The target phase values for each antenna pixel  400   a - x  may be selected to generate a target beamform for transmitting and/or receiving electromagnetic radiation. Each of the antenna elements ( 425 ,  426 , and  427  in  FIGS.  4 A and  4 B ) within a given antenna pixel  400   a - x  is associated with a distinct phase advance relative to the other antenna elements. Accordingly, one of the antenna elements within each antenna pixel  400   a - x  will be associated with a phase advance that most closely approximates the target phase value for the given antenna pixel  400   a - x.    
     The beamforming controller  490  may activate one individual antenna element within each antenna pixel  400   a - x  identified as having a phase advance closest to the target phase value of each respective antenna pixel  400   a - x.  The phase advance associated with each activated antenna element of each antenna pixel  400   a - x  may not exactly match the target phase value of each respective antenna pixel  400   a - x.  However, the beamforming controller  490  may adjust the phase of each of the activated (phase-adjustable) antenna elements to correspond to (e.g., be equal to, approximate, or more closely approximate) the identified target phase value for each respective antenna pixel  400   a - x.    
       FIG.  5 A  illustrates a top view of an example antenna pixel  500  with four offset antenna elements  525 ,  526 ,  527 , and  528  associated with a waveguide or sections of waveguides (illustrated as pattern-filled striplines)  510 ,  511 ,  512 , and  513 . As explicitly labeled for antenna element  525 , each of the antenna elements  525 ,  526 ,  527 , and  528  includes an iris  530 , a diode  540 , and a patch  550 . While many of the illustrated examples include patch-and-iris antenna elements with diodes for activation, it is appreciated that any of a wide variety of alternative types of antenna elements may be utilized, as described herein. A controller may activate one of the staggered antenna elements  525 ,  526 ,  527 , and  528  and/or phase-tune one of the staggered antenna elements  525 ,  526 ,  527 , and  528  to have a particular phase response. The staggered layout provides increased spatial separation to reduce or eliminate cross-coupling between an activated and phase-tuned antenna element and adjacent un-activated or inactive antenna element. 
     As in other embodiments, each of the antenna elements  525 ,  526 ,  527 , and  528  may be associated with a different phase advance and have limited phase-adjustability. Collectively, however, the antenna pixel  500  may have a full 2π phase range even though each antenna element  525 ,  526 ,  527 , and  528  has access to only a portion of the 2π phase range (e.g., each antenna element  525 ,  526 , and  527  may have a phase adjustability of 1/2π or 90 degrees). 
     As previously described, a similar configuration may also be used in a system that provides the antenna pixel  500  with less than the full tunability of a 2π phase range. For example, each of the antenna elements  525 ,  526 ,  527 , and  528  may only offer phase tunability between −30 degrees and +30 degrees, in which case the maximum tunability of the antenna pixel  500  would be 240 degrees. The specific range of tunability depends on the physical spacing of the antenna elements  525 ,  526 ,  527 , and  528  and/or the phase advance provided to each individual antenna element  525 ,  526 ,  527 , and  528 . 
       FIG.  5 B  illustrates a cross-sectional view of one antenna element  525  of the example antenna pixel  500  of  FIG.  5 A . In the illustrated example, a wall, such as a via fence in a printed circuit board (PCB)  595 , may form a waveguide that includes a stripline  510 . The region  531  may comprise an air-filled gap or a substrate material, according to various embodiments. The phase-adjustable antenna element  525  includes an iris  530 , diode  540 , and contact patch  550 . A voltage bias applied to the diode  540  activates and controls the overall phase response of the antenna element  525 . 
       FIG.  5 C  illustrates an antenna system  505  with an example 8×8 antenna array  500   x - n  of antenna pixels, such as the antenna pixel  500  illustrated in  FIG.  5 A . Each of the antenna pixels may include four antenna elements similar to the antenna element  525  illustrated in  FIG.  5 B . As illustrated, the antenna elements within each antenna pixel may be offset with respect to one another and with respect to the antenna elements of adjacent antenna pixels. 
     A beamforming controller  507  may receive, calculate, determine, or otherwise identify a target phase value for each antenna pixel  500  in the array  500   x - n  of antenna pixels. The pattern of target phase values for the array  500   x - n  of antenna elements corresponds to a target beamform of electromagnetic radiation for an operating wavelength or range of wavelengths. The controller may activate the antenna element within each antenna pixel that is associated with a phase advance that most closely approximates the target phase value for each given antenna pixel. The other antenna elements in each antenna pixel may remain deactivated. The controller may adjust the phase of the activated antenna element to deviate from the phase advance value to a phase value more closely approximating the target phase value for each respective antenna pixel. 
       FIG.  6 A  illustrates a block diagram of a top view of an example cavity-based antenna element  625 . As illustrated, the antenna element may include a stripline  610  within a waveguide adjacent to a cavity  631  bounded by walls  695 . The antenna element  625  includes an iris  630  and a voltage-controlled diode  640 . 
       FIG.  6 B  illustrates a block diagram of a cross-sectional view of the example cavity-based antenna element  625 . The illustrated example shows the stripline  610  within a waveguide bounded by walls  695 . A cavity  631  adjacent to the stripline  610  may comprise, for example, PCB material and be excited by the stripline  610  when the diode  640  is activated. Electromagnetic radiation radiates through the iris  630  and out of the antenna element  625  when the diode  640  is activated. A controller may adjust a voltage applied to the diode  640  to attain a target phase of the emitted electromagnetic radiation. 
       FIG.  6 C  illustrates a graph of the phase control region of an example antenna element that is tunable between −45 degrees and +45 degrees. The left vertical axis  645  corresponds to the radiated phase output of the antenna element with respect to the normalized voltage bias shown on the x-axis. The radiated phase output is graphed using a dashed line  635 . The right vertical axis  648  corresponds to the relative strength of the radiated field relative to the normalized voltage bias on the x-axis and is graphed using a solid line  637 . 
     With zero volts applied to the tunable element (e.g., a diode) of the antenna element, the output strength of the antenna element is very low (e.g., approximately −27 dB, as shown on the right vertical axis  648 ). At approximately 0.65 volts, the output strength of the antenna element peaks and has a phase offset of approximately zero degrees, as shown on the left vertical axis  645 . The output strength remains relatively high between approximately 0.61 volts and 0.71 volts while exhibiting a phase variation between −45 degrees and +45 degrees. This is illustrated on the graph as a shadowed 45-degree phase control region  650 . 
     Alternative embodiments may utilize voltage variations between, for example, 0.63 volts and 0.67 volts for a more even output strength with a smaller range of phase control. Different configurations, sizes of cavities, patch materials, diode types, and other variations in the specific antenna element may be utilized to modify the exact amplitude and phase characteristics relative to the voltage input. For example, a different configuration may use a voltage-controlled diode with an adjustable phase response between −30 degrees and 30 degrees for applied voltages between 2 and 3 volts. As another example, tunable elements such as mems devices, varactor diodes, liquid crystal tunable elements, and the like may be utilized that have different phase and amplitude responses. 
     An antenna pixel (such as any of the various antenna pixels described herein) may include multiple antenna elements with a response similar (e.g., identical or a variation thereof) to that shown in  FIG.  6 C . Each of the antenna elements within the antenna pixel may be associated with a different phase advance. A controller may identify a target phase value for the antenna pixel and identify which of the antenna elements is associate with a phase advance closest to the target phase value. The controller may activate the identified antenna element by applying a voltage bias. The voltage may be varied to select a specific phase shift relative to the base phase—i.e., the phase advance provided by the waveguide. In alternative embodiments, a current may be used to adjust the phase of the antenna element. 
       FIG.  7 A  illustrates a portion of an example antenna  700  with four parallel elongated waveguides with phase-adjustable antenna elements  725 - 758  coupled thereto. As in various embodiments described herein, each of the antenna elements  725 - 758  may be associated with a specific phase advance provided by the waveguide. Each of the antenna elements  725 - 758  may be phase adjustable within a range of phases. Each row of antenna elements may contribute one antenna element to an antenna pixel. In the illustrated example, the antenna elements in each row are offset from those in the adjacent row. In the illustrated example, a first antenna pixel  701  includes antenna elements  725 ,  735 ,  745 , and  755 . A second antenna pixel  702  includes antenna elements  726 ,  736 ,  746 , and  756 . A third antenna pixel includes antenna elements  727 ,  737 ,  747 , and  757 . A fourth antenna pixel includes antenna elements  728 ,  738 ,  748 , and  758 . A controller may activate and adjust the phase response of one of the antenna elements in each antenna pixel  701 - 704  to select a phase value for each respective antenna pixel. Any number of rows and columns of parallel elongated waveguides may be combined to form antennas of varying sizes for different applications, beamforming capabilities, and steerability. 
     As illustrated, multiple parallel elongated waveguides may be connected to the same source and/or detector. The parallel elongated waveguides may be connected via ports  770 ,  773 , and  775  with defined phase shifts to ensure that each subsequent row of antenna elements is provided with the correct phase advance. 
       FIG.  7 B  illustrates a simulated activation and phase adjustment of one antenna element  728 ,  737 ,  746 , and  755  in each antenna pixel  701 ,  702 ,  703 , and  704  of the example antenna  700 . A controller may tune each of the activated antenna elements to have a phase response approximating a target phase value for each respective antenna pixel. 
       FIG.  8    illustrates a portion of an example antenna  800  with four parallel elongated waveguides connected with meandering turns with phase-adjustable antenna elements that provide the defined phase shifts described in conjunction with  FIG.  7 A . Antenna elements  825 - 858  are connected to the four parallel elongated waveguides to form four distinct antenna pixels  801 ,  802 ,  803 , and  804  (shown divided by dashed lines). 
     The four parallel elongated waveguides are connected via meandering turns that provide a specific phase advance to the adjacent waveguide section. In the illustrated example, each of the meandering turns  890  provides 135 degrees of relative phase shift, while meandering turn  895  provides −45 degrees of relative phase shift. The specific examples are merely illustrative, and it is appreciated that variations may be utilized for a specific application to attain any desired or target phase advance between adjacent waveguides. 
       FIG.  9    illustrates a flowchart of an example method  900  of beamforming by activating one antenna element within each subwavelength antenna region (e.g., antenna pixel). A controller may identify, at  910 , a target beamform. The controller may identify, at  920 , a target phase value for each antenna region of an antenna array. The controller may activate, at  930 , one antenna element in each antenna region and then tune, at  940 , the activated antenna element in each respective antenna region to approximate the respective target phase value. 
       FIG.  10    illustrates a flowchart of an example method  1000  of beamforming by selectively activating one antenna element within each region of an array of subwavelength-spaced antenna elements. A region of the reconfigurable antenna may define an antenna pixel. For example, the region may define an antenna pixel with a dimension of one-half of an operational wavelength or less to achieve full phase tunability. Other embodiments may utilize antenna pixels with larger sizes with slightly reduced functionality that may be suitable for some applications. 
     In the specific example described, a controller may identify, at  1010 , a target beamform for a reconfigurable antenna with a plurality of antenna pixels, each of which includes at least two antenna elements. The controller may identify, at  1020 , a target phase value for each antenna pixel to attain an antenna phase pattern corresponding to the target beamform. 
     The controller may activate, at  1030 , the one antenna element in each antenna pixel that is identified as being associated with a phase advance approximating the target phase value for each respective antenna pixel. The controller may adjust, at  1040 , a phase response of each activated antenna element to approximate the antenna phase pattern corresponding to the target beamform. In embodiments in which each antenna pixel includes only two antenna elements, one-half of the antenna elements are activated and phase-adjusted to generate the target beamform. In embodiments in which each antenna pixel includes four antenna elements, one-fourth of the antenna elements are activated and phase-adjusted to generate the target beamform. Similarly, in embodiments in which each antenna pixel includes six antenna elements, one-sixth of the antenna elements are activated and phase-adjusted to generate the target beamform. 
       FIG.  11 A  illustrates a simplified block diagram of four antenna pixels, labeled Pixel 0, Pixel 1, Pixel 2, and Pixel 3. Each antenna pixel includes four antenna elements, with the antenna elements  1101 ,  1102 ,  1103 , and  1104  labeled within Pixel 0. The location at which the first antenna element  1101  radiates electromagnetic radiation can be described in terms of a relative horizontal and vertical displacement, (X 1 , Y 1 ). The location at which the second antenna element  1102  radiates electromagnetic radiation can be described in terms of a relative horizontal and vertical displacement, (X 2 , Y 2 ). The location at which the third antenna element  1103  radiates electromagnetic radiation can be described in terms of a relative horizontal and vertical displacement, (X 3 , Y 3 ). The location at which the fourth antenna element  1104  radiates electromagnetic radiation can be described in terms of a relative horizontal and vertical displacement, (X 4 , Y 4 ). The center location  1100  of the antenna pixel can be described in terms of a relative horizontal and vertical displacement (X 0 , Y 0 ). 
       FIG.  11 B  illustrates a flowchart of an example method  1150  of beamforming by activating one antenna element within each antenna pixel, with reference to the antenna element locations and/or the center location  1100  of the antenna pixel shown in  FIG.  11 A . A system may identify, at  1152 , a target beamform for an antenna. The system may identify, at  1154 , target phase values for the location of each antenna element within each antenna pixel to attain the target beamform. With reference to  FIG.  11 A , the system may determine a target phase value for each location (X 1 , Y 1 ), (X 2 , Y 2 ), (X 3 , Y 3 ), and (X 4 , Y 4 ) associated with each of the first, second, third, and fourth antenna elements, respectively. The target phase values for each antenna element within each antenna pixel may vary since they are in slightly different locations in the antenna. 
     For each antenna pixel, the system may evaluate, at  1156 , if any antenna element can be tuned to its unique target phase value. If one or more of the antenna elements can be tuned to its calculated target phase value, the antenna element that requires the least amount of tuning is activated and tuned to attain the target phase value, at  1158 . Only one antenna element in each antenna pixel is activated. 
     If none of the antenna elements in the antenna pixel can be tuned to their unique target phase values, then the system may calculate, at  1160 , a target phase value for the center of the antenna pixel (X 0 , Y 0 ). The system may then identify and activate, at  1162 , which of the antenna elements within the antenna pixel can be tuned to (or most closely approximate) the target phase value calculated for the center of the antenna pixel. The evaluation process is completed for each of the antenna pixels sequentially or in parallel. 
     This disclosure has been made with reference to various exemplary embodiments, including the best mode. However, those skilled in the art will recognize that changes and modifications may be made to the exemplary embodiments without departing from the scope of the present disclosure. While the principles of this disclosure have been shown in various embodiments, many modifications of structure, arrangements, proportions, elements, materials, and components may be adapted for a specific environment and/or operating requirements without departing from the principles and scope of this disclosure. These and other changes or modifications are intended to be included within the scope of the present disclosure. 
     This disclosure is to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope thereof. As used herein, all references to number ranges in the description and claims are intended to be inclusive of the bounding numbers, unless explicitly stated otherwise. For example, a range described as being between 1 and 10 is understood to encompass all numbers from 1 to 10, including the numbers 1 and 10. Various benefits, advantages, or solutions to problems may be described above with regard to the various embodiments. However, benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential feature or element. This disclosure should, therefore, be determined to encompass at least the following claims and permutations thereof.