Waveform complexity measurement method, device and equipment based on waveform feature vector

Abstract

This invention provides a method, apparatus, and device for measuring waveform complexity based on waveform feature vectors. The waveform complexity measurement method based on waveform feature vectors constructs a set of observed waveform feature vector matrices using multi-dimensional waveform feature vectors, and performs complexity analysis on this basis. This data modeling approach breaks through the limitations of traditional one-dimensional sequence analysis, avoiding the separation of multivariable signals for analysis, thus maintaining the integrity of the interdependencies between waveform signals. Furthermore, the use of fuzzy membership functions to calculate the similarity between waveform matrices effectively improves the robustness and accuracy of the system when handling noise and uncertain signals. This invention decomposes the complexity analysis task into multiple execution modules, employing a step-by-step processing flow, reducing the computational burden and error accumulation during waveform data processing, and improving analysis efficiency and accuracy.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and specifically to a method, apparatus, and device for measuring waveform complexity based on waveform feature vectors. Background Technology

[0002] With the rapid development of modern communication technologies, wireless communication, satellite communication, and shortwave communication systems are becoming increasingly complex, exhibiting a trend towards diversification in signal forms and data structures. In these systems, signal transmission is not only affected by noise and interference but also involves interactions across multiple signal dimensions, such as multiple-input multiple-output (MIMO) systems, cognitive radio networks, and multi-band satellite communication systems. Therefore, accurately measuring the complexity of communication waveforms is crucial for analyzing system behavior, optimizing information transmission characteristics, and improving overall communication performance. However, traditional complexity analysis methods are mostly based on one-dimensional sequences, making it difficult to fully capture the complex relationships between multivariable signals, thus limiting the accuracy and reliability of analysis results in multidimensional signal environments.

[0003] To address the limitations of one-dimensional complexity analysis methods, various algorithms have been applied to time series complexity analysis, such as approximate entropy, sample entropy, and fuzzy entropy algorithms. These algorithms demonstrate certain advantages in evaluating the complexity of univariate time series, quantifying the frequency of new patterns in signals and enhancing robustness to noise. However, these algorithms are primarily designed for processing one-dimensional scalar sequences. When dealing with multidimensional signals, they typically need to be decomposed into multiple one-dimensional signals for individual analysis. This not only increases computational complexity but may also lead to the loss of crucial information during the decomposition process, thus failing to accurately reflect the complex relationships between multivariate signals.

[0004] While existing one-dimensional complexity analysis methods have some application value in univariate time series analysis, their limitations are becoming increasingly apparent when dealing with multidimensional signals in modern communication systems. First, these methods lack support for multidimensional data, failing to comprehensively capture the coupling relationships and interaction patterns between signals from multiple channels or antennas. Second, their insufficient multivariate analysis capabilities make it difficult to accurately assess the interdependencies between signals in complex communication scenarios. Furthermore, with the rapid increase in the scale of communication data, existing algorithms face severe challenges in terms of computational efficiency and scalability, struggling to meet the demands of real-time processing and dynamic optimization. Therefore, there is an urgent need for a new method capable of performing complexity analysis on multidimensional signals to overcome the shortcomings of existing technologies and improve the signal analysis capabilities and overall performance of communication systems. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides a waveform complexity measurement method, apparatus, and device based on waveform feature vectors.

[0006] The technical problem to be solved by this invention is achieved through the following technical solution:

[0007] In a first aspect, the present invention provides a waveform complexity measurement method based on waveform feature vectors, comprising:

[0008] S101. Obtain the multidimensional waveform feature vector of the signal to be analyzed and construct the waveform feature sample space;

[0009] S102. Construct a set of observation waveform feature vector matrices based on the waveform feature sample space and the preset embedding dimension;

[0010] S103. Based on the observed waveform feature vector matrix group, fuzzy membership function, and preset similarity tolerance, determine the similarity between the current waveform matrix and the remaining waveform matrix, and calculate the average value to obtain the current similarity result; the remaining waveform matrix consists of all waveform matrices in the observed waveform feature vector matrix group except for the current waveform matrix.

[0011] S104. Obtain the first similarity level by using the current similarity results corresponding to all current waveform matrices;

[0012] S105. Expand the preset embedding dimension to obtain the expanded embedding dimension value, and use the expanded embedding dimension value as the preset embedding dimension to re-execute S102-S104 to obtain the second similarity.

[0013] S106. Calculate the waveform complexity fuzzy entropy using the first and second similarity levels to obtain the waveform complexity measurement result.

[0014] Optionally, S103 specifically includes:

[0015] Calculate the maximum distance between waveform matrices in the observed waveform feature vector matrix group;

[0016] Based on the fuzzy membership function, preset similarity tolerance, and maximum distance, the similarity between the current waveform matrix and each remaining waveform matrix is ​​determined, and the mean value is calculated to obtain the current similarity result.

[0017] Optionally, the maximum distance between waveform matrices in the observed waveform feature vector matrix group is calculated, including:

[0018] The maximum distance between waveform matrices in the observed waveform feature vector matrix group is calculated using Euclidean distance.

[0019] Optionally, the similarity between the current waveform matrix and the remaining waveform matrix can be calculated based on the following formula:

[0020]

[0021] d[A(i),A(j)] represents the similarity between the current waveform matrix A(i) and the remaining waveform matrix A(j) under the preset embedding dimension m, r represents the preset similarity tolerance, and exp represents the exponential function.

[0022] Optionally, the signal to be analyzed includes any one of the following: frequency hopping waveform, constellation scrambling waveform, and frequency hopping waveform with constellation scrambling, or a combination waveform composed of frequency hopping waveform, constellation scrambling waveform, and frequency hopping waveform with constellation scrambling.

[0023] Optionally, S102 specifically includes:

[0024] Using a sliding window approach and with a preset embedding dimension as the window size, the waveform feature sample space is segmented to obtain the observed waveform feature vector matrix group.

[0025] Optionally, the preset embedding dimension m is 2, and the preset similarity tolerance r is 0.5.

[0026] Optionally, the waveform complexity fuzzy entropy is represented as:

[0027] FuzzyEn(m,r,N)=lnΦ m,N (r)-lnΦ m+1,N (r);

[0028] Where FuzzyEn(m,r,N) represents the waveform complexity fuzzy entropy corresponding to the total number of waveform feature sample spaces N under a preset embedding dimension m and a preset similarity tolerance r, Φ m,N (r) represents the first degree of similarity, Φ m+1,N (r) indicates the second degree of similarity.

[0029] Secondly, the present invention provides a waveform complexity measurement device based on waveform feature vectors, the waveform complexity measurement device based on waveform feature vectors includes: an acquisition unit, a construction unit, a calculation unit, and a loop processing unit;

[0030] The acquisition unit is used to: acquire the multidimensional waveform feature vector of the signal to be analyzed and construct the waveform feature sample space;

[0031] The construction unit is used to: construct a group of observed waveform feature vector matrices based on the waveform feature sample space and the preset embedding dimension;

[0032] The calculation unit is used to: determine the similarity between the current waveform matrix and the remaining waveform matrix based on the observed waveform feature vector matrix group, the fuzzy membership function, and the preset similarity tolerance, and calculate the average value to obtain the current similarity result; the remaining waveform matrix consists of all waveform matrices in the observed waveform feature vector matrix group except for the current waveform matrix;

[0033] The building unit is also used to: obtain the first similarity level through the current similarity results corresponding to all current waveform matrices;

[0034] The loop processing unit is used to: expand the preset embedding dimension to obtain the expanded embedding dimension value, and use the expanded embedding dimension value as the preset embedding dimension to re-execute the actions of the construction unit and the calculation unit to obtain the second similarity;

[0035] The calculation unit is also used to: calculate the waveform complexity fuzzy entropy using the first similarity degree and the second similarity degree, and obtain the waveform complexity measurement result.

[0036] Thirdly, the present invention provides a waveform complexity measurement device based on waveform feature vectors, comprising: a processor, a storage medium and a bus, wherein the storage medium stores machine-readable instructions executable by the processor, and when the waveform complexity measurement device based on waveform feature vectors is running, the processor communicates with the storage medium via the bus, and the processor executes the machine-readable instructions to perform the steps of the waveform complexity measurement method based on waveform feature vectors as described in the first aspect above.

[0037] This invention provides a method, apparatus, and device for measuring waveform complexity based on waveform feature vectors. The method includes: S101, acquiring multi-dimensional waveform feature vectors of the signal to be analyzed and constructing a waveform feature sample space; S102, constructing an observation waveform feature vector matrix group based on the waveform feature sample space and a preset embedding dimension; S103, determining the similarity between the current waveform matrix and the remaining waveform matrices based on the observation waveform feature vector matrix group, a fuzzy membership function, and a preset similarity tolerance, and calculating the average value to obtain the current similarity result; the remaining waveform matrices are all waveform matrices in the observation waveform feature vector matrix group except for the current waveform matrix; S104, obtaining a first similarity degree through the current similarity results corresponding to all current waveform matrices; S105, expanding the preset embedding dimension to obtain an expanded embedding dimension value, and re-executing S102-S104 using the expanded embedding dimension value as the preset embedding dimension to obtain a second similarity degree; S106, calculating the waveform complexity fuzzy entropy using the first and second similarity degrees to obtain the waveform complexity measurement result. In this invention, a set of observation waveform feature vector matrices is constructed using multidimensional waveform feature vectors, and complexity analysis is performed on this basis. This data modeling method breaks through the limitations of traditional one-dimensional sequence analysis, avoids splitting multivariate signals for analysis, and thus maintains the integrity of the interdependence between waveform signals. In addition, fuzzy membership functions are used to calculate the similarity between waveform matrices, which effectively improves the robustness and accuracy of the system when dealing with noise and uncertain signals. Furthermore, this invention decomposes the complexity analysis task into multiple execution modules and adopts a step-by-step calculation process, which reduces the computational burden and error accumulation in the waveform data processing process and improves the analysis efficiency and accuracy.

[0038] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0039] Figure 1 A flowchart illustrating a waveform complexity measurement method based on waveform feature vectors provided in an embodiment of the present invention;

[0040] Figure 2 The waveform variation curves based on the method of the present invention under different observation lengths are illustrated by way of example;

[0041] Figure 3 The waveform variation curves of the fuzzy entropy-based detection method under different observation lengths are shown as an example.

[0042] Figure 4 A schematic diagram of the structure of a waveform complexity measurement device based on waveform feature vectors provided in an embodiment of the present invention;

[0043] Figure 5 This is a schematic diagram of the structure of a waveform complexity measurement device based on waveform feature vectors, provided for an embodiment of the present invention. Detailed Implementation

[0044] This invention provides a waveform complexity measurement method based on waveform feature vectors, which extends the measurement of complexity to multi-dimensional waveform feature vector sequences. It uses the high-performance fuzzy entropy algorithm to analyze waveform complexity and realizes the complexity measurement of multi-dimensional waveform feature vector sequences based on the fuzzy entropy algorithm.

[0045] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0046] To reduce the computational burden and error accumulation during waveform data processing, while improving the efficiency and accuracy of waveform data analysis, this invention provides a waveform complexity measurement method based on waveform feature vectors. Figure 1 This is a flowchart illustrating a waveform complexity measurement method based on waveform feature vectors, provided as an embodiment of the present invention. Figure 1 As shown, it includes:

[0047] S101. Obtain the multidimensional waveform feature vector of the signal to be analyzed and construct the waveform feature sample space.

[0048] Optionally, the signal to be analyzed includes any one of the following: frequency hopping waveform, constellation scrambling waveform, and frequency hopping waveform with constellation scrambling, or a combination waveform composed of frequency hopping waveform, constellation scrambling waveform, and frequency hopping waveform with constellation scrambling. The frequency hopping waveform performs frequency hopping on 16 frequency slots at a hopping rate of 200 times per second; the constellation scrambling waveform uses 12 modulation schemes, switching 200 times per second; the frequency hopping waveform with constellation scrambling switches 200 times per second on 16 frequency slots, and also switches the same 12 modulation schemes 200 times per second. The 12 modulation schemes correspond to: BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying), 8PSK (Eight-Phase Phase Shift Keying), 16QAM (Hexadecimal Quadrature Amplitude Modulation), 32QAM (32-base Quadrature Amplitude Modulation), 64QAM (64-base Quadrature Amplitude Modulation), 128QAM (128-base Quadrature Amplitude Modulation), 256QAM (256-base Quadrature Amplitude Modulation), FSK (Frequency Shift Keying), GMSK (Gaussian Minimum Frequency Shift Keying), OFDM (Orthogonal Frequency Division Multiplexing), and DPSK (Differential Phase Shift Keying).

[0049] In this embodiment, the multidimensional waveform feature vector can be composed of waveform feature vectors in D dimensions, such as frequency, modulation, and polarization.

[0050] The t-th waveform feature sample space v(t) can be represented as:

[0051] v(t) = [u1(t), u2(t), ..., u D [(t)], t∈(1,N);

[0052] Among them, u D v(t) represents the waveform feature vector of the Dth dimension corresponding to v(t), and N represents the total number of waveform feature sample spaces. All v(t) can form the waveform feature sample space {v(t)|t=1,2,…,N}.

[0053] It should be further noted that the waveform feature sample space contains multiple waveform feature samples, and v(t) is specifically the t-th sample in the waveform feature sample space.

[0054] It is understood that, in this embodiment of the invention, by using multi-dimensional waveform feature vector modeling and modular computation, the limitations of information loss in traditional one-dimensional analysis are avoided, achieving comprehensive capture and accurate analysis of multivariable signals. This design effectively improves the system's analytical accuracy and provides strong support for the performance optimization of complex communication systems.

[0055] S102. Construct a set of observation waveform feature vector matrices based on the waveform feature sample space and the preset embedding dimension.

[0056] Optionally, S102 specifically includes:

[0057] Using a sliding window approach and with a preset embedding dimension as the window size, the waveform feature sample space is segmented to obtain the observed waveform feature vector matrix group.

[0058] In this embodiment, the observed waveform feature vector matrix group can be represented as:

[0059] A(1),A(2),...,A(i),...,A(N-m+1);

[0060] Among them, A(i)=[v(i),v(i+1),...,v(i+m-1)]-v0(i), i represents the index of the waveform matrix in the observed waveform feature vector matrix group, v0(i) represents the arithmetic mean of v(i), v(i+1), ..., v(i+m-1)], and m represents the preset embedding dimension.

[0061] S103. Based on the observed waveform feature vector matrix group, fuzzy membership function and preset similarity tolerance, determine the similarity between the current waveform matrix and the remaining waveform matrix, and calculate the average value to obtain the current similarity result.

[0062] Optionally, S103 may specifically include:

[0063] Calculate the maximum distance between waveform matrices in the observed waveform feature vector matrix group;

[0064] Based on the fuzzy membership function, preset similarity tolerance, and maximum distance, the similarity between the current waveform matrix and each remaining waveform matrix is ​​determined, and the mean value is calculated to obtain the current similarity result.

[0065] Optionally, the maximum distance between waveform matrices in the observed waveform feature vector matrix group is calculated, including:

[0066] The maximum distance between waveform matrices in the observed waveform feature vector matrix group is calculated using Euclidean distance.

[0067] Optionally, the similarity between the current waveform matrix and the remaining waveform matrix can be calculated based on the following formula:

[0068]

[0069] d[A(i),A(j)] represents the similarity between the current waveform matrix A(i) and the remaining waveform matrix A(j) under the preset embedding dimension m, r represents the preset similarity tolerance, and exp represents the exponential function.

[0070] in,

[0071] Current similarity results between A(i) and the remaining waveform matrix A(j) It can be represented as:

[0072]

[0073] The first similarity level can be obtained by averaging the current similarity results corresponding to all current waveform matrices. The first similarity level Φ is... m,N (r) can be represented as:

[0074]

[0075] The second degree of similarity can be expressed as:

[0076]

[0077] In this embodiment, the fuzzy membership function transforms the similarity of waveforms at different times into a membership value between 0 and 1. The closer the membership value is to 1, the higher the similarity of the waveforms at the two times; the closer the membership value is to 0, the lower the similarity of the waveforms at the two times.

[0078] Optionally, the preset embedding dimension m is 2, and the preset similarity tolerance r is 0.5.

[0079] In this context, the embedding dimension *m* determines the local complexity of the signal, and can also be viewed as the size of each window in fuzzy entropy calculation, i.e., how many signal sampling points are needed to construct an effective feature vector. Increasing the value of *m* increases the signal's complexity and information content. The similarity tolerance *r* measures the similarity of signals; this value is usually determined experimentally and directly affects the accuracy of similarity judgment in subsequent steps. Through extensive experiments, the applicant has determined that using *m* = 2 and *r* = 0.5 as the final values ​​effectively improves the accuracy and robustness of signal processing.

[0080] The remaining waveform matrix consists of all waveform matrices in the observed waveform feature vector matrix group except for the current waveform matrix.

[0081] S104. Obtain the first similarity level by using the current similarity results corresponding to all current waveform matrices.

[0082] S105. Expand the preset embedding dimension to obtain the expanded embedding dimension value, and use the expanded embedding dimension value as the preset embedding dimension to re-execute S102-S104 to obtain the second similarity.

[0083] S106. Calculate the waveform complexity fuzzy entropy using the first and second similarity levels to obtain the waveform complexity measurement result.

[0084] Optionally, the waveform complexity fuzzy entropy is represented as:

[0085] FuzzyEn(m,r,N)=lnΦ m,N (r)-lnΦ m+1,N (r);

[0086] Where FuzzyEn(m,r,N) represents the waveform complexity fuzzy entropy corresponding to the total number of waveform feature sample spaces N under a preset embedding dimension m and a preset similarity tolerance r, Φ m,N (r) represents the first degree of similarity, Φ m+1,N (r) indicates the second degree of similarity.

[0087] It should be noted that the waveform complexity measurement method based on waveform feature vectors provided by this invention can be widely applied to communication application scenarios, including but not limited to MIMO systems and multi-antenna communication, and can also be applied to complex network scenarios such as cognitive radio, satellite communication, and the Internet of Things. Its general algorithm structure allows it to flexibly adapt to the needs of various communication environments, providing an efficient tool for performance analysis and optimization of various systems.

[0088] This invention provides a waveform complexity measurement method based on waveform feature vectors. It constructs a set of observed waveform feature vector matrices using multidimensional waveform feature vectors and performs complexity analysis on this basis. This data modeling approach breaks through the limitations of traditional one-dimensional sequence analysis, avoiding the separation of multivariable signals for analysis and thus maintaining the integrity of the interdependencies between waveform signals. Furthermore, it employs fuzzy membership functions to calculate the similarity between waveform matrices, effectively improving the robustness and accuracy of the system when handling noise and uncertain signals. Moreover, this invention decomposes the complexity analysis task into multiple execution modules, adopting a step-by-step processing flow, reducing the computational burden and error accumulation during waveform data processing, and improving analysis efficiency and accuracy.

[0089] To verify the effectiveness of the waveform complexity measurement method based on waveform feature vectors provided in this embodiment of the invention, simulation verification was also performed.

[0090] Specifically, Figure 2 The waveform variation curves based on the method of the present invention under different observation lengths are illustrated exemplarily. To demonstrate the superiority of the method of the present invention, a traditional fuzzy entropy detection method is used for comparison, and the results are as follows. Figure 3 As shown. Among them, Figure 2 and Figure 3 The horizontal axis represents the observation length, and the vertical axis represents the value of fuzzy entropy (waveform complexity fuzzy entropy).

[0091] from Figure 2 Simulation results show that the method of this invention can distinguish the complexity of traditional single-dimensional agility methods such as frequency hopping and constellation perturbation from that of multi-dimensional agility waveforms. Furthermore, the frequency hopping waveform with constellation perturbation exhibits the highest fuzzy entropy value, indicating that this waveform has the highest complexity, which aligns with the waveform parameter settings. The waveform complexity measurement method based on waveform feature vectors of this invention innovatively employs waveform tensors, enabling simultaneous detection of multi-dimensional waveform parameters and clearly distinguishing the complexity of multi-dimensional complex waveforms. Therefore, the method of this invention can be used for measuring the complexity of complex waveforms.

[0092] from Figure 3 Simulation results show that the complexity of frequency-hopping waveforms is similar. Therefore, traditional fuzzy entropy measurement methods cannot distinguish the complexity of frequency-hopping waveforms from that of constellation-disrupted frequency-hopping waveforms. Furthermore, the complexity of constellation-disrupted waveforms is zero, which is clearly inconsistent with reality. This is because traditional fuzzy entropy detection methods only focus on detecting single-dimensional frequency-hopping sequence parameters and cannot simultaneously detect the parameters of constellation-disrupted waveforms, thus resulting in constellation-disrupted waveforms having zero complexity. Additionally, traditional fuzzy entropy detection methods also struggle to distinguish multi-dimensional complex waveforms employing multiple modulation schemes.

[0093] Depend on Figure 2 and Figure 3 The comparison clearly demonstrates the innovation and practicality of the method of this invention in multidimensional complexity measurement technology, and reflects the application value of the method of this invention in complex communication systems.

[0094] In summary, the waveform complexity measurement method based on waveform feature vectors provided by this invention mainly solves the problems of insufficient accuracy, information loss, low computational efficiency, and poor scalability faced by traditional complexity analysis techniques in high-dimensional data processing. First, this invention expands a single-dimensional signal into a multi-dimensional waveform feature vector matrix, comprehensively capturing the complex relationships between different variables and avoiding the loss of key information caused by the simplification of signals in traditional methods. This design is particularly suitable for complex communication scenarios such as multi-channel and multi-antenna systems, helping to more accurately analyze system performance and dynamic characteristics. Second, this invention introduces a fuzzy membership function, enhancing the robustness of complexity analysis. By calculating the similarity between samples, this method can effectively cope with uncertainties and noise in signals, thereby improving the accuracy of analysis results. This design improves the system's adaptability to noisy environments, making it suitable for signal processing in variable environments such as satellite communication and the Internet of Things. Furthermore, this invention adopts a modular, step-by-step computation strategy, gradually improving the stability and consistency of computation through iterative optimization. This method decomposes the complexity calculation task into multiple steps, reducing accumulated errors in large-scale data processing and ensuring high-precision analysis results even in big data environments. These advantages enable the method of the present invention not only to meet the requirements of real-time signal processing in communication systems, but also to perform rapid analysis and optimization in complex scenarios such as MIMO systems and cognitive radio.

[0095] The method provided in this embodiment of the invention can be applied to electronic devices. Specifically, the electronic device can be a desktop computer, a portable computer, a smart mobile terminal, a server, etc., and this embodiment of the invention does not limit the application to such devices.

[0096] Based on the same inventive concept, embodiments of the present invention also provide a waveform complexity measurement device based on waveform feature vectors. Figure 4 This is a schematic diagram of a waveform complexity measurement device based on waveform feature vectors, provided as an embodiment of the present invention. Figure 4 As shown, it includes:

[0097] The system includes an acquisition unit 401, a construction unit 402, a calculation unit 403, and a loop processing unit 404.

[0098] The acquisition unit 401 is used to: acquire the multidimensional waveform feature vector of the signal to be analyzed and construct the waveform feature sample space;

[0099] The construction unit 402 is used to: construct a group of observed waveform feature vector matrices based on the waveform feature sample space and the preset embedding dimension;

[0100] The calculation unit 403 is used to: determine the similarity between the current waveform matrix and the remaining waveform matrix based on the observed waveform feature vector matrix group, the fuzzy membership function and the preset similarity tolerance, and calculate the average value to obtain the current similarity result; the remaining waveform matrix is ​​all waveform matrices in the observed waveform feature vector matrix group except for the current waveform matrix;

[0101] The construction unit 402 is also used to: obtain the first similarity level through the current similarity results corresponding to all current waveform matrices;

[0102] The loop processing unit 404 is used to: expand the preset embedding dimension to obtain the expanded embedding dimension value, and use the expanded embedding dimension value as the preset embedding dimension to re-execute the actions of the construction unit 402 and the calculation unit 403 to obtain the second similarity.

[0103] The calculation unit 403 is also used to: calculate the waveform complexity fuzzy entropy using the first similarity degree and the second similarity degree to obtain the waveform complexity measurement result.

[0104] Figure 5 A schematic diagram of a waveform complexity measurement device based on waveform feature vectors provided in an embodiment of the present invention includes: a processor 510, a storage medium 520, and a bus 530. The storage medium 520 stores machine-readable instructions executable by the processor 510. When the waveform complexity measurement device based on waveform feature vectors is running, the processor 510 and the storage medium 520 communicate via the bus 530, and the processor 510 executes the machine-readable instructions to perform the steps of the above-described method embodiment. Specific implementation methods and technical effects are similar and will not be described in detail here.

[0105] The storage medium may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the storage medium may also be at least one storage device located remotely from the aforementioned processor.

[0106] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0107] It should be noted that the terms "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.

[0108] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0109] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the accompanying drawings and the disclosure, will understand and implement other variations of the disclosed embodiments in carrying out the claimed invention. In the description of the invention, the word "comprising" does not exclude other components or steps, "a" or "an" does not exclude a plurality, and "a plurality" means two or more, unless otherwise explicitly specified. Furthermore, while different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.

[0110] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the inventive concept, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method of measuring complexity of a waveform based on a waveform feature vector, characterized by, Comprising: S101, acquire the multi-dimensional waveform feature vector of the signal to be analyzed, and construct a waveform feature sample space; wherein the multi-dimensional waveform feature vector is composed of waveform feature vectors of dimensions; the dimensions include at least a frequency dimension, a modulation dimension, and a polarization dimension; the waveform feature sample space is represented as , , represents the waveform feature vector of the corresponding dimension, represents the total number of waveform feature sample spaces; S102, based on a sliding window manner, and taking a preset embedding dimension as a window size, the waveform feature sample space is divided to obtain an observation waveform feature vector matrix group, which is represented as: ； wherein, , , denotes the sequence number of a waveform matrix in the waveform feature vector matrix group, denotes the arithmetic mean value of denotes a preset embedding dimension; S103, the maximum distance between the waveform matrices in the observation waveform feature vector matrix group is calculated by using the Euclidean distance; based on the fuzzy membership function, the preset similarity tolerance degree and the maximum distance, the similarity between the current waveform matrix and each remaining waveform matrix is determined, and the average value is obtained to obtain the current similarity result; the remaining waveform matrix is all waveform matrices in the observation waveform feature vector matrix group except the current waveform matrix; S104, the first similarity degree is obtained through the current similarity result corresponding to all current waveform matrices; S105, the preset embedding dimension is expanded to obtain an embedding dimension expansion value, and the embedding dimension expansion value is taken as the preset embedding dimension to re-execute S102-S104 to obtain a second similarity degree; S106, the waveform complexity fuzzy entropy is calculated by using the first similarity degree and the second similarity degree to obtain a waveform complexity measure result.

2. The method of claim 1, wherein the wave complexity measure is based on a wave feature vector. The similarity between the current waveform matrix and the remaining waveform matrix is calculated based on the following formula: ； denotes the current waveform matrix denotes the remaining waveform matrix in the preset embedding dimension denotes the similarity, denotes denotes the maximum distance between denotes the preset similarity tolerance degree denotes the exponential function.

3. The method of claim 1, wherein the wave complexity measure is based on a wave feature vector. The signal to be analyzed includes any one of a frequency hopping waveform, a constellation scrambling waveform, and a constellation scrambled frequency hopping waveform, or a combination waveform composed of the frequency hopping waveform, the constellation scrambling waveform, and the constellation scrambled frequency hopping waveform.

4. The method of claim 1, wherein the wave complexity measure is based on a wave feature vector. The preset embedding dimension The preset similarity tolerance is 2. It is 0.

5.

5. The method of claim 1, wherein the wave complexity measure is based on a wave feature vector. The waveform complexity fuzzy entropy is represented as: ； wherein, represents a preset embedding dimension and a preset similarity tolerance degree the total number of waveform feature sample spaces corresponding to the waveform complexity fuzzy entropy, represents the first similarity degree, represents the second similarity degree.

6. A waveform complexity measure apparatus based on waveform feature vectors, characterized by, The waveform complexity measure device based on the waveform feature vector comprises an acquisition unit, a construction unit, a calculation unit and a loop processing unit; The acquisition unit is used for acquiring a multi-dimensional waveform feature vector of a signal to be analyzed, and constructing a waveform feature sample space; wherein the multi-dimensional waveform feature vector is composed of waveform feature vectors of dimensions; the dimensions at least include a frequency dimension, a modulation dimension and a polarization dimension; the waveform feature sample space is represented as , , represents a corresponding waveform feature vector of the dimension, represents a total number of waveform feature sample spaces.​ The construction unit is configured to: based on a sliding window manner, and taking a preset embedding dimension as a window size, the waveform feature sample space is divided to obtain an observation waveform feature vector matrix group; the observation waveform feature vector matrix group is represented as: ； wherein, , , denotes the sequence number of a waveform matrix in the waveform feature vector matrix group, denotes the arithmetic mean of , denotes a preset embedding dimension; The calculation unit is configured to: the maximum distance between the waveform matrices in the observation waveform feature vector matrix group is calculated by using the Euclidean distance; based on the fuzzy membership function, the preset similarity tolerance degree and the maximum distance, the similarity between the current waveform matrix and each remaining waveform matrix is determined, and the average value is obtained to obtain the current similarity result; the remaining waveform matrix is all waveform matrices in the observation waveform feature vector matrix group except the current waveform matrix; The construction unit is further configured to: the first similarity degree is obtained through the current similarity result corresponding to all current waveform matrices; The loop processing unit is configured to: the preset embedding dimension is expanded to obtain an embedding dimension expansion value, and the embedding dimension expansion value is taken as the preset embedding dimension to re-execute the actions of the construction unit and the calculation unit to obtain a second similarity degree; The calculation unit is further configured to: the waveform complexity fuzzy entropy is calculated by using the first similarity degree and the second similarity degree to obtain a waveform complexity measure result.

7. A waveform complexity measure device based on waveform feature vectors, characterized by, Comprising: A processor, a storage medium storing machine readable instructions executable by the processor, and a bus for communications between the processor and the storage medium when the waveform feature vector based waveform complexity measure device is in operation, wherein the processor executes the machine readable instructions to perform the steps of the waveform feature vector based waveform complexity measure method of any one of claims 1-5.

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