Unmanned aerial vehicle channel flatness bandwidth and composite doppler analysis method and system

Abstract

The application discloses a method and system for analyzing channel smooth bandwidth and composite Doppler of an unmanned aerial vehicle, comprising: obtaining a time delay domain autocorrelation function by using a time-varying channel impulse response, then obtaining a frequency-time joint power spectrum density function by Fourier transform to the frequency domain, and then determining a smooth interval by the autocorrelation function of the frequency-time joint power spectrum density function; dividing an ultra-wideband channel into several smooth subintervals, and establishing corresponding channel transfer functions; through coordinate system conversion, calculating Doppler frequency offsets of unmanned aerial vehicle movement, attitude change and propeller jitter respectively and integrating them into a composite Doppler frequency offset; combining the channel transfer function and the composite Doppler frequency offset, normalizing the channel coefficient and calculating the frequency correlation function and the time correlation function of the channel. The application realizes accurate division of the frequency domain smooth bandwidth of the ultra-wideband channel and integrated representation of multi-factor Doppler effect, and provides support for reliable design of the unmanned aerial vehicle communication system.

Description

Technical Field

[0001] This invention relates to the field of low-altitude unmanned aerial vehicle (UAV) technology, specifically to a method and system for analyzing the channel stability bandwidth and composite Doppler of UAVs. Background Technology

[0002] The deployment of low-altitude unmanned aerial vehicles (UAVs) in various applications such as surveillance, delivery, and collaborative missions is increasing, placing higher demands on the reliability of communication systems. The communication channel is the core transmission medium connecting the transmitter and receiver in a communication system, and its characteristics directly determine the quality, rate, and reliability of signal transmission. Currently, ultra-wideband technology is often required in low-altitude scenarios to achieve high-speed data transmission or precise target positioning, causing the channel to exhibit significant frequency-varying characteristics over a wide bandwidth. Simultaneously, low-altitude UAVs themselves possess dynamic characteristics, including frequent attitude adjustments for maneuvering and jitter caused by propeller vibration, which leads to rapid and significant changes in the communication channel.

[0003] In the development of ultra-wideband low-altitude unmanned aerial vehicle (UAV) communication systems, frequency-varying characteristics and airframe dynamics both contribute to significant channel non-stationarity. Failure to consider these factors when characterizing non-stationary UAV channels hinders the proper design of low-altitude communication systems, potentially leading to connection interruptions, reduced data rates, and compromised mission success rates. Existing research on low-altitude UAV channel characteristics largely focuses on narrowband or relatively stable frequency bands, with insufficient consideration of airframe dynamics, making it difficult to support the development and optimization of communication systems in ultra-wideband application scenarios. Therefore, there is an urgent need to conduct characteristic research on low-altitude UAV channels in ultra-wideband scenarios, taking into account UAV attitude changes, propeller oscillations, and frequency-varying characteristics under high bandwidth conditions.

[0004] The characterization of channel frequency domain non-stationary characteristics largely depends on the allocation of stationary bandwidths. Existing research mainly includes: characterizing channel characteristics within stationary bandwidths using two-state Markov models; allocating two-dimensional stationary bandwidths based on Pearson-Moscowitz spectra, but without considering the influence of UAV trajectories; allocating stationary bandwidths by turning radius and turning frequency, and verifying their effect on frequency domain fading; and designing collaborative stationary bandwidths based on cluster common visibility to achieve integrated characterization of multi-node frequency domain non-stationary characteristics. However, existing methods generally fail to comprehensively and accurately reflect the inherent frequency domain non-stationarity in ultra-wideband scenarios.

[0005] The Doppler effect is a core component of channel modeling, and its accurate representation is crucial for UAV communication systems. For example, while Rayleigh and Rice channel models have explored Doppler frequency shifts related to UAV speed and altitude, they haven't addressed the modeling challenges of high-speed UAV motion scenarios. Geometric channel modeling methods have been employed to analytically derive the Doppler spread function induced by UAV motion. Attitude-induced Doppler frequency shifts have been incorporated into low-altitude UAV channel models, but micro-Doppler effects caused by propeller jitter have not been accounted for. Studies on UAV rotor jitter and propeller echoes have achieved high-resolution representation of non-stationary micro-Doppler effects, but the composite Doppler effect caused by the UAV's three-dimensional attitude motion has not been considered. Assuming the values ​​of multiple frequency offset components are linearly added, due to factors such as multipath fluctuations in different frequency bands and mismatched scattering energy proportions across different bandwidths, frequency domain fading within a broadband channel can lead to mutual interference between various Doppler frequency offset components and deviations in the calculation of correlation characteristics between the frequency domain and time dimensions. Ultimately, this results in distorted channel simulations and insufficient accuracy in Doppler frequency offset representation.

[0006] In summary, current research on the channel characteristics analysis of low-altitude unmanned aerial vehicles (UAVs) still faces challenges in bandwidth allocation and Doppler shift calculation. Existing bandwidth allocation studies largely rely on time-varying power delay distributions, which can characterize channel delay domain characteristics and delineate multipath components. However, focusing solely on the delay dimension fails to accurately reflect frequency non-stationarity and capture frequency domain variation patterns in ultra-wideband scenarios, leading to decreased model physical interpretability and practical adaptability. Simultaneously, in Doppler shift calculation, existing studies generally only consider the relative translational motion of the transmitter and receiver, neglecting Doppler phase changes caused by UAV attitude variations and the slight Doppler frequency shift caused by propeller jitter. This results in calculation results deviating from actual channel characteristics, making it difficult to accurately characterize the time-varying features of the channel. These two shortcomings are mutually reinforcing and restrictive. On the one hand, the differences in multipath fluctuations across different frequency bands directly amplify the calculation errors of various Doppler frequency offsets. When linearly superimposing translation, attitude, and micro-jitter frequency offsets, it is impossible to match the differentiated scattering energy proportions of each frequency band. On the other hand, the evolution of composite Doppler phase and time delay offsets in different frequency bands cannot be accurately distinguished, further exacerbating the coupling distortion between frequency domain fading and time-varying Doppler effects. Ultimately, this results in a significant decrease in the physical interpretability and practical adaptability of the model, and a significant deviation in the characterization of channel time-varying features.

[0007] Therefore, this invention studies stationary bandwidth partitioning and composite Doppler to overcome the challenge of characterizing non-stationary channels in ultra-wideband scenarios, laying the foundation for the reliable design of low-altitude UAV communication systems. Summary of the Invention

[0008] To address the challenges faced by low-altitude unmanned aerial vehicle (UAV) communications, such as the inadequacy of traditional channel models to fully consider the dynamic characteristics of low-altitude scenarios and their inability to meet the requirements of system design and performance evaluation, this invention proposes a method and system for analyzing stationary bandwidth and compound Doppler effects in UAV channels. By combining frequency-dependent stationary bandwidth and the compound Doppler effect, the non-stationary channel characteristics of UAVs are characterized. The proposed frequency-varying power delay distribution bandwidth partitioning criterion effectively captures the time-frequency non-stationary characteristics of the channel. The compound Doppler model, which integrates UAV attitude and propeller jitter, improves the accuracy of Doppler frequency shift calculation. Numerical simulation results show that changes in frequency points lead to alterations in coherent bandwidth and cluster number, while jitter also negatively impacts the level crossover rate and average fading duration.

[0009] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0010] In a first aspect, the present invention discloses a method for analyzing the channel stability bandwidth and composite Doppler of an unmanned aerial vehicle (UAV), the method comprising the following steps:

[0011] S1, Input configuration parameters, including: signal bandwidth, carrier frequency, carrier wavelength, UAV speed, UAV pitch angle, roll angle and yaw angle, antenna body coordinates, propeller jitter amplitude, angular frequency and initial phase, stationary bandwidth threshold and Rice factor.

[0012] S2, calculate the time-delay domain autocorrelation function using the time-varying channel impulse response, perform a Fourier transform on the time-delay dimension of the time-delay domain autocorrelation function to obtain the frequency-time-delay joint power spectral density function; using the frequency-delay joint power spectral density function as the statistical basis, simultaneously take the maximum value of the power spectrum integral at two frequency points as the normalized denominator to construct the autocorrelation function of the frequency-time-delay scattering function.

[0013] S3. Combining the stationary bandwidth threshold and the autocorrelation function of the frequency-delay scattering function, traverse different frequency intervals to find the maximum frequency interval that satisfies the autocorrelation function value not being lower than the stationary bandwidth threshold, and take this maximum frequency interval as the frequency domain stationary bandwidth; using the frequency domain stationary bandwidth as the segmentation standard, continuously divide the signal bandwidth to divide the ultra-wideband channel into several frequency domain stationary sub-intervals; combining the Rice factor and the antenna body coordinates, establish the channel transfer function between the transmitting antenna element and the receiving antenna element in each frequency domain stationary sub-interval respectively;

[0014] S4, based on the input pitch angle, roll angle and yaw angle, transforms the inertial coordinate system of the UAV into the body coordinate system; based on the coordinate transformation result, combined with the UAV speed, calculates the Doppler frequency offset caused by the UAV motion, combined with the attitude angle, solves the Doppler frequency offset caused by attitude change, combined with the amplitude, angular frequency and initial phase of propeller jitter, calculates the Doppler frequency offset caused by propeller jitter, and then combined with the carrier frequency and carrier wavelength to complete the conversion of the three types of frequency offsets, and adds them together to obtain the composite Doppler frequency offset;

[0015] S5, the composite Doppler frequency offset is used as a phase correction term and applied to the channel transfer function of each stationary sub-interval obtained in step S3 to calculate the normalized channel coefficient of the UAV channel, and key statistical characteristic indicators are calculated for channel analysis. The key statistical characteristic indicators include at least the frequency correlation function and the time correlation function.

[0016] Step S2 further includes:

[0017] The time-delay domain autocorrelation function is calculated using the time-varying channel impulse response, and is expressed as:

[0018] ;

[0019] in For channel impulse response, For the observation time, For the propagation delay of electromagnetic waves, This is the time delay offset. It is the expectation operator, superscript Represents the conjugate operation for complex numbers;

[0020] Taking the Fourier transform of the time-delay domain autocorrelation function yields the frequency-time-delay joint power spectral density function, expressed as:

[0021] ;

[0022] The autocorrelation function of the frequency-time delay scattering function is calculated and expressed as:

[0023] ;

[0024] In the formula, f is the reference frequency. The frequency interval between two frequency points. Represents an imaginary number.

[0025] Furthermore, in step S3, the frequency domain stationary bandwidth Represented as;

[0026] ;

[0027] in, This represents a preset stationary bandwidth threshold, adaptively selected based on the channel modeling accuracy and computational efficiency requirements of the UAV communication scenario. It is used to determine the channel stationary boundary corresponding to the frequency domain autocorrelation function. Indicates time t, frequency point f, and frequency interval. The autocorrelation function of the corresponding frequency-time delay scattering function.

[0028] Furthermore, in step S3, the first The channel transfer function for each stationary subinterval in the frequency domain is expressed as:

[0029] ;

[0030] In the formula, Indicates the first Rice factor for each stationary interval in the frequency domain. and These represent the time delays for the line-of-sight path and the non-line-of-sight path, respectively. For the first The number of non-line-of-sight paths in each frequency-domain stationary sub-interval. It is the first The number of sub-paths in a non-line-of-sight path For the propagation delay of electromagnetic waves, For the observation time, As the reference frequency, For frequency domain stationary bandwidth, Indicates the first The center frequency within each stationary sub-interval in the frequency domain This represents the power correction factor for the line-of-sight path caused by obstruction due to the fuselage structure. This is the power correction factor for frequency-dependent non-line-of-sight paths. and These represent the equivalent Doppler phases for the line-of-sight path and the non-line-of-sight path, respectively. and The antenna pattern function takes into account attitude changes. Numbering the transmitting antenna elements, For the receiving antenna element number, the superscript L corresponds to the line-of-sight (LOS) path, and the superscript NL corresponds to the non-line-of-sight (NLOS) scattering path. The variable is the integral variable, representing continuous frequency points within a frequency-stationary sub-interval. For the first The first transmitting antenna element and the first The channel impulse response between the receiving antenna elements is expressed as:

[0031] ;

[0032] Then the channel coefficient and Further modeling is as follows:

[0033] ;

[0034] ;

[0035] In the formula, Represents 0 to The uniformly distributed variable is used to represent the random initial phase of the line-of-sight path and the non-line-of-sight path. This represents the composite Doppler frequency offset within a stationary sub-interval in the frequency domain. and These are the spatially corrected phases of the multi-input multi-output antenna elements for line-of-sight and non-line-of-sight paths, respectively.

[0036] Further, in step S4, the composite Doppler frequency offset is expressed as:

[0037] ;

[0038] The Doppler frequency shift caused by the drone's motion is represented as follows:

[0039] ;

[0040] In the formula, Indicates the carrier frequency of the transmitted signal. Indicates the speed of the drone. This indicates the angle between the direction of the drone's movement and the direction of signal propagation. Indicates the speed of propagation of electromagnetic waves;

[0041] The Doppler frequency shift caused by the change in the attitude of the UAV is:

[0042] ;

[0043] In the formula, This represents the angular velocity vector of the UAV rotating around its center of mass. , , These represent the pitch, roll, and yaw angles of the UAV, respectively. The superscript dot indicates the first derivative with respect to time. Indicates that the antenna is in Installation position in the coordinate system Indicates that the antenna is in Position in the coordinate system Let R represent the coordinate vector of the ground vehicle in the global inertial coordinate system, and let R represent the transformation matrix. This represents the position vector of the transmitting antenna in the body coordinate system.

[0044] The Doppler frequency shift caused by drone propeller vibration is:

[0045] ;

[0046] In the formula, the jitter speed Represented as

[0047] ;

[0048] In the formula, These represent the jitter amplitudes in the x, y, and z directions, respectively. The dithering angular frequency, These are the initial phases of the jitter in the x, y, and z directions, respectively. The unit direction vector in the body coordinate system. This represents the instantaneous displacement vector of the transmitting antenna in the body coordinate system caused by the vibration of the propeller.

[0049] Further, in step S5, the process of using the composite Doppler frequency offset as a phase correction term and applying it to the channel transfer function of each stationary sub-interval obtained in step S3 to calculate the normalized channel coefficients of the UAV channel includes:

[0050] Composite Doppler frequency shift Integrating over time yields the time-varying Doppler phase, which is then multiplied as a complex exponential correction term into the line-of-sight component and each non-line-of-sight sub-path component of the channel transfer function to obtain the time-domain response of the line-of-sight channel after superimposed Doppler effects. and ;

[0051] By performing maximum / minimum normalization on the time-domain responses corresponding to all frequency points within the same stationary sub-interval in the same frequency domain, the normalized channel coefficients of the UAV channel are calculated and expressed as:

[0052] ;

[0053] ;

[0054] Further, in step S5, based on the path power correction factor, Doppler phase, and time delay parameters corresponding to the normalized channel coefficients of each frequency-domain stationary sub-interval, a channel frequency correlation function and a time correlation function are constructed respectively; the frequency correlation function and the time correlation function are respectively expressed as:

[0055] ;

[0056] ;

[0057] in, It is the expectation operator.

[0058] Secondly, the present invention discloses a UAV channel stationary bandwidth and composite Doppler analysis system, the system comprising a user configuration unit, a stationary bandwidth partitioning unit, a composite Doppler and statistical characteristic calculation unit, and an output unit;

[0059] The user configuration unit is used to input configuration parameters, which include: signal bandwidth, carrier frequency, carrier wavelength, UAV speed, UAV pitch angle, roll angle and yaw angle, antenna body coordinates, propeller jitter amplitude, angular frequency and initial phase, stationary bandwidth threshold and Rice factor.

[0060] The stationary bandwidth partitioning unit is used to calculate the time-delay domain autocorrelation function using the time-varying channel impulse response. A Fourier transform of the time-delay dimension is performed on the time-delay domain autocorrelation function to obtain the frequency-time-delay joint power spectral density function. Using the frequency-delay joint power spectral density function as a statistical basis, the maximum value of the power spectrum integrals at two frequency points is simultaneously taken as the normalized denominator to construct the autocorrelation function of the frequency-time-delay scattering function. Then, combining the stationary bandwidth threshold and the autocorrelation function of the frequency-delay scattering function, different frequency intervals are traversed to find the maximum frequency interval that satisfies the autocorrelation function value not being lower than the stationary bandwidth threshold. This maximum frequency interval is taken as the frequency-domain stationary bandwidth. Using the frequency-domain stationary bandwidth as the segmentation standard, the signal bandwidth is continuously divided, dividing the ultra-wideband channel into several frequency-domain stationary sub-intervals.

[0061] The composite Doppler and statistical characteristic calculation unit is used to call Rice factor and antenna body coordinates to establish the channel transfer function between the transmitting antenna unit and the receiving antenna unit in each stationary sub-interval; at the same time, based on the input pitch angle, roll angle and yaw angle, the inertial coordinate system of the UAV motion is converted into the body coordinate system; based on the coordinate transformation result, the Doppler frequency offset caused by the UAV motion is calculated by combining the UAV speed, the Doppler frequency offset caused by attitude change is solved by combining the attitude angle, the Doppler frequency offset caused by propeller jitter is calculated by combining the amplitude, angular frequency and initial phase of propeller jitter, and then the conversion of the three types of frequency offset is completed by combining the carrier frequency and carrier wavelength, and the composite Doppler frequency offset is obtained by adding them together;

[0062] The output unit is used to apply the composite Doppler frequency offset as a phase correction term to the channel transfer function of each stationary sub-interval, calculate the normalized channel coefficients of the UAV channel, and calculate key statistical characteristic indicators for channel analysis. The key statistical characteristic indicators include at least the frequency correlation function and the time correlation function.

[0063] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0064] First, the UAV channel stationary bandwidth and composite Doppler analysis method and system of the present invention proposes a bandwidth partitioning criterion based on the frequency-varying power delay distribution function. This solves the shortcomings of traditional power delay distribution methods that only focus on the delay dimension and ignore the two-dimensional non-stationarity of the ultra-wideband channel in time and frequency. It can accurately capture the differentiated multipath fluctuation characteristics in the broadband frequency band, realize the fine-grained stationary sub-interval partitioning of the total signal bandwidth, and effectively improve the physical interpretability and scenario adaptability of ultra-wideband channel frequency domain modeling.

[0065] Second, the UAV channel stable bandwidth and composite Doppler analysis method and system of the present invention comprehensively consider three types of motion interference: high-speed translational motion of UAV, three-dimensional attitude rotation and propeller micro-jitter. It constructs a multi-component coupled composite Doppler frequency offset calculation system, improves the solution method of key parameters such as channel path phase and frequency offset, accurately characterizes the time-varying fading characteristics of UAV channel in complex low-altitude scenarios, and solves the problems of missing micro-Doppler effect and distortion of composite motion representation in the prior art.

[0066] Third, the UAV channel stationary bandwidth and composite Doppler analysis method and system of the present invention calculates Rice factor for each stationary sub-interval after segmentation, which solves the technical pain point of traditional models that use globally fixed Rice factor and cannot adapt to the differences in multipath energy ratio in different sub-intervals, and greatly improves the calculation accuracy of energy allocation of non-line-of-sight scattering components in each frequency band.

[0067] Fourth, the UAV channel stationary bandwidth and composite Doppler analysis method and system of the present invention solves the problem of the disconnect and superposition of defects between the bandwidth division and time-varying Doppler modeling in the prior art by synergistic optimization of frequency domain stationary segmentation modeling and composite Doppler coupling correction. It realizes the joint and accurate characterization of the time-frequency two-dimensional non-stationary characteristics of the ultra-wideband UAV channel and the multi-motion coupled Doppler effect, and provides reliable model support for channel simulation, system design and performance optimization of complex low-altitude UAV ultra-wideband communication. Attached Figure Description

[0068] Figure 1 This is a flowchart illustrating the method for analyzing the channel stability bandwidth and composite Doppler of an unmanned aerial vehicle (UAV) proposed in this invention.

[0069] Figure 2 A schematic diagram of the proposed channel model for low-altitude communication;

[0070] Figure 3 This is a diagram showing the normalized channel coefficients output by the antenna pair Tx1 and Rx1 in this invention.

[0071] Figure 4 The graph shows the frequency correlation function results of the model proposed in this invention.

[0072] Figure 5The graph shows the time correlation function results of the model proposed in this invention. Detailed Implementation

[0073] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0074] See Figure 1 This invention discloses a method for analyzing the channel stationary bandwidth and composite Doppler of unmanned aerial vehicles (UAVs). The method includes the following steps:

[0075] S1, Input configuration parameters, including: signal bandwidth, carrier frequency, carrier wavelength, UAV speed, UAV pitch angle, roll angle and yaw angle, antenna body coordinates, propeller jitter amplitude, angular frequency and initial phase, stationary bandwidth threshold and Rice factor.

[0076] S2, calculate the time-delay domain autocorrelation function using the time-varying channel impulse response, perform a Fourier transform on the time-delay dimension of the time-delay domain autocorrelation function to obtain the frequency-time-delay joint power spectral density function; using the frequency-delay joint power spectral density function as the statistical basis, simultaneously take the maximum value of the power spectrum integral at two frequency points as the normalized denominator to construct the autocorrelation function of the frequency-time-delay scattering function.

[0077] S3. Combining the stationary bandwidth threshold and the autocorrelation function of the frequency-delay scattering function, traverse different frequency intervals to find the maximum frequency interval that satisfies the autocorrelation function value not being lower than the stationary bandwidth threshold, and take this maximum frequency interval as the frequency domain stationary bandwidth; using the frequency domain stationary bandwidth as the segmentation standard, continuously divide the signal bandwidth to divide the ultra-wideband channel into several frequency domain stationary sub-intervals; combining the Rice factor and the antenna body coordinates, establish the channel transfer function between the transmitting antenna element and the receiving antenna element in each frequency domain stationary sub-interval respectively;

[0078] S4, based on the input pitch angle, roll angle and yaw angle, transforms the inertial coordinate system of the UAV into the body coordinate system; based on the coordinate transformation result, combined with the UAV speed, calculates the Doppler frequency offset caused by the UAV motion, combined with the attitude angle, solves the Doppler frequency offset caused by attitude change, combined with the amplitude, angular frequency and initial phase of propeller jitter, calculates the Doppler frequency offset caused by propeller jitter, and then combined with the carrier frequency and carrier wavelength to complete the conversion of the three types of frequency offsets, and adds them together to obtain the composite Doppler frequency offset;

[0079] S5, the composite Doppler frequency offset is used as a phase correction term and applied to the channel transfer function of each stationary sub-interval obtained in step S3 to calculate the normalized channel coefficient of the UAV channel, and key statistical characteristic indicators are calculated for channel analysis. The key statistical characteristic indicators include at least the frequency correlation function and the time correlation function.

[0080] In step S2, the time-delay domain autocorrelation function is calculated using the time-varying channel impulse response, expressed as:

[0081] ;

[0082] in For channel impulse response, For the observation time, For the propagation delay of electromagnetic waves, This is the time delay offset. It is the expectation operator, superscript Represents the conjugate operation for complex numbers;

[0083] Taking the Fourier transform of the time-delay domain autocorrelation function yields the frequency-time-delay joint power spectral density function, expressed as:

[0084] ;

[0085] The autocorrelation function of the frequency-time delay scattering function is calculated and expressed as:

[0086] ;

[0087] In the formula, f is the reference frequency. The frequency interval between two frequency points. Represents an imaginary number.

[0088] Furthermore, in step S3, the frequency domain stationary bandwidth Represented as;

[0089] ;

[0090] in, This represents a preset stationary bandwidth threshold, adaptively selected based on the channel modeling accuracy and computational efficiency requirements of the UAV communication scenario. It is used to determine the channel stationary boundary corresponding to the frequency domain autocorrelation function. Indicates time t, frequency point f, and frequency interval. The autocorrelation function of the corresponding frequency-time delay scattering function.

[0091] In step S3, the first The channel transfer function for each stationary subinterval in the frequency domain is expressed as:

[0092] ;

[0093] In the formula, Indicates the first Rice factor for each stationary interval in the frequency domain. and These represent the time delays for the line-of-sight path and the non-line-of-sight path, respectively. For the first The number of non-line-of-sight paths in each frequency-domain stationary sub-interval. It is the first The number of sub-paths in a non-line-of-sight path For the propagation delay of electromagnetic waves, For the observation time, As the reference frequency, For frequency domain stationary bandwidth, Indicates the first The center frequency within each stationary sub-interval in the frequency domain This represents the power correction factor for the line-of-sight path caused by obstruction due to the fuselage structure. This is the power correction factor for frequency-dependent non-line-of-sight paths. and These represent the equivalent Doppler phases for the line-of-sight path and the non-line-of-sight path, respectively. and The antenna pattern function takes into account attitude changes. Numbering the transmitting antenna elements, For the receiving antenna element number, the superscript L corresponds to the line-of-sight (LOS) path, and the superscript NL corresponds to the non-line-of-sight (NLOS) scattering path. The variable is the integral variable, representing continuous frequency points within a frequency-stationary sub-interval. For the first The first transmitting antenna element and the first The channel impulse response between the receiving antenna elements is expressed as:

[0094] ;

[0095] Then the channel coefficient and Further modeling is as follows:

[0096] ;

[0097] ;

[0098] In the formula, Represents 0 to The uniformly distributed variable is used to represent the random initial phase of the line-of-sight path and the non-line-of-sight path. This represents the composite Doppler frequency offset within a stationary sub-interval in the frequency domain. and These are the spatially corrected phases of the multi-input multi-output antenna elements for line-of-sight and non-line-of-sight paths, respectively.

[0099] The antenna pattern functions for line-of-sight and non-line-of-sight paths can be expressed as follows:

[0100] ;

[0101] ;

[0102] in, and These represent the vertical and horizontal components of the radiation pattern of the transmitting antenna, respectively. and These represent the vertical and horizontal components of the radiation pattern of the receiving antenna, respectively. and Let these represent the unit departure direction vector and the unit arrival direction vector of the line-of-sight path, respectively. and Let represent the unit departure direction vector and the unit arrival direction vector for non-line-of-sight paths, respectively. and The initial phase for different polarization combinations along the line-of-sight path. , , and The initial phase for different polarization combinations along non-line-of-sight paths. Indicates the cross-polarization power ratio. and These are the attitude matrices of the transmitting and receiving ends, respectively.

[0103] Furthermore, in step S4, two coordinate systems are introduced to describe the motion of the UAV. The first is an inertial coordinate system, whose origin is fixed at the ground station. The axis points due east horizontally. The axis points to true north. The axis points vertically upwards. The second type is the body coordinate system, whose origin is located at the UAV's center of mass. The shaft moves forward along the machine head. The shaft runs along the fuselage to the right. The axis is perpendicular to the fuselage and points upwards. A transformation matrix is ​​used. The transformation matrix for converting the UAV's inertial coordinate system to its body coordinate system can be expressed as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] In the formula, , , These represent pitch angle, roll angle, and yaw angle, respectively.

[0108] The composite Doppler frequency shift is expressed as:

[0109] ;

[0110] The Doppler frequency shift caused by the drone's motion is represented as follows:

[0111] ;

[0112] In the formula, Indicates the carrier frequency of the transmitted signal. Indicates the speed of the drone. This indicates the angle between the direction of the drone's movement and the direction of signal propagation. Indicates the speed of propagation of electromagnetic waves;

[0113] The Doppler frequency shift caused by the change in the attitude of the UAV is:

[0114] ;

[0115] In the formula, This indicates the rotation of the drone, that is, in The angular velocity vector of the UAV rotating about its center of mass in the coordinate system. The single-point superscript indicates the first derivative with respect to time. Indicates that the antenna is in Installation position in the coordinate system Indicates that the antenna is in Position in the coordinate system Let R represent the coordinate vector of the ground vehicle in the global inertial coordinate system, and let R represent the transformation matrix. This represents the position vector of the transmitting antenna in the body coordinate system.

[0116] The Doppler frequency shift caused by drone propeller vibration is:

[0117] ;

[0118] In the formula, the jitter speed Represented as

[0119] ;

[0120] In the formula, These represent the jitter amplitudes in the x, y, and z directions, respectively. The dithering angular frequency, These are the initial phases of the jitter in the x, y, and z directions, respectively. The unit direction vector in the body coordinate system. This represents the instantaneous displacement vector of the transmitting antenna in the body coordinate system caused by the vibration of the propeller.

[0121] Further, in step S5, the process of using the composite Doppler frequency offset as a phase correction term and applying it to the channel transfer function of each stationary sub-interval obtained in step S3 to calculate the normalized channel coefficients of the UAV channel includes:

[0122] Composite Doppler frequency shift Integrating over time yields the time-varying Doppler phase, which is then multiplied as a complex exponential correction term into the line-of-sight component and each non-line-of-sight sub-path component of the channel transfer function to obtain the time-domain response of the line-of-sight channel after superimposed Doppler effects. and ;

[0123] By performing maximum / minimum normalization on the time-domain responses corresponding to all frequency points within the same stationary sub-interval in the same frequency domain, the normalized channel coefficients of the UAV channel are calculated and expressed as:

[0124] ;

[0125] ;

[0126] Further, in step S5, based on the path power correction factor, Doppler phase, and time delay parameters corresponding to the normalized channel coefficients of each frequency-domain stationary sub-interval, a channel frequency correlation function and a time correlation function are constructed respectively; the frequency correlation function and the time correlation function are respectively expressed as:

[0127] ;

[0128] ;

[0129] in, It is the expectation operator.

[0130] Example

[0131] This embodiment uses a typical low-altitude ultra-wideband UAV communication scenario. Figure 2 The proposed channel model for low-altitude communication is shown in Table 1 below. The specific values ​​of each key configuration parameter are set as follows.

[0132] Table 1 Configuration Parameters

[0133]

[0134] The time-varying channel impulse response obtained The time-delay domain autocorrelation function is obtained, and then a Fourier transform is performed on the time-delay domain autocorrelation function to obtain the frequency-time-delay joint power spectral density function. The autocorrelation function of the frequency-time-delay joint power spectral density function is calculated, and finally, the stationary bandwidth is obtained using its autocorrelation function.

[0135] ;

[0136] Subsequently, the total 2 GHz of ultra-wideband channels were evenly divided into Segmental stationary subintervals (i.e.) Each segment has a bandwidth of 200 MHz.

[0137] Within a single 200 MHz stationary sub-interval, the scattering environment experienced by signals at different frequencies is considered consistent. Taking the first sub-band... (center frequency) Taking GHz as an example, calculate the key parameters of its channel transfer function:

[0138] Determining line-of-sight path delay based on ray tracing technology Non-line-of-sight path delay distribution in .

[0139] Setting the power correction factor caused by fuselage obstruction Frequency-dependent power correction factor Substituting the parameters into the channel impulse response model, we obtain:

[0140] ;

[0141] The inertial coordinate system of the UAV's motion is converted to the body coordinate system, taking into account the effects of translation, attitude rotation, and propeller jitter:

[0142] (1) Doppler frequency shift during centroid translation:

[0143] ;

[0144] (2) Doppler frequency shift of attitude change:

[0145] First, the rotational angular velocity of the computer body. With antenna position vector The cross product of is:

[0146] ;

[0147] Projecting this rotational velocity along the line of sight yields the effective linear velocity. The resulting Doppler frequency shift is:

[0148] ;

[0149] (3) Propeller vibration micro-Doppler frequency deviation:

[0150] The instantaneous velocity of the antenna due to mechanical jitter is:

[0151] ;

[0152] This leads to the following micro-Doppler extreme values:

[0153] ;

[0154] (4) Total composite Doppler frequency offset:

[0155] Combining the above three components, the total composite Doppler frequency offset is defined as follows:

[0156] ;

[0157] By combining the channel transfer function and the composite Doppler frequency offset, the channel coefficients are normalized. Figure 3 This is a diagram showing the normalized channel coefficients output by the antenna pair Tx1 and Rx1 in this invention. The obtained normalized channel coefficients are then used to calculate the channel's frequency correlation function and time correlation function:

[0158] (1) Frequency correlation function: Based on a normalized threshold of 0.7, the coherence bandwidth is calculated to be approximately 1.26 MHz. When the frequency interval is taken as... When the frequency correlation function is 0.78, the frequency correlation function can be obtained.

[0159] (2) Time correlation function: Simulation results show that the channel coherence time is approximately 82.73 ms. Taking a minimal time interval... The time correlation function is 0.91. Figure 4 The graph shows the frequency correlation function results of the model proposed in this invention. Figure 5 The graph shows the time correlation function results of the model proposed in this invention.

[0160] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0161] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for analyzing the channel stationary bandwidth and composite Doppler of an unmanned aerial vehicle (UAV), characterized in that, The method includes the following steps: S1, Input configuration parameters, including: signal bandwidth, carrier frequency, carrier wavelength, UAV speed, UAV pitch angle, roll angle and yaw angle, antenna body coordinates, propeller jitter amplitude, angular frequency and initial phase, stationary bandwidth threshold and Rice factor. S2, calculate the time-delay domain autocorrelation function using the time-varying channel impulse response, perform a Fourier transform on the time-delay dimension of the time-delay domain autocorrelation function to obtain the frequency-time-delay joint power spectral density function; using the frequency-delay joint power spectral density function as the statistical basis, simultaneously take the maximum value of the power spectrum integral at two frequency points as the normalized denominator to construct the autocorrelation function of the frequency-time-delay scattering function. S3. Combining the stationary bandwidth threshold and the autocorrelation function of the frequency-delay scattering function, traverse different frequency intervals to find the maximum frequency interval that satisfies the autocorrelation function value not being lower than the stationary bandwidth threshold, and take this maximum frequency interval as the frequency domain stationary bandwidth; using the frequency domain stationary bandwidth as the segmentation standard, continuously divide the signal bandwidth to divide the ultra-wideband channel into several frequency domain stationary sub-intervals; combining the Rice factor and the antenna body coordinates, establish the channel transfer function between the transmitting antenna element and the receiving antenna element in each frequency domain stationary sub-interval respectively; S4, based on the input pitch angle, roll angle and yaw angle, transforms the inertial coordinate system of the UAV into the body coordinate system; based on the coordinate transformation result, combined with the UAV speed, calculates the Doppler frequency offset caused by the UAV motion, combined with the attitude angle, solves the Doppler frequency offset caused by attitude change, combined with the amplitude, angular frequency and initial phase of propeller jitter, calculates the Doppler frequency offset caused by propeller jitter, and then combined with the carrier frequency and carrier wavelength to complete the conversion of the three types of frequency offsets, and adds them together to obtain the composite Doppler frequency offset; S5, the composite Doppler frequency offset is used as a phase correction term and applied to the channel transfer function of each stationary sub-interval obtained in step S3 to calculate the normalized channel coefficient of the UAV channel, and key statistical characteristic indicators are calculated for channel analysis. The key statistical characteristic indicators include at least the frequency correlation function and the time correlation function.

2. The UAV channel stationary bandwidth and composite Doppler analysis method according to claim 1, characterized in that, Step S2 further includes: The time-delay domain autocorrelation function is calculated using the time-varying channel impulse response, and is expressed as: ； in For channel impulse response, For the observation time, For the propagation delay of electromagnetic waves, This is the time delay offset. It is the expectation operator, superscript Represents the conjugate operation for complex numbers; Taking the Fourier transform of the time-delay domain autocorrelation function yields the frequency-time-delay joint power spectral density function, expressed as: ； The autocorrelation function of the frequency-time delay scattering function is calculated and expressed as: ； In the formula, As the reference frequency, The frequency interval between two frequency points. Represents an imaginary number.

3. The UAV channel stationary bandwidth and composite Doppler analysis method according to claim 1, characterized in that, In step S3, the frequency domain stable bandwidth Represented as; ； in, This represents a preset stationary bandwidth threshold, adaptively selected based on the channel modeling accuracy and computational efficiency requirements of the UAV communication scenario. It is used to determine the channel stationary boundary corresponding to the frequency domain autocorrelation function. express Time and frequency Frequency interval The autocorrelation function of the corresponding frequency-time delay scattering function.

4. The UAV channel stationary bandwidth and composite Doppler analysis method according to claim 1, characterized in that, In step S3, the first The channel transfer function for each stationary subinterval in the frequency domain is expressed as: ； In the formula, Indicates the first Rice factor for each stationary interval in the frequency domain. and These represent the time delays for the line-of-sight path and the non-line-of-sight path, respectively. For the first The number of non-line-of-sight paths in each frequency-domain stationary sub-interval. It is the first The number of sub-paths in a non-line-of-sight path For the propagation delay of electromagnetic waves, For the observation time, As the reference frequency, For frequency domain stationary bandwidth, Indicates the first The center frequency within each stationary sub-interval in the frequency domain This represents the power correction factor for the line-of-sight path caused by obstruction due to the fuselage structure. This is the power correction factor for frequency-dependent non-line-of-sight paths. and These represent the equivalent Doppler phases for the line-of-sight path and the non-line-of-sight path, respectively. and The antenna pattern function takes into account attitude changes. Numbering the transmitting antenna elements, For the receiving antenna element number, the superscript L corresponds to the line-of-sight (LOS) path, and the superscript NL corresponds to the non-line-of-sight (NLOS) scattering path. The variable is the integral variable, representing continuous frequency points within a frequency-stationary sub-interval. For the first The first transmitting antenna element and the first The channel impulse response between the receiving antenna elements is expressed as: ； Then the channel coefficient and Further modeling is as follows: ； ； In the formula, Represents 0 to The uniformly distributed variable is used to represent the random initial phase of the line-of-sight path and the non-line-of-sight path. This represents the composite Doppler frequency offset within a stationary sub-interval in the frequency domain. and These are the spatially corrected phases of the multi-input multi-output antenna elements for line-of-sight and non-line-of-sight paths, respectively.

5. The UAV channel stationary bandwidth and composite Doppler analysis method according to claim 1, characterized in that, In step S4, the composite Doppler frequency offset is expressed as: ； The Doppler frequency shift caused by the drone's motion is represented as follows: ； In the formula, Indicates the carrier frequency of the transmitted signal. Indicates the speed of the drone. This indicates the angle between the direction of the drone's movement and the direction of signal propagation. Indicates the speed of propagation of electromagnetic waves; The Doppler frequency shift caused by the change in the attitude of the UAV is: ； In the formula, This represents the angular velocity vector of the UAV rotating around its center of mass. , , These represent the pitch angle, roll angle, and yaw angle of the UAV, respectively, with the superscript dot indicating the first derivative with respect to time. Indicates that the antenna is in Installation position in the coordinate system Indicates that the antenna is in Position in the coordinate system Let R represent the coordinate vector of the ground vehicle in the global inertial coordinate system, and let R represent the transformation matrix. This represents the position vector of the transmitting antenna in the body coordinate system. The Doppler frequency shift caused by drone propeller vibration is: ； In the formula, the jitter speed Represented as ； In the formula, These represent the jitter amplitudes in the x, y, and z directions, respectively. The dithering angular frequency, These are the initial phases of the jitter in the x, y, and z directions, respectively. The unit direction vector in the body coordinate system. This represents the instantaneous displacement vector of the transmitting antenna in the body coordinate system caused by the vibration of the propeller.

6. The UAV channel stationary bandwidth and composite Doppler analysis method according to claim 1, characterized in that, In step S5, the process of using the composite Doppler frequency offset as a phase correction term and applying it to the channel transfer function of each stationary sub-interval obtained in step S3 to calculate the normalized channel coefficients of the UAV channel includes: Composite Doppler frequency shift Integrating over time yields the time-varying Doppler phase, which is then multiplied as a complex exponential correction term into the line-of-sight component and each non-line-of-sight sub-path component of the channel transfer function to obtain the time-domain response of the line-of-sight channel after superimposed Doppler effects. and ; By performing maximum / minimum normalization on the time-domain responses corresponding to all frequency points within the same stationary sub-interval in the same frequency domain, the normalized channel coefficients of the UAV channel are calculated and expressed as: ； 。 7. The UAV channel stationary bandwidth and composite Doppler analysis method according to claim 6, characterized in that, In step S5, based on the path power correction factor, Doppler phase, and time delay parameters corresponding to the normalized channel coefficients of each frequency domain stationary sub-interval, a channel frequency correlation function and a time correlation function are constructed respectively; the frequency correlation function and the time correlation function are respectively expressed as: ； ； in, It is the expectation operator.

8. A system for analyzing the channel stationary bandwidth and composite Doppler of an unmanned aerial vehicle (UAV), characterized in that, The system includes a user configuration unit, a stable bandwidth allocation unit, a composite Doppler and statistical characteristic calculation unit, and an output unit; The user configuration unit is used to input configuration parameters, which include: signal bandwidth, carrier frequency, carrier wavelength, UAV speed, UAV pitch angle, roll angle and yaw angle, antenna body coordinates, propeller jitter amplitude, angular frequency and initial phase, stationary bandwidth threshold and Rice factor. The stable bandwidth partitioning unit is used to calculate the time-delay domain autocorrelation function using the time-varying channel impulse response of the channel, and to perform a Fourier transform on the time-delay dimension of the time-delay domain autocorrelation function to obtain the frequency-time-delay joint power spectral density function. Based on the frequency-time delay joint power spectral density function, the maximum value of the power spectrum integral at two frequency points is taken simultaneously as the normalized denominator to construct the autocorrelation function of the frequency-time delay scattering function. Then, combining the stationary bandwidth threshold and the autocorrelation function of the frequency-time delay scattering function, different frequency intervals are traversed to find the maximum frequency interval that satisfies the autocorrelation function value not lower than the stationary bandwidth threshold. This maximum frequency interval is taken as the frequency domain stationary bandwidth. Using the frequency domain stationary bandwidth as the segmentation standard, the signal bandwidth is continuously divided into several frequency domain stationary sub-intervals. The composite Doppler and statistical characteristic calculation unit is used to call Rice factor and antenna body coordinates to establish the channel transfer function between the transmitting antenna unit and the receiving antenna unit in each stationary sub-interval; at the same time, based on the input pitch angle, roll angle and yaw angle, the inertial coordinate system of the UAV motion is converted into the body coordinate system; based on the coordinate transformation result, the Doppler frequency offset caused by the UAV motion is calculated by combining the UAV speed, the Doppler frequency offset caused by attitude change is solved by combining the attitude angle, the Doppler frequency offset caused by propeller jitter is calculated by combining the amplitude, angular frequency and initial phase of propeller jitter, and then the conversion of the three types of frequency offset is completed by combining the carrier frequency and carrier wavelength, and the composite Doppler frequency offset is obtained by adding them together; The output unit is used to apply the composite Doppler frequency offset as a phase correction term to the channel transfer function of each stationary sub-interval, calculate the normalized channel coefficients of the UAV channel, and calculate key statistical characteristic indicators for channel analysis. The key statistical characteristic indicators include at least the frequency correlation function and the time correlation function.

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