Method and System for Cracking UAV Communication Link Based on Chaotic Modulation Waveform

Abstract

The present application provides a method and system for cracking the UAV communication link based on chaotic modulation waveforms. Specifically, the present application uses a hybrid-index multi-carrier chaotic signal to generate a received signal matrix, separates the index bit features and modulation bit features mixed and superimposed in the matrix, and generates a set of independently modulated carrier components. Then, according to the frequency band distribution range of the set, the beamforming direction of the multi-channel antenna array is adjusted to generate carrier component signals. Subsequently, the carrier component signals are subjected to matrix reconstruction to remove environmental noise components and extract the corresponding chaotic waveform basis vectors. Finally, according to its mapping relationship with the modulation symbols of the target UAV, a spread spectrum code sequence is generated. The technical solution provided by the present application solves the problems of poor adaptability of traditional methods to aperiodic chaotic signals and insufficient decoupling accuracy of mixed features, improves the anti-interference ability of target signals, and realizes the efficient reverse analysis of UAV communication protocols and the accurate reconstruction of spread spectrum codes in complex electromagnetic environments.

Description

Technical Field

[0001] This application relates to the field of signal processing technology, and in particular, to a method and system for cracking an unmanned aerial vehicle (UAV) communication link based on a chaotic modulation waveform. Background Art

[0002] With the wide application of UAVs in fields such as military reconnaissance, disaster relief, and logistics transportation, the security of their communication links faces severe challenges. In scenarios such as countering malicious UAV invasions and cracking enemy communication protocols, it is necessary to achieve high-precision signal parsing and link reverse reconstruction for complex modulation mechanisms, while overcoming problems such as multi-UAV signal overlap and interference suppression in low signal-to-noise ratio environments.

[0003] Existing solutions mainly rely on traditional spectrum analysis, deep learning models, or multi-antenna beamforming techniques. Some methods separate carrier components through spectrum energy detection and matched filtering, and extract modulation features by combining time-frequency analysis; other solutions use deep learning models to classify the time-frequency diagrams of received signals, infer modulation rules, and generate pseudo-spreading codes; in addition, multi-antenna beamforming techniques are used to enhance the intensity of target signals, supplemented by compressive sensing algorithms to reduce the impact of noise.

[0004] However, the existing solutions have the following defects. Traditional spectrum analysis methods rely on the periodicity assumption of signals and are difficult to adapt to the non-periodic time-varying characteristics of chaotic modulation, resulting in insufficient carrier separation accuracy; deep learning models rely on a large amount of labeled data for training, have weak generalization ability for the dynamically changing carrier-index coupling relationship in hybrid index modulation, and the bit error rate increases significantly in complex scenarios; existing beamforming techniques do not combine the frequency band sparsity characteristics of carrier components, are difficult to accurately focus under multi-target interference, and the low-rank noise reduction algorithm fails to reconstruct spreading codes with a high failure rate due to ignoring the coupling relationship between indexes and modulation bits. Summary of the Invention

[0005] This application provides a method and system for cracking an unmanned aerial vehicle (UAV) communication link based on a chaotic modulation waveform, which is used to solve the problems in the prior art of poor adaptability to non-periodic chaotic modulation signals, insufficient accuracy in separating hybrid index multi-carrier characteristics, weak beamforming focusing ability under multi-target interference, and low-rank noise reduction failure and high spreading code reconstruction failure rate caused by the coupling between indexes and modulation bits.

[0006] In a first aspect, this application provides a method for cracking an unmanned aerial vehicle (UAV) communication link based on a chaotic modulation waveform, including:

[0007] Using a multi-channel antenna array to obtain a hybrid index multi-carrier chaotic signal transmitted by a target UAV, and generating a received signal matrix including the correlation relationship between the time dimension and the frequency dimension;

[0008] Based on the carrier distribution characteristics of the hybrid-index multi-carrier chaotic signal, a random sequence scrambling algorithm is used to separate the hybrid superposed index bit features and modulation bit features in the received signal matrix, and an independently modulated carrier component set is generated;

[0009] According to the frequency band distribution range of the carrier component set, the beamforming direction of the multi-channel antenna array is dynamically adjusted to generate a carrier component signal enhanced by beamforming;

[0010] Perform matrix reconstruction on the carrier component signal enhanced by beamforming, use the low-rank distribution characteristics to estimate and remove the environmental noise component in the matrix reconstruction result, and extract the chaotic waveform basis vectors corresponding to the main components in the matrix reconstruction result after removing the environmental noise component;

[0011] According to the mapping relationship between the chaotic waveform basis vectors and the modulation symbols of the target UAV, a spreading code sequence matching the hybrid-index multi-carrier differential chaotic modulation communication link is generated.

[0012] Optionally, based on the carrier distribution characteristics of the hybrid-index multi-carrier chaotic signal, using a random sequence scrambling algorithm to separate the hybrid superposed index bit features and modulation bit features in the received signal matrix includes:

[0013] According to the frequency interval and power density distribution of each carrier in the hybrid-index multi-carrier chaotic signal, a random reference sequence matching the carrier distribution characteristics is generated, where the length of the random reference sequence is the same as the number of columns of the received signal matrix;

[0014] Perform a point-by-point multiplication operation on the random reference sequence and the time-domain sampling points of each row in the received signal matrix to generate a scrambled signal component matrix;

[0015] Based on the time-domain sparse characteristics corresponding to the index bits in the scrambled signal component matrix, decompose the signal component matrix into an index bit feature matrix and a modulation bit feature matrix.

[0016] Optionally, generating an independently modulated carrier component set includes:

[0017] According to the row vector amplitude distribution of the index bit feature matrix, screen out the index selection modes with row vector amplitudes higher than a preset threshold to generate an effective index mode set;

[0018] According to the phase continuity of the column vectors of the modulation bit feature matrix, filter out the modulation symbols whose phase jumps exceed the constraints of the chaotic modulation symbol period, and use the remaining modulation symbols after filtering as an effective modulation symbol set;

[0019] Orthogonally project and match the set of valid index patterns with the set of valid modulation symbols to generate a set of carrier components including independent carrier frequencies, independent modulation symbols, and corresponding index selection patterns.

[0020] Optionally, according to the frequency band distribution range of the set of carrier components, dynamically adjust the beamforming direction of the multi-channel antenna array to generate a beamformed enhanced carrier component signal, including:

[0021] Determine the target frequency band coverage interval of the multi-channel antenna according to the frequency distribution range of each independently modulated carrier component in the set of carrier components, and extract the set of central frequencies of all carrier components within the target frequency band coverage interval;

[0022] Based on the frequency value of each carrier component in the set of central frequencies, calculate the delay compensation parameter corresponding to each antenna element in the multi-channel antenna array, and generate a beamforming weight vector matching the set of central frequencies according to the delay compensation parameter;

[0023] Perform complex weighted superposition of the beamforming weight vector and the original signal received by the multi-channel antenna array to generate a beamforming signal matrix for the target frequency band coverage interval;

[0024] According to the signal intensity distribution of different carrier components in the beamforming signal matrix, dynamically adjust the phase offset of the beamforming weight vector to make the signal intensity of the carrier component corresponding to the target UAV in the beamforming signal matrix reach a preset gain threshold, and generate the beamformed enhanced carrier component signal.

[0025] Optionally, perform matrix reconstruction on the beamformed enhanced carrier component signal, estimate and remove the environmental noise component in the matrix reconstruction result using the low-rank distribution characteristic, and extract the chaotic waveform basis vector corresponding to the main component in the matrix reconstruction result after removing the environmental noise component, including:

[0026] Construct a multi-dimensional signal reconstruction matrix according to the mapping relationship between the carrier frequency and the time sampling points of the beamformed enhanced carrier component signal;

[0027] Based on the frequency band distribution sparsity of the carrier components in the multi-dimensional signal reconstruction matrix, estimate the low-rank distribution characteristic of the reconstruction matrix to obtain an estimation result;

[0028] Based on the estimation result, decompose the reconstruction matrix into a low-rank matrix component and a noise matrix component;

[0029] Iteratively optimize the low-rank matrix component according to the statistical distribution characteristic of the elements in the noise matrix component;

[0030] Extract the singular vectors corresponding to the top preset number of largest singular values from the optimized low-rank matrix components to generate chaotic waveform basis vectors, where the value of the preset number is equal to the number of valid modulation symbols in the carrier component set.

[0031] Optionally, based on the sparsity of the frequency band distribution of the carrier components in the multidimensional signal reconstruction matrix, estimate the low-rank distribution characteristics of the reconstruction matrix to obtain an estimation result, including:

[0032] Calculate the sparsity parameter of the multidimensional signal reconstruction matrix according to the number of independently modulated carriers in the carrier component set and the sparsity of the frequency band distribution of the multidimensional signal reconstruction matrix, where the sparsity parameter is the proportion of the number of rows occupied by non-zero carrier components in the reconstruction matrix;

[0033] Based on the sparsity parameter and the power density distribution of each carrier component in the carrier component set, determine the initial rank value of the low-rank matrix component;

[0034] Perform singular value threshold decomposition on the multidimensional signal reconstruction matrix according to the initial rank value, and decompose the multidimensional signal reconstruction matrix into an initial low-rank matrix component and an initial noise matrix component, where the number of singular values of the initial low-rank matrix component is equal to the initial rank value;

[0035] Modify the initial rank value according to the amplitude distribution of the elements in the initial noise matrix component and the power density difference of the chaotic modulation symbols in the carrier component set to generate an optimized low-rank matrix rank value;

[0036] Based on the optimized low-rank matrix rank value, perform a second singular value threshold decomposition on the multidimensional signal reconstruction matrix to generate an optimal low-rank matrix component and an optimal noise matrix component as the estimation result of the low-rank distribution characteristic estimation.

[0037] Optionally, generate a spread spectrum code sequence matching the hybrid index multi-carrier differential chaos modulation communication link according to the mapping relationship between the chaotic waveform basis vectors and the modulation symbols of the target UAV, including:

[0038] Determine the segmented length of the chaotic waveform basis vector corresponding to each modulation symbol according to the mapping relationship between the time domain length of the chaotic waveform basis vector and the modulation symbol period of the target UAV, where the segmented length is proportional to the number of carrier components within the modulation symbol period;

[0039] Divide the chaotic waveform basis vector into multiple basis vector sub-segments according to the segmented length of the chaotic waveform basis vector, and generate an orthogonal projection coefficient set corresponding to each basis vector sub-segment according to the sparsity of the frequency band distribution of each carrier component in the carrier component set;

[0040] Based on the set of orthogonal projection coefficients, perform an orthogonal modulation operation on each basis vector sub - segment and the symbol sequence in the modulation symbol mapping relationship to generate a set of segmented spread - spectrum codes corresponding one - to - one with each carrier component;

[0041] According to the carrier index rule of the hybrid - index multi - carrier differential chaos modulation, perform time - domain superposition on the segmented spread - spectrum codes belonging to the same carrier index pattern in the set of segmented spread - spectrum codes to generate a combined spread - spectrum code corresponding to an independent carrier index;

[0042] In accordance with the arrangement order of the carrier frequencies in the hybrid - index multi - carrier modulation, perform phase - synchronization calibration on the combined spread - spectrum code and the frequency offset of the corresponding carrier component to generate the spread - spectrum code sequence.

[0043] In a second aspect, the present application provides a UAV communication link cracking system based on a chaotic modulation waveform, including:

[0044] An acquisition module, configured to use a multi - channel antenna array to acquire a hybrid - index multi - carrier chaotic signal transmitted by a target UAV, and generate a received signal matrix including the correlation relationship between the time dimension and the frequency dimension;

[0045] A separation module, configured to, based on the carrier distribution characteristics of the hybrid - index multi - carrier chaotic signal, perform a separation operation on the mixed - superposed index bit features and modulation bit features in the received signal matrix by using a random sequence scrambling algorithm, and generate a set of independently modulated carrier components;

[0046] An adjustment module, configured to dynamically adjust the beamforming direction of the multi - channel antenna array according to the frequency band distribution range of the set of carrier components, and generate a carrier component signal enhanced by beamforming;

[0047] An extraction module, configured to perform matrix reconstruction on the carrier component signal enhanced by beamforming, estimate and remove the environmental noise component in the matrix reconstruction result by using the low - rank distribution characteristic, and extract the chaotic waveform basis vectors corresponding to the main components in the matrix reconstruction result after removing the environmental noise component;

[0048] A generation module, configured to generate a spread - spectrum code sequence matching the hybrid - index multi - carrier differential chaos modulation communication link according to the mapping relationship between the chaotic waveform basis vectors and the modulation symbols of the target UAV.

[0049] In a third aspect, an embodiment of the present application provides a computing device, including a processing component and a storage component; the storage component stores one or more computer instructions; the one or more computer instructions are used to be called and executed by the processing component to implement the method for cracking a UAV communication link based on a chaotic modulation waveform as described in the first aspect above.

[0050] Fourthly, an embodiment of the present application provides a computer storage medium storing a computer program, which when executed by a computer, implements the method for cracking an unmanned aerial vehicle communication link based on a chaotic modulation waveform as described in the first aspect.

[0051] In the embodiment of the present application, a multi-channel antenna array is used to capture a hybrid-index multi-carrier chaotic signal and generate a received signal matrix. Combining with a random sequence scrambling algorithm, the accurate separation of the index and modulation bit features is realized, solving the problems of poor adaptability of traditional methods to aperiodic chaotic signals and insufficient decoupling accuracy of mixed features. Further, based on the carrier frequency band distribution, the beamforming direction is dynamically adjusted, significantly improving the anti-interference ability of the target signal. At the same time, using the low-rank distribution characteristics estimation and principal component extraction technology, the chaotic waveform basis vector is restored from the noise environment. Finally, a spread spectrum code sequence matching the target communication link is generated through modulation symbol mapping, forming a complete technical closed-loop from signal capture, feature separation, noise suppression to link reverse analysis, and achieving a high success rate of link cracking in a multi-unmanned aerial vehicle collaborative scenario.

[0052] Furthermore, through point-by-point multiplication operation, the time-domain scrambling of the received signal matrix is performed, and the decomposition of the index and modulation bit feature matrices is realized by using the time-domain sparse characteristics of the index bits, effectively solving the problem of feature separation failure caused by carrier-index dynamic coupling in the prior art. The length of the generated random reference sequence is strictly consistent with the number of columns of the signal matrix, ensuring that the scrambling operation does not damage the frequency band correlation of the original signal. The decomposed index and modulation bit matrices are respectively used as input parameters for subsequent beamforming adjustment and spread spectrum code generation, forming a collaborative mechanism of feature separation and signal enhancement in the technical link, and significantly improving the reconstruction accuracy of carrier components in a hybrid-index multi-carrier modulation scenario.

[0053] These aspects or other aspects of the present application will be more clearly understood in the following description of the embodiments. Description of the Drawings

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0055] Figure 1 Shows a flowchart of the method for cracking an unmanned aerial vehicle communication link based on a chaotic modulation waveform provided by the present application;

[0056] Figure 2 Shows a schematic structural diagram of the system for cracking an unmanned aerial vehicle communication link based on a chaotic modulation waveform provided by the present application;

[0057] Figure 3 The structural schematic diagram of a computing device provided by the present application is shown. Specific embodiments

[0058] In order to enable those skilled in the art to better understand the solution of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present application.

[0059] In some processes described in the specification, claims and the above-mentioned drawings of the present application, a plurality of operations that appear in a specific order are included. However, it should be clearly understood that these operations may not be executed in the order in which they appear in this document or may be executed in parallel. The serial numbers of the operations, such as 101, 102, etc., are only used to distinguish different operations, and the serial numbers themselves do not represent any execution order. In addition, these processes may include more or fewer operations, and these operations may be executed in sequence or in parallel. It should be noted that the descriptions such as "first" and "second" in this document are used to distinguish different messages, devices, modules, etc., and do not represent a sequence, nor do they limit that "first" and "second" are of different types.

[0060] In the research process of the present application, it is found that the existing methods for cracking UAV communication links have technical bottlenecks in non-periodic chaotic signal processing, such as poor adaptability, insufficient accuracy in separating the characteristics of hybrid-index multi-carrier, weak anti-jamming ability of beamforming under multi-target interference, and high failure rates in low-rank noise reduction and spread-spectrum code reconstruction.

[0061] Based on this, a method for cracking UAV communication links based on chaotic modulation waveforms is provided. This method can separate the index and modulation bit characteristics through random sequence scrambling, dynamically optimize the beamforming direction by combining the sparsity of the carrier frequency band, and use low-rank distribution characteristics estimation and principal component extraction technology to achieve noise suppression and chaotic waveform restoration, and finally generate a spread-spectrum code sequence that matches the target communication link.

[0062] The technical solution of the present application is applicable to the reverse analysis of communication links using hybrid-index multi-carrier differential chaotic modulation in multi-UAV cooperative communication scenarios, and has significant advantages especially in complex electromagnetic environments with low signal-to-noise ratios and overlapping multi-signals.

[0063] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present application.

[0064] Figure 1The figure below is a flowchart of a method for cracking a UAV communication link based on a chaotic modulation waveform provided by an embodiment of this application. As Figure 1 shown, the method includes:

[0065] Step 101, use a multi-channel antenna array to obtain a hybrid-index multi-carrier chaotic signal transmitted by a target UAV, and generate a received signal matrix containing the correlation relationship between the time dimension and the frequency dimension;

[0066] In this step, the hybrid-index multi-carrier chaotic signal refers to a modulation method adopted in the target UAV communication link. Its characteristic is that the index bits (used to select carrier frequency bands) and modulation bits (used for chaotic waveform symbol mapping) are mixed and encoded onto multiple carriers, and the signal of each carrier is generated by a chaotic waveform, having non-periodic and wide-spectrum characteristics; the received signal matrix containing the correlation relationship between the time dimension and the frequency dimension refers to a two-dimensional matrix constructed after time-frequency analysis of the original signal received by the multi-channel antenna array. Its row dimension represents different carrier frequency bands, and the column dimension represents time series sampling points. The matrix element value is the signal amplitude or phase of the corresponding frequency band at a specific moment.

[0067] In the embodiment of this application, first, the radio frequency signal transmitted by the target UAV is received through a multi-channel antenna array (such as an 8-channel uniform linear array). Each antenna channel independently collects time-domain waveform data and records the time synchronization sampling sequence of each channel. Secondly, perform a short-time Fourier transform (STFT) or wavelet transform on the time-domain signal of each antenna channel to convert the time-domain signal into a frequency-domain - time joint distribution frequency band energy distribution map, and extract the amplitude and phase information of each carrier frequency band within the time window. Then, align the same-frequency data of different antenna channels according to the time sampling points to construct a three-dimensional tensor structure (number of channels × number of frequency bands × number of time points), and then perform coherent merging on the channel dimension to generate a two-dimensional received signal matrix, where the row index corresponds to the carrier frequency band number (such as frequency band 1 to frequency band N), and the column index corresponds to the time sampling point (such as t1 to tM). The matrix element is the merged complex signal value. For example, for 16 carrier frequency bands with hybrid-index modulation, a matrix of 16 rows × 1000 columns is generated, and each row represents the signals of 1000 sampling points of a carrier frequency band within a 1-millisecond time window.

[0068] For example, when the signal transmitted by the target UAV contains 8 carrier frequency bands (such as 8 sub - bands with an interval of 50 MHz within the 2.4 GHz band), after each channel of the multi - channel antenna array receives the signal, it is decomposed into 8 frequency - band components through fast Fourier transform (FFT), and the complex signal values (amplitude + phase) of each frequency band are recorded within each time window (such as 1 ms). The finally generated received signal matrix is a two - dimensional matrix of 8 rows (corresponding to 8 carrier frequency bands) × 100 columns (corresponding to 100 time sampling points). The element in the 3rd row and 50th column of the matrix represents the signal amplitude of the 3rd carrier frequency band at the 50th sampling moment.

[0069] Step 102: Based on the carrier distribution characteristics of the hybrid - index multi - carrier chaotic signal, use a random - sequence scrambling algorithm to separate the mixed - superposed index - bit features and modulation - bit features in the received signal matrix, and generate a set of independently modulated carrier components;

[0070] In this step, the random - sequence scrambling algorithm is an operation based on the point - by - point product of a pseudo - random sequence and the signal matrix. By introducing a random reference sequence that matches the carrier distribution characteristics, the mixed - superposition relationship between the index bits and modulation bits in the time domain is destroyed, thereby separating their features.

[0071] Index - bit features and modulation - bit features: Index bits are used to select carrier frequency bands (such as determining the activated carrier number at the current moment), and modulation bits are used to generate chaotic waveform symbols (such as generating phase or amplitude through chaotic mapping); the two are superposed due to mixed coding in the time domain.

[0072] The set of independently modulated carrier components refers to the set of separated carrier components. Each component contains an independent carrier frequency band, index - selection mode, and chaotic - modulation symbol, and is used for subsequent directional enhancement and signal reconstruction.

[0073] In the embodiments of the present application, first, according to the frequency interval of carriers in the received signal matrix (such as 50 MHz) and the power density distribution (such as the power difference of each carrier not exceeding 3 dB), a random reference sequence matching the carrier distribution characteristics is generated, and its length is consistent with the number of columns (time sampling points) of the received signal matrix. For example, if the received signal matrix is 16 rows × 1000 columns, the length of the random reference sequence is 1000. Secondly, the random reference sequence is subjected to a point-by-point multiplication operation with each row of the received signal matrix (corresponding to a carrier frequency band), so that the time-domain sparse pulses corresponding to the index bits (such as appearing once every 100 sampling points) are broadened after being modulated by the random sequence, while the continuous chaotic waveforms corresponding to the modulation bits are randomly phase perturbed. Then, a time-domain sparsity analysis is performed on the scrambled signal component matrix, and the compressed sensing algorithm is used to separate the index bit feature matrix (sparse pulse distribution) and the modulation bit feature matrix (continuous chaotic waveform). Finally, the effective index patterns are selected according to the row vector amplitudes of the index bit feature matrix (such as pulses with amplitudes higher than twice the noise floor), and the abnormal symbols are filtered out according to the phase continuity of the column vectors of the modulation bit feature matrix (such as the phase jump between adjacent sampling points not exceeding π / 2), generating a set of independently modulated carrier components.

[0074] For example, in the generated 8×1000 received signal matrix, the random reference sequence is a pseudo-random code with a length of 1000 (such as a Gold sequence). After multiplying the 1000 sampling points in the 3rd row carrier frequency band (2.45 GHz) with the random sequence point by point, the time-domain sparse pulses corresponding to the original index bits (such as the 50th, 150th, and 250th sampling points) are modulated into broadband signals by the random sequence, while the chaotic waveforms of the modulation bits are randomly phase perturbed. After sparse decomposition, the 3rd row in the index bit feature matrix shows that the effective pulses are located at the 50th, 150th, and 250th sampling points, while the 3rd column in the modulation bit feature matrix retains the chaotic symbols with continuous phase. Finally, a set of independent carrier components is generated, including the effective index pattern (activated once every 100 sampling points) in the 2.45 GHz frequency band and the corresponding chaotic modulation symbol sequence.

[0075] Step 103: Dynamically adjust the beamforming direction of the multi-channel antenna array according to the frequency band distribution range of the set of carrier components, and generate a carrier component signal enhanced by beamforming;

[0076] In this step, the beamforming direction means that by adjusting the phase and amplitude weights of each antenna element in the multi-channel antenna array, the main lobe of the radiation pattern of the antenna array is aligned with the direction of the target signal source, thereby enhancing the reception intensity of signals in a specific frequency band.

[0077] The carrier component signal enhanced by beamforming refers to an enhanced signal that suppresses interference and improves the signal-to-noise ratio after spatial filtering and signal superposition of the target carrier component through beamforming technology.

[0078] In the embodiments of the present application, first, according to the frequency distribution ranges of the independent modulated carriers in the carrier component set (such as 2.4 GHz to 2.48 GHz), determine the target frequency band interval to be covered by the multi-channel antenna array (such as 2.45 GHz ± 20 MHz), and extract the set of center frequencies of all carrier components within this interval (such as 2.42 GHz, 2.47 GHz, etc.). Secondly, for each center frequency, calculate the delay compensation parameters of each antenna element in the multi-channel antenna array (such as the delay τ_k of the k-th antenna element is d_k·sinθ / c, where d_k is the antenna spacing and θ is the signal incident angle), and generate a beamforming weight vector (complex weight value, including amplitude and phase adjustment parameters) that matches the center frequency. Then, perform complex weighted superposition of the weight vector and the original signal received by the multi-channel antenna to generate a beamforming signal matrix for the target frequency band (rows correspond to carrier frequency bands, and columns correspond to time sampling points). Finally, according to the real-time intensity distribution of each carrier component in the beamforming signal matrix (such as the signal intensity of 2.45 GHz is lower than the preset threshold), dynamically adjust the phase offset of the weight vector (such as increasing the phase compensation by 10°) to make the target carrier signal intensity reach the preset gain threshold, and output the enhanced carrier component signal.

[0079] For example, in the set of independent carrier components generated in step 102, there are 8 carrier frequency bands (such as 2.42 GHz, 2.45 GHz, 2.47 GHz, etc.). According to the frequency band distribution range (2.42 GHz to 2.47 GHz), the target frequency band interval is determined to be 2.4 GHz to 2.5 GHz. For the center frequency of 2.45 GHz, calculate the delay compensation parameters of each unit in the 8-channel antenna array (such as τ_1 = 0 ns, τ_2 = 1.2 ns), and generate a weight vector; after superimposing the weight vector and the original signal, the signal intensity of the 2.45 GHz frequency band is increased from -80 dBm to -60 dBm, while the signal in the interference frequency band (such as 2.6 GHz) is suppressed; by dynamically adjusting the phase offset, finally generate the enhanced carrier component signal.

[0080] Step 104, perform matrix reconstruction on the carrier component signal enhanced by beamforming, use the low-rank distribution characteristic estimation to estimate and remove the environmental noise component in the matrix reconstruction result, and extract the chaotic waveform basis vectors corresponding to the main components in the matrix reconstruction result after removing the environmental noise component;

[0081] In this step, the low-rank distribution characteristic estimation means assuming that the distribution of the effective carrier components in the signal matrix has low rank (that is, the rank of the matrix is much smaller than its dimension), while the noise components show high rank or random distribution, so as to separate the signal and noise through matrix decomposition.

[0082] The chaotic waveform basis vector refers to the singular vector extracted from the low-rank matrix component, whose amplitude and time-varying characteristics are consistent with the chaotic modulation waveform transmitted by the target UAV, and is used to reverse generate the spread spectrum code sequence.

[0083] In the embodiment of this application, first, the carrier component signal after beamforming enhancement (such as a complex matrix of 8 frequency bands × 1000 time points) is used to construct a multi-dimensional signal reconstruction matrix (rows correspond to carrier frequency bands, columns correspond to time points) according to the mapping relationship between the carrier frequency and the time sampling points. Secondly, based on the sparsity of the frequency band distribution of the carrier component (for example, only 3 frequency bands have valid signals), the sparsity parameter of the reconstruction matrix is calculated (for example, the proportion of non-zero rows is 37.5%), and the initial rank value of the low-rank component is determined accordingly (for example, rank = 3). Then, the reconstruction matrix is subjected to singular value threshold decomposition (SVT) to obtain the initial low-rank matrix component (rank = 3) and the initial noise matrix component. Then, according to the amplitude distribution of the noise matrix component (such as Gaussian distribution mean μ = 0.1) and the difference in carrier power density, the initial rank value is corrected (such as adjusted to rank = 4), and a second singular value decomposition is performed to generate the final low-rank matrix component (rank = 4) and the noise matrix component. Finally, the left singular vectors corresponding to the first 4 largest singular values are extracted from the low-rank matrix component as the chaotic waveform basis vectors.

[0084] For example, in the generated 8×1000 beamforming enhanced matrix, the carrier component set includes three effective frequency bands of 2.42 GHz, 2.45 GHz, and 2.47 GHz. After constructing the reconstruction matrix, the calculated sparsity parameter is 3 / 8 = 37.5%, and the initial rank value is set to 3. Through singular value decomposition, it is found that the amplitude mean (μ = 0.15) of the noise component is higher than the target carrier power density (μ = 0.05), and the rank value is corrected to 4. After the second decomposition, the first 4 singular vectors are extracted. The first singular vector corresponds to the chaotic waveform of the 2.45 GHz frequency band, and its amplitude shows an aperiodic fluctuation characteristic with time, which matches the chaotic modulation rule of the target UAV.

[0085] Step 105, generate a spread spectrum code sequence that matches the hybrid index multi-carrier differential chaos modulation communication link according to the mapping relationship between the chaotic waveform basis vector and the modulation symbols of the target UAV;

[0086] In this step, the modulation symbol mapping relationship refers to the corresponding rule between the chaotic waveform basis vector and the modulation symbols (such as binary symbols 0 / 1 or QPSK symbols) defined in the target UAV communication protocol. For example, a specific time-domain waveform segment of the basis vector is mapped to the symbol "0", and another segment is mapped to the symbol "1".

[0087] The spread spectrum code sequence refers to a pseudo-random code sequence generated through orthogonal modulation and time-domain superposition. Its frequency-domain characteristics are fully matched with the carrier index rule and chaotic modulation method of the target communication link, and it is used to reverse-analyze communication content or inject interference signals.

[0088] In the embodiments of this application, first, according to the modulation symbol period of the target unmanned aerial vehicle (UAV) (for example, each symbol lasts for 250 sampling points) and the time-domain length of the chaotic waveform basis vector (for example, 1000 sampling points), the segment length of the basis vector corresponding to each symbol is determined (for example, 250 sampling points). Secondly, the chaotic waveform basis vector is divided into multiple sub-segments according to the segment length (for example, 4 sub-segments), and according to the sparsity of the frequency band distribution of each carrier component in the carrier component set (for example, the 2.45 GHz frequency band occupies 3 sub-carriers), an orthogonal projection coefficient set corresponding to each sub-segment is generated (for example, the row vectors in the coefficient matrix correspond one-to-one with the carrier frequency bands). Then, each basis vector sub-segment is subjected to an orthogonal modulation operation (such as point-by-point complex multiplication and accumulation) with the modulation symbol sequence (for example, [0, 1, 0, 1]) to generate a set of segmental spread spectrum codes corresponding to each carrier. Then, according to the carrier index rule of the hybrid index modulation (for example, the carrier frequency band is switched every two symbols), the segmental spread spectrum codes under the same index mode are subjected to time-domain superposition (for example, the spread spectrum codes of 2.45 GHz and 2.47 GHz corresponding to symbol 1 are superimposed) to generate a combined spread spectrum code. Finally, according to the arrangement order of the carrier frequencies (for example, 2.42 GHz → 2.45 GHz → 2.47 GHz), the phase synchronization calibration is performed on the combined spread spectrum code (for example, compensating for the phase offset caused by the carrier frequency offset) to generate the final spread spectrum code sequence.

[0089] For example, among the 4 extracted chaotic waveform basis vectors, the length of basis vector 1 is 1000 points and it is divided into 4 sub-segments of 250 points. The carrier component set contains 3 sub-carriers in the 2.45 GHz frequency band, and the generated orthogonal projection coefficient set is a 3×4 matrix. After modulating the first sub-segment with the symbol sequence [1, 0], a segmental spread spectrum code (250 points) of 2.45 GHz is generated. According to the index rule (the carrier frequency is switched every symbol), the spread spectrum codes of 2.45 GHz and 2.47 GHz corresponding to symbol 1 are superimposed to generate a combined spread spectrum code of 500 points. The phase offset of the 2.45 GHz frequency band is calibrated (for example, compensating for 10°), and finally a spread spectrum code sequence matching the target communication link is generated.

[0090] In order to improve the problem of insufficient feature separation accuracy caused by carrier-index dynamic coupling in the prior art, based on this, in some embodiments, according to what is described in step 102, based on the carrier distribution characteristics of the hybrid index multi-carrier chaotic signal, a random sequence scrambling algorithm is used to perform a separation operation on the index bit features and modulation bit features mixed and superimposed in the received signal matrix, and an independent modulation carrier component set is generated, including:

[0091] Step 201: Generate a random reference sequence that matches the distribution characteristics of the carriers according to the frequency intervals and power density distributions of the respective carriers in the hybrid-index multi-carrier chaotic signal. Here, the length of the random reference sequence is the same as the number of columns of the received signal matrix.

[0092] In this step, the frequency interval refers to the frequency difference between adjacent carrier frequency bands in the hybrid-index multi-carrier modulation (such as 50 MHz), which reflects the spatial interval characteristics of the carrier distribution; the power density distribution refers to the signal power distribution characteristics of each carrier frequency band within the unit frequency band (such as the power of some carriers being significantly higher than that of other carriers), which reflects the energy distribution differences of the carriers; the random reference sequence refers to a pseudo-random sequence that matches the characteristics of the carrier frequency bands (frequency interval, power density), and its phase or amplitude distribution law is adapted to the characteristics of the target carrier signal, and is used for subsequent scrambling operations to separate the mixed characteristics.

[0093] In the embodiments of the present application, first, determine the length of the random reference sequence to be the same number of points (such as 1000 points) according to the number of columns of the received signal matrix (the number of time sampling points, such as 1000 points). Second, based on the frequency intervals (such as carrier 1 being 2.4 GHz, carrier 2 being 2.45 GHz, with an interval of 50 MHz) and power density distributions (such as the power of carrier 1 being 3 dB higher than that of carrier 2) of the hybrid-index multi-carrier chaotic signal, generate the corresponding pseudo-random sequence (such as the Gold sequence or the m sequence). Specifically, for each carrier frequency band, adjust the phase jump interval of the random sequence according to its frequency interval (such as for every 50 MHz, the phase is flipped every 200 sampling points in the sequence), and adjust the amplitude ratio of the sequence according to the power density distribution (such as the amplitude of the sequence corresponding to the high-power carrier is increased by 3 dB). Finally, verify the consistency between the length of the generated random reference sequence and the number of columns of the received signal matrix (such as both being 1000 points) to ensure the matrix dimension matching for subsequent scrambling operations.

[0094] Step 202: Perform a point-by-point multiplication operation between the random reference sequence and the time-domain sampling points of each row in the received signal matrix to generate a scrambled signal component matrix.

[0095] In this step, the point-by-point multiplication operation refers to the operation of multiplying the elements at the corresponding positions in two sequences of the same length to generate a new sequence. In this step, each element of the random reference sequence is multiplied one by one with all the time-domain sampling points of a certain row (carrier frequency band) in the received signal matrix; the scrambled signal component matrix refers to the matrix generated after the point-by-point multiplication operation, whose row dimension is the same as that of the received signal matrix (the number of carrier frequency bands), and the column dimension is the number of time sampling points, but the superposition relationship between the index bits and modulation bits in the original signal is destroyed by the random sequence, forming the basis for feature separation.

[0096] In the embodiments of the present application, first, the random reference sequence generated in step 201 (such as a 1000-point Gold sequence) is normalized according to the power density distribution corresponding to the line carrier frequency band (for example, the amplitude of the sequence corresponding to the high-power carrier is increased by 3 dB). Secondly, a point-by-point multiplication operation is performed on each row of the received signal matrix (such as 8 carrier frequency bands): each element of the random reference sequence (in complex form, including amplitude and phase) is multiplied by each time-domain sampling point (complex signal value) of the corresponding carrier row to generate a scrambled row vector. For example, 1000 sampling points of the 3rd row (2.45 GHz carrier) are respectively multiplied by 1000 elements of the random sequence to generate a new 1000-point signal. Then, the scrambled results of all carrier rows are integrated according to the original matrix structure to generate a scrambled signal component matrix (8 rows × 1000 columns), whose row index still corresponds to the original carrier frequency band, but the time-domain signal characteristics have been perturbed by the random sequence. Finally, verify the consistency between the dimension of the scrambled matrix and the original matrix to ensure that the input data format for subsequent decomposition operations is correct.

[0097] Step 203, based on the time-domain sparse characteristics corresponding to the index bits in the scrambled signal component matrix, decompose the signal component matrix into an index bit feature matrix and a modulation bit feature matrix;

[0098] To solve the problem of the reconstruction error of the carrier component set caused by invalid index patterns and abnormal modulation symbol residues in the prior art, based on this, in some embodiments, according to step 102, an independently modulated carrier component set is generated, including:

[0099] Step 301, according to the row vector amplitude distribution of the index bit feature matrix, screen out the index selection patterns with row vector amplitudes higher than a preset threshold to generate a set of valid index patterns;

[0100] In this step, the time-domain sparse characteristics refer to the distribution of index bits in the time domain presenting a non-continuous, low-duty-cycle pulse form (such as a high-amplitude pulse appears only once every 100 sampling points), while the chaotic waveform corresponding to the modulation bits has a continuous time-domain distribution characteristic; the index bit feature matrix refers to the time-domain sparse pulse distribution of index bits in each carrier frequency band, and its row vector represents the index selection patterns of different carriers (such as the periodic law of the activated frequency band); the modulation bit feature matrix refers to the chaotic waveform symbols corresponding to the modulation bits in each carrier frequency band, and its column vector represents the continuous time-domain modulation information of different carriers.

[0101] In the embodiments of the present application, first, perform time-domain sparsity analysis on the scrambled signal component matrix (such as an 8×1000 matrix): calculate the variance of the time-domain signal amplitudes of each row (carrier frequency band), select the rows with variances exceeding a preset threshold (such as variance > 0.5), and determine them as the sparse pulse carriers corresponding to the index bits. Second, for the sparse pulse carriers (such as the 2nd, 5th, and 7th rows), use a sparsity recovery algorithm (such as compressive sensing optimized based on the L1 norm) to separate the sparse pulse positions (such as the 100th, 300th, and 500th sampling points) and their amplitudes, and generate an index bit feature matrix (8 rows × 1000 columns, with the elements of the non-sparse carrier rows set to zero). Then, for the remaining continuous waveform carriers (such as the 1st, 3rd, 4th, 6th, and 8th rows), reconstruct the continuous chaotic waveform through a low-rank matrix completion algorithm, and generate a modulation bit feature matrix (8 rows × 1000 columns, with the elements at the sparse pulse positions set to zero). Finally, verify the dimensional consistency (the same as the original signal matrix) and data orthogonality (no overlapping non-zero elements at the same positions in the index matrix and the modulation matrix) of the two matrices to ensure the effectiveness of the decomposition result.

[0102] Step 302, according to the phase continuity of the column vectors of the modulation bit feature matrix, filter out the modulation symbols whose phase jumps exceed the constraints of the chaotic modulation symbol period, and use the remaining modulation symbols after filtering as the effective modulation symbol set;

[0103] In this step, phase continuity means that the phase change amount (such as Δθ = θ(t + 1) - θ(t)) of adjacent sampling points of the chaotic modulation symbol in the time domain conforms to the aperiodic but bounded jump rule of chaotic modulation (such as |Δθ| ≤ π / 2).

[0104] The chaotic modulation symbol period constraint refers to the time length of a single chaotic modulation symbol defined in the target UAV communication protocol (such as each symbol lasts for 100 sampling points), and the phase jumps within this period need to satisfy the inter-symbol consistency.

[0105] In the embodiments of the present application, first, traverse each column (time sampling point) of the modulation bit feature matrix, and calculate the phase jump amount Δθ between adjacent sampling points (such as the phase difference between the 50th and 51st sampling points). Second, according to the chaotic modulation symbol period constraint (such as a symbol period of 100 sampling points), set a phase jump tolerance threshold (such as |Δθ| ≤ π / 2), and filter out the modulation symbols exceeding this threshold (such as the sampling point with Δθ = π). Then, perform time-domain continuity verification on the filtered modulation symbols: if the number of phase jumps within a certain symbol period (such as the 1st - 100th sampling points) exceeds the threshold number of times (such as exceeding 5 times), then determine that this symbol is invalid and eliminate it. Finally, integrate all the modulation symbols passing the verification to generate an effective modulation symbol set, including the retained symbol indices, phase jump tolerance values, and the corresponding carrier frequency band numbers.

[0106] Step 303: Perform orthogonal projection matching on the set of valid index patterns and the set of valid modulation symbols to generate a set of carrier components including independent carrier frequencies, independent modulation symbols, and corresponding index selection patterns.

[0107] In this step, orthogonal projection matching means using the orthogonal space mapping relationship to align the index selection pattern and the modulation symbol sequence in the time-frequency domain, eliminating the interference components between them, and ensuring that the index activation time and the modulation symbol period in the same carrier frequency band are completely synchronized. The set of carrier components refers to the frequency band identification of the independent carrier, the modulation symbol sequence, and the corresponding index activation rule, which are used for subsequent beamforming enhancement and signal reconstruction.

[0108] In the embodiment of the present application, first, align each index selection pattern in the set of valid index patterns (for example, the activation times of the 2.45 GHz carrier are the 200th and 600th sampling points) with the symbol sequence of the corresponding carrier in the set of valid modulation symbols (for example, the symbol sequence [0, 1, 0, 1] of the 2.45 GHz carrier) in the time domain: divide the symbol period according to the index activation time (for example, each symbol period has 200 sampling points) to ensure that each index pulse corresponds to the modulation symbols within a complete symbol period. Second, perform spatial decoupling on the index pulse position and the modulation symbol sequence through an orthogonal projection algorithm (such as Gram - Schmidt orthogonalization) to eliminate the time - domain interference of the index pulse on the modulation symbol. For example, within the symbol period corresponding to the index pulse position (such as the 200th point), project the modulation symbol sequence onto the subspace orthogonal to the index pulse and retain the pure modulation waveform component. Finally, integrate the independent index patterns and modulation symbols of all carrier frequency bands to generate a set of carrier components, and each component includes an independent carrier frequency (such as 2.45 GHz); an independent modulation symbol (such as the symbol sequence [0, 1, 0, 1]); and an index selection pattern (such as the activation times [200, 600]).

[0109] To improve the problem of insufficient multi - target signal interference suppression ability caused by the lack of combination of carrier frequency band sparsity in beamforming in the prior art, in some embodiments, according to step 103, according to the frequency band distribution range of the set of carrier components, dynamically adjust the beamforming direction of the multi - channel antenna array to generate a carrier component signal enhanced by beamforming, including:

[0110] Step 401: Determine the target frequency band coverage interval of the multi - channel antenna according to the frequency distribution range of each independently modulated carrier component in the set of carrier components, and extract the set of central frequencies of all carrier components within the target frequency band coverage interval.

[0111] In this step, the target frequency band coverage range refers to the frequency band range that the multi-channel antenna array needs to enhance directionally, which is determined by the maximum and minimum values of the frequency distributions of all valid carriers in the carrier component set (such as 2.4 GHz to 2.5 GHz) to ensure coverage of all target carriers; the central frequency set refers to the list of central frequencies of each independent carrier component within the target frequency band coverage range (such as 2.42 GHz, 2.45 GHz, 2.47 GHz), which is used to calculate the beamforming weight parameters.

[0112] In the embodiment of the present application, first, traverse all independent carrier components in the carrier component set (such as 3 carriers: 2.42 GHz, 2.45 GHz, 2.47 GHz), extract their frequency values and sort them to determine the minimum value (2.42 GHz) and the maximum value (2.47 GHz) of the target frequency band coverage range, and generate an interval after expanding the boundaries (such as 2.4 GHz to 2.5 GHz). Secondly, screen out all carrier components within this interval (such as the above 3 carriers), and record their central frequency values to form a central frequency set ([2.42, 2.45, 2.47] GHz). Then, verify whether the frequency intervals between adjacent carriers in the central frequency set conform to the hybrid index modulation rule (such as a 50 MHz interval), and eliminate abnormal carriers (such as carriers with an interval deviation of ±10%). Finally, associate the target frequency band coverage range with the central frequency set as the input parameter for beamforming weight calculation.

[0113] Step 402: Calculate the delay compensation parameter corresponding to each antenna unit in the multi-channel antenna array based on the frequency value of each carrier component in the central frequency set, and generate a beamforming weight vector that matches the central frequency set according to the delay compensation parameter;

[0114] In this step, the delay compensation parameter refers to the phase adjustment amount calculated according to the carrier frequency and the signal incident direction to compensate for the signal propagation delay caused by the spatial position difference of different antenna units, which is used to align the multi-channel signals and enhance the receiving intensity in the target direction; the beamforming weight vector refers to a vector composed of complex weight values, and each element corresponds to an antenna unit. By complex weighting (amplitude scaling and phase rotation), the main lobe of the array beam is aligned with the target signal direction.

[0115] In the embodiments of the present application, first, for each carrier component in the central frequency set (such as 2.42 GHz, 2.45 GHz), according to the signal incident direction (such as azimuth angle θ = 30°) and the antenna array geometric structure (such as uniform linear array, adjacent antenna spacing d = λ / 2), the time delay compensation parameter τ_n = (n·d·sinθ) / c (n is the antenna number, c is the speed of light) of each antenna element is calculated. For example, the time delay τ_2 of the second antenna in an 8-channel array is τ_2 = (2×0.062 m×sin30°) / (3×10^8 m / s) ≈ 0.2 ns. Second, the time delay parameter is converted into a phase compensation amount φ_n = 2πf_c·τ_n (f_c is the carrier frequency), and the complex weight value w_n = e^{jφ_n} of each antenna is generated. Then, the weight values of all antenna elements are integrated to generate a beamforming weight vector (such as an 8-dimensional complex vector [w_1, w_2,..., w_8]) that matches the central frequency set. Finally, the orthogonality of the weight vector at different carrier frequencies is verified (such as the correlation coefficient between the weight vectors at 2.42 GHz and 2.45 GHz is less than 0.1) to ensure the spatial separation ability of multi-carrier signals.

[0116] Step 403, perform complex weighted superposition on the beamforming weight vector and the original signal received by the multi-channel antenna array to generate a beamforming signal matrix for the target frequency band coverage interval;

[0117] In this step, complex weighted superposition means applying complex weights (amplitude scaling and phase rotation) to the original signals of each antenna channel, and adding the weighted signals of all channels point by point in the time domain to form an enhanced signal after spatial filtering; the beamforming signal matrix refers to a two-dimensional matrix generated after beamforming processing, whose row dimension corresponds to the carrier frequency bands within the target frequency band coverage interval, the column dimension corresponds to the time sampling points, and the matrix elements are the enhanced complex signal values.

[0118] In the embodiments of the present application, first, for each carrier component within the target frequency band coverage interval (such as 2.42 GHz, 2.45 GHz), perform per-channel complex multiplication operations on the corresponding beamforming weight vector (such as an 8-dimensional complex vector) and the original signal of the multi-channel antenna array (such as an 8-channel × 1000 time-point matrix). For example, the weight vector of the second carrier (2.45 GHz) , ,..., is multiplied separately by the original signals of 8 channels (1000 sampling points per channel) to generate 8 weighted channel signals. Second, align the weighted channel signals according to the time sampling points and add them point by point (such as the superimposed value at the t-th sampling point is · ), generate an enhanced signal sequence (1×1000 vector) for this carrier. Then, repeat the above operations for all target carriers, and integrate to generate a beamforming signal matrix (such as 2 rows × 1000 columns, row 1 corresponding to 2.42 GHz, row 2 corresponding to 2.45 GHz). Finally, verify the signal strength of the target carriers in the matrix (such as the signal strength at 2.45 GHz is increased by 20 dB) and the interference suppression effect (such as the signal at 2.6 GHz is attenuated by 30 dB) to ensure the effectiveness of beamforming.

[0119] Step 404: Dynamically adjust the phase offset of the beamforming weight vector according to the signal strength distribution of different carrier components in the beamforming signal matrix, so that the signal strength of the carrier component corresponding to the target UAV in the beamforming signal matrix reaches a preset gain threshold, and generate the carrier component signal enhanced by beamforming;

[0120] In this step, the phase offset refers to the phase adjustment value applied to the complex weight of each antenna element in the beamforming weight vector, which is used to optimize the pointing accuracy of the main lobe of the beam and suppress the side lobe interference; the preset gain threshold is a signal strength threshold set according to the signal-to-noise ratio requirement of the target UAV communication link (such as -60 dBm) to ensure that the enhanced carrier component meets the subsequent processing requirements.

[0121] In the embodiment of the present application, first, traverse each carrier component in the beamforming signal matrix (such as 2.42 GHz, 2.45 GHz), and measure its signal strength distribution (such as the average strength at 2.45 GHz is -70 dBm). Secondly, compare the current strength with the preset gain threshold (-60 dBm). If it does not meet the standard (such as the difference Δ = 10 dB), then calculate the required phase offset increment (such as Δφ = 10°). Then, use the gradient descent algorithm to update the phase parameter of the beamforming weight vector: for the weight phase φ_n of each antenna element, adjust it according to φ_n' = φ_n + Δφ·sgn( S / φ_n) (where S / φ_n is the partial derivative of the signal strength with respect to the phase). Then, re-weight the adjusted weight vector and the original signal complexly and superpose them to generate a new beamforming signal matrix. Repeat the above process until the signal strength of the target carrier reaches the preset threshold, and output the enhanced carrier component signal (such as the signal strength at 2.45 GHz is increased to -58 dBm).

[0122] To solve the problem of incomplete noise suppression caused by the neglect of carrier distribution sparsity in low-rank matrix estimation in the prior art, in some embodiments, as described in step 104, matrix reconstruction is performed on the carrier component signal enhanced by beamforming, and the low-rank distribution characteristic is used to estimate and remove the environmental noise component in the matrix reconstruction result, and the chaotic waveform basis vector corresponding to the main component in the matrix reconstruction result after removing the environmental noise component is extracted, including:

[0123] Step 501, construct a multi-dimensional signal reconstruction matrix according to the mapping relationship between the carrier frequency and the time sampling points of the carrier component signal enhanced by beamforming;

[0124] In this step, the multi-dimensional signal reconstruction matrix refers to a two-dimensional complex matrix constructed through the mapping relationship between the carrier frequency (row dimension) and the time sampling points (column dimension). Its row vector represents the time-domain signal evolution of a specific carrier frequency band, and the column vector represents the frequency-domain distribution of different carriers at the same moment. The matrix element value is the complex signal (amplitude and phase) enhanced by beamforming.

[0125] In the embodiment of the present application, first, the time-domain signal sequences of each carrier frequency band are extracted from the carrier component signal enhanced by beamforming generated in step 404 (for example, both 2.42 GHz and 2.45 GHz contain 1000 time sampling points). Secondly, they are arranged in ascending order of the carrier frequency band numbers as rows (for example, row 1 is 2.42 GHz, and row 2 is 2.45 GHz), and the time sampling points are arranged in the order of time windows as columns (for example, columns 1 to 1000 correspond to 1 ms to 1000 ms) to construct a two-dimensional complex matrix. Then, verify the time-frequency alignment consistency of the matrix: ensure that the column index of each carrier row is strictly synchronized with the time sampling points (for example, column 500 corresponds to the signal value at the 500 ms moment). Finally, perform normalization processing on the matrix (for example, scale the overall amplitude to the [-1, 1] interval) to generate a standardized multi-dimensional signal reconstruction matrix.

[0126] Step 502, based on the frequency band distribution sparsity of the carrier components in the multi-dimensional signal reconstruction matrix, estimate the low-rank distribution characteristic of the reconstruction matrix to obtain an estimation result;

[0127] In this step, the low-rank distribution characteristic estimation is used to determine its potential low-rank structure by analyzing the correlation between the singular value decay characteristic of the signal matrix and the frequency band sparsity of the carrier components, providing a mathematical basis for separating the signal and the noise.

[0128] In this embodiment, in the embodiment of the present application, first, calculate the frequency band distribution sparsity parameter of the reconstruction matrix (for example, the ratio of non-zero carrier rows is 3 / 8), and combine the power density distribution of the carrier components (for example, the ratio of high-power carriers is 20%) to determine the initial low-rank value (for example, rank = 3). Secondly, perform singular value decomposition (SVD) on the reconstruction matrix to extract the singular value list (for example, = 150, = 100, = 50, = 0.8), determine the initial low-rank value as 3 according to the proportion of singular value energy (the energy of the first 3 singular values accounts for 98%) and the sparsity parameter. Then, estimate the noise floor (such as the noise energy corresponding to the smallest singular value = 0.8) to correct the initial rank value and generate the final low-rank estimation result (such as the optimized rank value = 2).

[0129] Step 503, based on the estimation result, decompose the reconstruction matrix into a low-rank matrix component and a noise matrix component;

[0130] In this step, the low-rank matrix component is composed of the first k principal singular values that dominate the signal energy in the reconstruction matrix and their corresponding singular vectors, representing the effective carrier signal components of the target UAV (k is the rank value estimated in step 502); the noise matrix component is composed of the singular vectors corresponding to the remaining small singular values, representing environmental noise, interference signals, and decomposition residuals.

[0131] In the embodiment of the present application, first, based on the low-rank value estimated in step 502 (such as k = 3), perform truncated singular value decomposition (TruncatedSVD) on the reconstruction matrix: retain the first k singular values ( = 150, = 100, = 50) and their corresponding left singular matrix U_k (the first k columns) and right singular matrix V_k (the first k columns) to generate the low-rank matrix component L = U_k·diag( , , ·V_kᴴ. Second, calculate the noise matrix component S = the original reconstruction matrix - L. Finally, verify the proportion of the signal energy of the low-rank component (such as the Frobenius norm ratio of L accounting for 98%) and the amplitude statistical characteristics of the noise matrix (such as the elements of S following a Gaussian distribution with a mean of 0 and a variance of 0.1) to ensure that the decomposition result meets the separation requirements of the target signal and noise.

[0132] Step 504, according to the statistical distribution characteristics of the elements in the noise matrix component, perform iterative optimization on the low-rank matrix component;

[0133] In this step, iterative optimization refers to dynamically adjusting the singular value threshold of the low-rank matrix and the noise suppression intensity by the alternating direction multiplier method or the weighted nuclear norm minimization algorithm, combined with the noise statistical characteristics (such as the variance of the Gaussian distribution, the noise sparsity ratio), so as to improve the separation accuracy of the signal and noise.

[0134] In the embodiments of the present application, first, an optimization objective function is set based on the statistical distribution characteristics of the noise matrix components (for example, the amplitude of the noise matrix elements follows a Gaussian distribution with a mean of zero and a variance of 0.1). The objective function needs to simultaneously minimize the nuclear norm of the low-rank matrix component (i.e., the sum of all singular values) and the L1 norm of the noise matrix component (i.e., the sum of the absolute values of all elements). Among them, the regularization coefficient lambda is calculated by the product of the noise standard deviation and the reciprocal of the square root of the maximum dimension of the matrix. For example, lambda is equal to the noise standard deviation divided by the square root of the larger value of the number of rows and columns of the matrix. Secondly, the following iterative optimization process is performed:

[0135] Fix the low-rank matrix and update the noise matrix. Sparsify the noise matrix through a soft-threshold operator. Specifically, for each element of the noise matrix, keep its sign (positive or negative), and reduce the element value whose absolute value exceeds the lambda threshold by the lambda value, and set the elements below the threshold to zero.

[0136] Fix the noise matrix and update the low-rank matrix. Subtract the updated noise matrix from the original reconstruction matrix, perform truncated singular value decomposition on the resulting matrix, and only retain the components with singular values greater than the current lambda threshold to generate a new low-rank matrix component.

[0137] Dynamically adjust the lambda value. According to the difference between the remaining energy of the noise matrix (for example, the sum of the absolute values of all elements of the noise matrix divided by the total number of matrix elements) and the target noise variance, gradually reduce the lambda value. For example, if the current noise energy is higher than the target variance, reduce the lambda value by 10%.

[0138] Repeat the above steps until the change amount of the nuclear norm of the low-rank matrix is less than a preset convergence threshold (for example, the difference in nuclear norms between two consecutive iterations is less than 1%), and finally output the optimized low-rank matrix component and noise matrix component.

[0139] Step 505: Extract the singular vectors corresponding to the first preset number of the largest singular values from the optimized low-rank matrix component to generate chaotic waveform basis vectors, where the value of the preset number is equal to the number of valid modulation symbols in the carrier component set;

[0140] In this step, the chaotic waveform basis vector refers to the singular vector extracted from the low-rank matrix component, whose amplitude and time-varying characteristics are consistent with the chaotic modulation waveform transmitted by the target UAV and is used to inversely generate the spread spectrum code sequence; the preset number is dynamically set according to the number of valid modulation symbols in the carrier component set (for example, if there are 3 valid symbols, extract the first 3 singular vectors) to ensure a one-to-one correspondence between the basis vectors and the modulation symbols.

[0141] In the embodiments of the present application, first, according to the number of valid modulation symbols in the carrier component set, a preset number k = 3 is determined. Secondly, the optimized low-rank matrix component (such as a matrix with rank = 3) is subjected to singular value decomposition to obtain a singular value list (such as = 200, = 150, = 100) and the corresponding left singular vector matrix U (such as an 8×3 matrix) and right singular vector matrix V (such as a 1000×3 matrix). Then, the first k columns of the left singular matrix U (such as columns 1 to 3) are extracted as the chaotic waveform basis vectors. Finally, it is verified whether the time-domain waveform of the basis vectors satisfies the aperiodic but bounded amplitude jump characteristic of chaotic modulation (such as the amplitude jump between adjacent sampling points does not exceed the maximum allowable value).

[0142] To improve the problem of low-rank estimation error accumulation caused by the sensitivity of single singular value decomposition to noise distribution in the prior art, in some embodiments, according to step 502, based on the frequency band distribution sparsity of the carrier components in the multidimensional signal reconstruction matrix, the low-rank distribution characteristic estimation of the reconstruction matrix is performed to obtain an estimation result, including:

[0143] Step 601, according to the number of independently modulated carriers in the carrier component set and the frequency band distribution sparsity of the multidimensional signal reconstruction matrix, calculate the sparsity parameter of the multidimensional signal reconstruction matrix, where the sparsity parameter is the proportion of the number of rows occupied by non-zero carrier components in the reconstruction matrix;

[0144] In this step, the sparsity parameter is used to quantify the sparsity degree of the effective carrier distribution in the multidimensional signal reconstruction matrix, and is specifically defined as "the percentage of the number of rows of effective carriers in the total number of rows of the frequency band". For example, if the total number of rows of the frequency band is 8 rows, and 3 rows carry effective signals, the sparsity is thirty-seven point five percent.

[0145] In the embodiments of the present application, first, the number of independently modulated effective carriers is obtained from the carrier component set (for example, 3 carriers with frequencies of 2.42 GHz, 2.45 GHz, and 2.47 GHz respectively), and the total number of rows of the frequency band of the multidimensional signal reconstruction matrix is determined (for example, 8 rows, corresponding to 8 sub-bands evenly divided within the 2.4 GHz to 2.5 GHz frequency band). Secondly, the number of rows actually containing effective signals in the reconstruction matrix is counted (for example, rows 2, 5, and 7), and the proportion of it in the total number of rows is calculated. For example, the number of effective rows is 3 rows, the total number of rows is 8 rows, and the sparsity parameter is thirty-seven point five percent. Finally, according to the sparsity rule of hybrid index modulation (for example, the sparsity is required to be lower than fifty percent), it is verified whether the calculation result is reasonable, and if it exceeds the threshold, abnormal carriers (such as invalid frequency bands or interference signals) are removed and re-counted.

[0146] Step 602: Determine the initial rank value of the low-rank matrix component based on the sparsity parameter and the power density distribution of each carrier component in the set of carrier components;

[0147] In this step, the initial rank value refers to the number of principal components preset in the low-rank matrix decomposition process, which is used to preliminarily separate signals and noise. Its value needs to take into account both signal sparsity (the number of effective carriers) and power density distribution (the proportion of energy of each carrier).

[0148] In this embodiment, first, according to the sparsity parameter of the multi-dimensional signal reconstruction matrix (for example, the total number of frequency band rows is 8 rows, and 3 rows carry effective signals, with a sparsity of 37.5%), the candidate initial rank value is initially set to the number of effective carriers, which is 3. Secondly, the candidate rank value is corrected in combination with the power density distribution of each carrier component in the set of carrier components (for example, the power ratios of the 3 effective carriers are 50%, 30%, and 20% respectively). By accumulating the power ratios of the first k carriers, it is verified whether the preset threshold (such as 85%) is reached. If the cumulative power ratio of the first 2 carriers is 80% (50% + 30%), which does not reach the threshold, then the third carrier needs to be included (cumulative 100%), so as to determine the initial rank value as 3. At the same time, it is verified whether this rank value meets the sparsity constraint (such as the upper limit of the effective number of rows corresponding to a sparsity of 37.5% is 3), and finally an initial rank value that matches the signal energy distribution and frequency band sparsity is generated.

[0149] Step 603: Perform singular value threshold decomposition on the multi-dimensional signal reconstruction matrix according to the initial rank value, and decompose the multi-dimensional signal reconstruction matrix into an initial low-rank matrix component and an initial noise matrix component, where the number of singular values of the initial low-rank matrix component is equal to the initial rank value;

[0150] In this step, singular value threshold decomposition is a matrix decomposition method based on a preset rank value. By retaining the first k largest singular values (k is the initial rank value) and their corresponding singular vectors, the dominant components (low-rank components) and residual noise (noise components) in the signal are separated.

[0151] In the embodiment of the present application, first, based on the initial rank value determined in step 602 (for example, k = 3), perform singular value decomposition on the multi-dimensional signal reconstruction matrix (such as an 8-row × 1000-column complex matrix) to obtain a list of singular values (such as =200, =150, =100, =0.5, etc.). Then, retain the first k singular values ( , , ), and the first k columns of the corresponding left singular vector matrix U and the first k columns of the right singular vector matrix V to construct the initial low-rank matrix component L_initial = U[:,:k]·diag( , , )·V[:,:k]^H. Subsequently, subtract the low-rank component from the original matrix to obtain the initial noise matrix component S_initial = original matrix - L_initial. Finally, verify the signal energy ratio of the initial low-rank component (for example, the Frobenius norm of L_initial accounts for 98% of the total energy of the original matrix) and the statistical characteristics of the noise component (for example, the element amplitudes of S_initial follow a Gaussian distribution with a mean of 0 and a variance of 0.1) to ensure that the decomposition result meets the requirements of signal and noise separation.

[0152] Step 604, according to the difference between the amplitude distribution of the elements in the initial noise matrix component and the power density of the chaotic modulation symbols in the carrier component set, correct the initial rank value to generate an optimized low-rank matrix rank value;

[0153] In this step, the difference between the amplitude distribution and the power density refers to the difference between the amplitude statistical characteristics (such as mean and variance) of the noise matrix elements and the power density of the effective chaotic modulation symbols (such as the symbol power is 20 dB higher than the noise floor), which is used to determine whether the initial rank value underestimates or overestimates the number of signal principal components.

[0154] In the embodiment of the present application, first, based on the amplitude distribution of the initial noise matrix component (such as the element amplitude mean is 0.1 and the variance is 0.15), calculate the noise floor energy (mean square value ≈ 0.1² + 0.15 = 0.115). Secondly, extract the power density of the chaotic modulation symbols in the carrier component set (such as the average power of the effective symbols is 1.2, the noise floor is 0.115, and the power density difference is 10.4 times). If the power density difference exceeds a preset threshold (such as 10 times), it is considered that the initial rank value may underestimate the number of signal principal components. Then, adopt an iterative correction strategy to increment the initial rank value k_initial = 3 to k = 4, re-perform singular value decomposition on the reconstructed matrix, and calculate the signal energy ratio corresponding to the newly added singular value (such as the 4th singular value = 5, energy ratio ² / (total energy) ≈ 0.6%). If the energy ratio of the newly added singular value is lower than the noise floor energy ratio (such as 0.6% < 0.115), then determine it as a noise component, terminate the correction and retain k = 3; otherwise, accept k = 4 as the optimized rank value; finally, generate an optimized low-rank matrix rank value according to the above logic (such as k = 3).

[0155] Step 605: Based on the optimized rank value of the low-rank matrix, perform a second singular value threshold decomposition on the multi-dimensional signal reconstruction matrix to generate an optimal low-rank matrix component and an optimal noise matrix component, which are used as the estimation result of the low-rank distribution characteristic estimation;

[0156] In this step, the second singular value threshold decomposition refers to a decomposition process that, based on the initial decomposition and combined with the optimized rank value, further eliminates noise interference and refines the extraction of the signal principal components, ensuring that the singular vectors of the low-rank component strictly match the target signal; the optimal low-rank matrix component is composed of the singular vectors corresponding to the singular values retained after the second decomposition, and its energy proportion is consistent with the power density distribution of the chaotic modulation symbols, and the rank value is optimized through noise floor verification.

[0157] In the embodiments of the present application, first, according to the generated optimized rank value (e.g., k = 3), perform a second singular value decomposition on the multi-dimensional signal reconstruction matrix (e.g., 8 rows × 1000 columns). Retain the first k singular values (e.g., = 200, σ2 = 150, = 100) and their corresponding left and right singular vectors to generate an optimal low-rank matrix component L_optimal = U[:, :k]·diag( , , ·V[:, :k]^H. Subsequently, calculate the optimal noise matrix component S_optimal = original matrix - L_optimal. Finally, verify whether the signal energy proportion of L_optimal (e.g., 98.5%) meets the preset threshold (e.g., > 95%), and check whether the element amplitude distribution of S_optimal (e.g., mean ≈ 0, variance ≈ 0.1) is consistent with the initial noise statistics to ensure the effectiveness of the decomposition result.

[0158] To solve the problem of link matching failure caused by the lack of consideration of carrier index rules and phase synchronization in the generation of spreading codes in the prior art, in some embodiments, according to what is described in step 105, based on the mapping relationship between the chaotic waveform basis vectors and the modulation symbols of the target UAV, generate a spreading code sequence that matches the hybrid index multi-carrier differential chaos modulation communication link, including:

[0159] Step 701: Based on the mapping relationship between the time domain length of the chaotic waveform basis vectors and the modulation symbol period of the target UAV, determine the segmented length of the chaotic waveform basis vectors corresponding to each modulation symbol, where the segmented length is proportional to the number of carrier components within the modulation symbol period;

[0160] In this step, the segment length refers to the number of time-domain sampling points contained in the sub-segments divided from the chaotic waveform basis vector, and its length needs to match the modulation symbol period of the target UAV (for example, each symbol lasts for 250 sampling points) and the number of carrier components (for example, 4 sub-carriers are activated within each symbol period), ensuring that the sub-segments after segmentation completely cover the multi-carrier modulation waveform within one symbol period.

[0161] In the embodiments of the present application, first, obtain the total time-domain length of the chaotic waveform basis vector (such as 1000 sampling points) and the modulation symbol period of the target UAV (such as each symbol lasts for 250 sampling points). Secondly, according to the number of carrier components within the modulation symbol period (such as 4 sub-carriers are activated within each symbol period), calculate the segment length: divide the total time-domain length by the number of symbol periods (such as 1000 / 250 = 4), and then multiply by the number of carrier components (such as 4×4 = 16), but it needs to be adjusted according to the actual mapping relationship. Specifically, if there is a linear relationship between the modulation symbol period and the number of carrier components (such as each symbol period corresponds to N sub-carriers, segment length = symbol period length × N), then set it directly according to this rule. Finally, verify whether the segment length meets the time-domain continuity constraint (such as the waveform phase jump within the sub-segment does not exceed the maximum value allowed by chaotic modulation), and correct the abnormal segmentation.

[0162] Step 702, divide the chaotic waveform basis vector into multiple basis vector sub-segments according to the segment length of the chaotic waveform basis vector, and generate an orthogonal projection coefficient set corresponding to each basis vector sub-segment according to the frequency band sparsity of each carrier component in the carrier component set;

[0163] In this step, the orthogonal projection coefficient set is a complex matrix generated through frequency band sparsity constraints and orthogonality mapping rules. Its rows correspond to different carrier frequency bands, and its columns correspond to the basis vector sub-segments, and are used to map the chaotic waveform sub-segments to the orthogonal carrier space to eliminate interference between frequency bands.

[0164] In the embodiments of the present application, first, according to the segmentation length determined in step 701 (e.g., 250 sampling points), the chaotic waveform basis vectors (such as the time-domain waveform with a length of 1000 points) are divided into multiple consecutive sub-segments (e.g., 4 sub-segments, each with 250 points). Then, based on the sparsity of the frequency band distribution of the effective carriers in the carrier component set (e.g., the total number of frequency bands is 8 rows, and only 3 rows of effective carriers), an orthogonal projection coefficient matrix is generated for each sub-segment. The specific process is as follows: for each sub-segment, its waveform time-domain features are extracted, and an orthogonal coefficient vector matching the effective carrier frequency band is generated through the Gram-Schmidt orthogonalization method. At the same time, the coefficients of the non-effective carrier rows (such as the remaining 5 rows) are set to zero to ensure the frequency band sparsity constraint. In addition, according to the power density distribution of the carrier components (e.g., the coefficient amplitude of the high-power carrier is increased by 3 dB), the coefficient amplitude ratio is adjusted, and finally an orthogonal projection coefficient matrix with the dimension of "number of effective carriers × number of sub-segments" (e.g., 3 effective carriers × 4 sub-segments) is formed.

[0165] Step 703, based on the set of orthogonal projection coefficients, perform an orthogonal modulation operation on each basis vector sub-segment and the symbol sequence in the modulation symbol mapping relationship to generate a set of segmented spread spectrum codes corresponding to each carrier component one by one;

[0166] In this step, the orthogonal modulation operation refers to the operation of linearly combining the basis vector sub-segment and the symbol sequence using the complex coefficients in the set of orthogonal projection coefficients to generate a spread spectrum code sequence with frequency band orthogonality and time-domain chaos characteristics; the set of segmented spread spectrum codes is composed of the spread spectrum code sequences corresponding to each carrier component, and the time-domain waveform of each spread spectrum code segment matches the chaotic modulation symbol and the carrier frequency band characteristics.

[0167] In the embodiments of the present application, first, the symbol sequence in the modulation symbol mapping relationship (e.g., the binary sequence [0, 1, 0, 1]) is time-domain aligned according to the segmentation length of the basis vector sub-segment (e.g., each symbol corresponds to 250 sampling points). Then, for each carrier component (such as 2.42 GHz, 2.45 GHz, 2.47 GHz), the coefficient vector corresponding to the carrier row is extracted from the set of orthogonal projection coefficients (e.g., the coefficients of the 2.42 GHz row are [0.8 + 0.1j, 0.2 - 0.3j, -0.4 + 0.5j, 0.6 + 0.7j]). Then, perform the orthogonal modulation operation: multiply each element of the symbol sequence (such as symbol 0 or 1) by the corresponding basis vector sub-segment (such as the 1st sub-segment 0 - 250 points) complexly, and then weighted and superimposed by the coefficient vector to generate the spread spectrum code sequence of this carrier. Specifically, symbol 0 is mapped to the product of the basis vector sub-segment and the first column of the coefficient vector, symbol 1 is mapped to the product with the second column, and so on. Finally, the spread spectrum code sequences of all carrier components are integrated to form a set of segmented spread spectrum codes, whose dimension is "number of carriers × total time-domain length" (such as 3 carriers × 1000 points).

[0168] Step 704: According to the carrier index rule of the hybrid index multi-carrier differential chaos modulation, perform time-domain superposition on the segmented spreading codes belonging to the same carrier index pattern in the segmented spreading code set to generate a combined spreading code corresponding to an independent carrier index;

[0169] In this step, the carrier index rule defines the activation pattern of carriers in different symbol periods in the target UAV communication protocol (for example, only one carrier is activated in each symbol period). Time-domain superposition means splicing or weighted fusion in chronological order the segmented spreading codes of the same carrier in different symbol periods to form a spreading code sequence that continuously covers the entire communication period, while ensuring that the signal amplitude in the non-activated period is zero.

[0170] In the embodiment of the present application, first, according to the carrier index rule of the hybrid index modulation (for example, the 2.45 GHz carrier is activated in symbol period 1 and the 2.42 GHz carrier is activated in period 2), extract the segments corresponding to the same carrier in different symbol periods from the segmented spreading code set (such as the segments from 0 to 250 points and 500 to 750 points of the 2.45 GHz carrier, and the segment from 250 to 500 points of the 2.42 GHz carrier). Subsequently, splice the segmented spreading codes without overlap in chronological order: if the carrier is activated in multiple non-consecutive symbol periods, fill zero-valued signals in the non-activated period (for example, set the 2.45 GHz carrier to zero in the 250 - 500 point interval); if there are multiple activations in the same period (such as the carrier is repeatedly activated in adjacent periods), perform Hamming window weighted superposition on the overlapping part for smooth transition. Finally, check whether the phase jump between adjacent segments exceeds the maximum value allowed by the chaos modulation (such as Δθ≤π / 2), and perform phase compensation on the segments with abnormal jumps to ensure the time-domain waveform continuity and chaos characteristics of the combined spreading code.

[0171] Step 705: According to the arrangement order of the carrier frequencies in the hybrid index multi-carrier modulation, perform phase synchronization calibration on the combined spreading code and the frequency offset of the corresponding carrier component to generate the spreading code sequence;

[0172] In this step, phase synchronization calibration means adjusting the initial phase of the spreading code according to the frequency offset of the carrier component (such as the difference between the carrier center frequency and the reference frequency) to ensure the phase continuity of the multi-carrier signal in the time-frequency domain, and avoid inter-carrier interference and inter-symbol interference; the spreading code sequence is composed of the calibrated combined spreading code, whose phase is strictly synchronized with the frequency offset and conforms to the time-frequency domain constraint conditions of the hybrid index modulation protocol.

[0173] In the embodiments of the present application, first, according to the carrier frequency arrangement order of hybrid index modulation (for example, from low frequency to high frequency are 2.42 GHz, 2.45 GHz, 2.47 GHz in sequence), the frequency offset of each carrier component is extracted (such as the offset of the 2.45 GHz carrier relative to the reference frequency is +10 MHz). Secondly, the phase compensation amount of each carrier spreading code is calculated: based on the frequency offset Δf and the symbol period length T (such as 1 ms), the phase compensation value Δφ = 2π·Δf·T (for example, Δf = 10 MHz, T = 1 ms, Δφ = 2π×10^7×10^{-3}=20π radians). Then, each carrier component of the combined spreading code is multiplied by the corresponding complex exponential phase compensation factor e^{-jΔφ} to eliminate the phase accumulation error caused by frequency offset. Finally, it is verified whether the phase of the calibrated spreading code is continuous at the symbol period boundary (such as the adjacent symbol phase jump ≤ π / 2), and the abnormal section is interpolated and smoothed; the generated spreading code sequence will be directly used to reversely generate the communication signal of the target UAV, and its phase synchronization characteristic (such as the phase of the 2.45 GHz carrier is zero) ensures that the receiving end can accurately demodulate the symbol through matched filtering. At the same time, the frequency offset parameter (such as +10 MHz) is derived from the signal reception parameter configuration, forming a cross-step frequency offset compensation closed loop.

[0174] Figure 2 FIG. is a schematic structural diagram of a UAV communication link cracking system based on a chaotic modulation waveform provided by an embodiment of the present application, as Figure 2 shown, the system includes:

[0175] An acquisition module 21, configured to use a multi-channel antenna array to acquire a hybrid index multi-carrier chaotic signal transmitted by a target UAV, and generate a received signal matrix including the correlation relationship between the time dimension and the frequency dimension;

[0176] A separation module 22, configured to perform a separation operation on the mixed superposition index bit feature and modulation bit feature in the received signal matrix by using a random sequence scrambling algorithm based on the carrier distribution characteristic of the hybrid index multi-carrier chaotic signal, and generate a set of independently modulated carrier components;

[0177] An adjustment module 23, configured to dynamically adjust the beamforming direction of the multi-channel antenna array according to the frequency band distribution range of the set of carrier components, and generate a carrier component signal enhanced by beamforming;

[0178] An extraction module 24, configured to perform matrix reconstruction on the carrier component signal enhanced by beamforming, estimate and remove the environmental noise component in the matrix reconstruction result by using the low-rank distribution characteristic, and extract the chaotic waveform basis vector corresponding to the main component in the matrix reconstruction result after removing the environmental noise component;

[0179] A generating module 25, configured to generate a spreading code sequence matching the hybrid-index multi-carrier differential chaos modulation communication link according to the mapping relationship between the chaotic waveform basis vectors and the modulation symbols of the target UAV. Figure 2 The UAV communication link cracking system based on chaotic modulation waveforms described above can execute Figure 1 The UAV communication link cracking method based on chaotic modulation waveforms in the embodiments shown, the implementation principle and technical effects will not be elaborated further. For the UAV communication link cracking system based on chaotic modulation waveforms in the above embodiments, the specific manners in which each module and unit perform operations have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0180] In a possible design, Figure 2 The UAV communication link cracking system based on chaotic modulation waveforms in the embodiments shown can be implemented as a computing device, such as Figure 3 As shown, the computing device may include a storage component 31 and a processing component 32;

[0181] The storage component 31 stores one or more computer instructions, wherein the one or more computer instructions are for the processing component 32 to call and execute.

[0182] The processing component 32 is used for the above Figure 1 UAV communication link cracking method based on chaotic modulation waveforms in the embodiments.

[0183] Wherein, the processing component 32 may include one or more processors to execute computer instructions to complete all or part of the steps in the above method. Of course, the processing component may also be implemented by one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors or other electronic components for executing the above method.

[0184] The storage component 31 is configured to store various types of data to support operations on the terminal. The storage component may be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk or optical disk.

[0185] Of course, the computing device will necessarily also include other components, such as input / output interfaces, display components, communication components, etc.

[0186] The input / output interface provides an interface between the processing component and the peripheral interface module, and the peripheral interface module may be an output device, an input device, etc.

[0187] The communication component is configured to facilitate communication between the computing device and other devices in a wired or wireless manner, etc.

[0188] Among them, the computing device may be a physical device or an elastic computing host provided by a cloud computing platform, etc. At this time, the computing device may refer to a cloud server, and the above-mentioned processing component, storage component, etc. may be basic server resources leased or purchased from a cloud computing platform.

[0189] The embodiment of the present application also provides a computer storage medium storing a computer program, and when the computer program is executed by a computer, it can implement the above-mentioned Figure 1 method for cracking an unmanned aerial vehicle communication link based on a chaotic modulation waveform shown in the embodiment.

[0190] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the above-described system, device, and unit can refer to the corresponding processes in the foregoing method embodiments, and will not be described herein again.

[0191] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative labor.

[0192] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0193] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than limiting them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present application.

Claims

1. A method for cracking the UAV communication link based on chaotic modulation waveforms, characterized in that, Including: Obtain the hybrid-index multi-carrier differential chaos signal transmitted by the target UAV using a multi-channel antenna array, and generate a received signal matrix containing the correlation relationship between the time dimension and the frequency dimension; Based on the carrier distribution characteristics of the hybrid-index multi-carrier differential chaos signal, use a random sequence scrambling algorithm to separate the hybrid-overlapped index bit features and modulation bit features in the received signal matrix, and generate a set of independently modulated carrier components; According to the frequency band distribution range of the set of carrier components, dynamically adjust the beamforming direction of the multi-channel antenna array to generate a carrier component signal enhanced by beamforming; Perform matrix reconstruction on the carrier component signal enhanced by beamforming, use the low-rank distribution characteristics to estimate and remove the environmental noise component in the matrix reconstruction result, and extract the chaotic waveform basis vectors corresponding to the principal components in the matrix reconstruction result after removing the environmental noise component; According to the mapping relationship between the chaotic waveform basis vectors and the modulation symbols of the target UAV, generate a spread spectrum code sequence that matches the modulation communication link of the hybrid-index multi-carrier differential chaos signal.

2. The method according to claim 1, wherein Based on the carrier distribution characteristics of the hybrid-index multi-carrier differential chaos signal, using a random sequence scrambling algorithm to separate the hybrid-overlapped index bit features and modulation bit features in the received signal matrix includes: Generate a random reference sequence that matches the carrier distribution characteristics according to the frequency interval and power density distribution of each carrier in the hybrid-index multi-carrier differential chaos signal, where the length of the random reference sequence is the same as the number of columns of the received signal matrix; Perform a point-by-point multiplication operation on the random reference sequence and the time-domain sampling points of each row in the received signal matrix to generate a scrambled signal component matrix; Based on the time-domain sparse characteristics corresponding to the index bits in the scrambled signal component matrix, decompose the signal component matrix into an index bit feature matrix and a modulation bit feature matrix.

3. The method according to claim 2, wherein Generating a set of independently modulated carrier components includes: According to the row vector amplitude distribution of the index bit feature matrix, screen out the index selection patterns with row vector amplitudes higher than a preset threshold to generate a set of effective index patterns; According to the column vector phase continuity of the modulation bit feature matrix, filter out the modulation symbols whose phase jumps exceed the chaos modulation symbol period constraint, and use the remaining modulation symbols after filtering as a set of effective modulation symbols; Perform orthogonal projection matching on the set of effective index patterns and the set of effective modulation symbols to generate a set of carrier components including independent carrier frequencies, independent modulation symbols, and corresponding index selection patterns.

4. The method according to claim 1, wherein According to the frequency band distribution range of the set of carrier components, dynamically adjust the beamforming direction of the multi-channel antenna array to generate a carrier component signal enhanced by beamforming, including: According to the frequency distribution range of each independently modulated carrier component in the set of carrier components, determine the target frequency band coverage interval of the multi-channel antenna array, and extract the set of center frequencies of all carrier components within the target frequency band coverage interval; Calculate the time delay compensation parameters corresponding to each antenna element in the multi-channel antenna array based on the frequency values of each carrier component in the central frequency set, and generate a beamforming weight vector matching the central frequency set according to the time delay compensation parameters; Perform complex weighted superposition of the beamforming weight vector and the original signal received by the multi-channel antenna array to generate a beamforming signal matrix for the target frequency band coverage interval; According to the signal intensity distribution of different carrier components in the beamforming signal matrix, dynamically adjust the phase offset of the beamforming weight vector so that the signal intensity of the carrier component corresponding to the target UAV in the beamforming signal matrix reaches a preset gain threshold, and generate the carrier component signal enhanced by beamforming; 5. The method according to claim 1, characterized in that Perform matrix reconstruction on the carrier component signal enhanced by beamforming, estimate and remove the environmental noise component in the matrix reconstruction result using the low-rank distribution characteristic, and extract the chaotic waveform basis vectors corresponding to the principal components in the matrix reconstruction result after removing the environmental noise component, including: Construct a multi-dimensional signal reconstruction matrix according to the mapping relationship between the carrier frequency and the time sampling points of the carrier component signal enhanced by beamforming; Estimate the low-rank distribution characteristic of the multi-dimensional signal reconstruction matrix based on the frequency band distribution sparsity of the carrier components in the multi-dimensional signal reconstruction matrix to obtain an estimation result; Based on the estimation result, decompose the multi-dimensional signal reconstruction matrix into a low-rank matrix component and a noise matrix component; Iteratively optimize the low-rank matrix component according to the statistical distribution characteristic of the elements in the noise matrix component; Extract the singular vectors corresponding to the first preset number of largest singular values from the optimized low-rank matrix component to generate chaotic waveform basis vectors, where the value of the preset number is equal to the number of valid modulation symbols in the carrier component set; 6. The method according to claim 5, wherein Estimate the low-rank distribution characteristic of the multi-dimensional signal reconstruction matrix based on the frequency band distribution sparsity of the carrier components in the multi-dimensional signal reconstruction matrix to obtain an estimation result, including: Calculate the sparsity parameter of the multi-dimensional signal reconstruction matrix according to the number of independently modulated carriers in the carrier component set and the frequency band distribution sparsity of the multi-dimensional signal reconstruction matrix, where the sparsity parameter is the proportion of the number of rows occupied by non-zero carrier components in the multi-dimensional signal reconstruction matrix; Determine the initial rank value of the low-rank matrix component based on the sparsity parameter and the power density distribution of each carrier component in the carrier component set; Perform singular value threshold decomposition on the multi-dimensional signal reconstruction matrix according to the initial rank value, and decompose the multi-dimensional signal reconstruction matrix into an initial low-rank matrix component and an initial noise matrix component, where the number of singular values of the initial low-rank matrix component is equal to the initial rank value; Correct the initial rank value according to the amplitude distribution of the elements in the initial noise matrix component and the power density difference of the chaotic modulation symbols in the carrier component set to generate an optimized low-rank matrix rank value; Based on the optimized rank value of the low-rank matrix, perform a second singular value threshold decomposition on the multi-dimensional signal reconstruction matrix to generate an optimal low-rank matrix component and an optimal noise matrix component, which are used as the estimation results of the low-rank distribution characteristic estimation.

7. The method according to claim 1, wherein According to the mapping relationship between the chaotic waveform basis vectors and the modulation symbols of the target UAV, generate a spreading code sequence that matches the modulation communication link of the hybrid-index multi-carrier differential chaotic signal, including: According to the mapping relationship between the time domain length of the chaotic waveform basis vectors and the modulation symbol period of the target UAV, determine the segmented length of the chaotic waveform basis vectors corresponding to each modulation symbol, where the segmented length is proportional to the number of carrier components within the modulation symbol period; Divide the chaotic waveform basis vectors into multiple basis vector sub-segments according to the segmented length of the chaotic waveform basis vectors, and generate an orthogonal projection coefficient set corresponding to each basis vector sub-segment according to the frequency band distribution sparsity of each carrier component in the carrier component set; Based on the orthogonal projection coefficient set, perform an orthogonal modulation operation on each basis vector sub-segment and the symbol sequence in the modulation symbol mapping relationship to generate a segmented spreading code set corresponding to each carrier component one by one; According to the carrier index rule of the hybrid-index multi-carrier differential chaos modulation, perform time domain superposition on the segmented spreading codes belonging to the same carrier index mode in the segmented spreading code set to generate a combined spreading code corresponding to an independent carrier index; According to the arrangement order of the carrier frequencies in the hybrid-index multi-carrier differential chaos modulation, perform phase synchronization calibration on the combined spreading code and the frequency offset of the corresponding carrier component to generate the spreading code sequence.

8. Drone communication link cracking system based on chaotic modulation waveform, characterized in that, Including: An acquisition module, configured to use a multi-channel antenna array to acquire a hybrid-index multi-carrier differential chaos signal transmitted by a target UAV, and generate a received signal matrix including the correlation relationship between the time dimension and the frequency dimension; A separation module, configured to perform a separation operation on the mixed superposition index bit feature and modulation bit feature in the received signal matrix by using a random sequence scrambling algorithm based on the carrier distribution characteristic of the hybrid-index multi-carrier differential chaos signal, and generate a set of independently modulated carrier components; An adjustment module, configured to dynamically adjust the beamforming direction of the multi-channel antenna array according to the frequency band distribution range of the carrier component set, and generate a carrier component signal enhanced by beamforming; An extraction module, configured to perform matrix reconstruction on the carrier component signal enhanced by beamforming, use low-rank distribution characteristic estimation to remove the environmental noise component in the matrix reconstruction result, and extract the chaotic waveform basis vectors corresponding to the main components in the matrix reconstruction result after removing the environmental noise component; A generation module, configured to generate a spreading code sequence that matches the modulation communication link of the hybrid-index multi-carrier differential chaos signal according to the mapping relationship between the chaotic waveform basis vectors and the modulation symbols of the target UAV.

9. A computing device, characterized in that, It includes a processing component and a storage component; the storage component stores one or more computer instructions; the one or more computer instructions are used to be called and executed by the processing component to implement the method for cracking the UAV communication link based on the chaotic modulation waveform according to any one of claims 1 to 7.

10. A computer storage medium, characterized in that, A computer program is stored, and when the computer program is executed by a computer, it implements the method for cracking the UAV communication link based on the chaotic modulation waveform according to any one of claims 1 to 7.

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