Patent Publication Number: US-2022239262-A1

Title: Phased array amplifier linearization

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to application titled ANTENNA ARRAY CALIBRATION SYSTEMS AND METHODS, Ser. No. 15/611,289, filed on Jun. 1, 2017, the disclosure of which is hereby incorporated by reference in its entirety herein. This application is also related to application titled SPATIAL DIGITAL PRE-DISTORTION, Ser. No. 15/372,723 filed Dec. 8, 2016, the disclosure of which is hereby incorporated by reference in its entirety herein. 
     This application is a continuation of U.S. patent application Ser. No. 17/303,021, filed May 18, 2021, which is a divisional application of U.S. patent application Ser. No. 15/801,232, filed Nov. 1, 2017, each of which is hereby incorporated by reference in its entirety herein. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     Embodiments of the invention generally relate to antennas, and in particular, to predistortion in connection with phased-array antennas. 
     Description of the Related Art 
     Radio frequency (RF) power amplifiers are used in a variety of applications, such as telecommunications, radars and the like. When a signal is amplified by an RF power amplifier, the amplified signal can become distorted due to non-linearities in RF power amplification. An upconversion process can also result in non-linearities. The presence of distortion can cause problems such as intermodulation distortion, out-of-band emissions, and interference. 
     One technique to linearize an RF power amplifier is by predistortion. With predistortion, the input signal to the RF power amplifier is predistorted in a manner that is complementary to the distortion added by the RF power amplifier to reduce the resulting distortion in the output of the RF power amplifier. Such techniques can also be applied to linearize the combination of an upconverter and RF power amplifier. 
     However, conventional predistortion techniques cannot be used with analog beamformers. What is needed is a technique to apply predistortion to the phased array amplifier of an analog beamformer. 
     SUMMARY OF THE DISCLOSURE 
     One embodiment includes an apparatus for radio frequency (RF) linearization of multiple amplifiers of a phased array, wherein the apparatus includes: a plurality of return paths configured to carry at least RF sample signals of a plurality of RF power amplifiers; a hardware RF power combiner configured to combine the RF sample signals to generate a combined signal; a plurality of return-side phase shifters configured to adjust a phase shift of the RF sample signals such that the RF sample signals are phase aligned at the hardware RF power combiner; and a predistorter configured to predistort an input signal to generate a predistorted signal and configured to adapt predistortion coefficients for predistortion based at least partly on observations of a signal derived from the combined signal. 
     One embodiment includes a method of linearization of multiple amplifiers of a phased array, wherein the method includes: phase shifting radio frequency (RF) sample signals of a plurality of RF power amplifiers such that the RF sample signals are phase aligned at a hardware RF power combiner; combining the RF sample signals the hardware RF power combiner to generate a combined signal; and predistorting an input signal with a predistorter to generate a predistorted signal, wherein predistortion coefficients are based at least partly on comparisons between portions of the input signal and corresponding portions of a signal derived from the combined signal. 
     One embodiment includes a phased array element for a phased array, wherein the phased array element includes: a switch for switching an antenna element between either a transmit side or a receive side for time-division duplex operation; and a return path separate from a transmit path, wherein the return path is configured to provide a radio frequency (RF) sample of a transmitted signal, wherein the return path further comprises a phase shifter configured to adjust a phase of the RF sample. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These drawings and the associated description herein are provided to illustrate specific embodiments of the invention and are not intended to be limiting. 
         FIG. 1A  is a schematic block diagram of a symmetric routing schematic for a 4-by-4 antenna array according to an embodiment. 
         FIG. 1B  is a schematic block diagram of an asymmetric routing schematic for a 2-by-8 antenna array according to another embodiment. 
         FIG. 2A  is an illustration of a horizontal wavefront according to an embodiment. 
         FIG. 2B  is an illustration of an angled wavefront according to an embodiment. 
         FIG. 2C  is a schematic block diagram of a series of transceivers according to an embodiment. 
         FIG. 2D  is an illustration of a planar array and an associated electromagnetic pattern according to an embodiment. 
         FIG. 3A  is a schematic block diagram of a probe with a power detector disposed between two antenna elements according to an embodiment. 
         FIGS. 3B-1 and 3B-2  are flow diagrams for calibration using a probe with a power detector disposed between two antenna elements according to an embodiment. 
         FIG. 3C  is a schematic block diagram of a probe with a mixer disposed between two antenna elements according to an embodiment. 
         FIG. 3D  is a flow diagram for calibration using a probe with a mixer disposed between two antenna elements according to an embodiment. 
         FIG. 4  is a schematic block diagram of probes disposed between four antenna elements according to an embodiment. 
         FIG. 5A  is a schematic block diagram of probes disposed between an array of three by four antenna elements according to an embodiment. 
         FIG. 5B  is a flow diagram for calibration using probes disposed between an array of three by four antenna elements according to an embodiment. 
         FIG. 6A  is a schematic block diagram of a probe with an RF power source disposed between two antenna elements according to an embodiment. 
         FIG. 6B  is a flow diagram for calibration using a probe with an RF power source disposed between two antenna elements according to an embodiment. 
         FIG. 7  illustrates a phased array with predistortion. 
         FIG. 8A  illustrates an embodiment of a phased array element. 
         FIG. 8B  illustrates another embodiment of a phased array element. 
         FIG. 8C  illustrates another embodiment of a phased array element. 
         FIG. 9  illustrates a method of arranging signal for collection of data for the determination of predistortion coefficients. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The following detailed description of certain embodiments presents various descriptions of specific embodiments. However, the innovations described herein can be embodied in a multitude of different ways, for example, as defined and covered by the claims. In this description, reference is made to the drawings where like reference numerals can indicate identical or functionally similar elements. It will be understood that elements illustrated in the figures are not necessarily drawn to scale. Moreover, it will be understood that certain embodiments can include more elements than illustrated in a drawing and/or a subset of the elements illustrated in a drawing. Further, some embodiments can incorporate any suitable combination of features from two or more drawings. 
     An antenna array can enable a beamformer to steer an electromagnetic radiation pattern in a particular direction, which generates a main beam in that direction and side lobes in other directions. The main beam of the radiation pattern is generated based on constructive inference of the signals based on the transmitted signals&#39; phases. Furthermore, the amplitudes of the antenna elements determine side-lobe levels. A beamformer can generate desired antenna patterns by, for example, providing phase shifter settings for the antenna elements. However, over time, the amplitudes of signals and the relative phases among the antenna elements can drift from the values set when the antenna was originally calibrated. The drift can cause the antenna pattern to degrade, which can, for example, reduce the gain in a main lobe. Thus, what is needed is a way to accurately measure and control the phase and amplitude of antenna elements in an array system even after an antenna array has been fielded. Furthermore, the calibration process itself can be relatively labor intensive, time consuming, and costly. Thus, there is a need for a method of calibration without the need for expensive test equipment and facilities and having to relocate the antenna to a particular location. These disclosed techniques are also applicable to the manufacturing test environment and can be used to speed production, thus lowering costs. In one embodiment, the calibration data is used by the beamformer and combined with other data, such as pre-calculated or pre-stored antenna pattern data, to generate appropriate settings for beamforming. 
     The present disclosure enables an antenna array to perform calibration using relative measurements of phase and/or absolute measurements of amplitude. A probe is placed between antenna elements and the phase and/or amplitude of the antenna elements are measured. Then, the phase or amplitude can be assessed to determine adjustments that are made to the transmitter, receiver, or transceiver connected to the antenna elements. In some embodiments, the antenna elements can transmit signals, and the phase of one or more antenna elements can be adjusted until a relatively high or maximum and/or relatively low or minimum power level is reached. Upon determining a relatively high or maximum power level, the phase adjuster or shifter values are recorded as those corresponding to in phase, and for a relatively low or minimum power level, the phase values are recorded as 180 degrees out of phase. Although embodiments describe the use of a probe, it is appreciated that other structures (e.g. conductors) that can transmit and/or receive signals may also be used (e.g. slots, monopole, small patches, other coupling structures, etc). 
     In some embodiments, the probe should be disposed symmetrically between the antenna elements. For example, if there are two antenna elements, the probe can be placed in between the two antenna elements. In another example, if there are four antenna elements, the probe can be placed diagonally between the four antenna elements equidistant from each of the four antenna elements. Placing the probe symmetrically between antenna elements reduces or eliminates the possible variation that may occur in the propagation of the radiation pattern to or from the probe and the antenna elements. 
     In some embodiments, the antenna elements can be used to transmit signals to the probe, the probe receiving the transmitted signals. The probe can detect power (e.g. by using a power detector) or detect both power and phase (e.g. by using a mixer). Alternatively, the probe can be used as a transmitter, transmitting a signal to the antenna elements, where the antenna elements receive the transmitted signal. 
     Using a single probe to calibrate multiple antennas is advantageous. Having a single probe that may be used to transmit to the antenna elements and/or receive signals from antenna elements may itself introduce variation to the signal. However, since the same probe and components connected to the probe (e.g. mixer) are used to measure the signal, there is advantageously no part-to-part or channel-to-channel variation with the disclosed techniques. For example, the probe and the components connected to the probe will introduce the same variation to a signal received at the probe from a first and second antenna element. 
     By contrast, couplers used to measure phase and amplitude of a signal to calibrate antenna elements would introduce variation. A separate coupler would be connected to the transmit path of each antenna element. Then, the signal would travel along the signal route to components connected to each coupler. The routing path from each coupler to their associated connected components would introduce channel to channel variation. Each coupler may be connected to its own set of components, which despite possibly being of the same kind of components, the components themselves introduce part to part variability. Furthermore, the couplers themselves use additional hardware such as switches. The couplers themselves, often made of metallic substances, may interfere with the radiation signal making it harder to obtain higher isolation between the antenna elements. These drawbacks are reduced or eliminated by embodiments of the invention. 
     Embodiments of the present disclosure including using a probe disposed between antenna elements are advantageous in that the probes can be used to calibrate the array based on near field radiation measurements. Thus, the array can be calibrated without the need for far field measurements. Typically, electromagnetic anechoic chambers, (also called echo-free chambers) can be used to simulate an open space situation. The time and space in these chambers may be difficult to schedule, may be expensive, and time consuming. However, embodiments of the present disclosure avoid the need of having to place the antenna in an anechoic chamber because near-field measurements are used instead of far-field measurements. Furthermore, anechoic chambers may be practical for initial calibration, but not for later calibration. Some embodiments of the antenna array of the present disclosure may be calibrated repeatedly and at the field. The probes can be permanently placed in between antenna elements. The antenna array may be configured to allow temporary installment of the probes in between the antenna elements as well. Some embodiments of the near-field calibration of the present disclosure may also be helpful for small signal difference. 
     The calibration method and system can be used to calibrate arrays of different sizes. For example, the system can calibrate a planar array by calibrating a first set of antenna elements (or calibration group) that are equidistant to one probe, then calibrating a second set of antenna elements equidistant to another probe where the first and second set of antenna elements share at least one antenna element. Then, the shared antenna element can be used as a reference point to calibrate the other antenna elements. 
     Although the disclosure may discuss certain embodiments with the probe as the receiver and the antenna elements as the transmitter, it is understood that the probe can act as a transmitter and the antenna elements as a receiver, and vice versa. 
       FIG. 1A  is a schematic block diagram of a symmetric routing schematic  100  according to an embodiment. The symmetric routing schematic  100  includes antenna elements,  102 A,  102 B,  102 C,  102 N,  102 E,  102 F,  102 G,  102 H,  102 I,  102 J,  102 K,  102 L,  102 M,  102 N,  102 O, and  102 P (collectively referred to herein as  102 ). The symmetric routing schematic  100  also includes a chip  104 A,  104 E,  104 I, and  104 M (collectively referred to herein as  104 ). The symmetric routing schematic  100  includes a transceiver  110  and routing paths  106 A,  106 B,  106 C,  106 D,  106 E,  106 F,  106 G,  106 H,  106 I,  106 J,  106 K,  106 L,  106 M,  106 N,  106 O,  106 P,  108 A,  108 E,  108 I, and  108 M (collectively referred to herein as  106 ) from the transceiver  110  to the antenna elements  102 . 
       FIG. 1A  refers to a symmetric routing schematic  100  for a 4-by-4 antenna array. The schematic refers to symmetric routing because the routes on the routing paths  106  from the transceiver  110  to the antenna elements  102  are of the same distance. For example, the routing path from transceiver  110  to antenna element  102 A is a combination of the routing paths  108 A and  106 A, while the routing path from transceiver  110  to antenna element  102 B is a combination of the routing paths  108 A and  106 B. The routing paths are generated to minimize variation in the distance the signal travels from the transceiver  110  to the antenna element  102 . This type of configuration helps to mitigate the variation that may cause difficulties in calibration due to different lengths of routing paths the signal travels from the transceiver  110  to the antenna element  102 . 
     The antenna elements  102  may be radiating elements or passive elements. For example, the antenna elements  102  may include dipoles, open-ended waveguides, slotted waveguides, microstrip antennas, and the like. Although some embodiments illustrate a certain number of antenna elements  102 , it is appreciated that the some embodiments may be implemented on an array of two or more antenna elements. 
       FIG. 1B  is a schematic block diagram of an asymmetric routing schematic  150  for a 2-by-4 antenna array according to another embodiment. The asymmetric routing schematic  150  includes antenna elements  152 A,  152 B,  152 C,  152 D,  152 E,  152 F,  152 G, and  152 H (collectively referred to herein as  152 ). The asymmetric routing schematic  150  also includes a chip  154 . The asymmetric routing schematic  150  includes routing paths  156 A,  156 B,  156 C, and  156 D (collectively referred to herein as  156 ) from the chip  154  to the antenna elements  152 .  FIG. 1B  is directed to asymmetric routing because the routing paths  156  from the chip  154  to the antenna elements  152  are different in lengths. Thus, the phase and amplitude varies differently from channel to channel. For example, the transmitted signal at the antenna element  152  may be different from element to element even though the same signal was transmitted from the chip  154 . In some embodiments, the received signal at the antenna elements  152  may be the same, but different when received at the chip  154  as a result of the different lengths of the routing paths  156 . 
       FIG. 2A  is an illustration of a horizontal wavefront  200  according to an embodiment. Each antenna element  102  may radiate in a spherical radiation pattern. However, the radiation patterns collectively generate a horizontal wavefront  204 . The illustration  200  includes antenna elements  102 A,  102 B,  102 C,  102 N,  102 M- 1  and  102 M. The antenna elements  102 A,  102 B,  102 C, and  102 N may be arranged linearly, where the elements are arranged on a straight line in a single dimension. In this configuration, the beam may be steered in one plane. The antenna elements may also be arranged planarly, arranged on a plane in two dimensions (N direction and M direction). In this planar configuration, the beam may be steered in two planes. The antenna elements may also be distributed on a non-planar surface. The planar array may be rectangular, square, circular, or the like. It is appreciated that the antenna may be arranged in other configurations, shapes, dimensions, sizes, types, other systems that can implement an antenna array, and the like. The illustration of the horizontal wavefront  200  shows each of the antenna elements  102  transmitting a signal  202 A,  202 B,  202 C,  202 N,  202 M- 1 , and  202 M (collectively referred to herein as  202 ) creating a horizontal wavefront  204 . The illustration of  FIG. 2A  illustrates an antenna array creating a main beam that points upward, as shown by the horizontal wavefront  204 . The phases from the antenna elements  102  are constructively interfering in the upward direction. 
       FIG. 2B  is an illustration of an angled wavefront  220  according to an embodiment. The illustration of the angled wavefront  220  includes antenna elements  102 A,  102 B,  102 C,  102 N,  102 M- 1  and  102 M. The antenna elements may be arranged similarly to that described for  FIG. 2A . The illustration of an angled wavefront  220  shows the antenna elements  102  transmitting a signal  222 A,  222 B,  222 C,  222 N,  222 M- 1 , and  222 M (collectively referred to herein as  222 ) creating a wavefront  224  that propagates at an angle, different from the direction of the wavefront  204  in  FIG. 2A . The phases of the signals  222  are constructively interfering in the direction that the angled wavefront  220  is traveling (e.g. up-right direction). Here, each of the phases of the antenna elements  102  may be shifted by the same degree to constructively interfere in a particular direction. 
     The antenna elements  102  can be spaced apart equidistant from one another. In some embodiments, the antenna elements  102  are spaced at different distances from each other, but with a probe equidistant from at least two antenna elements  102 . 
     Although the disclosure may discuss certain embodiments as one type of antenna array, it is understood that the embodiments may be implemented on different types of antenna arrays, such as time domain beamformers, frequency domain beamformers, dynamic antenna arrays, active antenna arrays, passive antenna arrays, and the like. 
       FIG. 2C  is a schematic block diagram of a series of transceivers  240 A,  240 B,  240 N (collectively referred to herein as  240 ) according to an embodiment. In some embodiments, a single transceiver  240  feeds to a single antenna element  102 . However, it is appreciated that a single transceiver  240  may feed to multiple antenna elements  102 , or a single antenna element  102  may be connected to a plurality of transceivers  240 . Furthermore, it is appreciated that the antenna element  102  may be linked to a receiver and/or a transmitter. 
     In some embodiments, the transceiver  240  may include a switch  242 A,  242 B,  242 N (collectively referred to herein as  242 ) to switch the path from the antenna element  102  to the receiver or the transmitter path. The transceiver  240  includes another switch  248 A,  248 B,  248 N (collectively referred to herein as  248 ) that switches the path from the signal processor (not shown) to the receiver or the transmitter path. The transmitter path has a phase adjuster  244 A,  244 B,  244 N (collectively referred to herein as  244 ) and a variable gain amplifier  246 A,  246 B,  246 N (collectively referred to herein as  246 ). The phase adjuster  244  adjusts the phase of the transmitted signal at the antenna element  102  and the variable gain amplifier  246  adjusts the amplitude of the transmitted signal at the antenna element  102 . Although the embodiments describe the transceiver  240  including a phase adjuster  244  and a variable gain amplifier  246 , other components can be used to adjust the magnitude of the signal and/or the phase of the signal. Furthermore, although a switch is shown to switch from the transmitter path to the receive path, other components can be used, such as a duplexer. 
     The receiver path may also have a phase adjuster  250 A,  250 B,  250 N (collectively referred to herein as  250 ), and a variable gain amplifier  252 A,  252 B,  252 N (collectively referred to herein as  252 ). The phase adjuster  250  and the variable gain amplifier  252  can be used to adjust the received signal from the antenna element  102  before going to the signal processor (not shown). 
       FIG. 2D  is an illustration of a planar phased array  260  and an associated electromagnetic pattern according to an embodiment.  FIG. 2D  includes antenna elements  102 A,  102 B,  102 N,  102 M- 1 , and  102 M.  FIG. 2D  also includes a beam pattern with a main beam  262 , and side lobes  264 A,  264 B,  264 C. The antenna elements  102  are transmitting a signal where the phase of the signal is constructively interfering in the direction of the main beam  262 . The precision of the amplitude of the antenna elements  102  controls the side-lobe levels. For example, the more uniform the amplitudes of the transmitted signals from the antenna elements  102  are, the lower the side lobe levels will be. The antenna elements  102  may be disposed on a single die, or multiple dies. 
       FIG. 3A  is a schematic block diagram  300  of a probe  310 A with a power detector  312 A disposed between two antenna elements  102 A,  102 B according to an embodiment. In this block diagram  300 , the probe is disposed equidistant between the two antenna elements  102 A,  102 B. The probe  310 A may be a slot, a probe, a coupling element, any component that can be used to detect signals, or the like. The probe can be used as a transmitter. 
       FIGS. 3B-1 and 3B-2  is a flow diagram for calibration using a probe with a power detector disposed between two antenna elements according to an embodiment. 
       FIG. 3B-1  illustrates a flow diagram  320  for measuring and comparing all power levels for the two antenna elements  102 A,  102 B. At block  322 , the transmitter tied to the antenna element  102 B is turned off. At block  324 , a signal is transmitted from the first antenna element  102 A. A signal is generated from the mixer  302 A, amplified by the variable gain amplifier  246 A, shifted in phase by the phase adjuster  244 A, and transmitted from the antenna element  102 A. At block  326 , the probe  310 A detects the transmitted signal from the antenna element  102 A and the power detector  312 A detects power values of the detected signal. At block  327 , the system can determine whether all power and/or phase levels are measured. If yes, then the system can continue to block  328 . If not, then the power and/or phase can be adjusted in block  323 , and proceed back to block  324 . For example, a combination of each power level and each phase level can be measured. In some embodiments, the phase and amplitude are decoupled such that each power level can be measured and each phase level measured independently without having to measure every combination of each power level and each phase level. 
     At block  328 , the transmitter tied to the antenna element  102 A is turned off. At block  330 , a signal is transmitted from the second antenna element  102 B. A signal is generated from the mixer  302 B, amplified by the variable gain amplifier  246 B, shifted in phase by the phase adjuster  244 B, and transmitted from the antenna element  102 B. At block  332 , the probe  310 A detects the transmitted signal from the antenna element  102 B and the power detector  312 A detects power values of the detected signal. 
     At block  334 , once the detected signals from the transmitted signals of antenna elements  102 A and  102 B are stored, the power values are compared to calibrate the transmitter connected to the antenna element  102 A relative to the transmitter connected to the antenna element  102 B, and/or vice versa. The power values are calibrated by adjusting the gain of the variable gain amplifier  246 A and/or  246 B. In some embodiments, the calibration is performed during, before, or after other blocks in  FIG. 3B . After comparing power values to calibrate the antenna elements at block  334 , the flow can continue to  FIG. 3B-2 . 
       FIG. 3B-2  illustrates a flow diagram  321  for calibrating the phase for the two antenna elements  102 A,  102 B. At block  325 , a signal of the same power level is transmitted from both antenna elements  102 A,  102 B. This can be achieved using data obtained from the steps in  FIG. 3B-1 . At block  329 , the phase of the first antenna element  102 A is changed. Then at block  335 , the total power can be measured by a power detector  312 A. The system determines whether the maximum power level is measured at block  336 . If not, then the system continues to change the phase of the first antenna element  102 A and continues the flow diagram from block  329 . If the maximum power level is measured at block  336 , then the phase can be determined to be in an in-phase condition. The phases that provide the maximum power level at block  336  is recorded for the antenna elements at block  337 . 
     At block  338 , the phase of the first antenna element  102 A is changed, and at block  339 , the total power is measured using the power detector  312 A. At block  340 , the system determines whether the minimum power level is measured. If not, then the phase of the first antenna element  102 A is changed and the flowchart continues from block  338 . If the minimum power level is measured, then the system records the phase calibration information for the antenna elements at block  341 . This can be considered a 180 degrees out of phase condition. 
       FIG. 3C  is a schematic block diagram  330  of a probe  310 A with a mixer  342 A disposed between two antenna elements  102 A,  102 B according to an embodiment. The probe  310 A may be disposed equidistant from the antenna elements  102 A and  102 B. The probe  310 A is connected to the mixer  342 A. 
       FIG. 3D  is a flow diagram  360  for calibration using a probe with a mixer disposed between two antenna elements according to an embodiment. The mixer can be used to measure phase and/or amplitude. At block  362 , the transmitter connected to antenna element  102 B is turned off. At block  364 , a signal is generated from the mixer  302 A, amplified by the variable gain amplifier  246 A, phase shifted by the phase adjuster  244 A, and transmitted by the antenna element  102 A. At block  366 , the probe  310 A detects the transmitted signal and using the mixer, the signal processor measures and records the amplitude and phase values. At block  367 , the system can determine whether all power and/or phase levels have been measured. If yes, then the system can proceed to block  368 . If no, then the system can adjust power and/or phase levels in block  363 , and return to block  324 . 
     At block  368 , the transmitter connected to the antenna element  102 A is turned off. At block  370 , a signal is generated from the mixer  302 B, amplified by the variable gain amplifier  246 B, shifted in phase by the phase adjuster  244 B, and transmitted by the antenna element  102 B. At block  372 , the probe  310 A detects the signal, the mixer mixes the signal, and the signal processor measures and records the phase and amplitude values. At block  373 , the system can determine whether all power and/or phase levels have been measured. If yes, then the system can proceed to block  374 . If no, then the system can adjust power and/or phase levels in block  369 , and return to block  370 . 
     At block  374 , based on a comparison between the amplitudes of the signals transmitted by the antenna element  102 A and  102 B, the variable gain amplifiers  246 A,  246 B are adjusted such that the amplitudes are calibrated to transmit substantially the same power based on the same signal generated. Furthermore, based on a correlation between the phases of the signals transmitted by the antenna element  102 A and  102 B, the phase adjusters  244 A and  244 B are adjusted such that the phases are calibrated to transmit at substantially the same phase for the same generated signal. 
     The values of the variable gain amplifier  246 A,  246 B and/or the phase adjusters  244 A,  244 B may be controlled using a digital command sent through the beam steering interface, such as the beam steering chip or the signal processor. The phase adjuster may be an n-bit phase adjuster providing control of the phase in a total of a particular number of phase degrees. Thus, the calibration process may be calibrated to be the state that allows for the closest phase value. In some embodiments, the calibration is performed during, before, or after other blocks in  FIG. 3D . 
       FIG. 4  is a schematic block diagram  400  of probes  310 A,  310 B,  310 C disposed between four antenna elements  102 A,  102 B,  102 C,  102 N according to an embodiment. In the block diagram  400 , probe  310 A is disposed equidistant from antenna element  102 A and antenna element  102 B. The probe  310 B is disposed equidistant from antenna element  102 B and antenna element  102 C. The probe  310 C is disposed equidistant from antenna element  102 C and antenna element  102 N. The antenna elements  102 A,  102 B,  102 C, and  102 N are disposed linearly. 
     In this embodiment, antenna elements  102 A and  102 B are calibrated first. The transmitters connected to the antenna elements  102 B,  102 C, and  102 N are turned off. The mixer  302 A generates a signal, the signal shifted in phase by the phase adjuster  244 A, the signal amplified by a variable gain amplifier  246 A, and transmitted from the antenna element  102 A. The probe  310 A receives the signal. Next, the antenna  102 B transmits a signal that the same probe  310 A detects. In this embodiment, the probe  310 A is connected to a power detector  312 A. Antenna elements  102 A and  102 B are calibrated similar to the process described in  FIG. 3A . However, the probe  310 A may be connected to mixers and may be calibrated similar to the process described in  FIG. 3B . Other ways of calibration are possible. For example, other components may be connected to the probe  310 A to measure phase and/or amplitude. Furthermore, other methods of calibration may be used using relative measurements of phase and/or amplitude. 
     Next, antenna elements  102 B and  102 C are calibrated. Then,  102 C and  102 N are calibrated. In this embodiment, the calibration occurs serially. However, calibration may occur in different time steps. For example, when antenna element  102 B is transmitting a signal to calibrate with antenna  102 A, not only can probe  310 A be detecting the signal, but also probe  310 B may detect the signal. Thus, while antenna elements  102 A and  102 B are being calibrated, the calibration between antenna elements  102 B and  102 C can begin in parallel. In this embodiment, neighboring antenna elements are being calibrated. However, it is appreciated that any set of antenna elements that are equidistant from the probe can be calibrated. For example, the first and fourth antenna element  102 A,  102 N can be calibrated with a probe  310 B between the second and third antenna element  102 B,  102 C. 
       FIG. 5A  is a schematic block diagram of probes disposed between an array of three by four antenna elements according to an embodiment. The probes  310 A,  310 B,  310 C . . .  310 M (collectively referred to herein as  310 ) are disposed symmetrically between a set of four antenna elements  102 . In this embodiment, the probe  310  is equidistant from each antenna element  102  in the set of four antenna elements. However, it is appreciated that the probe  310  may be placed at some distance that is equidistant from at least two antenna elements  102 . 
       FIG. 5B  is a flow diagram for calibration using probes disposed between an array of three by four antenna elements according to an embodiment. 
     At block  522 , all transmitters connected to all antenna elements  102  are turned off. At block  524 , the first set of four antenna elements is calibrated together. Then, the first antenna element  102 A transmits a signal. The probe  310 A receives this signal, measures the power using the power detector  312 A, and records the power. This is repeated for the other three antenna elements  102  that are equidistant from the first probe  310 A. Then, the gain of each antenna element  102  within the set of four antenna elements is adjusted to be calibrated in relation to one another. Then, all four antenna elements  102  transmit a signal, the phase adjusted, and the phase recorded to identify the phase configurations that provide maximized power (e.g. the phase values are equal). The same test is performed for when the power is minimized (e.g. phases are 180 degrees apart). Calibration can be performed in a similar manner to that described in  FIG. 3A, 3B , and other ways described in this disclosure. 
     Although the disclosure may discuss certain embodiments as calibrating four antennas at once, it is understood that the embodiments may be implemented using a different number of transmitters, antenna elements, probes, and the like. For example, the power can be calibrated for four antenna elements at once (e.g. once power is recorded for four antenna elements, the gain for each of the four antenna elements can be adjusted to meet a reference gain value), while the phase can be calibrated in pairs (e.g. calibrate antenna elements  102 A and  102 B first, then calibrate antenna elements  102 A and  102 M- 1  next). 
     After the antenna elements  102  within the set of four antenna elements have been calibrated in reference to one another, the calibration procedure may calibrate the next set of four antenna elements  102 . Antenna elements except for the antenna elements in the next set are turned off at block  526 . At block  528 , an antenna element that is in both the first and second set is identified. Then at block  530 , the next set of antenna elements are calibrated with the identified antenna element as a reference. The next set of four antenna elements  102  may be equidistant from the next probe  310 B. The same or a different calibration method may be used for the next set of four antenna elements  102 . After the sets of antenna elements  102  across the row of elements are calculated, the process can be repeated for the following column of a set of four antenna elements  102 . For example, after the set of antenna elements  102  have been calibrated using the probes  310 A,  310 B, and  310 C, then the next set of four antenna elements  102  to be calibrated may be those that are equidistant from the probe  310 M. 
     Once the power values are calibrated, the transmitter connected to the antenna element  102 A and the transmitter connected to the antenna element  102 B are turned on. Based on the power calibration, the antenna elements  102 A and  102 B transmit signals at substantially the same power level. Adjust one or both of the phase adjuster  244 A or  244 B. The probe  310 A will receive both signals from antenna elements  102 A and  102 B and detect the power values at the power detector  312 A. When the power is maximized, the phase adjuster  244 A and  244 B are aligned (e.g. the phase values are equal). When the power is minimized, the phase adjuster  244 A and  244 B are opposite (e.g. phase of one equals the phase of the other plus 180 degrees). Using this relative relationship, the system can calibrate the phase of one antenna element relative to the other antenna element. 
       FIG. 6A  is a schematic block diagram of a probe  310 A with an RF power source  610  disposed between two antenna elements  102 A,  102 B according to an embodiment. In this block diagram  600 , the probe  310 A is disposed equidistant between the two antenna elements  102 A,  102 B. The probe  310 A may transmit a signal for the antenna elements  102 A and  102 B to receive. 
       FIG. 6B  is a flow diagram for calibration using a probe with an RF power source disposed between two antenna elements according to an embodiment. At block  622 , the probe  310 A is a radiating element that transmits a signal. The probe  310 A can be connected to an RF power source  610 . At block  624 , the antenna elements  102 A,  102 B receives the signal transmitted from the probe  310 A. The antenna elements  102 A,  102 B can be connected to a phase adjuster  604 A and  604 B, the variable gain amplifier  606 A,  606 B, and an I/Q mixer  602 A,  602 B. The antenna elements  102 A,  102 B receives the signal and detects the phase and amplitude using the I/Q mixer  602 A,  602 B. At block  626 , the antenna elements are calibrated based on a comparison of the detected phase and amplitude measurements. 
       FIG. 7  illustrates a phased array with predistortion linearization. In one embodiment, the phased array corresponds to an analog phased array or to a hybrid phased array and is used in connection with a time-division duplex (TDD) communication system, such as a mobile phone base station. Other systems, such as radar systems, are also applicable. As will be explained in greater detail later in connection with  FIGS. 8A-8C , the phased array elements  702   a - 702   n  can include phase shifters and variable gain amplifiers to adjust a pattern or “beam” of the phased array for both transmitting and receiving. In some embodiments, the amount of phase shift and gain adjustment to be applied to each phased array element for a desired pattern can be determined by the techniques described earlier in connection with  FIGS. 1A to 6B . However, other techniques can alternatively be used. 
     A predistorter  704  includes a digital signal processor (DSP)  706  and an adaptive control  708 . An input signal V S (t) is provided as an input to the DSP  706 . For example, the input signal V S (t) can be generated by a modulator of a modem and correspond to a baseband complex modulation envelope. The DSP  706  can perform predistortion on the input signal V S (t) on a sample-by-sample basis to generate a predistorted drive signal V P (t) that complements the nonlinearities collectively introduced by the RF power amplifiers of the phased array elements  702   a - 702   n . In the illustrated embodiment, the same predistortion provided by the predistorter  704  is applied to multiple or to all RF power amplifiers of the phased array elements  702   a - 702   n  of the phased array. 
     A wide variety of algorithms can be used for predistortion. Moreover, the DSP  706  can correspond to a wide variety of signal processing circuits, such as, but not limited to, a finite impulse response (FIR) filter, a lookup table, or the like. The manner by which the DSP  706  predistorts the input signal V S (t) is determined by the particular predistortion algorithm being implemented and the coefficients within the DSP  706 . The adaptive control  708  can compare samples of the input signal V S (t) with corresponding samples of a digital feedback signal V DR (t) to determine appropriate coefficients for predistortion that are applied by the DSP  706 . These appropriate coefficients can vary with different amplifiers, over time, over temperature, over different drive levels, over varying beam pattern, or the like, and can be adaptively adjusted as needed by the adaptive control  708 . For discussions on predistortion and adaptive adjustment, see, for example, NAGATA, Y.,  Linear Amplification Technique for Digital Mobile Communications , IEEE Vehicular Technology Conference (1989), pgs. 159-164; and CAVERS, J. K.,  Amplifier Linearization Using A Digital Predistorter With Fast Adaptation And Low Memory Requirements , IEEE Transactions on Vehicular Technology, Vol. 39, No. 4, pp. 374-383, November 1990. 
     Adaptive adjustment and the collection of RF samples for adaptive adjustment need not be performed continuously and can instead be performed sporadically, such as periodically, or in response to changes, such as changes to beam angle/antenna pattern/gain/power levels. 
     The DSP  706  can be implemented in hardware, such as in an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or the like. Portions of the adaptive control  708  can be implemented in software/firmware by a processor executing machine-readable instructions for the particular predistortion algorithm. The computations performed by the adaptive control  708  do not need to be performed in real time and can be performed using data stored in and retrieved from a memory device. 
     A digital-to-analog converter (DAC)  710  converts the predistorted drive signal V P (t) from a digital form to an analog form and provides an analog predistorted drive signal V A (t) as an input to an upconverter  712 . The upconverter  712  converts the analog predistorted drive signal V A (t) to an upconverted signal V U (t). In the illustrated embodiment, the analog predistorted drive signal V A (t) is a baseband signal, and the upconverted signal V U (t) is a higher-frequency signal, and can be, for example, radio frequency, microwave frequency, millimeter wave (RF/MW/mmw). In the context of this disclosure, the term radio frequency (RF) will include, but is not limited to, microwave and millimeter wave frequencies. In one example, the upconverter  712  can correspond to a quadrature upconverter. Other types of upconverters can be used. The upconverter  712  can include, for example, a mixer, a filter, and a variable gain amplifier. 
     The upconverted signal V U (t) is provided as an input to a power divider  714 , which can include one or more Wilkinson power dividers. In contrast to conventional TDD systems, in some embodiments, the power divider  714  is dedicated to the transmit/forward path and is not used for the receive/return path. The power divider  714  provides the multiple phased array elements  702   a - 702   n  with the same predistorted signal as a drive signal. 
     The phased array elements  702   a - 702   n  include the RF power amplifiers to be linearized as well as other components. The number of phased array elements  702   a - 702   n  in the phased array can vary in a very broad range. While not restricted to a power of 2, a number that is a power of 2 can be easier to implement. In one example, the number of phased array elements  702   a - 702   n  is in a range between 16 and 1024. In some embodiments, each of the phased array elements  702   a - 702   n  can be manufactured to be identical to each other, but can vary during operation with different phase shifter and or gain/power settings. The phased array elements  702   a - 702   n  can have a transmit terminal T, a receive/return terminal R, and an antenna element terminal T. In contrast to a conventional phased array element for a TDD system, the transmit and receive/return paths in some embodiments of the invention can be separated or dedicated. This advantageously provides relatively large cost and size improvements over systems in which each RF amplifier of a phased array has its own predistortion linearization. For clarity, other terminals such as power and control terminals are not shown. Various embodiments for the phased array elements  702   a - 702   n  will be described in greater detail later in connection with  FIGS. 8A-8C . 
     In the illustrated embodiment, the return/receive paths are the same paths and are separate from the forward/transmit paths. In some embodiments, each receive path adjusts the phase of its received signal, such that all received signals are added in-phase. Amplitude adjustment in the receive path is also possible, to compensate for path mismatches, if any. A hardware RF power combiner  716  combines the signals from the return/receive paths to generate a combined signal V C (t), which is provided as an input to a downconverter  718 . During a transmit phase, the return/receive paths can carry RF sample signals. During a receive phase, the return/receive paths can carry received signals, such as signals transmitted by mobile phones. In some embodiments, the hardware RF power combiner  716  can include one or more Wilkinson combiners. The hardware RF power combiner  716  does not correspond to a multiplexer. 
     The downconverter  718  converts the combined signal V C (t), which is an RF signal, to a downconverted signal V D (t), which can be a baseband or intermediate frequency signal. The downconverter  718  can include a mixer and a filter, and in some embodiments, can include additional amplifiers. The downconverted signal V D (t) is provided as an input to an analog-to-digital converter (ADC)  720 , which converts the downconverted signal V D (t) to a digital downconverted signal V DR (t). 
     When the phased array is transmitting, selected samples of the digital downconverted signal V DR (t) can be collected for analysis for adaptive adjustment of predistortion. When the phased array is receiving, the digital downconverted signal V DR (t) can, for example, be provided as an input to a demodulator of the modem (not shown) to generate received data. 
     The adaptive control  708  can compare samples of the input signal V S (t) with corresponding samples of the digital downconverted signal V DR (t) to estimate the predistortion coefficients. For example, the samples from the input signal V S (t) can be scaled, rotated, and delayed to align with the samples of the digital downconverted signal V DR (t). In one example, an adaptive algorithm can tune its predistortion coefficients to minimize the total error (such as mean-squared error) between the input signal V S (t) and the digital downconverted signal V DR (t). 
       FIGS. 8A-8C  illustrate various embodiments of phased array elements  802 ,  822 ,  842 . Other variations are possible. These phased array elements  802 ,  822 ,  842  can be used for any of the phased array elements  702   a - 702   n  described earlier in connection with  FIG. 7 . To avoid repetition of description, components having the same or similar function may be referenced by the same reference number. 
     In the embodiment illustrated in  FIG. 8A , the transmit path and the receive/return path are separate. In a TDD system, transmitting and receiving occur at different times. When transmitting, the return/receive path can be used for providing RF samples of the transmitted signal. When receiving, the return/receive path is used to provide received signals. The phased array element  802  includes a transmit-side phase shifter  804 , a variable gain RF power amplifier  806 , a leaky switch  808 , a low-noise amplifier (LNA)  810 , and a return-side phase shifter  812 . The amount of phase shift provided by the transmit-side phase shifter  804  and the amount of gain of the variable gain RF power amplifier  806  are determined based on the antenna pattern or beamforming desired. 
     When transmitting, a relatively small amount of the transmitted power can be leaked across the leaky switch  808  from the transmit side to the return/receive side for collection of RF samples for adaptive adjustment. Ordinarily, the leaky switch  808  selects either the transmit side or the return/receive side for the antenna element. An appropriate amount of leakage between the transmit side and the return/receive side can be specified and deliberately introduced for the leaky switch  808 . The amount of leakage that will be applicable can vary in a very broad range and can vary with an amount of gain provided by the LNA  810 . This leaked power provides the return/receive side with an RF sample of the transmitted signal. 
     The LNA  810  can be present in the return/receive path for reception of signals from other sources, such as mobile phones, but is not needed for the RF sampling of the transmitted signal. During RF sampling, the gain of the LNAs  810  of the plurality of phased array elements  802  can be the same. During operation, the return-side phase shifter  812  can have different settings depending on whether the return/receive paths are being used for collection of RF samples for adaptive adjustment of predistortion or are being used for receiving. 
     When the return/receive paths are being used for collection of RF samples, the return-side phase shifters should be adjusted such that the return path signals are aligned in phase at the hardware RF power combiner  716  ( FIG. 7 ). In some embodiments, this can mean that the return-side phase shifter  812  effectively performs the opposite phase shift to the phase shift of the transmit-side phase shifter  804 . It will be understood that there can be variations in path lengths that can need to be taken into account by additional offsets. These variations can be determined during a manufacturing or calibration process and stored in a lookup table. When the return/receive paths are being used for receiving, the return-side phase shifters  812  can be adjusted to implement the desired antenna pattern. 
     In the embodiment illustrated in  FIG. 8B , transmit path and receive/return path are again separate or dedicated paths. The phased array element  822  includes a transmit-side phase shifter  804 , a variable gain RF power amplifier  806 , a directional coupler  824 , a switch  826 , a low-noise amplifier (LNA)  810 , and a return-side phase shifter  812 . In a TDD system, the switch  826  selects the transmit side for the antenna element when transmitting, and the switch  826  selects the receive side for the antenna element when receiving. 
     When transmitting, a relatively small amount of the transmitted power (known as an RF sample) is coupled via the directional coupler  824  from the transmit side to the return/receive side for collection of RF samples for adaptive adjustment. The coupling factor is not critical. For example, the coupling factor can be −10 decibels (dB), −20 dB, or the like. Other amounts are applicable for the coupling factor and will be readily determined by one of ordinary skill in the art. However, in some embodiments, the coupling factor is about the same for the directional couplers  824  of the phased array. The RF samples from the coupled output can be provided to the return/receive path ahead of or behind the LNA  810 , but should be provided ahead of the return-side phase shifter  812 . For example, switches can be used to provide the RF samples to the desired points in the signal path. 
     As described earlier in connection with  FIG. 8A , when the return/receive paths are being used for collection of RF samples, the return-side phase shifters  812  should be adjusted such that the return path signals are aligned in phase at the hardware RF power combiner  716  ( FIG. 7 ). When the return/receive paths are being used for receiving, the return-side phase shifters  812  can be adjusted to implement the desired antenna pattern. 
     In the embodiment illustrated in  FIG. 8C , transmit path and the receive path can be the same, and a dedicated return path can provide RF samples for adaptive adjustment. The phased array element  842  includes a transmit-side phase shifter  804 , a variable gain RF power amplifier  806 , a directional coupler  824 , a switch  826 , a low-noise amplifier (LNA)  810 , a return-side phase shifter  844 , and a receive-path phase shifter  846 . 
     In the embodiment illustrated in  FIG. 8C , the transmit and receive operations can be similar to those found in conventional phased array elements. The power divider  714  can provide combining functions for the receive path, and components such as the downconverter  718  and ADC  720  can be duplicated for the receive path and the return path, as the receive path and the return path are separate in  FIG. 8C . 
     The directional coupler  824  provides the RF samples to the return-side phase shifter  844 , which can be adjusted such that the return path signals are aligned in phase at the hardware RF power combiner  716  ( FIG. 7 ). The gain of the LNA  810  and the phase of the receive-path phase shifter  846  can be adjusted based on the desired antenna pattern or beamforming. 
       FIG. 9  illustrates a method of arranging signal for collection of data for the determination of predistortion coefficients. The process adjusts the phase of the RF sample signals such that the RF sample signals are phase aligned  902  at the hardware RF power combiner  716  ( FIG. 7 ). The phase alignment can be accomplished by providing phase adjustments to the phase shifters  812 ,  844  ( FIGS. 8A-8C ). These phase-aligned RF sample signals are combined  904  in the hardware RF power combiner  716  of the phased array to generate a combined signal. The adaptive adjustment algorithm can then determine  906  the appropriate predistortion coefficients to use based on comparisons between portions of the input signal and corresponding portions of a signal derived from the combined signal, such as from corresponding portions of a downconverted and digitally converted version of the combined signal. 
     Any of the principles and advantages discussed herein can be implemented in connection with any other systems, apparatus, or methods that benefit could from any of the teachings herein. For instance, any of the principles and advantages discussed herein can be implemented in connection with any devices with a need to adjust the amplitude or phase of a phased array. 
     Aspects of this disclosure can be implemented in various electronic devices. For instance, one or more of the above phased array embodiments can implemented in accordance with any of the principles and advantages discussed herein can be included in various electronic devices. Examples of the electronic devices can include, but are not limited to, cell phone base stations, radar systems, radar detectors, consumer electronic products, parts of the consumer electronic products such as semiconductor die and/or packaged modules, electronic test equipment, etc. Examples of the electronic devices can also include communication networks. The consumer electronic products can include, but are not limited to, a phone such as a smart phone, a laptop computer, a tablet computer, a wearable computing device such as a smart watch or an ear piece, an automobile, a camcorder, a camera, a digital camera, a portable memory chip, a washer, a dryer, a washer/dryer, a copier, a facsimile machine, a scanner, a multifunctional peripheral device, a wireless access point, a router, etc. Further, the electronic device can include unfinished products, including those for industrial and/or medical applications. 
     Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise,” “comprising,” “include,” “including,” and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to.” The words “coupled” or “connected”, as generally used herein, refer to two or more elements that may be either directly connected, or connected by way of one or more intermediate elements. Thus, although the various schematics shown in the figures depict example arrangements of elements and components, additional intervening elements, devices, features, or components may be present in an actual embodiment (assuming that the functionality of the depicted circuits is not adversely affected). Additionally, the words “herein,” “above,” “below,” and words of similar import, when used in this application, shall refer to this application as a whole and not to any particular portions of this application. Where the context permits, words in the Detailed Description of Certain Embodiments using the singular or plural number may also include the plural or singular number, respectively. The words “or” in reference to a list of two or more items, is intended to cover all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list. All numerical values or distances provided herein are intended to include similar values within a measurement error. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the disclosure. Indeed, the novel apparatus, systems, and methods described herein may be embodied in a variety of other forms. Furthermore, various omissions, substitutions and changes in the form of the methods and systems described herein may be made without departing from the spirit of the disclosure. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the disclosure.