Patent Publication Number: US-2022229155-A1

Title: Electronic Devices Having Spatial Ranging Calibration Capabilities

Description:
FIELD 
     This disclosure relates generally to electronic devices and, more particularly, to electronic devices with wireless circuitry. 
     BACKGROUND 
     Electronic devices are often provided with wireless capabilities. An electronic device with wireless capabilities has wireless circuitry that includes one or more antennas. The wireless circuitry is sometimes used to perform spatial ranging operations in which radio-frequency signals are used to estimate a distance between the electronic device and an external object. 
     It can be challenging to provide wireless circuitry that accurately estimates this distance. For example, the wireless circuitry will often introduce undesirable power droops and/or phase shifts to the radio-frequency signals. If care is not taken, these power droops and phase shifts can cause the wireless circuitry to inaccurately estimate the distance between the electronic device and the external object. 
     SUMMARY 
     An electronic device may include wireless circuitry. The wireless circuitry may include spatial ranging circuitry and antennas. In one implementation that is described herein as an example, the spatial ranging circuitry includes radar circuitry such as frequency modulated continuous wave (FMCW) radar circuitry. The antennas may include a transmit antenna for a transmit chain in the radar circuitry and a receive antenna for a receive chain in the radar circuitry. The transmit chain may include a transmit signal generator (e.g., a chirp generator), a digital-to-analog converter (DAC), a first mixer, and a signal splitter. The receive chain may include a second mixer (e.g., a de-chirp mixer) and measurement circuitry. A path (e.g., a de-chirp path) may couple the signal splitter to the second mixer. The transmit signal generator may generate transmit signals (e.g., chirp signals) that are transmitted by the transmit antenna and received by the receive antenna. Doppler shifts in the received signals may be processed to estimate or detect a velocity of an external object. A time-dependent frequency difference between the transmitted and received signals may be processed to estimate or detect a range between the device and the external object. Angle of arrival of the received signals may also be estimated. 
     If care is not taken, the components of the radar circuitry may impose an undesirable power droop and phase shift to the chirp signals, which can limit the accuracy of the estimated position and/or velocity. Control circuitry may calibrate the radar circuitry to mitigate these issues. During calibration, the DAC may transmit a multi-tone calibration signal. The multi-tone calibration signal includes two or more tones that are separated by a frequency gap. The first mixer may upconvert the multi-tone calibration signal, which is transmitted over the antennas or a loopback path prior to receipt at the second mixer. If desired, an additional mixer may upconvert the multi-tone calibration signal to higher frequencies prior to transmission over the antennas or loopback path and an additional mixer may downconvert the multi-tone calibration signal received over the loopback path or the antennas. The second mixer may mix the multi-tone calibration signal output by the first mixer with the multi-tone calibration signal received over the antennas or loopback path to produce a baseband multi-tone calibration signal. The baseband multi-tone calibration signal will be offset from DC by the frequency gap. This may prevent DC noise, LO leakage, or other system/process noise from interfering with the baseband multi-tone calibration signal. 
     The control circuitry may sweep the first mixer (or the additional mixers in embodiments where the radar circuitry includes additional mixers) over different frequencies of operation of the radar circuitry while the second mixer continues to generate baseband multi-tone calibration signals. The measurement circuitry may measure magnitudes and phases of the baseband multi-tone calibration signals. The control circuitry may estimate the power droop and phase shift of the radar circuitry based on the magnitude and phase measurements. Distortion circuitry such as predistortion circuitry in the transmit chain may then predistort the transmit signals to invert the power droop and phase shift effects of the radar circuitry, thereby ensuring that accurate range, position, and/or velocity estimates can be obtained over the lifetime of the device. 
     An aspect of the disclosure provides wireless communication circuitry for performing spatial ranging operations on an external object using transmit signals. The wireless circuitry can include a digital-to-analog converter (DAC) configured to generate a multi-tone calibration signal having a first tone and a second tone separated from the first tone by a frequency gap. The wireless circuitry can include a first mixer configured to upconvert the multi-tone calibration signal from a first frequency band to a second frequency band. The wireless circuitry can include a second mixer having a first input configured to receive the multi-tone calibration signal in the second frequency band via a signal path from an output of the first mixer, and having a second input configured to receive the multi-tone calibration signal in the second frequency band via intermediate circuitry communicatively coupled between the output of the first mixer and the second input. The second mixer can be configured to generate a baseband multi-tone calibration signal. The wireless circuitry can include measurement circuitry configured to measure a magnitude of the baseband multi-tone calibration signal. The wireless circuitry can include control circuitry configured to estimate a power droop of the intermediate circuitry based on the magnitude measured by the measurement circuitry. The control circuitry can be configured to distort the transmit signals based on the estimated power droop. 
     An aspect of the disclosure provides a method for calibrating radar circuitry. The method can include, with a digital-to-analog converter (DAC) in a transmit chain of the radar circuitry, generating a multi-tone calibration signal having a first tone and a second tone separated from the first tone by a frequency gap of less than 20 MHz. The method can include, with a first mixer in the transmit chain, upconverting the multi-tone calibration signal from baseband to a first frequency band. The method can include, with a second mixer in the transmit chain, upconverting the multi-tone calibration signal from the first frequency band to a second frequency band. The method can include, with a third mixer in a receive chain of the radar circuitry, downconverting the multi-tone calibration signal upconverted by the second mixer from the second frequency band to the first frequency band. The method can include, with a de-chirp mixer in the receive chain, generating a baseband multi-tone calibration signal by mixing the multi-tone calibration signal upconverted by the first mixer with the multi-tone calibration signal downconverted by the third mixer, the baseband multi-tone calibration signal being separated from a direct current (DC) frequency by the frequency gap. The method can include, with control circuitry, estimating a power droop and phase shift of the radar circuitry based on the baseband multi-tone calibration signal generated by the de-chirp mixer. The method can include, with predistortion circuitry in the transmit chain, predistorting chirp signals transmitted over the transmit chain based on the power droop and phase shift estimated by the control circuitry. 
     An aspect of the disclosure provides an electronic device. The electronic device can include a first antenna. The electronic device can include a second antenna. The electronic device can include radar circuitry configured to generate transmit signals that are transmitted using the first antenna. The second antenna can be configured to receive a reflected version of the transmit signals transmitted using the first antenna. The electronic device can include control circuitry configured to perform spatial ranging operations based on the reflected version of the transmit signals received using the second antenna. The electronic device can include a digital-to-analog converter (DAC) in the radar circuitry. The DAC can be configured to generate a multi-tone calibration signal that is transmitted using the first antenna. The multi-tone calibration signal can have a first tone and a second tone that is separated from the first tone by a frequency gap of less than 20 MHz. The control circuitry can be configured to estimate a power droop of the radar circuitry using the multi-tone calibration signal. The control circuitry can be configured to distort the transmit signals based on the estimated power droop. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a functional block diagram of an illustrative electronic device having calibrated spatial ranging circuitry in accordance with some embodiments. 
         FIG. 2  is a circuit diagram of illustrative spatial ranging circuitry that is calibrated using a multi-tone calibration signal in accordance with some embodiments. 
         FIG. 3  is flow chart of illustrative operations involved in calibrating spatial ranging circuitry using a multi-tone calibration signal in accordance with some embodiments. 
         FIG. 4  is a frequency diagram of an illustrative multi-tone calibration signal that may be used to estimate the power droop and/or phase shift of spatial ranging circuitry in accordance with some embodiments. 
         FIG. 5  is a plot of illustrative power droops that may be estimated using a multi-tone calibration signal in accordance with some embodiments. 
         FIG. 6  is a diagram showing how illustrative digital predistortion circuitry may be used to compensate for an estimated power droop and/or phase shift of spatial ranging circuitry in accordance with some embodiments. 
         FIG. 7  is a diagram of illustrative spatial ranging circuitry having at least first and second mixers that may be calibrated using a multi-tone calibration signal in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Electronic device  10  of  FIG. 1  may be a computing device such as a laptop computer, a desktop computer, a computer monitor containing an embedded computer, a tablet computer, a cellular telephone, a media player, or other handheld or portable electronic device, a smaller device such as a wristwatch device, a pendant device, a headphone or earpiece device, a device embedded in eyeglasses or other equipment worn on a user &#39;s head, or other wearable or miniature device, a television, a computer display that does not contain an embedded computer, a gaming device, a navigation device, an embedded system such as a system in which electronic equipment with a display is mounted in a kiosk or automobile, a wireless internet-connected voice-controlled speaker, a home entertainment device, a remote control device, a gaming controller, a peripheral user input device, a wireless base station or access point, equipment that implements the functionality of two or more of these devices, or other electronic equipment. 
     As shown in the functional block diagram of  FIG. 1 , device  10  may include components located on or within an electronic device 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, metal alloys, etc.), other suitable materials, or a combination of these materials. In some situations, parts or all 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 include control circuitry  14 . Control circuitry  14  may include storage such as storage circuitry  16 . Storage circuitry  16  may include 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. Storage circuitry  16  may include storage that is integrated within device  10  and/or removable storage media. 
     Control circuitry  14  may include processing circuitry such as processing circuitry  18 . Processing circuitry  18  may be used to control the operation of device  10 . Processing circuitry  18  may include on one or more microprocessors, microcontrollers, digital signal processors, host processors, baseband processor integrated circuits, application specific integrated circuits, central processing units (CPUs), etc. Control circuitry  14  may be configured to perform operations in device  10  using hardware (e.g., dedicated hardware or circuitry), firmware, and/or software. Software code for performing operations in device  10  may be stored on storage circuitry  16  (e.g., storage circuitry  16  may include non-transitory (tangible) computer readable storage media that stores the software code). The software code may sometimes be referred to as program instructions, software, data, instructions, or code. Software code stored on storage circuitry  16  may be executed by processing circuitry  18 . 
     Control circuitry  14  may be used to run software on device  10  such as satellite navigation applications, 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  14  may be used in implementing communications protocols. Communications protocols that may be implemented using control circuitry  14  include internet protocols, wireless local area network (WLAN) protocols (e.g., IEEE 802.11 protocols—sometimes referred to as Wi-Fi®), protocols for other short-range wireless communications links such as the Bluetooth® protocol or other wireless personal area network (WPAN) protocols, IEEE 802.11ad protocols (e.g., ultra-wideband protocols), cellular telephone protocols (e.g., 3G protocols, 4G (LTE) protocols, 5G protocols, etc.), antenna diversity protocols, satellite navigation system protocols (e.g., global positioning system (GPS) protocols, global navigation satellite system (GLONASS) protocols, etc.), antenna-based spatial ranging protocols (e.g., radio detection and ranging (RADAR) protocols or other desired range detection protocols for signals conveyed at millimeter and centimeter wave frequencies), or any other desired communications protocols. Each communications protocol may be associated with a corresponding radio access technology (RAT) that specifies the physical connection methodology used in implementing the protocol. 
     Device  10  may include input-output circuitry  20 . Input-output circuitry  20  may include input-output devices  22 . Input-output devices  22  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  22  may include user interface devices, data port devices, and other input-output components. For example, input-output devices  22  may include touch sensors, displays (e.g., touch-sensitive and/or force-sensitive displays), light-emitting components such as displays without touch sensor capabilities, buttons (mechanical, capacitive, optical, etc.), scrolling wheels, touch pads, key pads, keyboards, microphones, cameras, buttons, speakers, status indicators, audio jacks and other audio port components, digital data port devices, motion sensors (accelerometers, gyroscopes, and/or compasses that detect motion), capacitance sensors, proximity sensors, magnetic sensors, force sensors (e.g., force sensors coupled to a display to detect pressure applied to the display), etc. In some configurations, keyboards, headphones, displays, pointing devices such as trackpads, mice, and joysticks, and other input-output devices may be coupled to device  10  using wired or wireless connections (e.g., some of input-output devices  22  may be peripherals that are coupled to a main processing unit or other portion of device  10  via a wired or wireless link). 
     Input-output circuitry  20  may include wireless circuitry  24  to support wireless communications. Wireless circuitry  24  (sometimes referred to herein as wireless communications circuitry  24 ) may include two or more antennas  40 . Wireless circuitry  24  may also include baseband processor circuitry, transceiver circuitry, amplifier circuitry, filter circuitry, switching circuitry, radio-frequency transmission lines, and/or any other circuitry for transmitting and/or receiving radio-frequency signals using antennas  40 . 
     Wireless circuitry  24  may transmit and/or receive radio-frequency signals within a corresponding frequency band at radio frequencies (sometimes referred to herein as a communications band or simply as a “band”). The frequency bands handled by wireless circuitry  24  may include wireless local area network (WLAN) frequency bands (e.g., Wi-Fi® (IEEE 802.11) or other WLAN communications bands) such as a 2.4 GHz WLAN band (e.g., from 2400 to 2480 MHz), a 5 GHz WLAN band (e.g., from 5180 to 5825 MHz), a Wi-Fi® 6E band (e.g., from 5925-7125 MHz), and/or other Wi-Fi® bands (e.g., from 1875-5160 MHz), wireless personal area network (WPAN) frequency bands such as the 2.4 GHz Bluetooth® band or other WPAN communications bands, cellular telephone frequency bands (e.g., bands from about 600 MHz to about 5 GHz, 3G bands, 4G LTE bands, 5G New Radio Frequency Range 1 (FR1) bands below 10 GHz, 5G New Radio Frequency Range 2 (FR2) bands between 20 and 60 GHz, etc.), other centimeter or millimeter wave frequency bands between 10-300 GHz, near-field communications frequency bands (e.g., at 13.56 MHz), satellite navigation frequency bands (e.g., a GPS band from 1565 to 1610 MHz, a Global Navigation Satellite System (GLONASS) band, a BeiDou Navigation Satellite System (BDS) band, etc.), ultra-wideband (UWB) frequency bands that operate under the IEEE 802.15.4 protocol and/or other ultra-wideband communications protocols, communications bands under the family of 3GPP wireless communications standards, communications bands under the IEEE 802.XX family of standards, and/or any other desired frequency bands of interest. 
     Antennas  40  may be formed using any desired antenna structures. For example, antennas  40  may include antennas with resonating elements that are formed from loop antenna structures, patch antenna structures, inverted-F antenna structures, slot antenna structures, planar inverted-F antenna structures, helical antenna structures, monopole antennas, dipoles, hybrids of these designs, etc. Filter circuitry, switching circuitry, impedance matching circuitry, and/or other antenna tuning components may be adjusted to adjust the frequency response and wireless performance of antennas  40  over time. 
     The radio-frequency signals handled by antennas  40  may be used to convey wireless communications data between device  10  and external wireless communications equipment (e.g., one or more other devices such as device  10 ). Wireless communications data may be conveyed by wireless circuitry  24  bidirectionally or unidirectionally. The wireless communications data may, for example, include data that has been encoded into corresponding data packets such as wireless data associated with a telephone call, streaming media content, internet browsing, wireless data associated with software applications running on device  10 , email messages, etc. 
     Wireless circuitry  24  may additionally or alternatively perform spatial ranging operations using antennas  40 . In scenarios where wireless circuitry  24  both conveys wireless communications data and performs spatial ranging operations, one or more of the same antennas  40  may be used to both convey wireless communications data and perform spatial ranging operations. In another implementation, wireless circuitry  24  may include a set of antennas  40  that only conveys wireless communications data and a set of antennas  40  that is only used to perform spatial ranging operations. 
     When performing spatial ranging operations, antennas  40  may transmit radio-frequency signals  36 . Wireless circuitry  24  may transmit radio-frequency signals  36  in a corresponding radio frequency band such (e.g., a frequency band that includes frequencies greater than around 10 GHz, greater than around 20 GHz, less than 10 GHz, etc.). Radio-frequency signals  36  may reflect off of objects external to device  10  such as external object  34 . External object  34  may be, for example, the ground, a building, a wall, furniture, a ceiling, a person, a body part, an animal, a vehicle, a landscape or geographic feature, an obstacle, or any other object or entity that is external to device  10 . Antennas  40  may receive reflected radio-frequency signals  38 . Reflected signals  38  may be a reflected version of the transmitted radio-frequency signals  36  that have reflected off of external object  34  and back towards device  10 . 
     Control circuitry  14  may process the transmitted radio-frequency signals  36  and the received reflected signals  38  to detect or estimate the range R between device  10  and external object  34 . If desired, control circuitry  14  may also process the transmitted and received signals to identify a two or three-dimensional spatial location (position) of external object  34 , a velocity of external object  34 , and/or an angle of arrival of reflected signals  38 . In one implementation that is described herein as an example, wireless circuitry  24  performs spatial ranging operations using a frequency-modulated continuous-wave (FMCW) radar scheme. This is merely illustrative and, in general, other radar schemes or spatial ranging schemes may be used (e.g., an OFDM radar scheme, an FSCW radar scheme, a phase coded radar scheme, etc.). 
     In order to support spatial ranging operations, wireless circuitry  24  may include spatial ranging circuitry such as radar circuitry  26 . In one embodiment that is sometimes described herein as an example, radar circuitry  26  includes FMCW radar circuitry that performs spatial ranging using an FMCW radar scheme. Radar circuitry  26  may therefore sometimes be referred to herein as FMCW radar circuitry  26 . Radar circuitry  26  may use one or more antennas  40  to transmit radio-frequency signals  36  (e.g., as a continuous wave of radio-frequency energy under an FMCW radar scheme). One or more antennas  40  may also receive reflected signals  38  (e.g., as a continuous wave of radio-frequency energy under the FMCW radar scheme). Radar circuitry  26  may process radio-frequency signals  36  and reflected signals  38  to identify/estimate range R, the position of external object  34 , the velocity of external object  34 , and/or the angle-of-arrival of reflected signals  38 . In embodiments where radar circuitry  26  uses an FMCW radar scheme, doppler shifts in the continuous wave signals may be detected and processed to identify the velocity of external object  34  and the time dependent frequency difference between radio-frequency signals  36  and reflected signals  38  may be detected and processed to identify range R and/or the position of external object  34 . Use of continuous wave signals for estimating range R may allow control circuitry  10  to reliably distinguish between external object  34  and other background or slower-moving objects, for example. 
     As shown in  FIG. 1 , radar circuitry  26  may include transmit (TX) signal generator circuitry such as transmit signal generator  28 . Transmit signal generator  28  may generate transmit signals for transmission over antenna(s)  40 . In some implementations that are described herein as an example, transmit signal generator  28  includes a chirp generator that generates chirp signals for transmission over antenna(s)  40  (e.g., in embodiments where radar circuitry  26  uses an FMCW radar scheme). Transmit signal generator  28  may therefore sometimes be referred to herein as chirp generator  28 . Transmit signal generator  28  may, for example, produce chirp signals that are transmitted as a continuous wave of radio-frequency signals  36 . The chirp signals may be formed by periodically ramping up the frequency of the transmitted signals in a linear manner over time, for example. Radar circuitry  26  may also include digital-to-analog converter (DAC) circuitry such as DAC  32 . DAC  32  may convert the transmit signals (e.g., the chirp signals) from the digital domain to the analog domain prior to transmission by antennas  40  (e.g., in radio-frequency signals  36 ). Radar circuitry  26  may also include analog-to-digital converter (ADC) circuitry such as ADC  42 . ADC  42  may convert signals from the analog domain to the digital domain for subsequent processing by control circuitry  14 . While control circuitry  14  is shown separately from wireless circuitry  24  in the example of  FIG. 1  for the sake of clarity, wireless circuitry  24  may include processing circuitry that forms a part of processing circuitry  18  and/or storage circuitry that forms a part of storage circuitry  16  of control circuitry  14  (e.g., portions of control circuitry  14  may be implemented on wireless circuitry  24 ). 
     In practice, the components in wireless circuitry  24  may introduce a frequency-dependent power droop and/or a phase shift to the radio-frequency signals transmitted by antennas  40 . The power droop may, for example, be caused by circuit, filter, and/or cabling frequency dependencies, as well as by directivity/gain limitations over frequency for antennas  40 . When using an FMCW radar scheme, the frequency-dependent power droop increases the width of the main target lobe in the baseband (BB) spectrum, which can reduce the range resolution of radar circuitry  26 . In addition, signal-to-noise ratio (SNR) in the baseband signal can be reduced due to discrete and fixed gain stages in wireless circuitry  24 . It may therefore be desirable to be able to avoid or compensate for any power droop or phase shift introduced by wireless circuitry  24  when performing spatial ranging operations. 
     In order to compensate for the power droop and phase shift introduced by wireless circuitry  24  while performing spatial ranging operations, wireless circuitry  24  may estimate or track the power droop and phase shift introduced by wireless circuitry  24  during operation over the lifetime of device  10 . DAC  32  may generate a multi-tone calibration signal that is used to estimate the power droop and phase shift. The multi-tone calibration signal includes two or more tones that are separated by a relatively small gap in frequency space (sometimes referred to herein as frequency gap Δf). Once the power droop and/or phase shift have been estimated, radar circuitry  26  may distort the transmit signals (e.g., chirp signals) generated by transmit signal generator  28  using distortion circuitry  30 . Distortion circuitry  30  may include predistortion circuitry that predistorts the transmit signals prior to transmission by antennas  40  and/or may include post-distortion circuitry that distorts received signals. The distortion introduced by distortion circuitry  30  may serve to invert the effects of the power droop and phase shift, thereby ensuring that radar circuitry  26  can continue to produce accurate estimates of range R, position, velocity, and/or angle-of-arrival, even if the power droop or phase shift change over time. Distortion circuitry  30  may be implemented using hardware and/or software on control circuitry  14 , using one or more processors in radar circuitry  26  and/or control circuitry  14 , using digital logic on radar circuitry  26  (e.g., a standalone digital predistortion circuit block), using analog circuitry in radar circuitry  26  (e.g., a standalone analog predistortion circuit block), etc. The distortion circuitry may include, for example, multipliers, look-up tables, memory, and/or any other desired components for distorting an input signal to produce a distorted output signal (e.g., a predistorted output signal in embodiments where distortion circuitry  30  includes predistortion circuitry). 
       FIG. 2  is a circuit diagram of radar circuitry  26  (e.g., in embodiments where radar circuitry  26  performs multiple up-conversions prior to transmission by antennas  40 ). If desired, the components of radar circuitry  26  may be mounted to a common substrate (e.g., a shared rigid or flexible printed circuit board) or may be formed on a common integrated circuit (IC) or package. As shown in  FIG. 2 , radar circuitry  26  may include a transmit chain  52  (sometimes referred to herein as transmitter chain  52 , transmit line-up  52 , or transmit path  52 ) and a receive chain  54  (sometimes referred to herein as receiver chain  54 , receive line-up  54 , or receive path  52 ). 
     Radar circuitry  26  may have a first (transmit) port coupled to a first antenna  40  such as transmit antenna  40 TX (e.g., transmit antenna  40 TX may form a part of transmit chain  52 ). Radar circuitry  26  may have a second (receive) port coupled to a second antenna  40  such as receive antenna  40 RX (e.g., receive antenna  40 RX may form a part of receive chain  54 ). A signal path such as de-chirp path  48  may couple transmit chain  52  to receive chain  54 . 
     Transmit chain  52  may include transmit signal generator  28  (e.g., a chirp generator), DAC  32 , an first mixer such as mixer  56 , amplifier circuitry such as amplifiers  58  and  66  (e.g., power amplifiers), a signal splitter such as splitter  62 , and a second radio-frequency mixer such as mixer  64 . Receive chain  54  may include ADC  42 , phase and magnitude measurement circuitry  88 , filter circuitry such as low pass filter (LPF)  76 , a third mixer such as de-chirp mixer  74 , a fourth mixer such as mixer  72 , and amplifier circuitry such as amplifier  70  (e.g., a low noise amplifier (LNA)). 
     As shown in  FIG. 2 , the output of transmit signal generator  28  may be coupled to the input of DAC  32  (e.g., transmit signal generator  28  may be formed from digital logic in radar circuitry  26  and may operate in the digital domain). The output of DAC  32  may be coupled to a first input of mixer  56  (e.g., over an I/Q signal path). Mixer  56  may have a second input that receives a local oscillator (LO) signal from frequency band 1 local oscillator (FB1LO)  50 . The output of mixer  56  may be coupled to the input of amplifier  58 . The output of amplifier  58  may be coupled to the input of splitter  62 . Splitter  62  may have a first output terminal coupled to a first input of mixer  64 . Mixer  64  may have a second input that receives a LO signal from frequency band 2 local oscillator (FB2LO)  46 . The output of mixer  64  may be coupled to the input of amplifier  66 . The output of amplifier  66  may be coupled to transmit antenna  40 TX (e.g., over one or more radio-frequency transmission lines). 
     In receive chain  54 , the input of amplifier  70  may be coupled to receive antenna  40 RX. The output of amplifier  70  may be coupled to a first input of mixer  72 . Mixer  72  may have a second input that receives the LO signal from FB2LO  46 . The output of mixer  72  may be coupled to a first input of de-chirp mixer  74 . De-chirp mixer  74  may have a second input that is coupled to a second output terminal of splitter  62  over de-chirp path  48 . If desired, an amplifier such as amplifier  68  may be interposed on de-chirp path  48 . While not shown in the example of  FIG. 2  for the sake of clarity, de-chirp path  48  may also include a signal splitter having first and second output terminals coupled to de-chirp mixer  74 , where a 90-degree phase delay is applied to the second output terminal (e.g., so de-chirp mixer  74  can operate on I/Q signals). The output of de-chirp mixer  74  may be coupled to the input of LPF  76  (e.g., over an I/Q signal path). The output of LPF  76  may be coupled to the input of phase and magnitude measurement circuitry  88 . The output of phase and magnitude measurement circuitry  88  may be coupled to the input of ADC  42 . The output of ADC  42  may be coupled to control circuitry  14  ( FIG. 1 ) over digital output path  78 . If desired, an optional loopback path  80  may couple the output of amplifier  66  in transmit chain  52  to the input of amplifier  70  in receive chain  54 . A radio-frequency coupler and/or switching circuitry may be interposed on loopback path  80  if desired. Loopback path  80  may be used to calibrate radar circuitry  26  in scenarios where antennas  40 TX and  40 RX are not used for calibration. 
     Transmission lines in wireless circuitry  24  (e.g., radio-frequency transmission lines used to couple mixer  64  to transmit antenna  40 TX, radio-frequency transmission lines used to couple receive antenna  40 RX to mixer  72 , etc.) may include coaxial cables, microstrip transmission lines, stripline transmission lines, edge-coupled microstrip transmission lines, edge-coupled stripline transmission lines, transmission lines formed from combinations of transmission lines of these types, etc. One or more of the transmission lines may be integrated into rigid and/or flexible printed circuit boards if desired. 
     The example of  FIG. 2  is merely illustrative. In general, other circuit architectures may be used to form radar circuitry  26 . Mixers  56  and  74  may be I/Q mixers. Additional filters, amplifiers, switches, delay stages, splitters, and/or other circuit components may be formed at other locations in radar circuitry  26 . For example, a bandpass filter may be interposed between amplifier  58  and splitter  62 . Phase and magnitude measurement circuitry  88  may be formed at other locations or at multiple locations if desired (e.g., measurement circuitry  88  may be coupled to the output ADC  42 , the input of ADC  42 , and/or the input of LPF  76 ). If desired, mixers  64  and  72  and FB2LO  46  may be omitted. De-chirp mixer  74  may operate in the digital domain if desired (e.g., the output of ADC  42  may be coupled to the input of de-chirp mixer  74 , ADC  42  may be interposed on receive chain  54  at any desired location between receive antenna  40 RX and the input of de-chirp mixer  74 , etc.). Digital predistortion circuitry and/or analog predistortion circuitry from distortion circuitry  30  of  FIG. 1  may be interposed on transmit chain  52  and/or receive chain  54  at any desired location(s). In addition to being used to perform spatial ranging operations for radar circuitry  26 , transmit antenna  40 TX and/or receive antenna  40 RX may also be used to transmit and/or receive wireless communications data if desired (e.g., using other transceiver circuitry and frequency/time domain multiplexing circuitry not shown in  FIG. 2  for the sake of clarity). Radar circuitry  26  may, for example, form part of a transmitter such as a 5G NR transmitter. 
     When performing spatial ranging operations, transmit signal generator  28  may generate digital transmit signals (e.g., digital chirp signals) for subsequent transmission by transmit antenna  40 TX (e.g., using a continuous wave of radio-frequency energy). DAC  32  may convert the digital transmit signals into corresponding analog transmit signals (e.g., analog chirp signals). DAC  32  may provide the analog transmit signals (e.g., as I/Q signals) to mixer  56 . Mixer  56  may upconvert the analog transmit signals from baseband to a first frequency band FB1 band using FB1LO  50 . 
     First frequency band FB1 may be at higher frequencies than baseband and lower frequencies than the radio-frequency signals  36  transmitted by transmit antenna  40 TX (e.g., in the arrangement of  FIG. 2  in which multiple up-conversions are performed). As one example, radio-frequency signals  36  may be transmitted in a second frequency band FB2 such as a radio-frequency (RF) band. Frequency band FB2 may include frequencies greater than 10 GHz (e.g., an RF band around 25 GHz, greater than 20 GHz, greater than 30 GHz, greater than 50 GHz, etc.) and/or frequencies less than 10 GHz. Frequency band FB1 may include frequencies less than frequency band FB2 (e.g., frequencies less than 10 GHz, less than 5 GHz, etc.). Frequency band FB1 may sometimes be referred to herein as an intermediate frequency (IF) band. In embodiments where mixers  64  and  72  are omitted, frequency band FB1 may be any desired frequency band (e.g., an RF band) higher than baseband. 
     Amplifier  58  may amplify the FB1 transmit signals (e.g., FB1 chirp signals) for transmission to splitter  62 . Distributing the transmit signals in frequency band FB1 rather than in the higher frequency band FB2 may serve to minimize signal attenuation as the signals are distributed to locations in device  10  that are relatively far away from DAC  32 , particularly when frequency band FB2 is at relatively high frequencies that are otherwise subject to significant signal attenuation (e.g., frequencies greater than 10 GHz). Splitter  62  may transmit the FB1 transmit signals to mixer  64  and de-chirp path  48  (e.g., splitter  62  may split the FB1 transmit signals between mixer  64  and de-chirp path  48 ). Mixer  64  may upconvert the FB1 transmit signals from frequency band FB1 to frequency band FB2 for transmission by transmit antenna  40 TX. Amplifier  66  may amplify the FB2 transmit signals (e.g., FB2 chirp signals) and transmit antenna  40 TX may transmit the FB2 transmit signals (e.g., as radio-frequency signals  36 ). In embodiments where mixers  64  and  72  are omitted, transmit antenna  40 TX may transmit the FB1 transmit signals as radio-frequency signals  36 . 
     Receive antenna  40 RX may receive reflected signals  38  (e.g., a reflected version of the FB2 transmit signals transmitted by transmit antenna  40 TX but that have reflected off of external object  34  of  FIG. 1 ). In examples where the transmit signals include chirp signals, reflected signals  38  may sometimes be referred to herein as reflected chirp signals. Amplifier  70  may amplify the reflected signals. Mixer  72  may downconvert the reflected signals from frequency band FB2 to frequency band FB1 for distribution to de-chirp mixer  74  (e.g., as FB1 reflected signals). De-chirp path  48  may convey the FB1 transmit signals from splitter  62  to de-chirp mixer  74 . Amplifier  68  may amplify the FB1 transmit signals on de-chirp path  48  (e.g., to compensate for attenuation associated with splitter  62 ). De-chirp mixer  74  may mix the FB1 transmit signals received over de-chirp path  48  with the FB1 reflected signals received from mixer  72  to produce baseband signals (e.g., baseband chirp signals). In embodiments where mixers  64  and  72  are omitted, de-chirp mixer  74  may mix the FB1 transmit signals received over de-chirp path  48  with the FB1 reflected signals received by receive antenna  40 RX. De-chirp mixer  74  may provide the baseband signals to LPF  76 . LPF  76  may low-pass filter the baseband signals to remove noise, harmonic effects, etc. The baseband signals may be conveyed to ADC  42  (e.g., via phase and magnitude measurement circuitry  88 ). ADC  42  may convert the baseband signals to digital signals (e.g., digital chirp signals). Control circuitry  14  may process the baseband signals to estimate range R, the position of external object  34 , and/or the velocity of external object  34  ( FIG. 1 ). 
     In practice, transmit antenna  40 TX, receive antenna  40 RX, the transmission lines, filter circuitry (which typically cannot support the full FMCW bandwidth), and the other components in transmit chain  52  and receive chain  54  can introduce an undesirable power droop and/or phase shift to radar circuitry  26 . For example, the components along dashed path  82  may introduce a power droop and/or phase shift to the signals provided to de-chirp mixer  74 , which can be characterized by complex weight values k 1  and k 3 . Similarly, the components along dashed path  84  (or dashed path  86  in scenarios where loopback path  80  is used for calibration rather than antennas  40 TX and  40 RX) may introduce a power droop and/or phase shift to the signals provided to de-chirp mixer  74 , which can be characterized by complex weight values k 2  and k 4 . 
     If care is not taken, the power droop and phase shift may cause control circuitry  14  to generate inaccurate estimates of range R, position, and/or velocity. In addition, the amount of power droop and phase shift can change over time. Control circuitry  14  and radar circuitry  26  may perform calibration operations to estimate the power droop and phase shift and to compensate for the estimated power droop and phase shift even if the power droop and phase shift change over time, thereby ensuring that control circuitry  14  can accurately estimate range R and the position/velocity of external objects throughout the useful life of device  10 . 
     However, in practice, the presence of de-chirp path  48 , the relatively low baseband bandwidth of the system after de-chirping (e.g., 1-10 MHz) given the relatively high RF bandwidth of the system (e.g., 3-5 GHz), and the presence of DC/flicker noise or other process noise (e.g., LO leakage) at baseband can make it particularly difficult to estimate the power droop and/or phase shift of radar circuitry  26 . In order to mitigate these issues and to ensure that accurate estimates of the power droop and phase shift are gathered, radar circuitry  26  may be calibrated using a multi-tone calibration signal. The multi-tone calibration signal may include two or more tones (e.g., two tones, three tones, four tones, five tones, six tones, more than six tones, etc.) that are separated by a relatively small frequency gap Δf in frequency space. 
     As shown in  FIG. 2 , during the calibration operations, DAC  32  may generate multi-tone calibration signal mtone at baseband frequencies. Transmit signal generator  28  may refrain from transmitting signals (e.g., chirp signals) during the calibration operations. Mixer  56  may upconvert multi-tone calibration signal mtone to frequency band FB1 using FB1LO  50 . Amplifier  58  may amplify and transmit multi-tone calibration signal mtone. Splitter  62  may provide multi-tone calibration signal mtone to mixer  64 . Splitter  62  may also provide multi-tone calibration signal mtone to de-chirp mixer  74  over de-chirp path  48 . Mixer  64  may upconvert multi-tone calibration signal mtone to frequency band FB2, amplifier  66  may amplify multi-tone calibration signal mtone, and transmit antenna  40 TX may transmit multi-tone calibration signal mtone. 
     Receive antenna  40 RX may receive the multi-tone calibration signal mtone transmitted by transmit antenna  40 TX (e.g., directly over-the-air in a closed-loop path). In another implementation, loopback path  80  may be used to convey multi-tone calibration signal mtone from the output of amplifier  66  to the input of amplifier  70 . In this example, transmit antenna  40 TX is not used to transmit the multi-tone calibration signal. Amplifier  70  may amplify the multi-tone calibration signal mtone received using receive antenna  40 RX or loopback path  80 . 
     Mixer  72  may downconvert the received multi-tone calibration signal mtone to frequency band FB1 using FB2LO  46 . De-chirp mixer  74  may mix the multi-tone calibration signal mtone in frequency band FB1 received over de-chirp path  48  with the multi-tone calibration signal mtone in frequency band FB1 received from mixer  72  to produce baseband multi-tone calibration signal mtone′. LPF  76  may filter baseband multi-tone calibration signal mtone′ to remove high frequency mixer products from the baseband multi-tone calibration signal. Phase and magnitude measurement circuitry  88  may measure the magnitude and/or phase of baseband multi-tone calibration signal mtone′ and may provide the measured magnitude and/or phase values to ADC  42 . ADC  42  may convert the magnitude and/or phase values into digital data dat. Digital data dat may be provided to control circuitry  14  over digital output path  78 . Control circuitry  14  may store digital data dat at storage circuitry  16  for subsequent processing. This example is merely illustrative and, if desired, phase and magnitude measurement circuitry  88  may be located at other points or multiple points within receive chain  54 . 
     This process may be repeated while sweeping over different frequency bands FB2 (e.g., while changing the radio frequency of multi-tone calibration signal mtone as produced by mixer  64 ). This may serve to produce a full estimate of the power droop and/or phase shift of FMCW radar circuitry  26  across the operating (radio) frequencies of radar circuitry  26 . Once each of the desired radio frequencies have been characterized, distortion circuitry  30  ( FIG. 1 ) may distort subsequently-transmitted transmit signals (e.g., chirp signals) to invert the estimated power droop and/or phase shifts as estimated using multi-tone calibration signal mtone. The distorted chirp signals may then be used to produce accurate and reliable estimates of range R, velocity, and/or position. 
       FIG. 3  is a flow chart of illustrative operations that may be performed by radar circuitry  26  and control circuitry  14  in calibrating radar circuitry  26  (e.g., in embodiments where radar circuitry  26  performs multiple up-conversions prior to transmission by antennas  40 ). The operations of  FIG. 3  may be performed during manufacture, assembly, or testing of radar circuitry  26  or device  10  (e.g., in a manufacturing system or factory) and/or may be performed during regular operation of device  10  by an end user (e.g., during the useful life of device  10 ). 
     At operation  100 , DAC  32  may generate multi-tone calibration signal mtone. DAC  32  may generate the multi-tone calibration signal such that each tone is separated from one or two adjacent tones (in frequency) by a selected frequency gap Δf. Frequency gap Δf may be large enough so that each tone is distinct in frequency but small enough so that each tone experiences approximately the same power droop and so that frequency gap Δf lies within the relatively small bandwidth of ADC  42 . As examples, frequency gap Δf may be 20 MHz, 15 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, less than 20 MHz, less than 15 MHz, less than 10 MHz, less than 7 MHz, less than 6 MHz, less than 5 MHz, less than 4 MHz, or other values. 
     At operation  102 , mixer  56  may upconvert multi-tone calibration signal mtone from baseband to frequency band FB1. Amplifier  58  may pass multi-tone calibration signal mtone in frequency band FB1 to splitter  62 . Splitter  62  may transmit multi-tone calibration signal mtone to de-chirp mixer  74  over de-chirp path  48 . Splitter  62  may also transmit multi-tone calibration signal mtone to mixer  64 . 
     At operation  104 , control circuitry  14  may select a first FB2 frequency (e.g., a first RF band) to use for transmitting multi-tone calibration signal mtone. The frequency may be the first frequency in a sweep over the operating radio frequencies of radar circuitry  26  that is performed in calibrating the radar circuitry. The frequency may be greater than 10 GHz or 20 GHz or less than 10 GHz, as examples. 
     At operation  106 , mixer  64  may upconvert multi-tone calibration signal mtone from frequency band FB1 to the selected FB2 frequency (e.g., using FB2LO  46 ). Amplifier  66  may amplify the radio-frequency multi-tone calibration signal mtone. Transmit antenna  40 TX may transmit the radio-frequency multi-tone calibration signal mtone and receive antenna  40 RX may receive the transmitted radio-frequency multi-tone calibration signal mtone. In time, the transmit antenna transmits each of the tones in the radio-frequency multi-tone calibration signal mtone concurrently and, if desired, with the same polarization. In another implementation, the radio-frequency multi-tone calibration signal mtone may be conveyed to receive chain  54  over loopback path  80  rather than being transmitted by transmit antenna  40 TX. 
     At operation  108 , de-chirp mixer  74  may receive the multi-tone calibration signal mtone in frequency band FB2 over de-chirp path  48 . Mixer  72  may downconvert the radio-frequency multi-tone calibration signal mtone received over receive antenna  40 TX or loopback path  80  to frequency band FB1. De-chirp mixer  74  may mix the multi-tone calibration signal mtone in frequency band FB1 received over de-chirp path  48  with the multi-tone calibration signal mtone in frequency band FB1 produced by mixer  72  to generate baseband multi-tone calibration signal mtone′. 
     At operation  110 , LPF  76  may filter baseband multi-tone calibration signal mtone′ to remove high frequency mixer products from the baseband multi-tone calibration signal. Phase and magnitude measurement circuitry  88  may measure the magnitude and/or phase of baseband multi-tone calibration signal mtone′. In scenarios where a single tone is used for calibration, the single tone after down-conversion by de-chirp mixer  74  is at DC and is subject to interference from DC noise and other LO leakage. However, in scenarios where multi-tone calibration signal mtone is used for calibration, each of the tones in baseband multi-tone calibration signal mtone′ is offset from DC by frequency gap Δf. This may serve to prevent DC/flicker noise or other process noise (e.g., LO leakage) at baseband from interfering with baseband multi-tone calibration signal mtone′, thereby allowing for a more accurate estimate of power droop and/or phase shift to be obtained than in scenarios where only a single tone is used for calibration. ADC  42  may convert the magnitude and phase values to corresponding digital data dat. Control circuitry  14  may store digital data dat for subsequent processing. 
     If frequencies remain in the sweep of FB2 frequencies for estimating the power droop and phase shift, processing may proceed to operation  114  as shown by path  112 . At operation  114 , control circuitry  14  may select a new FB2 frequency to use for the next transmission of multi-tone calibration signal mtone. Processing may then loop back to operation  106 , as shown by path  116 , to continue to gather magnitude and/or phase values from baseband multi-tone calibration signal mtone for each of the FB2 frequencies in the sweep. This may allow control circuitry  14  to gather a full estimate of the power droop and/or phase of FMCW radar circuitry  26  as a function of frequency (e.g., across the range of operating frequencies of radar circuitry  26 ) for use in distorting subsequently transmitted chirp signals. 
     If no frequencies remain in the sweep of FB2 frequencies for estimating the power droop and phase shift, processing may proceed to operation  120  via path  118 . At operation  120 , control circuitry  14  may process the digital data dat (e.g., as stored at each iteration of operations  106 - 110 ) to estimate the amplitude and/or phase shift effects introduced by the components of radar circuitry  26 . The amplitude effects may be indicative of the power droop of the system. 
     At operation  122 , radar circuitry  26  may resume transmission of transmit signals for determining the range R between device  10  and external object  34  ( FIG. 1 ). Transmit signal generator  28  may transmit signals (e.g., chirp signals). Control circuitry  14  may predistort and/or post-distort the signals using distortion circuitry  30 . Distortion circuitry  30  ( FIG. 1 ) may distort the signals based on the estimated power droop and/or phase shift effects (e.g., as identified at operation  120 ). Distortion circuitry  30  may include digital predistortion circuitry that predistorts the chirp signals in the digital domain prior to conversion by DAC  32 , analog predistortion circuitry that predistorts the chirp signals after conversion by DAC  32 , and/or post-distortion circuitry that distorts received signals. 
     At operation  124 , transmit antenna  40 TX may radiate the transmit signals. Receive antenna  40 RX may receive a reflected version of the transmitted signals that have reflected off of external object  34  (e.g., as reflected signals  38  of  FIG. 1 ). The distortion performed at operation  124  may be an inverse of the estimated power droop and/or phase shift effects such that, after passing through transmit chain  52 , the distorted chirp signals are transmitted by transmit antenna  40 TX and received by receive antenna  40 RX as if there was no power droop or phase shift introduced by radar circuitry  26 . Distortion circuitry  30  may perform the distortion by complex-multiplying the transmit signals by complex values that serve to invert the estimated power droop and/or phase shift, as well as any I/Q imbalance in the system, for example. 
     If desired, radar circuitry  26  and control circuitry  14  may re-calibrate radar circuitry  26  (e.g., by looping back to operation  100 ) periodically (e.g., after a predetermined time period has elapsed), upon receipt of a user input or application call instructing device  10  to calibrate radar circuitry  26 , upon a detected change in the operating conditions of device  10 , upon detection of deterioration in the wireless performance of device  10 , or in response to any other desired trigger condition. This may allow radar circuitry  26  to continue to generate accurate estimates of range R, position, and velocity throughout the operating life of device  10 . In another implementation, radar circuitry  26  may be calibrated only once. 
       FIG. 4  includes frequency diagrams that show how an exemplary multi-tone calibration signal mtone may be used to produce baseband multi-tone calibration signal mtone′ for estimating power droop and/or phase shift. The example of  FIG. 4  illustrates the simplest case in which multi-tone calibration signal mtone is a dual-tone calibration signal having two tones separated by frequency gap Δf. The dual-tone calibration signal may sometimes also be referred to herein as a dual-tone pair or a pair of tones. This example is merely illustrative and, in general, multi-tone calibration signal mtone may include any desired number of two or more tones that are each separated from one or two other tones by frequency gap Δf. 
     As shown by frequency diagram  126  of  FIG. 4 , DAC  32  may generate multi-tone calibration signal mtone in a first frequency band 1 (e.g., baseband). DAC  32  may generate multi-tone calibration signal mtone using a tone generator, synthesizer, or other digital circuitry/logic. The tones in multi-tone calibration signal mtone are separated by frequency gap Δf. Mixer  56  may upconvert multi-tone calibration signal mtone to a second frequency band B2 (e.g., in frequency band FB1), as shown by arrow  130 . This signal may be provided to mixer  64  and to de-chirp path  48 . 
     Mixer  64  may upconvert multi-tone calibration signal mtone to a third frequency band B3 (e.g., in frequency band FB2), as shown by arrow  132 . Frequency gap Δf is preserved after each up-conversion. The multi-tone calibration signal mtone in frequency band B3 may be transmitted by transmit antenna  40 TX or loopback path  80 . Mixer  72  may downconvert the multi-tone calibration signal mtone from frequency band B3 back to frequency band B2. De-chirp mixer  74  may mix the multi-tone calibration signal mtone in frequency band B2 as received over de-chirp path  48  with the multi-tone calibration signal mtone in frequency band B2 as down-converted by mixer  72  to recover baseband multi-tone calibration signal mtone,′ as shown by arrow  136 . 
     As shown by frequency diagram  128  of  FIG. 4 , baseband multi-tone calibration signal mtone′ has an amplitude A1, which is measured by phase and magnitude measurement circuitry  88  and converted to a digital value in digital data dat by ADC  42 . The next radio frequency in the sweep of FB2 frequencies may then be used (e.g., during a subsequent iteration of operations  106 - 110  of  FIG. 3 ). This may produce a multi-tone calibration signal mtone at another frequency in frequency band B3, such as the multi-tone calibration signal mtone represented by dashed arrows  135  in frequency diagram  126 . The amplitude of this multi-tone calibration signal may be different than for the previously transmitted multi-tone calibration signal due to the power droop of the system (e.g., as shown by power droop  134 ). After mixing by de-chirp mixer  74 , the resulting baseband multi-tone calibration signal mtone′ may have amplitude A2, as shown by dashed arrow  129  in frequency diagram  128 . Amplitude A2 may be measured by phase and magnitude measurement circuitry  88  and converted to a digital value in digital data dat by ADC  42 . 
     Amplitude A2 is less than amplitude A1 due to the frequency-dependent power droop imposed by the components of wireless circuitry  24 . This may be repeated for each FB2 frequency in the sweep to recover a full estimate of the power droop  134  across operating frequencies as exhibited by wireless circuitry  24 . In other words, radar circuitry  26  may shift the generated dual-tones of multi-tone calibration signal mtone along the frequency axis (e.g., by iterating over operations  106 - 110  of  FIG. 3 ), while maintaining a constant frequency gap Δf, until the operating frequency range of radar circuitry  26  is sufficiently covered or sampled with dual-tones. In general, the finer the shift in radio frequency between each iteration, the more granularly the droop function (e.g., power droop  134 ) can be estimated. In embodiments where radar circuitry  26  only performs a single upconversion, the sweep over operating frequency may be performed within band B2 without further upconversion to band B3 (e.g., radar circuitry  26  may transmit multi-tone calibration signals across different FB1 frequencies, where power droop  134  is observed within frequency band FB1). Control circuitry  14  may process the stored amplitudes in digital data dat to estimate power droop  134 . The phase of each baseband multi-tone calibration signal mtone′ may also be estimated if desired to identify any phase shifts imposed by the components of radar circuitry  26 . 
     In scenarios where only a single-tone calibration signal is used, the resulting baseband tone would be recovered at DC in frequency diagram  128 , where any measurement of amplitude/phase would be negatively affected by DC noise or LO leakage. However, by generating multi-tone calibration signal mtone with two or more tones separated by frequency gap Δf, the output of the mixing operation performed by de-chirp mixer  74  (baseband multi-tone calibration signal mtone′) will be offset in frequency from DC by frequency gap Δf. Frequency gap Δf may therefore be selected such that baseband multi-tone calibration signal mtone′ does not overlap with any DC noise, LO leakage, or other baseband system noise. This may allow more accurate measurements of magnitude (e.g., amplitudes A1, A2, etc.) and thus power droop to be gathered than in scenarios where a single tone calibration signal is used, thereby allowing accurate estimates of range R, position, and velocity to be obtained over time. 
       FIG. 5  is a plot showing three examples of potential power droops that may be estimated by radar circuitry  26  and control circuitry  14  from the magnitude of baseband multi-tone calibration signals mtone′ for use in predistorting chirp signals. As shown in  FIG. 5 , curve CA shows a linear power droop that may be estimated by radar circuitry  26  and control circuitry  14 . Curve CC shows a parabolic power droop that may be estimated by radar circuitry  26  and control circuitry  14 . Curve CB shows a combination of linear and parabolic power droops that may be estimated by radar circuitry  26  and control circuitry  14 . Each point on curves CA, CB, and CC may correspond to a respective radio frequency in the sweep of radio frequencies used in transmitting multi-tone calibration signals mtone. Linear power droops such as that associated with curve CA are often associated with the droop effects of cabling. Parabolic power droops such as that associated with curve CC are often associated with the droop effects of antennas  40 TX and  40 RX. A combination of linear and parabolic power droops such as that associated with curve CB may represent the combination of the droop effects of cabling and antennas  40 TX and  40 RX, for example. These examples are merely illustrative and, in practice, the estimated power droop may have other shapes. 
     In the simplest case where multi-tone calibration signal mtone is a dual-tone calibration signal (e.g., as shown in  FIG. 4 ), the dual-tone pair may be represented as complex tones using equation 1, for example. 
       ( k   1   e   jωt   +k   1   e   j(1+Δ)ωt )*·( k   2   e   jωt   +k   2   e   j(1+Δ)ωt )*=2 k   1   *k   2 (1+cos(Δω t ))  (1)
 
     In equation 1, co is angular frequency, Δ is the frequency gap Δf in units of angular frequency, “*” is the complex conjugate operator, “·” is the dot product operator, t is time, and j is the square root of −1. By performing the operations of  FIG. 3 , control circuitry  14  may estimate power droop and/or phase shift effects introduced by radar circuitry  26  and thus may estimate complex weight values k 1  and k 2 . Complex weight values k 1  and k 2  may then be used to form the value that is used to predistort the chirp signals (e.g., the chirp signals may be multiplied by a value such as 1/(k 1 *k 2 ) to predistort the chirp signals, thereby inverting the subsequent power droop and phase shift effects imparted by the components of radar circuitry  26 ). 
     In the baseband of transmit chain  52 , the dual-tone calibration signal may be represented by one complex tone or two real tones that consist of four symmetric complex tones, as given by equation 2. 
       cos(ω t )+cos((1+Δ)ω t )=0.5(( e   −jωt   +e   jωt )+( e   −j(1+Δ)ωt   +e   j(1+Δ)ωt ))  (2)
 
     In the FB2 (e.g., RF) domain, the complex tone pairs are frequency-dependent attenuated, where the mixer path is represented by expression 3 and the antenna path is represented by expression 4. 
       ((k 1 e −jωt k 3 e jωt )+(k 1 e −j(1+Δ)ωt k 3 e j(1+Δ)ωt )) 8   (3)
 
       (k 2 e −jωt k 4 e jωt )+(k 2 e −j(1+Δ)ωt k 4 e j(1+Δ)ωt ) 8   (4)
 
     In the baseband of receive chain  54 , after mixing by de-chirp mixer ∝(a process sometimes referred to herein as de-chirping), several mixing products are generated. The ±n·ω mixing products that are 1 GHz are attenuated by LPF  76 . The ±Δ·ω mixing products that are less than 20 MHz (e.g., 1 MHz) may be evaluated for estimating the power droop. More generally, one complex tone may be modeled using expression 5, two complex tones may be modeled using expression 6, and four complex tones (e.g., two real tones) may be modeled using expression 7. 
     
       
         
           
             
               
                 
                   
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     In expressions 6 and 7, “T” is the transpose operator and n is an integer index. Expression 6 represents five equations, where two of the equations are linear dependent on the other three. Two parameters of interest, k 1 *k 2  (lower frequency) and k 3 *k 4  (higher frequency) are simultaneously estimated. IQ-imbalance correction may be performed before droop estimation. Use of two real tones may allow radar circuitry  26  to be produced at a lower manufacturing cost than use of two complex tones. However, the two paths may be separately calibrated when two complex tones are used whereas the two paths may not be separately calibrated when two real tones are used. In order to support generation of two complex tones, the sin/cos tables used to produce multi-tone calibration signal mtone may be doubled in size or may be run at half rate, where the signal is interpolated in I/Q and a complex mix is used to arrive in the appropriate frequency band, as examples. 
     The distortion performed by distortion circuitry  30  may be performed in the digital domain or in the analog domain.  FIG. 6  is a diagram showing one example of how distortion circuitry  30  may include predistortion circuitry in the digital domain. As shown in  FIG. 6 , the input of DAC  32  may be coupled to digital circuitry  140 . Digital circuitry  140  may include transmit signal generator  28  and predistortion circuitry  146  (e.g., distortion circuitry  30  may include digital predistortion (DPD) circuitry such as predistortion circuitry  146 ). The input of predistortion circuitry  146  may be coupled to the output of transmit signal generator  28 . The output of predistortion circuitry  146  may be coupled to the input of DAC  32 . DAC  32  may have an output  142  coupled to mixer  56  ( FIG. 2 ). Predistortion circuitry  146  may have a control path  144  that receives control signals ctrl from control circuitry  14 . 
     Transmit signal generator  28  may generate transmit signals (e.g., chirp signals). Predistortion circuitry  146  may multiply the transmit signals by a value that serves to predistort the transmit signals such that the predistortion in the transmit signals will counteract the estimated power droop, phase shift, and/or any I/Q imbalance imparted by the components of radar circuitry  26 . Control signals ctrl may include the values that are used by predistortion circuitry  146  to predistort the chirp signals. As the estimated power droop and/or phase shift changes over time, control signals ctrl may change the values that are used by predistortion circuitry  146  to predistort the transmit signals. DAC  32  may convert the predistorted transmit signals from the digital domain to the analog domain. The example of  FIG. 6  is merely illustrative. Other predistortion schemes or architectures may be used. Predistortion circuitry  146  may alternatively be implemented in the analog domain. Distortion circuitry  30  may additionally or alternatively include post-distortion circuitry that operates on received signals to compensate for power droop and phase shift. 
     In this way, device  10  may perform power droop estimation for the complete radio-frequency bandwidth of radar circuitry  26 , even if receive chain  54  does not support the complete radio-frequency bandwidth. At the same time, no direct access to the radio-frequency signals is required for performing the power droop estimation. This may serve to reduce the receive chain bandwidth and therefore lower current consumption in the system. Calibrating radar circuitry  26  using multi-tone calibration signal mtone may allow device  10  to choose the baseband offset frequency (e.g., via selection of frequency gap Δf) to be a system-dependent ideal tone position, such that there is no influence of system impairments, LO noise, etc. on baseband multi-tone calibration signal mtone′. Power droop estimation and compensation may be performed during the final production test of device  10  and/or over the lifetime of device  10  to adapt the droop compensation to any potential aging effects in device  10 . In addition, droop tracking and compensation over the lifetime of device  10  may be used to check for changes in the operation of device  10 , such as scenarios where a case or cover is attached to device  10 , thereby allowing device  10  to adapt system configurations (e.g., gain settings, background cancellation, etc.) accordingly. 
     The example of  FIGS. 2-4  in which radar circuitry  26  performs multiple upconversions is merely one illustrative implementation showing how radar circuitry  26  may be calibrated using multi-tone calibration signal mtone. In general, radar circuitry  26  may perform any desired number of one or more upconversions and may include any desired number of two or more mixers.  FIG. 7  is a circuit diagram of radar circuitry  26  in an example where radar circuitry  26  performs at least one upconversion and includes at least two mixers. 
     As shown in  FIG. 7 , radar circuitry  26  may include a first mixer such as mixer  150  coupled to the output of DAC  32  (e.g., over an I/Q path), a signal splitter such as splitter  154  having an input coupled to the output of mixer  150 , a second mixer such as mixer  152  (e.g., a de-chirp mixer) having a first input coupled to a first output of splitter  154  over signal (e.g., de-chirp) path  158 , and circuitry  156  (e.g., one or more line up droops) coupled between a second output of splitter  154  and a second input of mixer  152 . Other circuit components such as amplifiers, filters, an ADC (e.g., ADC  42  of  FIG. 2 ), or other components may be interposed at any desired locations within radar circuitry  26 . Circuitry  156  may include other portions of radar circuitry  26  that introduce power droops and phase shifts to radar circuitry  26  (e.g., antennas, loopback paths, transmission lines, amplifiers, filters, etc.). Circuitry  156  may, for example, include mixers  64  and  72 , amplifiers  66  and  70 , and antennas  40 TX and  40 RX in embodiments where radar circuitry  26  performs multiple upconversions as shown in  FIG. 2 . Circuitry  156  may sometimes be referred to herein as intermediate circuitry. 
     During spatial ranging operations, DAC  32  may pass transmit signals generated using transmit signal generator  28  ( FIG. 2 ) (e.g., chirp signals) to mixer  150 . Mixer  150  may use LO  160  to upconvert the transmit signals to higher frequencies such as frequencies in frequency band FB1 or frequency band FB2 of  FIG. 2  (e.g., LO  160  may include FB1LO  50  or FB2LO  46  of  FIG. 2 ). Splitter  154  may pass the up-converted transmit signals to mixer  152  over signal path  158  and to circuitry  156 . Circuitry  156  may transmit the up-converted transmit signals (e.g., as radio-frequency signals  36  of  FIG. 1 ) and may receive corresponding reflected signals (e.g., reflected signals  38  of  FIG. 1 ). Circuitry  156  may pass the received reflected signals to mixer  152 . Mixer  152  may mix the received signals with the transmit signals received over signal path  158  to produce corresponding baseband signals at output path  162 . Control circuitry  14  ( FIG. 1 ) may process the baseband signals and the transmit signals to identify range R, position, and/or velocity for external object  34 . 
     During calibration, DAC  32  may transmit multi-tone calibration signal mtone. Mixer  150  may up-convert the multi-tone calibration signal. Splitter  154  may transmit the up-converted multi-tone calibration signal to mixer  152  over signal path  158  and to circuitry  156 . Circuitry  156  may transmit the up-converted multi-tone calibration signal (e.g., in a closed loop over the air or over a loop back path), which is then received at mixer  152 . Mixer  152  may mix the up-converted multi-tone calibration signals received over signal path  158  with the up-converted multi-tone calibration signals received from circuitry  156  to produce baseband multitone calibration signal mtone′. Control circuitry  14  may repeat this process while sweeping mixer  150  over different frequencies (e.g., the frequencies of operation of radar circuitry  26 ). Control circuitry  14  may use the baseband multitone calibration signals produced by mixer  152  to estimate the power droop and/or phase shifts of circuitry  156 . Control circuitry  14  may then use distortion circuitry  30  ( FIG. 1 ) to distort subsequently transmitted signals to mitigate the power droop and phase shifts of circuitry  156 . In other words, radar circuitry  26  of  FIG. 7  may be calibrated using multi-tone calibration signals mtone according to the operations of  FIG. 3  (e.g., in embodiments where radar circuitry  26  only performs a single upconversion, an FB1 frequency may be selected at operation  104  of  FIG. 3  instead of an FB2 frequency, the upconversion at operation  106  may be omitted, FB1 frequencies may be processed in determining whether to proceed along paths  112  or  118 , and a new FB1 frequency may be selected at operation  114 ). 
     The methods and operations described above in connection with  FIGS. 1-7  may be performed by the components of device  10  using software, firmware, and/or hardware (e.g., dedicated circuitry or hardware). Software code for performing these operations may be stored on non-transitory computer readable storage media (e.g., tangible computer readable storage media) stored on one or more of the components of device  10  (e.g., storage circuitry  16  of  FIG. 1 ). The software code may sometimes be referred to as software, data, instructions, program instructions, or code. The non-transitory computer readable storage media may include drives, non-volatile memory such as non-volatile random-access memory (NVRAM), removable flash drives or other removable media, other types of random-access memory, etc. Software stored on the non-transitory computer readable storage media may be executed by processing circuitry on one or more of the components of device  10  (e.g., processing circuitry  18  of  FIG. 1 , etc.). The processing circuitry may include microprocessors, central processing units (CPUs), application-specific integrated circuits with processing circuitry, or other processing circuitry. The components of  FIGS. 2, 6, and 7  may be implemented using hardware (e.g., circuit components, digital logic gates, etc.) and/or using software where applicable. 
     The foregoing is merely illustrative and various modifications can be made to the described embodiments. The foregoing embodiments may be implemented individually or in any combination.