PATENT DOCUMENT

Publication Number: US-12044788-B2
Application Number: US-202117383275-A
Country: US
Kind Code: B2

Title: Electronic device having angle of arrival detection capabilities

Abstract:
An electronic device may be provided with wireless circuitry that includes first, second, and third antennas used to determine the position and orientation of the electronic device relative to external equipment. The antennas may include patch elements on respective substrates mounted to a flexible printed circuit. Each substrate may include fences of conductive vias that are coupled to ground and that laterally surround the corresponding patch element. Control circuitry may identify phase differences between the first and second antennas and between the second and third antennas and may identify an angle of arrival of received ultra-wideband signals using the phase differences. The control circuitry may compare the phase differences to a set of predetermined surfaces of phase differences to identify environmental loading conditions for the antenna. The control circuitry may correct the angle of arrival using offsets identified based on the environmental loading conditions.

Claims:
What is claimed is: 
     
       1. An electronic device comprising:
 first and second antennas configured to receive radio-frequency signals; and 
 control circuitry coupled to the first and second antennas, wherein the control circuitry is configured to:
 identify a phase difference between the radio-frequency signals received by the first antenna and the radio-frequency signals received by the second antenna, 
 identify an angle of arrival value for the radio-frequency signals based on the identified phase difference, 
 identify an offset value based on the identified phase difference and a predetermined set of phase difference values, and 
 generate a corrected angle of arrival value by adjusting the angle of arrival value using the identified offset value. 
 
 
     
     
       2. The electronic device defined in  claim 1 , wherein the predetermined set of phase difference values comprises a plurality of curves of phase difference values, each curve corresponding to a respective impedance loading condition for the first and second antennas. 
     
     
       3. The electronic device defined in  claim 2 , wherein the control circuitry is configured to identify the offset value by identifying a curve in the plurality of curves that matches the identified phase difference. 
     
     
       4. The electronic device defined in  claim 2 , wherein the respective impedance loading conditions include a condition indicative of the electronic device being loaded by a removable case for the electronic device. 
     
     
       5. The electronic device defined in  claim 2 , wherein the respective impedance loading conditions include a condition indicative of one of the first and second antennas being loaded by a body part. 
     
     
       6. The electronic device defined in  claim 1 , wherein the radio-frequency signals comprise ultra-wideband signals at a frequency between 5.0 GHz and 8.3 GHz. 
     
     
       7. The electronic device defined in  claim 1  further comprising:
 a third antenna configured to receive the radio-frequency signals, wherein the control circuitry is configured to:
 identify an additional phase difference between the radio-frequency signals received by the second antenna and the radio-frequency signals received by the third antenna, the angle of arrival value for the radio-frequency signals being further associated with the identified additional phase difference. 
 
 
     
     
       8. The electronic device defined in  claim 7 , wherein the angle of arrival value for the radio-frequency signals comprises a three-dimensional angle of arrival value for the radio-frequency signals. 
     
     
       9. The electronic device defined in  claim 8 , wherein the control circuitry is configured to identify the three-dimensional angle of arrival value based on the identified phase difference between the radio-frequency signals received by the first antenna and the radio-frequency signals received by the second antenna and based on the identified additional phase difference between the radio-frequency signals received by the second antenna and the radio-frequency signals received by the third antenna, the three-dimensional angle of arrival value being indicative of an azimuth angle and an elevation angle. 
     
     
       10. The electronic device defined in  claim 7 , wherein the predetermined set of phase difference values include a first subset of phase difference values indicative of phase differences between signals received by the first and second antennas under a corresponding first set of impedance loading conditions and a second subset of phase difference values indicative of phase differences between signals received by the second and third antennas under a corresponding second set of impedance loading conditions. 
     
     
       11. The electronic device defined in  claim 10 , wherein the offset value is indicative of an impedance loading condition in one of the first or second sets of impedance loading conditions. 
     
     
       12. The electronic device defined in  claim 1 , wherein the offset value is indicative of one or more shifts in phase values, based on a presence of an external object. 
     
     
       13. The electronic device defined in  claim 1 , wherein the control circuitry is configured to identify information indicative of the first and second antennas operating in a non-free-space environment prior to identifying the offset value. 
     
     
       14. The electronic device defined in  claim 13 , wherein the control circuitry is configured to identify the information indicative of the first and second antennas operating in the non-free-space environment by comparing the identified phase difference between the radio-frequency signals received by the first antenna and the radio-frequency signals received by the second antenna with a predetermined free-space phase difference associated with the first and second antennas. 
     
     
       15. The electronic device defined in  claim 14 , wherein the control circuitry is configured to store the predetermined free-space phase difference and the predetermined set of phase difference values. 
     
     
       16. The electronic device defined in  claim 1  further comprising:
 phase measurement circuitry coupled to the first and second antennas and configured to generate a first phase measurement based on the radio-frequency signals received by the first antenna and to generate a second phase measurement based on the radio-frequency signals received by the second antenna. 
 
     
     
       17. The electronic device defined in  claim 16 , wherein the control circuitry is configured to identify the phase difference between the radio-frequency signals received by the first antenna and the radio-frequency signals received by the second antenna by subtracting the second phase measurement from the first phase measurement. 
     
     
       18. A method of operating wireless communications circuitry, the method comprising:
 receiving radio-frequency signals using first and second antennas; 
 identifying a phase difference between the radio-frequency signals received using the first antenna and the radio-frequency signals received using the second antenna; 
 identifying an angle of arrival value for the radio-frequency signals based on the identified phase difference; 
 identifying an offset value based on the identified phase difference and a predetermined set of phase difference values; and 
 generating a corrected angle of arrival value by adjusting the angle of arrival value using the identified offset value. 
 
     
     
       19. The method defined in  claim 18  further comprising:
 receiving the radio-frequency signals using a third antenna; 
 identifying an additional phase difference between the radio-frequency signals received using the second antenna and the radio-frequency signals received using the third antenna, wherein the angle of arrival value for the radio-frequency signals comprises a three-dimensional angle of arrival value for the radio-frequency signals; and 
 identifying the three-dimensional angle of arrival value based on the identified phase difference between the radio-frequency signals received using the first antenna and the radio-frequency signals received using the second antenna and based on the identified additional phase difference between the radio-frequency signals received using the second antenna and the radio-frequency signals received using the third antenna. 
 
     
     
       20. An electronic device comprising:
 first, second, and third antennas configured to receive radio-frequency signals; and 
 control circuitry coupled to the first, second, and third antennas, wherein the control circuitry is configured to:
 identify a first phase difference between the radio-frequency signals received by the first antenna and the radio-frequency signals received by the second antenna and a second phase difference between the radio-frequency signals received by the second antenna and the radio-frequency signals received by the third antenna, 
 identify a three-dimensional angle of arrival for the radio-frequency signals based on the first and second identified phase differences, 
 identify an offset value based on the first and second identified phase differences and based on a predetermined set of phase difference values, and 
 generate an updated three-dimensional angle of arrival by adjusting the identified three-dimensional angle of arrival using the identified offset value.

Description:
This application is a divisional of U.S. patent application Ser. No. 16/035,325, filed Jul. 13, 2018, and hereby incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     This relates generally to electronic devices and, more particularly, to electronic devices with wireless communications circuitry. 
     Electronic devices often include wireless communications circuitry. For example, cellular telephones, computers, and other devices often contain antennas and wireless transceivers for supporting wireless communications. 
     It can be challenging to form electronic device antenna structures with desired attributes. In some wireless devices, antennas are bulky. In other devices, antennas are compact, but are sensitive to the position of the antennas relative to external objects. If care is not taken, antennas may become detuned, may emit wireless signals with a power that is more or less than desired, or may otherwise not perform as expected. 
     Some electronic devices perform location detection operations to detect the location of an external device based on an angle of arrival of signals received from the external device (using multiple antennas). If care is not taken, external objects can block or load one or more of the antennas and can make it difficult to accurately estimate the angle of arrival. 
     It would therefore be desirable to be able to provide wireless circuitry for electronic devices having improved angle of arrival detection capabilities. 
     SUMMARY 
     An electronic device may be provided with wireless circuitry and control circuitry. The wireless circuitry may include multiple antennas and transceiver circuitry. The wireless circuitry may include antenna structures used to determine the position and orientation of the electronic device relative to external wireless equipment. The antenna structures may determine the position and orientation of the electronic device relative to external wireless equipment at least in part by measuring the angle of arrival of radio-frequency signals from the external wireless equipment. 
     An antenna module may include a flexible printed circuit and first, second, and third substrates mounted to the flexible printed circuit. A first patch antenna may include a first antenna resonating element on the first substrate. A second patch antenna may include a second antenna resonating element on the second substrate. A third patch antenna may include a third antenna resonating element on the third substrate. Ground traces may be formed in the first, second, and third substrates. Fences of conductive vias may extend through the first, second, and third substrates and may laterally surround the corresponding antenna resonating elements. 
     The electronic device may include a dielectric cover layer and a conductive layer coupled to the dielectric cover layer. The antenna module may be mounted within the electronic device so that the first, second, and third antennas are aligned with one or more apertures in the conductive layer. The dielectric cover layer may form a rear housing wall for the electronic device. 
     The first, second, and third antennas may receive radio-frequency signals such as ultra-wideband signals from external wireless equipment. Control circuitry in the electronic device may measure a first phase difference between the first and second antennas and may measure a second phase difference between the second and third antennas from the received ultra-wideband signals. The control circuitry may generate an angle of arrival value for the received ultra-wideband signals based on the first and second phase differences. The control circuitry may compare the first and second phase differences to a set of predetermined environment-specific curves or surfaces of phase difference values. The control circuitry may identify predetermined curves or surfaces in the set that match the first and second phase differences. The control circuitry may determine an environmental loading condition for the antennas based on the identified curves or surfaces. The control circuitry may identify predetermined offset values corresponding to the determined environmental loading condition. The control circuitry may generate a corrected angle of arrival value by adjusting the angle of arrival value using the identified offset values. 
     The corrected angle of arrival may accurately reflect the location of the wireless communications equipment relative to the electronic device. In this way, the control circuitry may accurately determine the location of the wireless communications equipment regardless of whether the antennas are being loaded by external objects. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a perspective view of an illustrative electronic device in accordance with an embodiment. 
         FIG.  2    is a schematic diagram of illustrative circuitry in an electronic device in accordance with an embodiment. 
         FIG.  3    is a diagram of illustrative wireless circuitry in accordance with an embodiment. 
         FIG.  4    is a diagram of an illustrative electronic device in wireless communication with an external node in a network in accordance with an embodiment. 
         FIG.  5    is a diagram showing how the location (e.g., range and angle of arrival) of an external node in a network may be determined relative to an electronic device in accordance with an embodiment. 
         FIG.  6    is a diagram showing how illustrative antennas in an electronic device may be used for detecting angle of arrival in accordance with an embodiment. 
         FIG.  7    is a diagram of an illustrative patch antenna in accordance with an embodiment. 
         FIG.  8    is a top view of an illustrative ultra-wide band antenna module having three patch antennas for computing the angle of arrival of incoming radio-frequency signals in accordance with an embodiment. 
         FIG.  9    is a cross-sectional side view of an illustrative ultra-wide band antenna module mounted within an electronic device in accordance with an embodiment. 
         FIG.  10    is a flow chart of illustrative steps involved in operating an ultra-wide band antenna module to compute angle of arrival regardless of environmental loading conditions in accordance with an embodiment. 
         FIG.  11    is an illustrative plot of phase difference on arrival as a function of elevation angle for radio-frequency signals received by an antenna under different environmental loading conditions in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Electronic devices such as electronic device  10  of  FIG.  1    may be provided with wireless communications circuitry. The wireless communications circuitry may be used to support wireless communications in multiple wireless communications bands. Communications bands handled by the wireless communications circuitry can include satellite navigation system communications bands, cellular telephone communications bands, wireless local area network communications bands, near-field communications bands, ultra-wideband communications bands, or other wireless communications bands. 
     The wireless communications circuitry may include one or more antennas. The antennas can include patch antennas, loop antennas, inverted-F antennas, strip antennas, planar inverted-F antennas, slot antennas, hybrid antennas that include antenna structures of more than one type, or other suitable antennas. Conductive structures for the antennas may, if desired, be formed from conductive electronic device structures. 
     The conductive electronic device structures may include conductive housing structures. The housing structures may include peripheral structures such as peripheral conductive structures that run around the periphery of an electronic device. The peripheral conductive structures may serve as a bezel for a planar structure such as a display, may serve as sidewall structures for a device housing, may have portions that extend upwards from an integral planar rear housing (e.g., to form vertical planar sidewalls or curved sidewalls), and/or may form other housing structures. 
     Gaps may be formed in the peripheral conductive structures that divide the peripheral conductive structures into peripheral segments. One or more of the segments may be used in forming one or more antennas for electronic device  10 . Antennas may also be formed using an antenna ground plane and/or an antenna resonating element formed from conductive housing structures (e.g., internal and/or external structures, support plate structures, etc.). 
     Electronic device  10  may be a portable electronic device or other suitable electronic device. For example, electronic device  10  may be a laptop computer, a tablet computer, a somewhat smaller device such as a wrist-watch device, pendant device, headphone device, earpiece device, or other wearable or miniature device, a handheld device such as a cellular telephone, a media player, or other small portable device. Device  10  may also be a set-top box, a desktop computer, a display into which a computer or other processing circuitry has been integrated, a display without an integrated computer, or other suitable electronic equipment. 
     Device  10  may include a housing such as housing  12 . Housing  12 , which may sometimes be referred to as a case, may be formed of plastic, glass, ceramics, fiber composites, metal (e.g., stainless steel, aluminum, etc.), other suitable materials, or a combination of these materials. In some situations, parts of housing  12  may be formed from dielectric or other low-conductivity material (e.g., glass, ceramic, plastic, sapphire, etc.). In other situations, housing  12  or at least some of the structures that make up housing  12  may be formed from metal elements. 
     Device  10  may, if desired, have a display such as display  14 . Display  14  may be mounted on the front face of device  10 . Display  14  may be a touch screen that incorporates capacitive touch electrodes or may be insensitive to touch. The rear face of housing  12  (i.e., the face of device  10  opposing the front face of device  10 ) may have a substantially planar housing wall such as rear housing wall  12 R (e.g., a planar housing wall). Rear housing wall  12 R may have slots that pass entirely through the rear housing wall and that therefore separate portions of housing  12  from each other. Rear housing wall  12 R may include conductive portions and/or dielectric portions. If desired, rear housing wall  12 R may include a planar metal layer covered by a thin layer or coating of dielectric such as glass, plastic, sapphire, or ceramic. Housing  12  may also have shallow grooves that do not pass entirely through housing  12 . The slots and grooves may be filled with plastic or other dielectric. If desired, portions of housing  12  that have been separated from each other (e.g., by a through slot) may be joined by internal conductive structures (e.g., sheet metal or other metal members that bridge the slot). 
     Housing  12  may include peripheral housing structures such as peripheral structures  12 W. Peripheral structures  12 W and conductive portions of rear housing wall  12 R may sometimes be referred to herein collectively as conductive structures of housing  12 . Peripheral structures  12 W may run around the periphery of device  10  and display  14 . In configurations in which device  10  and display  14  have a rectangular shape with four edges, peripheral structures  12 W may be implemented using peripheral housing structures that have a rectangular ring shape with four corresponding edges and that extend from rear housing wall  12 R to the front face of device  10  (as an example). Peripheral structures  12 W or part of peripheral structures  12 W may serve as a bezel for display  14  (e.g., a cosmetic trim that surrounds all four sides of display  14  and/or that helps hold display  14  to device  10 ) if desired. Peripheral structures  12 W may, if desired, form sidewall structures for device  10  (e.g., by forming a metal band with vertical sidewalls, curved sidewalls, etc.). 
     Peripheral structures  12 W may be formed of a conductive material such as metal and may therefore sometimes be referred to as peripheral conductive housing structures, conductive housing structures, peripheral metal structures, peripheral conductive sidewalls, peripheral conductive sidewall structures, conductive housing sidewalls, peripheral conductive housing sidewalls, sidewalls, sidewall structures, or a peripheral conductive housing member (as examples). Peripheral conductive housing structures  12 W may be formed from a metal such as stainless steel, aluminum, or other suitable materials. One, two, or more than two separate structures may be used in forming peripheral conductive housing structures  12 W. 
     It is not necessary for peripheral conductive housing structures  12 W to have a uniform cross-section. For example, the top portion of peripheral conductive housing structures  12 W may, if desired, have an inwardly protruding lip that helps hold display  14  in place. The bottom portion of peripheral conductive housing structures  12 W may also have an enlarged lip (e.g., in the plane of the rear surface of device  10 ). Peripheral conductive housing structures  12 W may have substantially straight vertical sidewalls, may have sidewalls that are curved, or may have other suitable shapes. In some configurations (e.g., when peripheral conductive housing structures  12 W serve as a bezel for display  14 ), peripheral conductive housing structures  12 W may run around the lip of housing  12  (i.e., peripheral conductive housing structures  12 W may cover only the edge of housing  12  that surrounds display  14  and not the rest of the sidewalls of housing  12 ). 
     Rear housing wall  12 R may lie in a plane that is parallel to display  14 . In configurations for device  10  in which some or all of rear housing wall  12 R is formed from metal, it may be desirable to form parts of peripheral conductive housing structures  12 W as integral portions of the housing structures forming rear housing wall  12 R. For example, rear housing wall  12 R of device  10  may include a planar metal structure and portions of peripheral conductive housing structures  12 W on the sides of housing  12  may be formed as flat or curved vertically extending integral metal portions of the planar metal structure (e.g., housing structures  12 R and  12 W may be formed from a continuous piece of metal in a unibody configuration). Housing structures such as these may, if desired, be machined from a block of metal and/or may include multiple metal pieces that are assembled together to form housing  12 . Rear housing wall  12 R may have one or more, two or more, or three or more portions. Peripheral conductive housing structures  12 W and/or conductive portions of rear housing wall  12 R may form one or more exterior surfaces of device  10  (e.g., surfaces that are visible to a user of device  10 ) and/or may be implemented using internal structures that do not form exterior surfaces of device  10  (e.g., conductive housing structures that are not visible to a user of device  10  such as conductive structures that are covered with layers such as thin cosmetic layers, protective coatings, and/or other coating layers that may include dielectric materials such as glass, ceramic, plastic, or other structures that form the exterior surfaces of device  10  and/or serve to hide peripheral conductive structures  12 W and/or conductive portions of rear housing wall  12 R from view of the user). 
     Display  14  may have an array of pixels that form an active area AA that displays images for a user of device  10 . For example, active area AA may include an array of display pixels. The array of pixels may be formed from liquid crystal display (LCD) components, an array of electrophoretic pixels, an array of plasma display pixels, an array of organic light-emitting diode display pixels or other light-emitting diode pixels, an array of electrowetting display pixels, or display pixels based on other display technologies. If desired, active area AA may include touch sensors such as touch sensor capacitive electrodes, force sensors, or other sensors for gathering a user input. 
     Display  14  may have an inactive border region that runs along one or more of the edges of active area AA. Inactive area IA may be free of pixels for displaying images and may overlap circuitry and other internal device structures in housing  12 . To block these structures from view by a user of device  10 , the underside of the display cover layer or other layers in display  14  that overlaps inactive area IA may be coated with an opaque masking layer in inactive area IA. The opaque masking layer may have any suitable color. 
     Display  14  may be protected using a display cover layer such as a layer of transparent glass, clear plastic, transparent ceramic, sapphire, or other transparent crystalline material, or other transparent layer(s). The display cover layer may have a planar shape, a convex curved profile, a shape with planar and curved portions, a layout that includes a planar main area surrounded on one or more edges with a portion that is bent out of the plane of the planar main area, or other suitable shapes. The display cover layer may cover the entire front face of device  10 . In another suitable arrangement, the display cover layer may cover substantially all of the front face of device  10  or only a portion of the front face of device  10 . Openings may be formed in the display cover layer. For example, an opening may be formed in the display cover layer to accommodate a button. An opening may also be formed in the display cover layer to accommodate ports such as speaker port  16  or a microphone port. Openings may be formed in housing  12  to form communications ports (e.g., an audio jack port, a digital data port, etc.) and/or audio ports for audio components such as a speaker and/or a microphone if desired. 
     Display  14  may include conductive structures such as an array of capacitive electrodes for a touch sensor, conductive lines for addressing pixels, driver circuits, etc. Housing  12  may include internal conductive structures such as metal frame members and a planar conductive housing member (sometimes referred to as a backplate) that spans the walls of housing  12  (i.e., a substantially rectangular sheet formed from one or more metal parts that is welded or otherwise connected between opposing sides of peripheral conductive structures  12 W). The backplate may form an exterior rear surface of device  10  or may be covered by layers such as thin cosmetic layers, protective coatings, and/or other coatings that may include dielectric materials such as glass, ceramic, plastic, or other structures that form the exterior surfaces of device  10  and/or serve to hide the backplate from view of the user. Device  10  may also include conductive structures such as printed circuit boards, components mounted on printed circuit boards, and other internal conductive structures. These conductive structures, which may be used in forming a ground plane in device  10 , may extend under active area AA of display  14 , for example. 
     In regions  22  and  20 , openings may be formed within the conductive structures of device  10  (e.g., between peripheral conductive housing structures  12 W and opposing conductive ground structures such as conductive portions of rear housing wall  12 R, conductive traces on a printed circuit board, conductive electrical components in display  14 , etc.). These openings, which may sometimes be referred to as gaps, may be filled with air, plastic, and/or other dielectrics and may be used in forming slot antenna resonating elements for one or more antennas in device  10 , if desired. 
     Conductive housing structures and other conductive structures in device  10  may serve as a ground plane for the antennas in device  10 . The openings in regions  22  and  20  may serve as slots in open or closed slot antennas, may serve as a central dielectric region that is surrounded by a conductive path of materials in a loop antenna, may serve as a space that separates an antenna resonating element such as a strip antenna resonating element or an inverted-F antenna resonating element from the ground plane, may contribute to the performance of a parasitic antenna resonating element, or may otherwise serve as part of antenna structures formed in regions  22  and  20 . If desired, the ground plane that is under active area AA of display  14  and/or other metal structures in device  10  may have portions that extend into parts of the ends of device  10  (e.g., the ground may extend towards the dielectric-filled openings in regions  22  and  20 ), thereby narrowing the slots in regions  22  and  20 . 
     In general, device  10  may include any suitable number of antennas (e.g., one or more, two or more, three or more, four or more, etc.). The antennas in device  10  may be located at opposing first and second ends of an elongated device housing (e.g., ends at regions  22  and  20  of device  10  of  FIG.  1   ), along one or more edges of a device housing, in the center of a device housing, in other suitable locations, or in one or more of these locations. The arrangement of  FIG.  1    is merely illustrative. 
     Portions of peripheral conductive housing structures  12 W may be provided with peripheral gap structures. For example, peripheral conductive housing structures  12 W may be provided with one or more gaps such as gaps  18 , as shown in  FIG.  1   . The gaps in peripheral conductive housing structures  12 W may be filled with dielectric such as polymer, ceramic, glass, air, other dielectric materials, or combinations of these materials. Gaps  18  may divide peripheral conductive housing structures  12 W into one or more peripheral conductive segments. There may be, for example, two peripheral conductive segments in peripheral conductive housing structures  12 W (e.g., in an arrangement with two of gaps  18 ), three peripheral conductive segments (e.g., in an arrangement with three of gaps  18 ), four peripheral conductive segments (e.g., in an arrangement with four of gaps  18 ), six peripheral conductive segments (e.g., in an arrangement with six gaps  18 ), etc. The segments of peripheral conductive housing structures  12 W that are formed in this way may form parts of antennas in device  10 . 
     If desired, openings in housing  12  such as grooves that extend partway or completely through housing  12  may extend across the width of the rear wall of housing  12  and may penetrate through the rear wall of housing  12  to divide the rear wall into different portions. These grooves may also extend into peripheral conductive housing structures  12 W and may form antenna slots, gaps  18 , and other structures in device  10 . Polymer or other dielectric may fill these grooves and other housing openings. In some situations, housing openings that form antenna slots and other structure may be filled with a dielectric such as air. 
     In order to provide an end user of device  10  with as large of a display as possible (e.g., to maximize an area of the device used for displaying media, running applications, etc.), it may be desirable to increase the amount of area at the front face of device  10  that is covered by active area AA of display  14 . Increasing the size of active area AA may reduce the size of inactive area IA within device  10 . This may reduce the area behind display  14  that is available for antennas within device  10 . For example, active area AA of display  14  may include conductive structures that serve to block radio-frequency signals handled by antennas mounted behind active area AA from radiating through the front face of device  10 . It would therefore be desirable to be able to provide antennas that occupy a small amount of space within device  10  (e.g., to allow for as large of a display active area AA as possible) while still allowing the antennas to communicate with wireless equipment external to device  10  with satisfactory efficiency bandwidth. 
     In a typical scenario, device  10  may have one or more upper antennas and one or more lower antennas (as an example). An upper antenna may, for example, be formed at the upper end of device  10  in region  20 . A lower antenna may, for example, be formed at the lower end of device  10  in region  22 . The antennas may be used separately to cover identical communications bands, overlapping communications bands, or separate communications bands. The antennas may be used to implement an antenna diversity scheme or a multiple-input-multiple-output (MIMO) antenna scheme. 
     Antennas in device  10  may be used to support any communications bands of interest. For example, device  10  may include antenna structures for supporting local area network communications, voice and data cellular telephone communications, global positioning system (GPS) communications or other satellite navigation system communications, Bluetooth® communications, near-field communications, ultra-wideband communications, etc. 
     A schematic diagram showing illustrative components that may be used in device  10  is shown in  FIG.  2   . As shown in  FIG.  2   , device  10  may include storage and processing circuitry such as control circuitry  28 . Control circuitry  28  may include storage such as hard disk drive storage, nonvolatile memory (e.g., flash memory or other electrically-programmable-read-only memory configured to form a solid-state drive), volatile memory (e.g., static or dynamic random-access-memory), etc. Processing circuitry in control circuitry  28  may be used to control the operation of device  10 . This processing circuitry may be based on one or more microprocessors, microcontrollers, digital signal processors, application specific integrated circuits, etc. 
     Control circuitry  28  may be used to run software on device  10 , such as internet browsing applications, voice-over-internet-protocol (VOIP) telephone call applications, email applications, media playback applications, operating system functions, etc. To support interactions with external equipment, control circuitry  28  may be used in implementing communications protocols. Communications protocols that may be implemented using control circuitry  28  include internet protocols, wireless local area network (WLAN) protocols (e.g., IEEE 802.11 protocols—sometimes referred to as WiFi®), protocols for other short-range wireless communications links such as the Bluetooth® protocol or other wireless personal area network (WPAN) protocols, cellular telephone protocols, MIMO protocols, antenna diversity protocols, satellite navigation system protocols, millimeter wave communications protocols, IEEE 802.15.4 ultra-wideband communications protocols or other ultra-wideband communications protocols, etc. 
     Input-output circuitry  44  may include input-output devices  32 . Input-output devices  32  may be used to allow data to be supplied to device  10  and to allow data to be provided from device  10  to external devices. Input-output devices  32  may include user interface devices, data port devices, and other input-output components. For example, input-output devices  32  may include touch screens, displays without touch sensor capabilities, buttons, scrolling wheels, touch pads, key pads, keyboards, microphones, cameras, buttons, speakers, status indicators, light sources, audio jacks and other audio port components, vibrators or other haptic feedback engines, digital data port devices, light sensors (e.g., infrared light sensors, visible light sensors, etc.), light-emitting diodes, motion sensors (accelerometers), capacitance sensors, proximity sensors, magnetic sensors, force sensors (e.g., force sensors coupled to a display to detect pressure applied to the display), etc. 
     Input-output circuitry  44  may include wireless circuitry  34  (sometimes referred to herein as wireless communications circuitry  34 ). To support wireless communications, wireless circuitry  34  may include radio-frequency (RF) transceiver circuitry formed from one or more integrated circuits, power amplifier circuitry, low-noise input amplifiers, passive RF components, one or more antennas such as antennas  40 , transmission lines, and other circuitry for handling RF wireless signals. Wireless signals can also be sent using light (e.g., using infrared communications). 
     Wireless circuitry  34  may include radio-frequency transceiver circuitry  24  for handling various radio-frequency communications bands. For example, wireless circuitry  34  may include transceiver circuitry  42 ,  36 ,  38 ,  26 , and  30 . Transceiver circuitry  36  may be wireless local area network transceiver circuitry. Transceiver circuitry  36  may handle 2.4 GHz and 5 GHz bands for WiFi® (IEEE 802.11) communications or other WLAN bands and may handle the 2.4 GHz Bluetooth® communications band or other WPAN bands. Transceiver circuitry  36  may sometimes be referred to herein as WLAN transceiver circuitry  36 . 
     Wireless circuitry  34  may use cellular telephone transceiver circuitry  38  (sometimes referred to herein as cellular transceiver circuitry  38 ) for handling wireless communications in frequency ranges (communications bands) such as a low band (sometimes referred to herein as a cellular low band LB) from 600 to 960 MHz, a midband (sometimes referred to herein as a cellular midband MB) from 1400 MHz or 1700 MHz to 2170 or 2200 MHz, and a high band (sometimes referred to herein as a cellular high band HB) from 2200 or 2300 to 2700 MHz (e.g., a high band with a peak at 2400 MHz) or other communications bands between 600 MHz and 4000 MHz or other suitable frequencies (as examples). Cellular transceiver circuitry  38  may handle voice data and non-voice data. 
     Wireless circuitry  34  may include satellite navigation system circuitry such as Global Positioning System (GPS) receiver circuitry  42  for receiving GPS signals at 1575 MHz or for handling other satellite positioning data (e.g., GLONASS signals at 1609 MHz). Satellite navigation system signals for receiver  42  are received from a constellation of satellites orbiting the earth. Wireless circuitry  34  can include circuitry for other short-range and long-range wireless links if desired. For example, wireless circuitry  34  may include circuitry for receiving television and radio signals, paging system transceivers, near field communications (NFC) transceiver circuitry  30  (e.g., an NFC transceiver operating at 13.56 MHz or another suitable frequency), etc. 
     In NFC links, wireless signals are typically conveyed over a few inches at most. In satellite navigation system links, cellular telephone links, and other long-range links, wireless signals are typically used to convey data over thousands of feet or miles. In WLAN and WPAN links at 2.4 and 5 GHz and other short-range wireless links, wireless signals are typically used to convey data over tens or hundreds of feet. 
     Ultra-wideband (UWB) transceiver circuitry  26  may support communications using the IEEE 802.15.4 protocol and/or other wireless communications protocols (e.g., ultra-wideband communications protocols). Ultra-wideband wireless signals may be based on an impulse radio signaling scheme that uses band-limited data pulses. Ultra-wideband signals may have any desired bandwidths such as bandwidths between 499 MHz and 1331 MHz, bandwidths greater than 500 MHz, etc. The presence of lower frequencies in the baseband may sometimes allow ultra-wideband signals to penetrate through objects such as walls. In an IEEE 802.15.4 system, a pair of electronic devices may exchange wireless time stamped messages. Time stamps in the messages may be analyzed to determine the time of flight of the messages and thereby determine the distance (range) between the devices and/or an angle between the devices (e.g., an angle of arrival of incoming radio-frequency signals). Transceiver circuitry  26  may operate (i.e., convey radio-frequency signals) in frequency bands such as an ultra-wideband frequency band between about 5 GHz and about 8.3 GHz (e.g., a 6.5 GHz frequency band, an 8 GHz frequency band, and/or at other suitable frequencies). 
     Wireless circuitry  34  may include antennas  40 . Antennas  40  may be formed using any suitable antenna types. For example, antennas  40  may include antennas with resonating elements that are formed from patch antenna structures, slot antenna structures, loop antenna structures, antenna structures having parasitic elements, inverted-F antenna structures, planar inverted-F antenna structures, helical antenna structures, monopole antennas, dipole antenna structures, Yagi (Yagi-Uda) antenna structures, hybrids of these designs, etc. If desired, one or more of antennas  40  may be cavity-backed antennas. 
     Different types of antennas may be used for different bands and combinations of bands. For example, one type of antenna may be used in forming a local wireless link antenna and another type of antenna may be used in forming a remote wireless link antenna. Dedicated antennas may be used for receiving satellite navigation system signals or, if desired, antennas  40  can be configured to receive both satellite navigation system signals and signals for other communications bands (e.g., wireless local area network signals and/or cellular telephone signals). Antennas  40  can include two or more antennas for handling ultra-wideband wireless communication. In one suitable arrangement that is described herein as an example, antennas  40  include three antennas for handling ultra-wideband wireless communication. 
     Transmission line paths may be used to route antenna signals within device  10 . For example, transmission line paths may be used to couple antennas  40  to transceiver circuitry  24 . Transmission lines in device  10  may include coaxial probes realized by metalized vias, microstrip transmission lines, stripline transmission lines, edge-coupled microstrip transmission lines, edge-coupled stripline transmission lines, waveguide structures, transmission lines formed from combinations of transmission lines of these types, etc. 
     Transmission lines in device  10  may be integrated into rigid and/or flexible printed circuit boards. In one suitable arrangement, transmission lines in device  10  may also include transmission line conductors (e.g., signal and ground conductors) integrated within multilayer laminated structures (e.g., layers of a conductive material such as copper and a dielectric material such as a resin that are laminated together without intervening adhesive) that may be folded or bent in multiple dimensions (e.g., two or three dimensions) and that maintain a bent or folded shape after bending (e.g., the multilayer laminated structures may be folded into a particular three-dimensional shape to route around other device components and may be rigid enough to hold its shape after folding without being held in place by stiffeners or other structures). All of the multiple layers of the laminated structures may be batch laminated together (e.g., in a single pressing process) without adhesive (e.g., as opposed to performing multiple pressing processes to laminate multiple layers together with adhesive). Filter circuitry, switching circuitry, impedance matching circuitry, and other circuitry may be interposed within the transmission lines, if desired. 
     A schematic diagram of an antenna  40  coupled to transceiver circuitry  24  (e.g., ultra-wideband transceiver  26 ) is shown in  FIG.  3   . As shown in  FIG.  3   , transceiver circuitry  24  may be coupled to antenna feed  52  of antenna  40  using transmission line structures such as radio-frequency transmission line  46 . 
     Antenna feed  52  may include a positive antenna feed terminal such as positive antenna feed terminal  54  and may include a ground antenna feed terminal such as ground antenna feed terminal  56 . Transmission line  46  may be formed from metal traces on a printed circuit or other conductive structures and may have a positive transmission line signal path such as path  48  (sometimes referred to herein as signal conductor  48 ) that is coupled to positive antenna feed terminal  54 . Transmission line  46  may have a ground transmission line signal path such as path  50  (sometimes referred to herein as ground conductor  50 ) that is coupled to ground antenna feed terminal  56 . Filter circuitry, switching circuitry, impedance matching circuitry, tunable components, and other circuitry may be interposed within transmission line  46  and/or may be incorporated into antenna  40  if desired (e.g., to support antenna tuning, to support operation in desired frequency bands, etc.). 
     During operation, device  10  may communicate with external wireless equipment. If desired, device  10  may use radio-frequency signals conveyed between device  10  and the external wireless equipment to identify a location of the external wireless equipment relative to device  10 . Device  10  may identify the relative location of the external wireless equipment by identifying a range to the external wireless equipment (e.g., the distance between the external wireless equipment and device  10 ) and the angle of arrival (AoA) of radio-frequency signals from the external wireless equipment (e.g., the angle at which radio-frequency signals are received by device  10  from the external wireless equipment). 
       FIG.  4    is a diagram showing how device  10  may determine a distance D between the device  10  and external wireless equipment such as wireless network node  60  (sometimes referred to herein as wireless equipment  60 , wireless device  60 , external device  60 , or external equipment  60 ). Node  60  may include devices that are capable of receiving and/or transmitting radio-frequency signals such as signals  58 . Node  60  may include tagged devices (e.g., any suitable object that has been provided with a wireless receiver and/or a wireless transmitter), electronic equipment (e.g., an infrastructure-related device), and/or other electronic devices (e.g., devices of the type described in connection with  FIG.  1   , including some or all of the same wireless communications capabilities as device  10 ). 
     For example, node  60  may be a laptop computer, a tablet computer, a somewhat smaller device such as a wrist-watch device, pendant device, headphone device, earpiece device, headset device (e.g., virtual or augmented reality headset devices), or other wearable or miniature device, a handheld device such as a cellular telephone, a media player, or other small portable device. Node  60  may also be a set-top box, a camera device with wireless communications capabilities, a desktop computer, a display into which a computer or other processing circuitry has been integrated, a display without an integrated computer, or other suitable electronic equipment. Node  60  may also be a key fob, a wallet, a book, a pen, or other object that has been provided with a low-power transmitter (e.g., an RFID transmitter or other transmitter). Node  60  may be electronic equipment such as a thermostat, a smoke detector, a Bluetooth® Low Energy (Bluetooth LE) beacon, a WiFi® wireless access point, a wireless base station, a server, a heating, ventilation, and air conditioning (HVAC) system (sometimes referred to as a temperature-control system), a light source such as a light-emitting diode (LED) bulb, a light switch, a power outlet, an occupancy detector (e.g., an active or passive infrared light detector, a microwave detector, etc.), a door sensor, a moisture sensor, an electronic door lock, a security camera, or other device. 
     As shown in  FIG.  4   , device  10  may communicate with node  60  using wireless radio-frequency signals  58 . Radio-frequency signals  58  may include Bluetooth® signals, near-field communications signals, wireless local area network signals such as IEEE 802.11 signals, millimeter wave communication signals such as signals at 60 GHz, ultra-wideband radio frequency signals, other radio-frequency wireless signals, infrared signals, etc. In one suitable arrangement that is described herein by example, radio-frequency signals  58  are ultra-wideband signals conveyed in ultra-wideband frequency bands such as 6.5 GHz and 8 GHz frequency bands. Radio-frequency signals  58  may be used to determine and/or convey information such as location and orientation information. For example, control circuitry  28  in device  10  may determine the location of node  60  relative to device  10  using radio-frequency signals  58 . 
     In arrangements where node  60  is capable of sending or receiving communications signals, control circuitry  28  may determine distance D using wireless signals (e.g., radio-frequency signals  58  of  FIG.  4   ). Control circuitry  28  may determine distance D using signal strength measurement schemes (e.g., measuring the signal strength of radio-frequency signals from node  60 ) or using time-based measurement schemes such as time of flight measurement techniques, time difference of arrival measurement techniques, angle of arrival measurement techniques, triangulation methods, time-of-flight methods, using a crowdsourced location database, and other suitable measurement techniques. This is merely illustrative, however. If desired, control circuitry  28  may use information from Global Positioning System receiver circuitry  42  ( FIG.  2   ), proximity sensors (e.g., infrared proximity sensors or other proximity sensors), image data from a camera, motion sensor data from motion sensors, and/or using other circuitry in device  10  to help determine distance D. In addition to determining the distance D between device  10  and node  60 , control circuitry  28  may determine the orientation of device  10  relative to node  60 . 
       FIG.  5    illustrates how the position and orientation of device  10  relative to nearby nodes such as node  60  may be determined. In the example of  FIG.  5   , control circuitry  28  uses a horizontal polar coordinate system to determine the location and orientation of device  10  relative to node  60 . In this type of coordinate system, control circuitry  28  may determine an azimuth angle θ and/or an elevation angle φ to describe the position of nearby nodes  60  relative to device  10 . Control circuitry  28  may define a reference plane such as local horizon  64  and a reference vector such as reference vector  68 . Local horizon  64  may be a plane that intersects device  10  and that is defined relative to a surface of device  10  (e.g., the front or rear face of device  10 ). For example, local horizon  64  may be a plane that is parallel to or coplanar with display  14  of device  10  ( FIG.  1   ). Reference vector  68  (sometimes referred to as the “north” direction) may be a vector in local horizon  64 . If desired, reference vector  68  may be aligned with longitudinal axis  62  of device  10  (e.g., an axis running lengthwise down the center of device  10  and parallel to the longest rectangular dimension of device  10 , parallel to the Y-axis of  FIG.  1   ). When reference vector  68  is aligned with longitudinal axis  62  of device  10 , reference vector  68  may correspond to the direction in which device  10  is being pointed. 
     Azimuth angle θ and elevation angle φ may be measured relative to local horizon  64  and reference vector  68 . As shown in  FIG.  5   , the elevation angle φ (sometimes referred to as altitude) of node  60  is the angle between node  60  and local horizon  64  of device  10  (e.g., the angle between vector  70  extending between device  10  and node  60  and a coplanar vector  66  extending between device  10  and horizon  64 ). The azimuth angle θ of node  60  is the angle of node  60  around local horizon  64  (e.g., the angle between reference vector  68  and vector  66 ). In the example of  FIG.  5   , the azimuth angle θ and elevation angle φ of node  60  are greater than 0°. 
     If desired, other axes besides longitudinal axis  62  may be used to define reference vector  68 . For example, control circuitry  28  may use a horizontal axis that is perpendicular to longitudinal axis  62  as reference vector  68 . This may be useful in determining when nodes  60  are located next to a side portion of device  10  (e.g., when device  10  is oriented side-to-side with one of nodes  60 ). 
     After determining the orientation of device  10  relative to node  60 , control circuitry  28  may take suitable action. For example, control circuitry  28  may send information to node  60 , may request and/or receive information from  60 , may use display  14  ( FIG.  1   ) to display a visual indication of wireless pairing with node  60 , may use speakers to generate an audio indication of wireless pairing with node  60 , may use a vibrator, a haptic actuator, or other mechanical element to generate haptic output indicating wireless pairing with node  60 , may use display  14  to display a visual indication of the location of node  60  relative to device  10 , may use speakers to generate an audio indication of the location of node  60 , may use a vibrator, a haptic actuator, or other mechanical element to generate haptic output indicating the location of node  60 , and/or may take other suitable action. 
     In one suitable arrangement, device  10  may determine the distance between the device  10  and node  60  and the orientation of device  10  relative to node  60  using two or more ultra-wideband antennas. The ultra-wide band antennas may receive wireless communication signals from node  60 . Time stamps in the wireless communication signals may be analyzed to determine the time of flight of the wireless communication signals and thereby determine the distance (range) between device  10  and node  60 . Additionally, angle of arrival (AoA) measurement techniques may be used to determine the orientation of electronic device  10  relative to node  60  (e.g., azimuth angle θ and elevation angle φ). 
     In angle of arrival measurement, node  60  transmits a radio-frequency signal to device  10  (e.g., radio-frequency signals  58  of  FIG.  4   ). Device  10  may measure a delay in arrival time of the radio-frequency signal between the two or more ultra-wideband antennas. The delay in arrival time (e.g., the difference in received phase at each ultra-wideband antenna) can be used to determine the angle of arrival of the radio-frequency signal (and therefore the angle of node  60  relative to device  10 ). Once distance D and the angle of arrival have been determined, device  10  may have knowledge of the precise location of node  60  relative to device  10 . 
       FIG.  6    is a schematic diagram showing how angle of arrival measurement techniques may be used to determine the orientation of device  10  relative to node  60 . As shown in  FIG.  6   , device  10  may include multiple antennas (e.g., a first antenna  40 - 1  and a second antenna  40 - 2 ) coupled to transceiver circuitry  24  over respective transmission lines  46  (e.g., a first transmission line  46 - 1  and a second transmission line  46 - 2 ). 
     Antennas  40 - 1  and  40 - 2  may each receive radio-frequency signals  58  from node  60  ( FIG.  5   ). Antennas  40 - 1  and  40 - 2  may be laterally separated by a distance d 1 , where antenna  40 - 1  is farther away from node  60  than antenna  40 - 2  (in the example of  FIG.  6   ). Therefore, radio-frequency signals  58  travel a greater distance to reach antenna  40 - 1  than antenna  40 - 2 . The additional distance between node  60  and antenna  40 - 1  is shown in  FIG.  6    as distance d 2 .  FIG.  6    also shows angles x and y (where x+y=90°). 
     Distance d 2  may be determined as a function of angle y or angle x (e.g., d 2 =d 1 *sin(x) or d 2 =d 1 *cos(y)). Distance d 2  may also be determined as a function of the phase difference between the signal received by antenna  40 - 1  and the signal received by antenna  40 - 2  (e.g., d 2 =(PD)*λ/(2*π), where PD is the phase difference (sometimes written “Δϕ”) between the signal received by antenna  40 - 1  and the signal received by antenna  40 - 2 , and λ is the wavelength of radio-frequency signals  58 . Device  10  may include phase measurement circuitry coupled to each antenna to measure the phase of the received signals and to identify phase difference PD (e.g., by subtracting the phase measured for one antenna from the phase measured for the other antenna). The two equations for d 2  may be set equal to each other (e.g., d 1 *sin(x)=(PD)*λ/(2*π) and rearranged to solve for the angle x (e.g., x=sin −1 ((PD)*λ/(2*π*d 1 )) or the angle y. Therefore, the angle of arrival may be determined (e.g., by control circuitry  28 ) based on the known (predetermined) distance between antennas  40 - 1  and  40 - 2 , the detected (measured) phase difference PD between the signal received by antenna  40 - 1  and the signal received by antenna  40 - 2 , and the known wavelength (frequency) of the received signals  58 . 
     Distance d 1  may be selected to ease the calculation for phase difference PD between the signal received by antenna  40 - 1  and the signal received by antenna  40 - 2 . For example, d 1  may be less than or equal to one half of the wavelength (e.g., effective wavelength) of the received signal  58  (e.g., to avoid multiple phase difference solutions). 
     With two antennas for determining angle of arrival (as in  FIG.  6   ), the angle of arrival within a single plane may be determined. For example, antennas  40 - 1  and  40 - 2  in  FIG.  6    may be used to determine azimuth angle θ. A third antenna may be included to enable angle of arrival determination in multiple planes (e.g., azimuth angle θ and elevation angle φ may both be determined). Angles x and/or y of  FIG.  6    may be converted to spherical coordinates to obtain azimuth angle θ and elevation angle φ, for example. 
     Any desired antenna structures may be used for implementing antennas  40  that are used to compute angle of arrival. In one suitable arrangement that is sometimes described herein as an example, patch antenna structures may be used for implementing antennas  40 . Antennas  40  that are implemented using patch antenna structures may sometimes be referred to herein as patch antennas. An illustrative patch antenna is shown in  FIG.  7   . 
     As shown in  FIG.  7   , antenna  40  may have a patch antenna resonating element such as patch element  74  that is separated from a ground plane structure such as ground  72  (sometimes referred to as ground layer  72 , grounding layer  72 , or antenna ground  72 ). Patch element  74  and antenna ground  72  may be formed from metal foil, machined metal structures, metal traces on a printed circuit or a molded plastic carrier, electronic device housing structures, or other conductive structures in an electronic device such as device  10 . Patch element  74  may sometimes be referred to herein as patch  74 , patch antenna resonating element  74 , patch radiating element  74 , or antenna resonating element  74 . 
     Patch element  74  may lie within a plane such as the X-Y plane of  FIG.  7   . Antenna ground  72  may lie within a plane that is parallel to the plane of patch element  74 . Patch element  74  and antenna ground  72  may therefore lie in separate parallel planes that are separated by a distance H. In general, greater distances (heights) H may allow antenna  40  to exhibit a greater bandwidth than shorter distances H. However, greater distances H may consume more volume within device  10  (where space is often at a premium) than shorter distances H. 
     Conductive path  76  may be used to couple terminal  54 ′ to positive antenna feed terminal  54 . Antenna  40  may be fed using a transmission line with a signal conductor coupled to terminal  54 ′ (and thus to positive antenna feed terminal  54 ) and with a ground conductor coupled to ground antenna feed terminal  56 . Other feeding arrangements may be used if desired. If desired, patch element  74  and antenna ground  72  may have different shapes and orientations (e.g., planar shapes, curved patch shapes, patch element shapes with non-rectangular outlines, shapes with straight edges such as squares, shapes with curved edges such as ovals and circles, shapes with combinations of curved and straight edges, etc.). 
     Multiple antennas of the type shown in  FIG.  7    may be used by control circuitry  28  to determine angle of arrival and thus the location of node  60  ( FIG.  5   ) relative to device  10 .  FIG.  8    is a top-down view showing how three antennas  40  may be used to determine angle of arrival. 
     As shown in  FIG.  8   , device  10  may include an antenna module  80  for determining the angle of arrival of radio-frequency signals  58  received from node  60  ( FIG.  4   ) and the range between device  10  and node  60 . Antenna module  80  may include three or more antennas  40  such as a first antenna  40 - 1 , a second antenna  40 - 2 , and a third antenna  40 - 3 . Antennas  40  may be configured to radiate at ultra-wideband frequencies and antenna module  80  may therefore sometimes be referred to herein as ultra-wideband antenna module  80 . 
     Antennas  40 - 1 ,  40 - 2 , and  40 - 3  may be mounted to a substrate such as substrate  78 . Substrate  78  may be, for example, a rigid printed circuit board or a flexible printed circuit. Antennas  40 - 1  and  40 - 3  may be located along perpendicular axes about antenna  40 - 2  (e.g., antennas  40 - 1  and  40 - 2  may be aligned with an axis parallel to the Y-axis whereas antennas  40 - 2  and  40 - 3  are aligned with an axis parallel to the X axis of  FIG.  8   ). While two antennas  40  may enable control circuitry  28  to determine angle of arrival within a single plane (e.g., azimuth angle θ or elevation angle φ of  FIG.  5   ), using three antennas arranged along orthogonal axes such as antennas  40 - 1 ,  40 - 2 , and  40 - 3  of  FIG.  8    may enable control circuitry  28  to determine angle of arrival within multiple planes and thus in spherical coordinates (e.g., azimuth angle θ and elevation angle φ may both be determined). 
     Antenna  40 - 1  and antenna  40 - 3  may each be located at distance  81  from antenna  40 - 2 . Distance  81  may be, for example, approximately equal to one half of the wavelength of operation of antennas  40 - 1 ,  40 - 2 , and  40 - 3 . Distance  81  may serve as distance d 1  ( FIG.  6   ) between antennas  40 - 1  and  40 - 2  for computing angle of arrival within a single plane between antennas  40 - 1  and  40 - 2 . Similarly, distance  81  may serve as distance d 1  between antennas  40 - 2  and  40 - 3  for computing angle of arrival within a single plane between antennas  40 - 2  and  40 - 3 . If desired, substrate  78  may include a cut-out region  83  to accommodate other device components when antenna module  80  is mounted within device  10 . 
     As shown in  FIG.  8   , each of antennas  40 - 1 ,  40 - 2 , and  40 - 3  may include a respective patch element  74  mounted to a corresponding patch substrate  84 . Patch substrates  84  (sometimes referred to herein as dielectric substrates  84  or dielectric carriers  84 ) may be mounted to the surface of substrate  78  and may separate patch elements  74  from the surface of substrate  78  (e.g., patch substrates  84  may extend along the Z-axis above the lateral surface of substrate  78 ). Patch substrates  84  may include plastic, ceramic, polyimide, liquid crystal polymer, or any other desired dielectric materials. Patch elements  74  may be formed from conductive traces on the surface of patch substrates  84 . Patch substrates  84  may separate patch elements  74  from ground traces over, on, or within substrate  78  (e.g., antenna ground  72  of  FIG.  7   ). This may serve to maximize the bandwidth of antennas  40 - 1 ,  40 - 2 , and  40 - 3  (e.g., given the relatively thin profile of substrate  78 ). 
     If desired, each substrate  84  may include a respective set or fence of conductive vias  86  that extends through the patch substrate (e.g., parallel to the Z-axis of  FIG.  8   ) and laterally around the corresponding patch element  74 . For example, antenna  40 - 1  may include a fence of conductive vias  86  that laterally extends around (surrounds) each side of the patch element  74  in antenna  40 - 1 . Each via  86  in the fences of conductive vias may be separated from two adjacent vias  86  in that fence by one-fifteenth of a wavelength or less, as an example. This may allow the fences of vias  86  to appear as a solid conductive wall (e.g., an infinite impedance) for radio-frequency signals conveyed laterally by patch elements  74  (e.g., parallel to the X-Y plane of  FIG.  8   ). In this way, respective fences of conductive vias  86  may form conductive cavities for each patch element  74  and may serve to isolate each of antennas  40 - 1 ,  40 - 2 , and  40 - 3  from each other and from electromagnetic interference from other device components. 
     Radio-frequency transmission lines  46  may be integrated within substrate  78  for feeding antennas  40 - 1 ,  40 - 2 , and  40 - 3 . For example, a first radio-frequency transmission line  46 - 1  may be coupled to antenna  40 - 1 , a second radio-frequency transmission line  46 - 2  may be coupled to antenna  40 - 2 , and a third radio-frequency transmission line  46 - 3  may be coupled to antenna  40 - 3 . Radio-frequency transmission lines  46 - 1 ,  46 - 2 , and  46 - 3  may be formed from conductive signal traces and conductive ground traces on substrate  78 , for example. 
     Radio-frequency transmission lines  46 - 1 ,  46 - 2 , and  46 - 3  may each be coupled to UWB transceiver circuitry  26  ( FIG.  2   ) through radio-frequency connector  82 . Connector  82  may be a coaxial cable connector or any other desired radio-frequency connector. Transceiver circuitry  26  may be formed on a separate substrate such as a main logic board for device  10 . Radio-frequency transmission line  46 - 2  may be routed from radio-frequency connector  82  to antenna  40 - 2  around antenna  40 - 1  and cut-out region  83 . Similarly, radio-frequency transmission line  46 - 3  may be routed from radio-frequency connector  82  to antenna  40 - 3  around antennas  40 - 1  and  40 - 2  and cut-out region  83 . The example of  FIG.  8    is merely illustrative and, in general, substrate  78  may have any desired shape and radio-frequency transmission lines  46  may be provided with any desired routing arrangement. 
     Each of antennas  40 - 1 ,  40 - 2 , and  40 - 3  may have the same dimensions for covering the same frequencies, for example. The dimensions of patch elements  74  may be selected to radiate within one or more desired frequency bands. For example, each patch element  74  may have a length  88  and an orthogonal width  90 . Length  88  may be selected so that patch element  74  radiates in a first frequency band (e.g., length  88  may be approximately one-half of the wavelength corresponding to a frequency in a 6.5 GHz frequency band) and width  90  may be selected so that patch element  74  radiates in a second frequency band (e.g., length  90  may be approximately one-half of the wavelength corresponding to a frequency in the 8 GHz frequency band). Positive antenna feed terminals  54  ( FIG.  7   ) may be coupled to patch elements  74  at a location that is offset at a selected distance from the center of patch elements  74  to match the impedance of patch elements  74  to the corresponding radio-frequency transmission line  46  in these frequency bands. 
     The example of  FIG.  8    is merely illustrative and, if desired, patch elements  74  may have other shapes (e.g., shapes having curved and/or straight edges). If desired, other device components such as matching circuitry, radio-frequency front end circuitry, filter circuitry, switching circuitry, amplifier circuitry, phase shifter circuitry, phase measurement circuitry, a camera module, a speaker, a light emitter, an ambient light sensor, another antenna for covering wireless local area network communications or other non-ultra-wideband communications, a vibrator, display components, proximity sensor components, or any other desired device components may be mounted to antenna module  80  (e.g., on substrate  78 ). 
       FIG.  9    is a cross-sectional side view showing how antenna module  80  may be mounted within device  10 . As shown in  FIG.  9   , antenna module  80  may be mounted within device  10  adjacent to a dielectric cover layer such as dielectric cover layer  104 . Dielectric cover layer  104  may form a dielectric rear wall for device  10  (e.g., dielectric cover layer  104  of  FIG.  9    may form part of rear housing wall  12 R of  FIG.  1   ) or may form a display cover layer for device  10  (e.g., dielectric cover layer  104  of  FIG.  9    may be a display cover layer for display  14  of  FIG.  1   ), as examples. Dielectric cover layer  104  may be formed from a visually opaque material or may be provided with pigment so that dielectric cover layer  104  is visually opaque if desired. 
     A conductive layer such as conductive layer  100  may be coupled to an interior surface of dielectric cover layer  100 . Conductive layer  100  may form a part of rear housing wall  12 R of  FIG.  1    or may be formed from other device housing structures such as a conductive support plate for device  10 , as examples. Conductive layer  100  may include an aperture (opening)  102 . Antenna module  80  may be mounted within interior  106  of device  10  so that antenna  40  (e.g., one of antennas  40 - 1 ,  40 - 2 , or  40 - 3  of  FIG.  8   ) is aligned with aperture  102 . When mounted in this way, antenna  40  may receive radio-frequency signals  58  ( FIG.  4   ) through dielectric cover layer  104  and aperture  102 . Patch element  74  of antenna  40  may be pressed against dielectric cover layer  104 , may be coupled to dielectric cover layer  104  using a layer of adhesive, or may be spaced apart from dielectric cover layer  104 . 
     As shown in  FIG.  9   , antenna module  80  may include patch substrate  84  mounted to substrate  78 . Patch substrate  84  may be rigid whereas substrate  78  is flexible, in one example. In this scenario, the portion of substrate  78  under patch substrate  84  may be rigid whereas the portion of substrate  78  extending beyond patch substrate  84  is flexible (e.g., a flexible printed circuit tail). Patch substrate  84  may be coupled to substrate  78  using adhesive if desired. 
     Patch substrate  84  and/or substrate  78  may each include multiple stacked dielectric layers (e.g., multiple layers of printed circuit board substrate such as multiple layers of fiberglass-filled epoxy) or may each include a single dielectric layer. Patch substrate  84  may include any desired dielectric materials such as epoxy, plastic, ceramic, glass, foam, polyimide, liquid crystal polymer, or other materials. Flexible substrate  78  may include conductive traces  94  and conductive traces  96  (e.g., conductive traces formed on different dielectric layers of substrate  78 ). Conductive traces  94  and  96  may collectively form radio-frequency transmission line  46  for antenna  40 . Conductive traces  94  may form the signal conductor (e.g., signal conductor  48  of  FIG.  3   ) whereas conductive traces  96  form the ground conductor (e.g., ground conductor  50  of  FIG.  3   ) for antenna  40 , for example. 
     Ground traces  98  may be embedded within patch substrate  84  and may be held at a ground potential (e.g., ground traces  98  may be coupled to other ground structures in device  10  such as conductive traces  96 ). Patch element  74  may be formed from conductive traces on surface  97  of patch substrate  84 . In scenarios where patch substrate  84  is formed from multiple stacked dielectric layers, ground traces  98  may be formed from conductive traces on a first dielectric layer in patch substrate  84  whereas patch element  74  is formed from conductive traces on another dielectric layer in patch substrate  84 . Conductive traces  94  (e.g., the signal conductor for radio-frequency transmission line  46 ) may be coupled to positive antenna feed terminal  54  on patch element  74  by conductive feed via  92  extending through patch substrate  84  and an opening in ground traces  98 . 
     Conductive vias  86  may extend through patch substrate  84  from ground traces  98  to surface  97 . Conductive vias  86  may be coupled to conductive landing pads on surface  97  of patch substrate  84  (e.g., conductive contact pads that are co-planar with patch element  74 ). Conductive vias  86  may be separated from patch element  74  by distance  101  at surface  97  (e.g., the conductive landing pads may be laterally separated from patch element  74  by distance  101 ). Distance  101  may be large enough to allow for some tolerance in manufacturing antenna  40  while also being small enough to minimize the footprint of antenna  40  within device  10 . As an example, distance  101  may be between 0.4 mm and 0.6 mm (e.g., 0.5 mm). Conductive vias  86  may be formed at the peripheral edges of patch substrate  84  (e.g., may surround a periphery of patch substrate  84 ) or patch substrate  84  may laterally extend beyond conductive vias  86 . Conductive vias  86  may prevent radio-frequency signals handled by patch element  74  from laterally escaping into interior  106  of device  10  and may prevent electromagnetic signals within interior  106  from interfering with antenna  40 . 
     When configured in this way, antenna module  80  may exhibit a thickness  95  (e.g., parallel to the Z-axis of  FIG.  9   ). Thickness  95  may be between 0.2 and 0.4 mm, as an example. This relatively narrow profile may allow antenna module  80  to be mounted within relatively narrow spaces within device  10  and in close proximity to other device components. Conductive vias  86  may serve to electromagnetically isolate antennas  40  from other device components despite their close proximity to antenna  40 . 
     In practice, antennas  40 - 1 ,  40 - 2 , and  40 - 3  may be susceptible to impedance loading from external objects (e.g., objects at or adjacent to the exterior surface of dielectric cover  104 ) such as a user&#39;s hand, clothing, or other parts of the user&#39;s body, a removable protective case for device  10 , a dielectric film, or other objects. Loading from external objects can affect the phase of the radio-frequency signals received by antennas  40 - 1 ,  40 - 2 , and  40 - 3 . For example, control circuitry  28  ( FIG.  2   ) may measure a particular phase when a given antenna is in a free space environment and may measure a different phase when that antenna is covered by a user&#39;s finger, even though the phases were measured from a signal received by device  10  at the same angle of arrival. 
     These discrepancies in measured signal phase can cause control circuitry  28  to generate erroneous phase difference values PD between pairs of antennas. Because phase difference values PD are used to determine the angle of arrival, these errors in phase difference values PD can cause control circuitry  28  to generate erroneous angle of arrival data (e.g., control circuitry  28  may erroneously determine that node  60  of  FIG.  5    is located at an inaccurate angle with respect to device  10 ). It would therefore be desirable to be able to provide antenna module  80  with the ability to generate accurate angle of arrival information regardless of how the antennas are being loaded by external objects. 
       FIG.  10    is a flow chart of illustrative steps that may be performed by device  10  to generate accurate angle of arrival information regardless of the environmental loading conditions for antennas  40 - 1 ,  40 - 2 , and  40 - 3 . The steps of  FIG.  10    may, for example, be performed by control circuitry  28  of  FIG.  2    and antenna module  80  of  FIGS.  8  and  9   . 
     At step  108 , antennas  40 - 1 ,  40 - 2 , and  40 - 3  may receive radio-frequency signals  58  from node  60  ( FIG.  4   ). In one suitable arrangement described herein by example, the radio-frequency signals are ultra-wideband signals in one or more ultra-wideband frequency bands (e.g., a 6.5 GHz ultra-wideband frequency band and an 8 GHz ultra-wideband frequency band). 
     At step  110 , phase measurement circuitry on antenna module  80  may measure the phase of the ultra-wideband signals received by each of antennas  40 - 1 ,  40 - 2 , and  40 - 3  and may pass the measured phases to control circuitry  28 . For example, the phase measurement circuitry may generate a first phase measurement for antenna  40 - 1 , a second phase measurement for antenna  40 - 2 , and a third phase measurement for antenna  40 - 3 . 
     Control circuitry  28  may subtract the second phase measurement from the first phase measurement to generate a first phase difference value PD 12  (sometimes annotated “Δϕ 12 ”) between antennas  40 - 1  and  40 - 2  (sometimes referred to herein as phase difference PD 12 ). Similarly, control circuitry  28  may subtract the third phase measurement from the second phase measurement to generate a second phase difference value PD 23  (sometimes annotated “Δϕ 23 ”) between antennas  40 - 2  and  40 - 3  (sometimes referred to herein as phase difference PD 23 ). Control circuitry  28  may determine the three-dimensional angle of arrival for the received ultra-wideband signals (e.g., azimuth angle θ and elevation angle φ) based on phase difference values PD 12  and PD 23 . If desired, control circuitry  28  may also determine the range between device  10  and node  60  using the received ultra-wideband signals (e.g., range D of  FIGS.  4  and  5   ). 
     At step  112 , control circuitry  28  may generate a first difference value Δ 12  by subtracting phase difference value PD 12  from a predetermined phase difference value PD 12 ′ and may generate a second difference value Δ 23  by subtracting phase difference value PD 23  from a predetermined phase difference value PD 23 ′. Predetermined phase difference values PD 23 ′ and PD 12 ′ may be stored at control circuitry  28  (e.g., in non-volatile memory). Predetermined difference value PD 12 ′ may be a free-space phase difference value that is generated between antennas  40 - 1  and  40 - 2  in a free-space environment (e.g., an operating environment in which antennas  40 - 1  and  40 - 2  are not loaded by any external objects). Similarly, predetermined difference value PD 23 ′ may be a free-space phase difference value that is generated between antennas  40 - 2  and  40 - 3  in a free-space environment (e.g., an operating environment in which antennas  40 - 2  and  40 - 3  are not loaded by any external objects). Predetermined phase difference values PD 12 ′ and PD 23 ′ may, for example, be generated during calibration of wireless circuitry  34  (e.g., prior to assembling device  10  or prior to normal operation of device  10  by an end user). 
     At step  114 , control circuitry  28  may compare difference value Δ 12  and/or difference value Δ 23  to one or more predetermined threshold values to determine whether one of antennas  40 - 1 ,  40 - 2 , and  40 - 3  is not in a free-space environment (e.g., to determine whether one of antennas  40 - 1 ,  40 - 2 , and  40 - 3  is being loaded by an external object). For example, control circuitry  28  may compare each difference value to different respective threshold values, may compare each difference value to the same threshold value, or may compare a combination of the difference values to a threshold value. 
     If each difference value is less than corresponding threshold value(s), this may be indicative of antennas  40 - 1 ,  40 - 2 , and  40 - 3  being operated in a free-space environment and processing may loop back to step  108  as shown by path  116 . Control circuitry  28  may identify that the angle of arrival information generated during the preceding iteration of step  110  is accurate and may proceed to identify the location of node  60  relative to device  10  or perform any other desired operations based on the angle of arrival information. 
     If one or more difference value is greater than the threshold value(s), this may be indicative of antennas  40 - 1 ,  40 - 2 , and/or  40 - 3  being operated in a non-free-space environment in which one or more of antennas  40 - 1 ,  40 - 2 , and  40 - 3  is being loaded or blocked by an external object. Processing may subsequently proceed to step  120  as shown by path  118 . 
     At step  120 , control circuitry  28  may compare phase difference value PD 12  to a set of predetermined environment-specific PD 12  surfaces and/or may compare phase difference value PD 23  to a set of predetermined environment-specific PD 23  surfaces. The predetermined environment-specific PD 12  and PD 23  surfaces may be stored at control circuitry  28 . 
     The predetermined environment-specific PD 12  surfaces may include surfaces of phase difference values PD 12  generated using antennas  40 - 1  and  40 - 2  under different environmental loading conditions (e.g., as generated during calibration of device  10 ). Each surface may include expected PD 12  values over all possible measured angles of arrival under a corresponding environmental loading condition. For example, control circuitry  28  may store a first surface of expected PD 12  values for scenarios where device  10  has been placed within a removable protective case, a second surface of expected PD 12  values for scenarios where antenna  40 - 1  is being covered by a user&#39;s finger, a third surface of expected PD 12  values for scenarios where antenna  40 - 2  is being covered by a user&#39;s hand, etc. 
     Similarly, the predetermined environment-specific PD 23  surfaces may include surfaces of phase difference values PD 23  generated using antennas  40 - 2  and  40 - 3  under different environmental loading conditions (e.g., as generated during calibration of device  10 ). Each surface may include expected PD 23  values over all possible measured angles of arrival under a corresponding environmental loading condition. For example, control circuitry  28  may store a first surface of expected PD 23  values for scenarios where device  10  has been placed within a removable protective case, a second surface of expected PD 23  values for scenarios where antenna  40 - 2  is being covered by a user&#39;s finger while placed in a protective case, a third surface of expected PD 23  values for scenarios where antennas  40 - 2  and  40 - 3  are being covered by a user&#39;s hand without a protective case, etc. This example in which control circuitry  28  compares the phase difference values to three-dimensional surfaces of phase difference values is merely illustrative and, if desired, control circuitry  28  may compare the phase difference values to two-dimensional curves of phase difference values (e.g., curves lying on a surface given a fixed azimuthal or elevation angle). 
     Control circuitry  28  may select a predetermined environment-specific PD 12  surface (curve) that matches the measured phase difference value PD 12  and may select a predetermined environment-specific PD 23  surface (curve) that matches the measured phase difference value PD 23 . Control circuitry  28  may identify the environmental loading condition associated with matching predetermined PD 12  and PD 23  surfaces. For example, if the measured PD 12  value matches a predetermined PD 12  surface corresponding to antenna  40 - 1  being loaded by a user&#39;s finger and the measured PD 23  value matches a predetermined PD 23  surface associated with no objects loading antennas  40 - 2  and  40 - 3 , control circuitry  28  may determine that antenna  40 - 1  is being blocked by a user&#39;s finger. As another example, if the measured PD 12  value matches a predetermined PD 12  surface corresponding to antennas  40 - 2  and  40 - 1  being loaded by a removable dielectric case for device  10  and the measured PD 23  value matches a predetermined PD 23  surface corresponding to antennas  40 - 2  and  40 - 3  being loaded by a removable dielectric case for device  10 , control circuitry  28  may determine that device  10  is mounted within a removable dielectric case (e.g., that antennas  40 - 1 ,  40 - 2 , and  40 - 3  are being loaded by a removable dielectric case for device  10 ). Control circuitry  28  may include any desired number of predetermined environment-specific PD 12  and PD 23  surfaces associated with any desired loading of any desired combination of antennas  40 - 1 ,  40 - 2 , and  40 - 3  by any desired external objects. 
     At step  122 , control circuitry  28  may identify predetermined angle of arrival offset values based on the identified environmental loading conditions (e.g., based on the comparison performed while processing step  120 ). The offset values may be stored at control circuitry  28  and may be generated during calibration of device  10 . Because different environmental loading conditions may generate different deviations in the phases measured by antennas  40 - 1 ,  40 - 2 , and  40 - 3 , these deviations can be measured and characterized during calibration of device  10 . The predetermined offset values stored at control circuitry  28  may compensate for these pre-characterized effects. For example, control circuitry  28  may store a first set of offset values associated with antennas  40 - 1 ,  40 - 2 , and  40 - 3  being loaded by a dielectric case for device  10 , a second set of offset values associated with antenna  40 - 1  being blocked by a user&#39;s finger, a third offset value associated with antenna  40 - 3  being blocked by a user&#39;s finger, etc. 
     Control circuitry  28  may add or otherwise combine the identified offset values with the determined angle of arrival (e.g., as generated while processing step  110 ) to generate a corrected angle of arrival value (e.g., a corrected azimuth angle θ and a corrected elevation angle φ). The offset values may compensate for errors in the angle of arrival value generated on account of shifts in phase values measured by antennas  40 - 1 ,  40 - 2 , and/or  40 - 3  due to the presence of different external objects. 
     Consider one example in which a user&#39;s finger is placed over antenna  40 - 1 . The user&#39;s finger may shift the phase of the ultra-wideband signal received by antenna  40 - 1  away from the phase that the antenna would exhibit if the finger was not present. The magnitude of this shift is dependent upon the material that is placed over the antenna (e.g., the environmental loading conditions for the antenna). This shift also results in a shift in the measured phase difference value PD 12  away from the phase difference value that the antennas would exhibit if the finger were not present. The shifted phase difference value would be characteristic of node  60  being located at a different location than its actual location. When control circuitry  28  generates an angle of arrival value based on the shifted phase difference value, the angle of arrival would be erroneous and characteristic of node  60  being located at a location other than its actual location. However, by comparing the measured phase difference values to the predetermined surfaces of phase difference values (e.g., by performing the steps of  FIG.  10   ), control circuitry  28  may identify the environmental loading conditions for the antennas (e.g., information about which antennas are being covered by what type of material) based on phase differences measured between the antennas. The predetermined offset values may correspond to the particular environmental loading conditions that contributed to the measured phase differences. By adjusting the angle of arrival using the predetermined offset values, the erroneous angle of arrival may be corrected to reflect the accurate location of node  60 . 
     Processing may subsequently loop back to step  108  as shown by path  124 . In this way, control circuitry  28  may ensure that correct angle of arrival information is determined regardless of whether antennas  40 - 1 ,  40 - 2 , and/or  40 - 3  are being loaded by external objects. Control circuitry  28  may subsequently use the corrected angle of arrival information to determine the accurate location of node  60  with respect to device  10  ( FIG.  5   ). 
       FIG.  11    is a plot of phase difference on arrival as a function of elevation for a given one of antennas  40 - 1 ,  40 - 2 , and  40 - 3 . As shown in  FIG.  11   , the Y-axis plots phase difference on arrival PD (e.g., phase difference value PD 12  or phase difference value PD 23 ) whereas the X-axis plots elevation angle φ of the incoming ultra-wideband signals (e.g., for a fixed azimuth angle θ). 
     Curve  126  illustrates the expected phase difference on arrival for a free-space environment in which a pair of the antennas is not loaded by an external object. Curve  128  illustrates the expected phase difference on arrival when the pair of antennas is covered by a finger. As shown by curves  126  and  128 , the expected phase difference on arrival generally increases as the elevation angle of the received ultra-wideband signal increases. However, the manner in which the phase difference varies over elevation angle changes based on whether the antennas are being loaded by an external object. By performing the operations of  FIG.  10   , control circuitry  28  may compensate for these variations to ensure that angle of arrival information generated based on the measured phase difference is accurate. 
     Curves  126  and  128  may be predetermined phase difference curves that are stored at control circuitry  28 . Curves  126  and  128  may be generated during calibration of device  10 , for example. Curve  126  may represent a two-dimensional portion of predetermined three-dimensional free-space surface (e.g., for a fixed azimuth angle θ). Curve  128  may represent a two-dimensional portion of predetermined three-dimensional surface corresponding to an environment in which the pair of antennas is covered by a finger (e.g., for a fixed azimuth angle θ). Control circuitry  28  may, if desired, compare curve  126  to measured phase difference values while processing step  112  of  FIG.  10   . Control circuitry  28  may, if desired, compare curves  126  and  128  (or larger surfaces to which curves  126  and  128  belong) to measured phase difference values while processing step  120  of  FIG.  12   . If the measured phase difference values match curve  128 , control circuitry  28  may determine that a finger is loading the pair of antennas and may identify offset values corresponding to situations in which a finger is loading the pair of antennas. Control circuitry  28  may add the offset values to the measured angle of arrival to generate a corrected angle of arrival (e.g., while processing step  122  of  FIG.  10   ) that accurately reflects the location of node  60  ( FIG.  5   ). The example of  FIG.  11    is merely illustrative. Curves  126  and  128  may have other shapes. 
     The foregoing is merely illustrative and various modifications can be made by those skilled in the art without departing from the scope and spirit of the described embodiments. The foregoing embodiments may be implemented individually or in any combination.

Metadata:
Filing Date: 20210722
Publication Date: 20240723
Grant Date: 20240723
Priority Date: 20180713
Inventors: COOPER, AARON J.
TAYEBI, AMIN
DI NALLO, CARLO
WANG, ZHEYU
Assignee: APPLE INC
CPC Classifications: [{"code": "G01S3/72", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01S3/46", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01S3/023", "inventive": false, "first": false, "tree": "[]"}, {"code": "H01Q3/2605", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01S3/043", "inventive": false, "first": false, "tree": "[]"}, {"code": "H01Q1/523", "inventive": false, "first": false, "tree": "[]"}, {"code": "H01Q9/0407", "inventive": false, "first": false, "tree": "[]"}, {"code": "H01Q21/065", "inventive": false, "first": false, "tree": "[]"}, {"code": "H01Q5/25", "inventive": true, "first": false, "tree": "[]"}, {"code": "H01Q1/243", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01S3/48", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01S3/043", "inventive": true, "first": false, "tree": "[]"}, {"code": "H01Q3/2605", "inventive": true, "first": false, "tree": "[]"}, {"code": "H01Q9/0407", "inventive": true, "first": false, "tree": "[]"}, {"code": "H01Q21/065", "inventive": true, "first": false, "tree": "[]"}, {"code": "H01Q5/25", "inventive": true, "first": false, "tree": "[]"}, {"code": "H01Q1/48", "inventive": true, "first": false, "tree": "[]"}, {"code": "H01Q9/0407", "inventive": true, "first": false, "tree": "[]"}, {"code": "H01Q1/38", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01S3/48", "inventive": true, "first": true, "tree": "[]"}, {"code": "H01Q1/243", "inventive": true, "first": true, "tree": "[]"}, {"code": "H01Q1/22", "inventive": true, "first": true, "tree": "[]"}, {"code": "H01Q21/065", "inventive": false, "first": false, "tree": "[]"}, {"code": "H01Q9/0407", "inventive": false, "first": false, "tree": "[]"}, {"code": "H01Q3/2605", "inventive": false, "first": false, "tree": "[]"}, {"code": "H01Q1/523", "inventive": false, "first": false, "tree": "[]"}, {"code": "H01Q1/243", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01S3/72", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01S3/043", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01S3/023", "inventive": false, "first": false, "tree": "[]"}, {"code": "H01Q5/25", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01S3/46", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01S3/48", "inventive": true, "first": true, "tree": "[]"}]
Family ID: 69138805