Abstract:
Systems and associated methods for reducing Doppler shifts in the broadband signals between Unmanned Aerial Vehicles (UAVs) and ground stations are disclosed herein. In one embodiment, a method for reducing the Doppler shift of wireless signals includes estimating a velocity of the UAV based on a Global Positioning System (GPS) or an Inertial Measurement Unit (IMU) of the UAV and calculating the Doppler shift of an upload (UL) wireless signal based on the velocity of the UAV. The method further includes predistorting a frequency of the UL wireless signal at the ground station to reduce the Doppler shift at a UAV receiver (RX) and transmitting the UL wireless signal from a ground station transmitter (TX) to the UAV RX. In some embodiments, calculating the Doppler shift of the UL wireless signal is performed at the ground station.

Description:
TECHNICAL FIELD 
       [0001]    The present technology is generally related to the field of correcting Doppler shifts in the broadband signals between Unmanned Aerial Vehicles (UAVs) and ground stations. 
       BACKGROUND 
       [0002]    Wireless communication systems transfer data from a transmitter (TX) of one station to a receiver (RX) of another station. In some applications, one of the stations can be ground based (i.e., stationary) while the other station is carried by a flying object (e.g., a satellite in Earth&#39;s orbit or an airplane). In some applications, multiple stations (TX or RX) can be ground based and in communication with one or more flying objects (RX or TX). Such systems are sometimes used for Internet connections, especially if the land-based network is underdeveloped. A relative distance between the TX and RX changes in real time, depending on the direction and magnitude of the velocity of the flying object. As a result, the Doppler shift distorts the signal transmitted/received between the TX and RX. The Doppler frequency shift can be estimated as: 
         [0000]        f   D   =f   t   −f   r , 
         [0000]    where f t  represents frequency of the signal at TX, and f r  represents frequency of the signal at RX. The Doppler frequency shift can be calculated as: 
         [0000]    
       
         
           
             
               
                 f 
                 D 
               
               = 
               
                 
                   f 
                   c 
                 
                  
                 
                   
                     ( 
                     
                       
                         
                           V 
                           → 
                         
                         t 
                       
                       - 
                       
                         
                           V 
                           → 
                         
                         r 
                       
                     
                     ) 
                   
                   . 
                   
                     n 
                     → 
                   
                 
               
             
             , 
           
         
       
     
         [0000]    where {right arrow over (V)} t  and {right arrow over (V)} r  represent velocities of TX and RX, respectively, {right arrow over (n)} represents unity vector in the line of TX and RX, and “c” represents the speed of light. 
         [0003]    In practice, if an airplane TX transmits a wireless signal while traveling away from the ground station, the frequency of the signal sensed by the ground station RX is lower than the frequency of the wireless signal originally transmitted by the airplane&#39;s TX. Conversely, if, for example, the airplane receives the wireless signal while travelling toward the ground station, the frequency of the signal sensed by the airplane&#39;s RX is higher than the frequency of the wireless signal originally transmitted from the ground station&#39;s TX. This mismatch in the TX/RX frequencies of the wireless signals can result in an increased bit error ratio (BER) of the digital signal (i.e., number of the error bits divided by the total number of bits in the signal) reduced from the received wireless signal at the RX, which reduces the effective bandwidth of the wireless signal. 
         [0004]    Several conventional methods can counteract the mismatch between the TX and RX frequencies caused by the Doppler shift. For example, when the trajectory of the flying object is known a-priori (e.g., a commercial airplane on a scheduled route), the Doppler shift at the ground station can be calculated. Based on this predetermined Doppler shift, the wireless signal at, for example, airplane TX, can be predistorted through analogue circuitry such that the frequency shift of the wireless signal received by the ground station RX is eliminated or reduced. In other conventional systems, the a-priori known Doppler shift can be fed to appropriate electronic circuitry at the RX to correct the frequency of the signal received by the RX. The electronic circuitry required for the correction/predistortion can be either stored at the ground station or carried by the relatively large flying object (e.g., the satellite or airplane). With some other conventional systems, the flying object transmits a reference signal at known frequency in addition to the data-carrying wireless signal. The difference between the frequency of the reference signal as received by the RX and the a-priori known value of the emitted reference signal corresponds to the Doppler frequency shift. Since the wireless signal received by the RX is also subjected to the same Doppler shift, the wireless signal can be corrected using, for example, suitable electronic circuitry. 
         [0005]    In some applications, however, the trajectory of the flying object is not known a-priori and/or the reference signals may not be practical because the bandwidth required for the reference signal reduces the bandwidth available for the wireless data transmission. Accordingly, it would be advantageous to provide a robust correction for wireless signal Doppler shift that does not depend on the a-priori knowledge of the trajectory of the flying object or on the reference signals. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0006]      FIG. 1A  is a schematic representation of a position of an unmanned aerial vehicle (UAV) with respect to a ground station. 
           [0007]      FIG. 1B  is a graph of a Doppler frequency as a function of time. 
           [0008]      FIG. 2  is a schematic illustration of a system for signal correction at the ground station and UAV RX&#39;s in accordance with an embodiment of the present technology. 
           [0009]      FIG. 3  is a schematic illustration of a system for signal predistortion at the ground station TX and a signal correction at the ground station RX in accordance with an embodiment of the present technology. 
           [0010]      FIG. 4  is a schematic illustration of a system for the signal predistortion and correction at both the ground station and UAV in accordance with an embodiment of the present technology. 
           [0011]      FIG. 5  is a schematic illustration of a system for the signal correction/predistortion at the ground station and the perturbation correction/predistortion at the UAV in accordance with an embodiment of the present technology. 
           [0012]      FIG. 6  is a schematic illustration of the UAV and ground station correction algorithms in accordance with an embodiment of the present technology. 
           [0013]      FIG. 7A  is a schematic illustration of the digital and analog predistortion of the wireless signal emitted by the TX in accordance with an embodiment of the present technology. 
           [0014]      FIG. 7B  is a schematic illustration of the digital and analog correction of the wireless signal received by the RX in accordance with an embodiment of the present technology. 
           [0015]      FIG. 8A  is a schematic illustration of correction of the wireless signal at the ground station in accordance with an embodiment of the present technology. 
           [0016]      FIG. 8B  is a schematic illustration of correction of the wireless signal at the UAV station in accordance with an embodiment of the present technology. 
           [0017]      FIG. 9  is a flow diagram illustrating an embodiment of implementation of the Doppler shift correction. 
           [0018]      FIG. 10  is a flow diagram illustrating a method for correcting the Doppler shift. 
           [0019]      FIG. 11  is a graph of bit error rate (BER) with and without correcting the Doppler shift. 
       
    
    
     DETAILED DESCRIPTION 
       [0020]    The following disclosure describes various embodiments of systems and associated methods for correcting the Doppler shift of the wireless signal between a ground station and an unmanned aerial vehicle (UAV). In some embodiments, a broadband communication via High Altitude Long Endurance (HALE) UAV is capable of achieving low cost/high throughput wireless communication. The UAV based broadband communication can be especially useful in the areas where land based fiber networks are underdeveloped. However, the Doppler shift changes the frequency of the wireless signals due to the velocity of the UAV relative to the ground station. In general, the Doppler shift caused by the velocity of the UAV is not known a-priori because of the complex and changing trajectory of the UAV. In some embodiments of the present technology, the Doppler shift can be evaluated by calculating velocity of the UAV using a GPS (and/or other motion sensors) carried by the UAV. Based on thus calculated real time Doppler shift, the download (DL) signal received at the ground station RX can be corrected to eliminate or reduce its Doppler shift. In general, the corrected signal has a smaller bit error ratio (BER) than the originally received signal that includes the Doppler shift. The corrected signal can then be demodulated into its constitutive channels and provided to the users. In some embodiments, based on the estimated Doppler shift, the upload signal (UL) at the ground station TX can be predistorted such that the effects of the Doppler shift are eliminated or at least reduced when the signal is received at the UAV RX. 
         [0021]    In addition to or instead of the correction/predistortion at the ground station, the signal correction and/or predistortion can be done at the UAV RX/TX using the electronics carried by the UAV. For example, the outgoing DL signal can be predistorted at the UAV TX, while the outgoing upload (UL) signal can be predistorted at the ground station TX. Furthermore, the signals can be corrected at the corresponding ground station/UAV RX&#39;s. Since the weight and size of the correction/predistortion electronics reduces the flight time and/or payload of the UAV, in some embodiments a coarse correction/predistortion can be delegated to the ground station, while the fine (or perturbation) correction/predistortion is performed by a suitable electronics carried by the UAV (for example, digital signal processing (DSP) electronics). In general, suitable correction/predistortion of the wireless signal can be applied before and/or after the signal is digitized. 
         [0022]    The calculated values of the Doppler shift may lag behind the real-time Doppler shift because of (a) the travel time for the UAV position/velocity data to reach the computers at the ground station; and (b) the computational effort to calculate the Doppler shift. Therefore, in some embodiments, the UAV flight (e.g., trajectory, velocity) can be dynamically characterized (for example, based on the GPS and other flight sensors carried by the UAV) to proactively predict the Doppler shift of the wireless signal in real time or at least closer to real time. Then, the predicted Doppler shift can be used to correct/predistort the wireless signal. 
         [0023]    Various embodiments of the inventive technology are set forth in the following description and  FIGS. 1A-8 . The word “module” is used to describe hardware, software or a combination of hardware and software that executes the computing/control tasks in the system. Some examples of the hardware are programmable processors, application specific integrated circuits (ASICs), digital signal processors (DSPs) and the like. The software may include a sequence of instructions that can be executed by the hardware. Many of the details and features shown in the Figures are merely illustrative of particular embodiments of the disclosure and may not be drawn to scale. Accordingly, other embodiments can have other details and features without departing from the spirit and scope of the present disclosure. In addition, those of ordinary skill in the art will understand that further embodiments can be practiced without several of the details described below. Some details describing well-known structures and systems often associated with wireless signal systems are not set forth below to avoid unnecessarily obscuring the description of the various embodiments of the disclosure. Furthermore, various embodiments of the disclosure can include structures other than those illustrated in the Figures and are expressly not limited to the structures shown in the Figures. 
         [0024]      FIG. 1A  is a schematic view of a trajectory  101  of a UAV  100  with respect to a ground stations  110   a ,  110   b . The trajectory  101  may appear erratic to a hypothetical observer at the ground station  200  because of the frequent changes in the velocity direction and magnitude of the UAV  100  with respect to fixed frames of reference  120   a  (at the ground station  110   a ) and  120   b  (at the ground station  110   b ). These changes in the velocity and location of the UAV  100  cause the corresponding Doppler shifts in frequency and timing of the signals received by the RX&#39;s of the ground stations  110   a ,  110   b  and the UAV  100 . In general, the trajectory of the UAV is not known a-priori. Therefore, the corresponding shifts in the frequency and timing of the wireless signals are also not known a-priori. 
         [0025]      FIG. 1B  is a graph of a sample Doppler frequency shift sensed by the RX (either UAV based or ground station based) as a function of time. The vertical axis represents Doppler frequency shift in Hz, and the horizontal axis represents time. The illustrated Doppler frequency shift has a basic (coarse) shape  102  with the interposed (fine) perturbations  103  that may be caused by, for example, vibration and/or rotation of the UAV. In general, the perturbations of the UAV are relatively small in comparison to the changes in the overall trajectory of the UAV. Due to a smaller amplitude of the perturbations  103  in comparison to the basic (coarse) shape  102 , the perturbations appear superimposed over the basic shape  102  of the Doppler frequency shift. In some embodiments, the amplitude of the perturbations  103  may be an order of magnitude smaller than the amplitude of the basic shape  102 . In general, a higher amplitude of the basic shape  102  corresponds to the faster speed of the UAV (either moving away or toward the RX). Conversely, a higher amplitude of the perturbations  103  that is superimposed over the basic shape  102  corresponds, for example, to a larger amplitude of the vibration of the UAV. In the right hand side of the graph, a group of waveforms  104  has a generally higher frequency than the remainder of the Doppler frequency shift  102 . Such a higher frequency may be indicative of the UAV changing its direction toward/away from the ground station more frequently. If left uncorrected, this higher frequency caused by the Doppler shift may result in a higher bit error ratio (BER) when the signal is received at the RX and/or smaller bandwidth of the wireless signal. 
         [0026]      FIG. 2  is a schematic illustration of a system for signal correction at the RX&#39;s of the UAV  100  and ground station  200 . In some embodiments, the UAV  100  can carry one or more GPS&#39;s and/or inertial measurement units (IMU&#39;s)  120  capable of determining a position of the UAV in real time. In some embodiments, the IMU&#39;s can be accelerometers or gyroscopes. Generally, the accuracy of determining the position of the UAV improves with the number of the GPS&#39;s, IMU&#39;s and the altitude of the UAV. In the illustrated embodiment, the output of the GPS, IMU  120  is fed to a UAV Altitude and Velocity Detection module  110 . A person of ordinary skill would know suitable electronics and software that can estimate altitude and velocity of a UAV based on the GPS signal of the UAV. For example, a first derivative of the GPS (and/or IMU) signal as a function of time can be an estimate of the velocity of the UAV. As explained above, the velocity of the UAV  100  causes the Doppler shift in the frequency of the wireless signal received at the ground station RX. Furthermore, the location of the UAV  100  (i.e., the distance from the UAV to the ground station) determines the time required for the wireless signal to travel from the UAV  100  to the ground station  200  (i.e., a timing difference). A Doppler Shift Estimator module  150  can estimate the frequency and timing shifts of the wireless signal based in part on the output of the UAV Altitude and Velocity Detection module  110 . In general, the UL wireless signal received by the UAV RX includes a frequency shift caused by the Doppler effect. In at least some embodiments of the inventive technology, based on the calculations by the UAV Altitude and Velocity Detection module  110 , a UAV RX Correction module  131  can eliminate or at least reduce the frequency/timing shifts of the UL wireless signal at the UAV RX. After the correction, the UL wireless signal received at the UAV RX can have a reduced BER and/or an improved bandwidth. 
         [0027]    A UAV Flight Control module  112  can maintain the altitude and velocity of the UAV based at least in part on the UAV Altitude and Velocity Detection module  110 . For example, the UAV Flight Control module  112  can maintain the position of the UAV at a prescribed altitude and within a generally defined area by controlling the magnitude and direction of the velocity of the UAV  100 . In some embodiments, a UAV Flight Status module  114  can report the location, velocity and/or acceleration of the UAV to the ground station  200 . Based on the reports received from the UAV Flight Status module  114  and signal from a GPS  220  of the ground station  200 , a Doppler Shift Estimator module  250  of the ground station  200  can estimate the Doppler shift of the wireless signal received at the ground station RX. A person of ordinary skill would know suitable methods and systems for estimating a Doppler shift of the wireless signal based on the velocity of the UAV  100 , distance of the UAV  100  from the ground station  200 , and frequency of the wireless signal. Based on the estimate of the Doppler shift, a Ground Station RX Correction module  241  can process the incoming wireless signal to eliminate or reduce the effects of frequency/timing shifts of the DL wireless signal received at the ground station RX. 
         [0028]    Performing the Doppler shift correction of the UL wireless signal at the UAV has both advantages and drawbacks. An example of an advantage are the readily available UAV altitude and velocity reports that can be input to the Doppler Shift Estimator module  150  without appreciable delays caused by the signal travel among the relatively closely spaced components of the UAV. However, the weight and space of the Doppler Shift Estimator module  150  and UAV RX Correction module  131  may limit the payload and/or flight time of the UAV. Conversely, when the Doppler shift correction is performed at the ground station  200  (e.g., at the Ground Station RX Correction module  241 ), the weight/space limitations are less restrictive, but the time required for the, for example, transmission of the UAV flight status reports from the UAV  100  to the ground station  200  necessarily delays the implementation of the DL wireless signal correction. Therefore, different distributions of the correction/predistortion hardware are suitable for different situations. 
         [0029]      FIG. 3  is a schematic illustration of a system for signal predistortion at the ground station TX and a signal correction at the ground station RX in accordance with an embodiment of the present technology. As explained with reference to  FIG. 2  above, the weight and space of the components required for UAV based RX correction may limit the payload and/or flight time of the UAV. Therefore, in at least some embodiments of the present technology, the ground station  200  can include electronics and software both for correcting the DL wireless signal and for predistorting the UL wireless signal. With the illustrated embodiment, the Doppler Shift Estimator module  250  receives the status reports from the UAV  100  (e.g., position, velocity, acceleration of the UAV) and the output of the ground station based GPS, IMU  220 . Based on the received data, the Doppler Shift Estimator module  250  can estimate required correction and predistortion, and provide it to the Ground Station RX Correction module  241  and a Ground Station TX Predistortion module  232 , respectively. Based on the input from the Doppler Shift Estimator module  250 , the Ground Station RX Correction module  241  can correct the incoming DL wireless signal to eliminate or reduce the BER and/or to improve the bandwidth of the wireless signal. Furthermore, the Ground Station TX Predistortion module  232  can predistort the outgoing UL wireless signal by, for example, adjusting the frequency of the UL wireless signal such that the wireless signal received at the UAV RX has the frequency/timing that is representative of small or non-existent Doppler shifts. For example, if the UAV  100  moves away from the ground station  200  then the Ground Station TX Predistortion module  232  may increase the frequency of the UL wireless signal to offset the effects of the Doppler shift associated with the UAV velocity. In some embodiments, the precision of the Doppler shift elimination/reduction can be further improved by correcting/predistorting the wireless signal at the ground station  200  and UAV  100 . An example of such a system is described below with reference to  FIG. 4 . 
         [0030]      FIG. 4  is a schematic illustration of a system for the signal predistortion and correction at both the ground station and UAV in accordance with an embodiment of the present technology. With the illustrated embodiment, the DL wireless signal can be predistorted at the UAV TX Predistortion module  142  to eliminate or reduce the effects of the Doppler shift at the ground station RX. The remaining effects of the Doppler shift (if any) in the predistorted DL wireless signal can be eliminated/reduced at the Ground Station RX Correction module  241 . Conversely, the UL wireless signal can be predistorted at the Ground Station TX Predistortion module  232 , and then further corrected at the UAV RX Correction module  131 . In at least some embodiments of the present technology, the effects of the Doppler shifts are eliminated or reduced more thoroughly using both the predistortion and correction. 
         [0031]      FIG. 5  is a schematic illustration of a system for the signal correction/predistortion at the ground station and the perturbation correction/predistortion at the UAV in accordance with an embodiment of the present technology. With the illustrated embodiment, the wireless signal is corrected/predistorted both at the ground station  200  and the UAV  100 . Specifically, a coarse correction/predistortion is performed at the ground station  200 , while a perturbation correction/predistortion is performed at the UAV  100 . In at least some embodiments, such a distribution of the wireless signal correction/predistortion between the ground station and the UAV can decrease the BER of the resulting data reduced from a received wireless signal, while minimizing the weight/space required for the correction/predistortion modules. As explained with reference to  FIG. 1B , the Doppler shift can have a basic (coarse) shape with the interposed (fine) perturbations caused by, for example, vibration and/or rotation of the UAV, which can be measured by Flight Sensors  160  (e.g., accelerometers, gyroscopes). The outputs of the Flight Sensors  160  and the GPS, IMU  120  can be directed to a Perturbation Detection module  170  that includes suitable electronics and/or software for quantifying the perturbations of the UAV. In some embodiments, the perturbations can be differentiated from the basic Doppler frequency shift based on the amplitudes of the perturbation being significantly smaller (e.g., an order of magnitude smaller or two orders of magnitude smaller) than the Doppler frequency shift. The amplitude differences can be detected by suitable electronics, for example level detectors. In other embodiments, the perturbations can be differentiated from the Doppler frequency shift based on the frequency of the perturbations being different (e.g., smaller or larger) than the Doppler frequency shift. The frequency differences can be detected by, for example, applying Fourier transform to the time series and detecting peak power density at different frequencies: Doppler frequency shift and the perturbation frequency. In some embodiment of the present technology, the required signal processing is performed by dedicated digital or analog signal processing electronics. Based at least in part on this quantification (i.e., quantification of the perturbations), a UAV RX Perturbation Correction module  133  can eliminate or reduce the perturbations of the incoming UL wireless signal. Analogously, a UAV TX Perturbation Predistortion module  143  can eliminate or reduce the perturbations of the outgoing DL wireless signal. With the illustrated embodiment, the required electronics for the perturbation correction/predistortion is carried by the UAV. Therefore, the time delays for the signals that quantify the perturbations are generally small (in comparison with the time delays associated with the travel of the wireless signal to/from the ground station), which can improve the correction/predistortion of the perturbations. In at least some embodiments, the Ground Station TX Predistortion module  232  and Ground Station RX Correction module  241  can respectively predistort/correct the wireless signal to eliminate or reduce the coarse Doppler shift of the wireless signal. As explained with reference to  FIG. 1B , in some embodiments, the perturbations in the Doppler frequency (or timing) shifts can have substantially higher frequency and smaller amplitude in comparison with the coarse Doppler frequency/timing shifts. In general, the correction of the Doppler frequency/timing shifts at the RX may introduce errors or noise due to, for example, the errors in calculating signal travel delays between the TX and RX. Such errors/noise may be relatively less significant for the coarse Doppler shifts due to their relatively high amplitudes. Conversely, the errors/noise caused by the correction of the perturbation frequency/timing shifts may be relatively more significant due to the relatively small amplitudes of the perturbations in the Doppler shifts. Therefore, in at least some embodiments, the DL wireless signal may be appropriately predistorted by the UAV TX Perturbation Predistortion module  143 , while the Ground Station RX Correction module  241  can correct the wireless signal to eliminate or reduce the coarse Doppler shift of the wireless signal. Analogously, the UL wireless signal may be appropriately predistorted by the Ground Station Predistortion module  232  to reduce/eliminate the coarse Doppler shifts, while the perturbations in the UL wireless signal are reduced/eliminated by the UAV RX Perturbation Correction module  133 . 
         [0032]      FIG. 6  is a schematic illustration of a UAV correction algorithm  600   a  and a ground station correction algorithm  600   b  in accordance with an embodiment of the present technology. In some embodiments, a UAV Flight Modeling algorithm  252  provides estimates of the UAV flight trajectory and/or velocity. These estimates can, for example, include near future predictions of the UAV trajectory and/or velocity based on the UAV position/velocity/acceleration. Furthermore, for modeling the UAV flight the UAV Flight Modeling algorithm  252  may rely on a Model Characterization algorithm  251  (e.g., characterizations of the past modeling results) and a Delay Characterization algorithm  253  (e.g., delay in the wireless signal propagating from the UAL to the ground station, delays in generating UAV flight status reports, delays in applying the correction at the TX or RX, etc.). In at least some embodiments, the output of the UAV Flight Modeling algorithm  252  can be used with transmit/receive (TRX) filters  254   a  (DL) and  254   b  (UL) to improve the Doppler shift estimates. For example, the DL TRX Filter  254   a  and/or the UL TRX Filter  254   b  may include input from the UAV Flight Status Report module  114  and the UAV Flight Modeling algorithm  252  to better estimate the UAV trajectory/velocity. In some embodiments, the DL/UL TRX Filters may include optimal signal filter, such as Kalman filters that recursively estimate the trajectory/velocity of the UAV. A person of ordinary skill would know other filters that can estimate the trajectory/velocity of the UAV. The estimates of the trajectory/velocity of the UAV can be provided to DL/UL Doppler Shift Estimate algorithms  255   a / 255   b  to calculate the corresponding Doppler shift estimates. In at least some embodiments, the Doppler shift estimates are the coarse estimates that do not include small perturbations in the wireless signal. 
         [0033]    In some embodiments of the present technology, the Doppler frequency/timing shifts can also be calculated at the UAV. For example, the UAV Flight Control module  112  can receive inputs from the UAV Flight Sensors  160  (e.g., vibration, rotation of the UAV) and the GPS  120  (e.g., absolute position of the UAV) to control the flight of the UAV and to provide flight parameters to the UAV Flight Status module  114 . Additionally, flight models, for example, past modeling results, can be characterized by a Model Characterization algorithm  152  that may include Kalman filter or other filters. Such characterization can include predictions of the future UAV trajectory (e.g., relatively short term predictions based on the Model Characterization that is based on past history of the UAV trajectory). Based on these inputs, a Fine Doppler Correction/Predistortion algorithm  155   a  can calculate required correction/predistortion that eliminates or reduces the fine (i.e., perturbation) Doppler shifts. The correction/predistortion of the perturbations in the wireless signal is described, for example, with reference to  FIG. 5 . Furthermore, a Coarse Doppler Correction/Predistortion algorithm  155   b  can calculate required correction/predistortion that eliminates or reduces the coarse Doppler shifts. Such elimination/reduction of the coarse Doppler shifts in the wireless signal is described, for example, with references to  FIGS. 2 and 4  above. The coarse or fine (perturbation) correction/predistortion of the wireless signal is executed by suitable electronics. Some embodiments of the systems and methods for correction/predistortion of the wireless signal are described with reference to  FIGS. 7A and 7B  below. 
         [0034]      FIGS. 7A and 7B  are schematic illustrations of the digital and analog circuits that perform the Doppler correction/predistortion, respectively, of the wireless signal emitted by the TX or received by the RX in accordance with embodiments of the present technology.  FIG. 7A  illustrates a signal predistortion system  700   a  that can digitally and/or analogly predistort the wireless signal emitted by a TX of the ground station or the UAV. The system  700   a  can include a TX Waveform Generating module  710  capable of generating a UL wireless signal (at the ground station) or a DL wireless signal (at the UAV). As explained above, these wireless signals are subjected to the Doppler frequency and timing shifts when communicated from/to a UAV. To counteract the effects of the Doppler shifts, the TX waveforms can be predistorted by a Digital Predistortion module  720   a  and/or an Analog Predistortion module  760   a  such that, when received at the corresponding RX, the effects of the Doppler shifts of the wireless signal are eliminated or reduced. Signal predistortion can be calculated/estimated by the systems and methods described with reference to  FIG. 6 . In some embodiments, the digital predistortion can be applied at a Digital Equalizer module  730  that is capable of applying required predistortion on a per-frequency or a per-channel basis. A person of ordinary skill would know suitable digital filters that can apply predistortion on the, for example, per-channel basis. An example of such a digital equalizer is a Viterbi equalizer that minimizes a probability of an error in a signal sequence. Therefore, in at least some embodiments, the Digital Equalizer module  730  provides a stream of digital data that is digitally predistorted to account for the Doppler shifts. This stream of digital data can be converted to an analog wireless signal at a Digital to Analog Converter (DAC)/Filter module  740   a . The resulting analog signal can be routed to a Quadrature Up Conversion module  750  where the analog channels can be converted from baseband frequencies to physical (RF) frequencies. In some embodiments, the Analog Predistortion module  760   a  can further predistort the analog channels to, for example, further reduce the Doppler shift of the wireless signal once it is received by the RX. A Power Amplifier  770   a  can amplify the analog signal to produce amplified signals  780  that are wirelessly sent by an antenna  790  to a corresponding RX. 
         [0035]      FIG. 7B  illustrates a signal correction system  700   b  that can digitally and/or analogly correct the effects of the Doppler shift in a wireless signal received by an RX of the ground station or the UAV. Certain elements of the system  700   b  may be generally analogous to those of system  700   a , and are not described in detail here. As explained above, the incoming wireless signal may include Doppler shifts because of the relative velocity of the UAV with respect to the ground station. The signal correction system  700   b  may eliminate or reduce the effects of the Doppler shifts by using, for example, the signal correction systems and methods described with reference to  FIG. 6 . In an embodiment of the inventive technology, the incoming wireless signal is received by the antenna  790  and is routed through a Low Noise Amplifier (LNA)  770   b . An Analog Correction module  760   b  can apply the analog correction at a Quadrature Down Conversion module  750 . An Analog to Digital Converter (ADC)/Filter module  740   b  converts analog signal to digital signal, and may filter the signal. The Digital Equalizer module  730  receives the digital signal from the ADC/Filter module  740   b . After the Digital Equalizer module  730  processes the digital signal, a Demodulation module  705  can demodulate the digital signal and a Channel Estimation module  705  can estimate an appropriate channel for the digital signal. In some embodiments of the technology, a Digital Correction module  720   b  can apply digital correction to the signal at the Digital Equalizer module  730 , the Demodulation module  705 , and/or Channel Estimation module  706 . The digital correction can be performed using, for example, suitable digital signal processing (DSP) electronics. Therefore, the effects of the Doppler shifts are eliminated or reduced in the outgoing digital signal (e.g., routed per corresponding channels) resulting in an improved bit error ratio (BER) of the digital signal reduced from the received wireless signal. A sample result of such a reduction in the BER is shown in  FIG. 11  below. 
         [0036]      FIG. 8A  schematically illustrates correction of the wireless signal at the ground station in accordance with an embodiment of the present technology. A correction schematics  800   a  includes down-converting the incoming wireless signal at the module  750 , followed by A/D conversion and filtering the signal at the module  740 . An initial RX correction can be performed at a module  810 . The wireless signal can be passed through module  720  for DSP correction, followed by a module  840  for decoding demodulation. Searching/synchronizing is performed at module  820 . A channel estimation Timing and/or frequency error can be estimated at a module  845 . Next, an AFC module  855  provides wireless signal to a reference clock  860 . An estimated Doppler shift is also provided to the reference clock  860  and to a synthesizer  865  by a module  880 . The estimated Doppler shift can include optimal estimations provided by module  870 . A synthesizer module  865  feeds the corrected wireless signal to the down-converter module  750 . 
         [0037]      FIG. 8B  schematically illustrates correction of the wireless signal at the UAV station in accordance with an embodiment of the present technology. In the illustrated embodiment, a correction schematics  800   b  includes elements that are generally analogous to those illustrated in the correction schematics  800   a . However, the illustrated correction schematics  800   b  does not include the module  880  for estimating the Doppler shift and the module  870  for the optimal estimation. In at least some embodiments, the functions of the modules  870  and  880  can be executed at the ground station to reduce the weight of the UAV. 
         [0038]      FIG. 9  is a flow diagram illustrating an embodiment of implementation of the Doppler shift correction. The illustrated flow diagram can be implemented at the UAV and/or ground station using the electronics/software described in relation to  FIGS. 2-8B  above. Those having skills in the art will recognize that some process steps may be repeated, varied, omitted, or supplemented, and other (e.g., less important) aspects not shown may be readily implemented. 
         [0039]    In some embodiments, for UAV in high maneuvering conditions changes of Doppler frequency shift with time can be estimated via dynamic recursively as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0000]    where V represents velocity of the UAV, r represents distance between the TX and RX, and x, y and z are Cartesian coordinates.
 
Equation (1) can be also expressed as:
 
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         [0000]    In general, the Doppler frequency shift changes non-linearly as a function of UAV position, velocity and acceleration. Linear perturbations of Doppler frequency shift can be calculated as: 
         [0000]    
       
         
           
             
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         [0000]    where g represents gravitation acceleration and δ x  is a state vector of:
 
(δ{dot over (V)} x , δ{dot over (V)} y , δ{dot over (V)} z , δV, . . . , δx, δy, δz)
 
The order of the estimation models and corresponding parameters can be adjusted dynamically to adapt different UAV states. Doppler frequency shift predictions are impacted by:
 
(a) GPS, IMU time (e.g., time for the GPS, IMU signal to propagate),
 
(b) inaccuracies in the estimated initial position of the UAV,
 
(c) errors in the velocity estimates,
 
(d) errors caused by the local reference oscillators, and
 
(e) errors caused by multiple passes of the wireless signal from TX/RX to RX/TX.
 
In some embodiments, GPS and IMU calculations can be performed at ground station, and can be used for calculating Flight Dynamic Coefficients and to estimate Kalman Filter. Furthermore, coarse Doppler shift can be calculated and a time offset used for TX predistortion can be estimated. Coefficients A, B, C, and D for Kalman filter can be calculated and used for TX frequency shift. The coefficients A, B, C, and D can be used to estimate changes in Doppler frequency shift (coarse or perturbation) as shown in Eq. 3 below.
 
         [0000]      δ {dot over (f)}   d   =Aδf   d   +B·δx   Eq. (3)
 
         [0040]      FIG. 10  illustrates a flow diagram of a process flow  1000  for correcting the Doppler shift in accordance with an embodiment of the present technology. In general, the process flow  1000  is applicable for correcting the coarse and/or fine Doppler shifts. The routine  1000  can be performed by electronics and software described with reference to  FIGS. 2-8B  above. The process flow  1000  does not show all steps of correcting the Doppler shifts in the wireless signal, but instead provides an understanding of the process steps in some embodiments of the technology. Those having skills in the art will recognize that some process steps may be repeated, varied, omitted, or supplemented, and other (e.g., less important) aspects not shown may be readily implemented. 
         [0041]    The process flow  1000  starts in block  1010 . In block  1015  a location of the UAV is detected using, for example, one or more GPS, IMU units. In block  1020 , a velocity of UAV can be estimated based on, for example, change of the location of the UAV over time (e.g., using a first derivative of the location over the time). A person of ordinary skill would know how to calculate/estimate the velocity of the UAV based on the GPS, IMU signal at the UAV. 
         [0042]    Once the velocity of the UAV is estimated, in block  1025  a Doppler shift can be estimated. For example, the estimate of the Doppler shift can be based on a known location of the ground station and the estimated velocity (magnitude and direction) of the UAV. In some embodiments, the Doppler shift (e.g., frequency shift, timing shift) can be estimated using a Doppler Shift Estimator module  150 . 
         [0043]    In block  1030 , a decision is made whether to predistort the wireless signal. If the wireless signal is to be predistorted, then in block  1035  the predistortion can be applied to the TX of the UAV and/or the TX of the ground station. The predistortion can be applied to the perturbation (fine) and/or coarse Doppler shift. In some embodiments, the predistortion can be applied using the UAV TX Predistortion module  142  or the Ground Station Predistortion module  232 . 
         [0044]    In block  1040 , a decision is made whether to correct the wireless signal. If the wireless signal is to be corrected, then in block  1045  the correction can be applied to the RX of the ground station and/or the RX of the UAV. Some embodiments of the suitable hardware/software for the correction of the wireless signal are explained with reference to, for example, the UAV RX Perturbation Correction module  133 , the UAV RX Correction module  131 , the Ground Station RX Correction module  241 , and the signal correction system  700   b.    
         [0045]    In block  1050 , the flight models for the UAV are updated. As explained above, in some embodiment the flight models can be based on the applications of Kalman filter or other filters. The process flow  1000  for correcting/predistorting the wireless signal ends in block  1055 , and may be started again in block  1010 . 
         [0046]      FIG. 11  is a graph of the BER with and without correcting the Doppler shifts. The horizontal axis represents a signal to noise energy ratio in decibel. The vertical axis represents the BER ranging from about 10 −8  (in some applications, an acceptable BER) to about 10 −1  (typically, an unacceptably high BER for most applications). A solid line  1120  corresponds to the BER without the correction applied, and a dash line  1110  corresponds to the BER with the correction applied. The BER generally decreases as the signal to noise ratio increases (i.e., in the direction of increased values on the horizontal axis). However, in the illustrated example, the BER with the correction applied (line  1110 ) decreases faster than the BER without the correction applied (line  1120 ). As a result, as the signal to noise ratio reaches about 14, the BER with correction drops to a value of about 10 −8 , while the BER without correction remains at about 10 −2 . In at least some practical applications, the BER of about 10 −2  would be considered too high. The graph in  FIG. 11  illustrates an application of the signal correction, but a generally analogous graph can be made for an application of the signal predistortion or for an application of the signal correction and predistortion. 
         [0047]    From the foregoing, it will be appreciated that specific embodiments of the invention have been described herein for purposes of illustration, but that various modifications may be made without deviating from the spirit and scope of the various embodiments of the invention. For example, in some embodiments the wireless signals may be transmitted between two or more UAVs that are equipped with the predistortion/correction hardware and software. Furthermore, while various advantages and features associated with certain embodiments of the disclosure have been described above in the context of those embodiments, other embodiments may also exhibit such advantages and/or features, and not all embodiments need necessarily exhibit such advantages and/or features to fall within the scope of the disclosure. Accordingly, the disclosure is not limited, except as by the appended claims.