Radar signal reconstruction method based on maximum multiple correlation entropy

Abstract

The invention discloses a radar signal reconstruction method based on maximum multiple correlation entropy, which adopts a maximum multiple correlation entropy criterion to define an error function, and replaces an error function based on # imgabs0 # norm commonly used in a traditional tensor completion method, and in an abnormal value pollution environment, the maximum multiple correlation entropy criterion is used to determine the error function, and the maximum multiple correlation entropy criterion is used to replace the error function based on # imgabs0 # norm. The maximum multiple correlation entropy is generally more robust than a traditional # imgabs1 # error function, and can better suppress the influence of an abnormal value, so that the radar signal reconstruction model based on the maximum multiple correlation entropy can effectively suppress the interference of the abnormal value on the system performance, thereby improving the reconstruction precision of the radar signal; therefore, accurate reconstruction and recovery of the radar signal polluted by the abnormal value are realized, the problem of poor performance caused by the influence of the abnormal value on the reconstruction of the radar signal at present is solved, and the signal processing capability of the system in a complex electromagnetic environment is further improved.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and in particular to a radar signal reconstruction method based on maximum complex correlation entropy. Background Art

[0002] With the continuous advancement of radar technology, the structure and mechanism of radar systems are becoming increasingly complex, and their functions are gradually showing a trend of diversification and systematization. At the same time, the emergence of new application models such as multi-radar collaboration and drone clusters has further promoted the evolution of radar signal processing technology towards diversification. Currently, for radar signals received by reconnaissance equipment, direct measurement and estimation are usually used to extract key parameters and then generate pulse descriptor words (PDWs). Then, based on the PDW information, key tasks such as radiation source identification and radar operating mode classification can be further carried out.

[0003] Currently, tasks such as radar individual identification and radar operating mode recognition generally rely on PDW as key feature information. The PDW acquisition process mainly relies on direct measurement of received radar signals, such as pulse width, pulse repetition interval, carrier frequency and other parameters. However, due to the increasingly complex current electromagnetic environment, the radar signals received by radars or drones will be interfered with by the complex electromagnetic environment, and the adverse effects of outliers on the received signals will also be amplified; secondly, from the perspective of reconnaissance equipment, the processing of received radar signals is usually performed directly by measurement. However, if the received radar signal is contaminated by outliers in the electromagnetic environment, the PDW formed by the measurement will be incorrect, thereby affecting the performance of subsequent tasks.

[0004] Given that PDW measurement is highly dependent on the quality of the received signal, and the process is easily interfered by outliers, improving the robustness of the data processing stage to abnormal information has become a key breakthrough. Especially in high-dimensional radar data, how to reasonably characterize radar data and how to effectively recover contaminated signals have become the core challenges to ensure the accuracy of PDW and the performance of subsequent tasks. Among them, tensors, as a form of high-dimensional data representation, can be effectively used for modeling and expressing radar data. However, traditional tensor completion methods usually rely on low-rank assumptions and are based on The model is solved based on the error function of the norm, and The error function of the norm usually lacks robustness to outliers. Therefore, when there are outliers in the received data, these methods are easily interfered with by them, resulting in distortion of the completion results, which in turn affects the quality of signal reconstruction and the accuracy of subsequent feature extraction.

[0005] Therefore, based on the above-mentioned shortcomings, how to provide a radar signal reconstruction method based on maximum complex correlation entropy with high signal reconstruction quality has become an urgent problem to be solved. Summary of the Invention

[0006] The technical problem to be solved by the present invention is the problem of radar signal reconstruction quality. The purpose is to provide a radar signal reconstruction method based on maximum complex correlation entropy, which solves the problem of traditional technology using The radar signal reconstruction based on the error function of the norm is susceptible to interference from outliers, which will cause distortion of the completion result and reduce the quality of signal reconstruction.

[0007] The present invention is achieved through the following technical solutions: In a first aspect, a radar signal reconstruction method based on maximum complex correlation entropy is provided, comprising: Establish a baseband signal model for the radar signal received by the UAV; Sampling the baseband signal model to obtain sampled data, and constructing a signal tensor corresponding to the baseband signal model using the sampled data; Based on the signal tensor, a radar signal reconstruction model is established with maximum complex correlation entropy as an error function; Using a semi-quadratic optimization algorithm, the radar signal reconstruction model is converted into a weighted signal reconstruction model, wherein the weighted signal reconstruction model is a convex model; Based on the weighted signal reconstruction model, a complex conjugate gradient signal model is constructed; The complex conjugate gradient signal model is solved by using an alternating complex conjugate gradient optimization algorithm to obtain a reconstructed signal tensor after the solution, and a reconstructed radar signal is generated based on the reconstructed signal tensor.

[0008] Based on the above-disclosed content, the present invention establishes a baseband signal model of the radar signal received by the drone, samples it, and constructs a signal tensor using the sampled data; then, based on the signal tensor, establishes a radar signal reconstruction model with maximum complex correlation entropy as the error function; then, the non-convex radar signal reconstruction model is converted into a convex model, that is, converted into a weighted signal reconstruction model; then, based on the weighted signal reconstruction model, a complex conjugate gradient signal model is constructed, and the complex conjugate gradient signal model is solved to obtain a reconstructed signal tensor; finally, based on the reconstructed signal tensor, a reconstructed radar signal can be generated.

[0009] Through the above design, the present invention adopts the maximum complex correlation entropy criterion to define the error function, and replaces the traditional tensor completion method based on norm error function, where the maximum complex correlation entropy is usually better than the traditional The error function is more robust and can better suppress the influence of outliers. In this way, the radar signal reconstruction model based on the maximum complex correlation entropy can effectively suppress the interference of outliers on system performance, thereby improving the reconstruction accuracy of radar signals. Therefore, the present invention realizes the accurate reconstruction and recovery of radar signals contaminated by outliers, solves the problem that the current radar signal reconstruction is affected by outliers and causes poor performance, thereby improving the signal processing capability of the system in complex electromagnetic environments.

[0010] In one possible design, the radar signal received by the UAV includes multiple signal sequences, where each signal sequence includes several baseband signals. The total number of signal sequences is equal to the number of illuminations of the phased array radar scanning the UAV. The total number of baseband signals in any signal sequence is equal to the number of pulse signals emitted by the phased array radar to each beam speed under one illumination, and one baseband signal corresponds to one pulse signal emitted by the phased array radar. Among them, the baseband signal model of the radar signal received by the UAV is established, including: Generate a baseband signal corresponding to each pulse signal emitted by the phased array radar received by the UAV under each illumination, and use the baseband signal corresponding to each pulse signal under each illumination to form the baseband signal model; Among them, under the illumination of the phased array radar, the baseband signal corresponding to the mth pulse signal received by the drone is:

[0011] Where, represents the baseband signal corresponding to the mth pulse signal under one illumination, represents the mth pulse signal emitted by the phased array radar, represents the delay of the mth pulse signal, represents the center frequency, represents the baseband noise signal, Indicates the signal amplification factor of the receiver on the drone, is an imaginary unit, where ,and Indicates the number of pulse signals emitted to each wave velocity under one irradiation.

[0012] In one possible design, the baseband signal model is sampled to obtain sampled data, and a signal tensor corresponding to the baseband signal model is constructed using the sampled data, including: Performing Nyquist sampling on each baseband signal in the baseband signal model to obtain sampling data of each baseband signal; Based on the sampling data of each baseband signal, and according to the number of irradiation times and slow time sampling points of the phased array radar, the signal tensor is constructed, wherein the signal tensor , represents the number of sampled data of each baseband signal, the number of slow-time sampling points, and the number of irradiations of the phased array radar in sequence. The number of slow-time sampling points is the number of pulse signals emitted by the phased array radar to each wave velocity under one irradiation. represents the kth irradiation The pulse signal corresponds to the i-th sampling data in the baseband signal, represents the complex field, ,and A pointer to an entry representing a signal tensor.

[0013] In one possible design, a radar signal reconstruction model is established based on the signal tensor with maximum complex correlation entropy as an error function, including: Performing tensor decomposition on the signal tensor to obtain a decomposition tensor, wherein the decomposition tensor includes a first signal sub-tensor and a second signal sub-tensor; Calculating the maximum complex correlation entropy between the signal tensor and the decomposition tensor; Based on the maximum complex correlation entropy, a radar signal reconstruction model is constructed with the maximum complex correlation entropy as an error function.

[0014] In one possible design, the signal tensor is constructed by sampling each baseband signal in the baseband signal model and using the sampled data. Each baseband signal in the baseband signal model belongs to a different signal sequence. The total number of signal sequences is the number of irradiations of the phased array radar of the scanning drone. The dimension of the signal tensor is , It represents the number of sampled data of each baseband signal, the number of pulse signals transmitted by the phased array radar each time it is illuminated, and the number of illuminations, and one pulse signal corresponds to one baseband signal; Accordingly, based on the maximum complex correlation entropy, a radar signal reconstruction model is constructed with the maximum complex correlation entropy as the error function, which includes: According to the following formula, the radar signal reconstruction model is constructed;

[0015] Where, represents the radar signal reconstruction model, Indicates the indicated parameter, represents the first signal subtensor, represents the second signal subtensor, represents the maximum complex correlation entropy, represents the kernel width of the kernel function, represents the intermediate parameters, express conjugation of; in, , where Indicates that the j-th pulse signal in the k-th forward plane in the signal tensor corresponds to the i-th sampled data of the baseband signal. The k-th forward plane is the forward plane formed by the tensor consisting of the sampled data of all baseband signals received by the UAV under the k-th illumination of the phased array radar. and , where A pointer to an entry representing a signal tensor.

[0016] In one possible design, a semi-quadratic optimization algorithm is used to convert the radar signal reconstruction model into a weighted signal reconstruction model, including: Construct the conjugate function; The conjugate function is used to perform model conversion processing on the radar signal reconstruction model, so as to obtain the weighted signal reconstruction model after the model conversion processing.

[0017] In one possible design, using the conjugate function to perform model conversion processing on the radar signal reconstruction model to obtain the weighted signal reconstruction model after the model conversion processing includes: According to the following formula, the radar signal reconstruction model is converted to obtain a weighted signal reconstruction model;

[0018] Where, represents the first intermediate tensor, represents the conjugate function, and ; in, .

[0019] In one possible design, a complex conjugate gradient signal model is constructed based on a weighted signal reconstruction model, including: Performing model simplification processing on the weighted signal reconstruction model to obtain a simplified signal reconstruction model; Performing equivalent transformation on the simplified signal reconstruction model to obtain a complex conjugate gradient signal model after the equivalent transformation; Among them, the simplified signal reconstruction model is:

[0020] Where, represents the second intermediate tensor, represents the indicator tensor, represents the signal tensor, represents the Vandermonde product, represents the Frobenius norm; and , where Represents the value of the jth row and ith column in the kth forward face in the second intermediate tensor; Correspondingly, the complex conjugate gradient signal model is:

[0021] Where, represents the Fourier transform of the k-th forward face in the second intermediate tensor, represents the Fourier transform of the indicated tensor, represents the Fourier transform of the kth forward face in the signal tensor, represents the Fourier transform of the kth forward face in the first signal subtensor, represents the Fourier transform of the kth forward facet in the second signal subtensor.

[0022] In one possible design, the complex conjugate gradient signal model includes a first parameter term, a second parameter term, and a kernel width, wherein the first parameter term is a Fourier transform term of a forward plane of the first signal subtensor, the second parameter term is a Fourier transform term of a forward plane of the first signal subtensor, and the first signal subtensor and the second signal subtensor are obtained by performing tensor decomposition on the signal tensor; The alternating complex conjugate gradient optimization algorithm is used to solve the complex conjugate gradient signal model, so as to obtain a reconstructed signal tensor after solving the problem, including: Obtaining the first parameter item and the second parameter item at the nth iteration, wherein when n is 1, the first parameter item and the second parameter item at the nth iteration are initial values; Determine the kernel width at the nth iteration; Substituting the kernel width, the first parameter term, and the second parameter term at the nth iteration into the complex conjugate gradient signal model to obtain a conjugate model at the nth iteration; Calculate the model residual of the conjugate model at the nth iteration; Determine whether an iteration stopping condition is met, wherein the iteration stopping condition is that the relative error between the model residual at the nth iteration and the model residual at the (n-1)th iteration is less than a preset threshold; If not, the second parameter term in the conjugate model at the nth iteration is fixed, and the first parameter term in the conjugate model at the nth iteration is updated to obtain the first parameter term at the (n+1)th iteration; Using the first parameter term at the (n+1)th iteration, the conjugate model is updated to obtain an updated conjugate model; Fixing the first parameter term in the updated conjugate model, and updating the second parameter term in the updated conjugate model to obtain the second parameter term at the (n+1)th iteration; Increment n by 1, and re-obtain the first parameter term and the second parameter term at the nth iteration until the iteration stop condition is met, thereby obtaining the optimal Fourier transform term of the forward surface of the first signal subtensor and the optimal Fourier transform term of the forward surface of the second signal subtensor; The optimal Fourier transform items of the forward plane of the first signal sub-tensor and the second signal sub-tensor are sequentially subjected to inverse Fourier transform processing and tensor t-product processing, so as to obtain the reconstructed signal tensor after the tensor t-product processing.

[0023] In one possible design, the first parameter term in the conjugate model at the nth iteration is updated to obtain the first parameter term at the (n+1)th iteration, including: After fixing the second parameter term in the conjugate model at the nth iteration, calculating the first partial derivative of the conjugate model at the nth iteration with respect to the first parameter term at the nth iteration; Obtaining a second partial derivative of the conjugate model at the n-1th iteration with respect to the first parameter term at the n-1th iteration, and calculating a conjugate directional coefficient at the nth iteration based on the second partial derivative and the first partial derivative; Calculating the conjugate direction at the nth iteration based on the first partial derivative and the conjugate direction coefficient; Determine the optimal step size of the first parameter term of the nth iteration; The first parameter item at the nth iteration is updated using the conjugate direction at the nth iteration and the optimal step size to obtain the first parameter item at the (n+1)th iteration.

[0024] In a second aspect, a radar signal reconstruction device based on maximum complex correlation entropy is provided, comprising: A baseband signal generation unit, used to establish a baseband signal model of the radar signal received by the UAV; A tensor unit is used to sample the baseband signal model to obtain sampled data, and construct a signal tensor corresponding to the baseband signal model using the sampled data; A signal reconstruction unit, configured to establish, based on the signal tensor, a radar signal reconstruction model with maximum complex correlation entropy as an error function; a signal reconstruction unit, configured to convert the radar signal reconstruction model into a weighted signal reconstruction model using a semi-quadratic optimization algorithm, wherein the weighted signal reconstruction model is a convex model; A signal reconstruction unit, configured to construct a complex conjugate gradient signal model based on the weighted signal reconstruction model; The signal reconstruction unit is further configured to solve the complex conjugate gradient signal model using an alternating complex conjugate gradient optimization algorithm to obtain a reconstructed signal tensor after the solution, and generate a reconstructed radar signal based on the reconstructed signal tensor.

[0025] In a third aspect, another radar signal reconstruction device based on maximum complex correlation entropy is provided. Taking the device as an electronic device as an example, it includes a memory, a processor and a transceiver that are communicatively connected in sequence, wherein the memory is used to store computer programs, the transceiver is used to send and receive messages, and the processor is used to read the computer program and execute the radar signal reconstruction method based on maximum complex correlation entropy as described in the first aspect or any possible design of the first aspect.

[0026] In a fourth aspect, a storage medium is provided, on which instructions are stored. When the instructions are executed on a computer, the radar signal reconstruction method based on maximum complex correlation entropy as described in the first aspect or any possible design of the first aspect is executed.

[0027] In a fifth aspect, a computer program product comprising instructions is provided, which, when executed on a computer, causes the computer to execute the radar signal reconstruction method based on maximum complex correlation entropy as described in the first aspect or any possible design of the first aspect.

[0028] Compared with the prior art, the present invention has the following advantages and beneficial effects: (1) The present invention adopts the maximum complex correlation entropy criterion to define the error function, and replaces the traditional tensor completion method based on norm error function, where the maximum complex correlation entropy is usually better than the traditional The error function is more robust and can better suppress the influence of outliers. In this way, the radar signal reconstruction model based on the maximum complex correlation entropy can effectively suppress the interference of outliers on system performance, thereby improving the reconstruction accuracy of radar signals. Therefore, the present invention realizes the accurate reconstruction and recovery of radar signals contaminated by outliers, solves the problem that the current radar signal reconstruction is affected by outliers and causes poor performance, thereby improving the signal processing capability of the system in complex electromagnetic environments.

[0029] (2) The present invention introduces a semi-quadratic optimization method and, with the help of a tensor decomposition mechanism, transforms the radar signal reconstruction problem based on the maximum complex correlation entropy criterion into a weighted signal reconstruction model that can be solved by an alternating optimization strategy. In this way, the present invention avoids the repeated singular value decomposition operations in the traditional t-SVD method, thereby significantly reducing the overall computational complexity and improving the computational efficiency of the algorithm.

[0030] (3) The present invention adopts the alternating complex conjugate gradient descent method to solve the model. This method has a fast convergence speed on the basis of ensuring the stability and accuracy of the algorithm. It can effectively reconstruct the radar signal interfered by outliers in a short time. In this way, it can meet the dual requirements of real-time performance and robustness in the current complex electromagnetic environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the examples. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be considered as limiting the scope. A person of ordinary skill in the art can also derive other relevant drawings based on these drawings without inventive effort. In the drawings: Figure 1 A schematic flow chart of the steps of a radar signal reconstruction method based on maximum complex correlation entropy provided by an embodiment of the present invention; Figure 2 A schematic diagram of an original signal provided by an embodiment of the present invention; Figure 3 A schematic diagram of a signal contaminated by outliers provided by an embodiment of the present invention; Figure 4 A schematic diagram of a reconstructed radar signal provided by an embodiment of the present invention; Figure 5 A schematic structural diagram of a radar signal reconstruction device based on maximum complex correlation entropy provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0032] To make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the following examples and accompanying drawings. The exemplary embodiments of the present invention and their descriptions are intended only to explain the present invention and are not intended to limit the present invention. It should be understood that although the terms "first," "second," and so on may be used herein to describe various elements, these elements should not be limited by these terms. These terms are merely used to distinguish one element from another. For example, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element without departing from the scope of the exemplary embodiments of the present invention.

[0033] Example: See also Figure 1 As shown, the radar signal reconstruction method based on maximum complex correlation entropy provided in this embodiment adopts the maximum complex correlation entropy criterion to define the error function and replaces the traditional tensor completion method based on The error function of the norm is used to establish a radar signal reconstruction model based on this. Then, the radar signal reconstruction model is converted into a weighted signal reconstruction model that can be solved by an alternating optimization strategy. Finally, the weighted signal reconstruction model is converted into a complex conjugate gradient signal model and solved by an alternating complex conjugate gradient optimization algorithm to obtain the reconstructed radar signal. Among them, in an outlier pollution environment, the maximum complex correlation entropy is usually better than the traditional The error function is more robust and can better suppress the influence of outliers; thus, the method uses the error function defined by the maximum complex correlation entropy to reconstruct radar signals, which can effectively suppress the interference of outliers on system performance, thereby improving the reconstruction accuracy of radar signals; based on this, the method realizes the accurate reconstruction and recovery of radar signals contaminated by outliers, solves the problem that the current radar signal reconstruction is affected by outliers and causes poor performance, thereby improving the signal processing capability of the system in complex electromagnetic environments; among them, for example, the method can be but is not limited to running on the drone side. It can be understood that the aforementioned execution subject does not constitute a limitation on the embodiments of the present application. Accordingly, the operation steps of the method can be but are not limited to the following steps S1 to S6.

[0034] S1. Build a baseband signal model for the radar signal received by the UAV.

[0035] In specific implementation, assuming a given coherent pulse interval (CPI), the multi-function phased array radar (MFPAR) transmits a pulse to each beam within one frame period (i.e., one illumination). pulses, each with a limited pulse width, are transmitted repeatedly with a pulse repetition interval (PRI), then the pulses It can be expressed as ;in, represents the pulse repetition interval, Represents a linear frequency modulation waveform, and its expression is as follows: (1) In formula (1), z represents a variable. In this embodiment, ,in, represents the sweep rate of the phased array radar, , represents the sweep bandwidth of the phased array radar, represents the pulse width, t represents the time, Represents an imaginary unit.

[0036] Therefore, at the center frequency In the CPI, the mth pulse signal It can also be given by the following formula: (2) At the same time, assuming that the radar There is a plane at a constant speed A mobile reconnaissance aircraft intercepts the MFPAR signal, and the expression of the mth pulse signal reaching the UAV is: (3) In formula (3), Indicates the pulse signal reaching the drone, represents the transmission delay of the mth pulse signal, represents additive white Gaussian noise with a mean of 0, where the transmission delay of the mth pulse signal is expressed as: (4) In formula (4), c represents the propagation speed of electromagnetic waves in air.

[0037] In this way, after down-conversion processing, the radar transmission modulated carrier signal in the intercepted signal is removed to form a baseband signal. Based on this, since the aforementioned phased array radar will transmit M pulse signals each time it is irradiated, the drone will receive baseband signals corresponding to multiple pulse signals under multiple irradiations. In this way, the radar signal received by the aforementioned drone contains multiple signal sequences, wherein each signal sequence contains several baseband signals, and the total number of signal sequences is equal to the number of irradiations of the phased array radar scanning the drone. The total number of baseband signals in any signal sequence is equal to the number of pulse signals emitted by the phased array radar to each wave speed under one irradiation, and one baseband signal corresponds to one pulse signal emitted by the phased array radar.

[0038] Therefore, when establishing the baseband signal model, the baseband signal corresponding to each pulse signal emitted by the phased array radar received by the drone under each irradiation can be generated; then, the baseband signal corresponding to each pulse signal under each irradiation can be used to form the baseband signal model.

[0039] Based on this, under one illumination of the phased array radar, the baseband signal corresponding to the mth pulse signal received by the UAV can be, but is not limited to, as shown in the following formula (5).

[0040] (5) In formula (5), represents the baseband signal corresponding to the mth pulse signal under one illumination, represents the mth pulse signal emitted by the phased array radar, represents the delay of the mth pulse signal, represents the center frequency, represents the baseband noise signal, Indicates the signal amplification factor of the receiver on the drone, is an imaginary unit, where ,and Indicates the number of pulse signals emitted to each wave velocity under one irradiation.

[0041] Therefore, after generating the expression of each baseband signal received by the drone through the aforementioned formula (5), a baseband signal model can be generated based on the baseband signal corresponding to each pulse signal under each illumination; then, the baseband signal model can be used to generate a signal tensor, and the process is shown in the following step S2.

[0042] S2. Sampling the baseband signal model to obtain sampling data, and constructing a signal tensor corresponding to the baseband signal model using the sampling data. In a specific implementation, for example, but not limited to, Nyquist sampling can be performed on each baseband signal in the baseband signal model to obtain sampling data for each baseband signal; then, based on the sampling data of each baseband signal and in accordance with the number of illuminations and slow-time sampling points of the phased array radar, the signal tensor is constructed.

[0043] In this embodiment, the signal tensor is represented as ,in, represents the number of sampled data of each baseband signal, the number of slow time sampling points and the number of irradiation times of the phased array radar in turn, represents the complex domain, and the number of slow-time sampling points is the number of pulse signals emitted by the phased array radar to each wave velocity under one illumination.

[0044] Furthermore, the task of radar signal reconstruction is to reconstruct the tensor from the observed , recover the actual signal tensor, where The entry index representing the observed signal tensor (i.e. Specifically, if ,but is obtained by sampling, that is , and at the same time, the signal tensor represents the kth irradiation The pulse signal corresponds to the i-th sample data in the baseband signal; based on this, the signal tensor is equivalent to a data with three dimensions, that is, its dimension is , and the first dimension is the number of irradiations, the second dimension is the number of baseband signals corresponding to the pulse signals under the irradiation times, and the third dimension is the sampling data of each baseband signal.

[0045] In this way, after obtaining the signal tensor of the baseband signal model based on the aforementioned step S2, a radar signal reconstruction model with the maximum complex correlation entropy as the error function can be established based on the signal tensor. The process is shown in the following step S3.

[0046] S3. Based on the signal tensor, establish a radar signal reconstruction model with maximum complex correlation entropy as the error function.

[0047] In specific applications, before providing the improved radar signal reconstruction model in this embodiment, the definitions of t-SVD decomposition and tubal-rank of tensors are first disclosed, as shown below: For the t-SVD decomposition of a tensor: Assume an arbitrary tensor , which can be decomposed as follows: (6) In the above formula (6), , And it is an orthogonal tensor, is a diagonal tensor; the t-SVD decomposition of a tensor is similar to the SVD decomposition of a matrix; in particular, when When , the t-SVD decomposition result of the tensor is the same as the matrix SVD decomposition result.

[0048] Meanwhile, for the tubal-rank of a tensor: The tubal-rank of a tensor is defined as the tensor after t-SVD transformation The number of non-zero values ​​in , that is: (7) In formula (7), is the rank of each forward face matrix of the tensor.

[0049] Furthermore, to ensure the signal-to-noise ratio of the received echo, the MFPAR will stay in one beam for a certain period of time and transmit multiple beams, namely, the CPI. Therefore, the MFPAR's transmitted signal contains redundant and highly similar information, which ensures that the tensor formed by the UAV's intercepted signal has a low-tubal-rank structure. Therefore, the low-tubal-rank signal reconstruction problem can be defined as: (8) In the above formula (8), represents the reconstructed signal tensor, Representing a tensor tubal-rank, represents the Vandermonde product of two tensors, represents the signal tensor, An indicator tensor representing the signal tensor.

[0050] in, (9) From the above formula (8), we can see that the goal of reconstruction is to minimize the low rank of the tensor; however, directly solving formula (8) is NP-hard. The optimization target is a non-convex function, so the formula needs to be further processed to optimize it; at the same time, from the perspective of tensor decomposition, according to the definition of tensor t-product, a low-rank tensor can be expressed as a special operational product of two smaller tensors, thereby processing the smaller tensor.

[0051] In detail, a tensor Can be decomposed into two tensors and The tensor t product of , and is a tensor tubal rank; thus, using the tensor t product, the aforementioned objective function can be written as: (10) In formula (10), represents the Frobenius norm.

[0052] From the above formula (10), we can see that the above tensor completion optimization algorithm is usually based on The error function of the tensor norm (i.e., the Frobenius norm of the tensor) lacks robustness to outliers. Considering the complex electromagnetic environment, the intercepted signal is usually contaminated by outliers and noise. Therefore, it is necessary to adopt a new error function to replace the traditional Norm of the error function to reduce the influence of outliers.

[0053] Specifically, from the perspective of information theory, the correlation entropy reflects the local nonlinear similarity relationship between two random variables, which is more robust to outliers than the correlation entropy based on Therefore, this embodiment adopts an error function based on the maximum complex correlation entropy to generate a radar signal reconstruction model to reduce the influence of outliers.

[0054] The construction process of the radar signal reconstruction model may be, but is not limited to, steps S31 to S33 as shown below.

[0055] S31. Perform tensor decomposition on the signal tensor to obtain a decomposed tensor, wherein the decomposed tensor includes a first signal sub-tensor and a second signal sub-tensor; in this embodiment, the tensor decomposition has been described above, that is, decomposed into and ; Then, the maximum complex correlation entropy criterion can be introduced to calculate the maximum complex correlation entropy between the decomposition tensor and the original signal tensor, and the process is shown in the following step S32.

[0056] S32. Calculate the maximum complex correlation entropy between the signal tensor and the decomposition tensor.

[0057] In the specific implementation, this embodiment first gives the definition of the maximum complex correlation entropy, namely: Given any two real random variables and , whose joint probability density function (PDF) is given by Given, then and The similarity between them can be expressed by the correlation entropy: (11) In the above formula (11), represents the correlation entropy, represents the mathematical expectation, is the probability density function, A kernel with a width of The kernel function often uses the Gaussian kernel function, and its formula is: (12) Thus, given a sampling process, the sample can be represented as , therefore, using the Gaussian kernel function, and The correlation entropy of can be expressed by the sample mean of its sampling, as shown in the following formula (13).

[0058] (13) In the above formula (13), , which represents the intermediate parameter, Also called empirical correlation entropy.

[0059] At the same time, since the received radar signal is an I / Q data stream after baseband modulation, it is usually represented by complex numbers in mathematics. Therefore, it is necessary to extend the correlation entropy to complex form. Suppose there are two arbitrary complex random variables and ,in, ,and are all real numbers, then the complex correlation entropy is defined as: (14) In the above formula (14), represents the complex Gaussian sum function, Represents the conjugate of a complex number.

[0060] Based on this, the maximum complex correlation entropy between the signal tensor and the decomposition tensor can be calculated through the above formula (14). That is, since the signal tensor has three dimensions i, j, k, the formula (14) becomes , about to The calculation formula is replaced by a signal tensor, and is replaced by the decomposed tensor; so, The calculation formula is: ; Then, the sum and average of formula (14) are transformed into three dimensions i, j, and k, and the maximum complex correlation entropy between the signal tensor and the decomposition tensor can be calculated.

[0061] After obtaining the maximum complex correlation entropy, a radar signal reconstruction model can be constructed, and the process is shown in the following step S33.

[0062] S33. Based on the maximum complex correlation entropy, a radar signal reconstruction model is constructed with the maximum complex correlation entropy as the error function.

[0063] In this embodiment, the complex correlation entropy is used to replace the formula (10) based on The error function of the norm is used as the optimization target, and the maximum complex correlation entropy criterion MCCC can be obtained: (15) Therefore, by introducing the maximum complex correlation entropy, the radar signal reconstruction model can be expressed as: (16) In formula (16), represents the radar signal reconstruction model, Indicates the indicated parameter, represents the first signal subtensor, represents the second signal subtensor, represents the maximum complex correlation entropy, represents the kernel width of the kernel function, represents the intermediate parameters, express The conjugation of .

[0064] in, , where Indicates that the j-th pulse signal in the k-th forward plane in the signal tensor corresponds to the i-th sampled data of the baseband signal. The k-th forward plane is the forward plane formed by the tensor consisting of the sampled data of all baseband signals received by the UAV under the k-th illumination of the phased array radar. and , where A pointer to an entry representing a signal tensor.

[0065] After the radar signal reconstruction model based on the maximum complex correlation entropy is constructed through the aforementioned steps S31 to S33, the model can be solved, and the process is shown in the following steps S4 to S6.

[0066] S4. Using a semi-quadratic optimization algorithm, convert the radar signal reconstruction model into a weighted signal reconstruction model, wherein the weighted signal reconstruction model is a convex model.

[0067] In specific applications, we first verify whether the aforementioned formula (16) is a convex function. That is, considering that the radar signal is mathematically represented in the form of complex numbers, the radar signal reconstruction model is essentially a complex-valued function. Then, since formula (16) does not satisfy the Cauchy–Riemann condition, the standard derivation rule will no longer apply. Based on this, we need to use Wirtinger differential to solve the gradient and Hessian matrix of formula (16).

[0068] At the same time, due to is the indicator tensor, so the convexity of Eq. (16) is only related to Based on this, Performing Wirtinger integration yields: (17) Formula (17) represents the The partial derivative and The partial derivative of .

[0069] Similarly, its complex Hessian matrix is: (18) In formula (18), Indicates inclusion ( ), express The conjugation of .

[0070] It can be seen from the above formula (18) that the complex Hessian matrix is ​​not a positive definite matrix. Therefore, formula (16) is non-convex and needs to be transformed and solved using a corresponding method. Based on this, this embodiment introduces a conjugate function to transform the radar signal reconstruction model, that is, construct a conjugate function; then, the conjugate function is used to perform model conversion processing on the radar signal reconstruction model, so as to obtain the weighted signal reconstruction model after the model conversion processing.

[0071] Specifically, the process of introducing the conjugate function is: First, we introduce a real-valued exponential function ,in, At the same time, according to convex optimization theory, there exists a conjugate function ,in, , and satisfies , where represents the supremum, are variables used for function indication; further, the upper bound of the conjugate function is Therefore, the formula (16) use Substituting and using the conjugate function, we get: (19) in, Then it represents the constructed conjugate function.

[0072] Based on this, by substituting formula (19) into formula (16), the radar signal reconstruction model can be converted into a weighted signal reconstruction model belonging to a convex function, which is expressed as follows: (20) In formula (21), represents the first intermediate tensor, represents the conjugate function, and ,in, In formula (20), it is the first intermediate tensor.

[0073] in, (twenty one).

[0074] In summary, by constructing a conjugate function, the original non-convex optimization problem can be converted into an objective function that can be solved by an alternating optimization algorithm.

[0075] After the non-convex radar signal reconstruction model is converted into a weighted signal reconstruction model that can be solved by the alternating optimization algorithm, the model can be simplified, and then the alternating complex conjugate gradient optimization algorithm can be used to solve the simplified model; wherein, the model simplification process is shown in the following step S5.

[0076] S5. Based on the weighted signal reconstruction model, a complex conjugate gradient signal model is constructed. In this embodiment, for example, but not limited to, the weighted signal reconstruction model may be first simplified to obtain a simplified signal reconstruction model; then, using the properties of the tensor t-product, the simplified signal reconstruction model is equivalently transformed to obtain a complex conjugate gradient signal model after the equivalent transformation.

[0077] Specifically, the model is simplified as follows: rewrite the aforementioned weighted signal reconstruction model and multiply it by a coefficient of 1 / 2. Based on this, the simplified signal reconstruction model can be obtained, as shown in the following formula (22).

[0078] (twenty two) In formula (22), represents the second intermediate tensor, represents the indicator tensor, represents the signal tensor, represents the Vandermonde product, represents the Frobenius norm.

[0079] in, (twenty three) In the above formula (23), Represents the value of the j-th row and i-th column in the k-th forward facet of the second intermediate tensor.

[0080] After completing the model simplification, using the properties of tensor t-product, the optimization problem of formula (22) can be equivalent to: (twenty four) In formula (24), represents the Fourier transform of the k-th forward face in the second intermediate tensor, represents the Fourier transform of the indicated tensor, represents the Fourier transform of the kth forward face in the signal tensor, represents the Fourier transform of the kth forward face in the first signal subtensor, represents the Fourier transform of the kth forward face in the second signal subtensor, and They represent the Fourier transform of all forward faces in the first signal sub-tensor and the Fourier transform of all forward faces in the second signal sub-tensor, respectively.

[0081] At the same time, since each forward face of the first signal sub-tensor and the second signal sub-tensor that constitute the signal tensor is independent, the above formula (24) can be further simplified as follows: (25) The above formula (25) represents the complex conjugate gradient signal model.

[0082] Therefore, through the above formulas (22) to (25), a complex conjugate gradient signal model can be constructed based on the weighted signal reconstruction model; then, the complex conjugate gradient signal model can be solved to obtain a reconstructed signal tensor, so as to generate a reconstructed radar signal based on the reconstructed signal tensor, and the process is shown in the following step S6.

[0083] S6. Using an alternating complex conjugate gradient optimization algorithm, solve the complex conjugate gradient signal model to obtain a reconstructed signal tensor after the solution, and generate a reconstructed radar signal based on the reconstructed signal tensor.

[0084] In this embodiment, it can be seen from the above formula (25) that although it is a non-convex function from a global perspective, if or Fixed, it becomes a convex function, so the alternating optimization strategy can be used and the complex conjugate gradient optimization method can be used to solve it.

[0085] Furthermore, for ease of description, this embodiment replaces the parameters in formula (25) with parameter terms, that is, the complex conjugate gradient signal model includes three parameter terms, namely the first parameter term, the second parameter term and the kernel width, wherein the first parameter term is the Fourier transform term of the forward plane of the first signal subtensor (i.e. ), the second parameter term is the Fourier transform term of the forward surface of the first signal subtensor (i.e. ), and the first signal sub-tensor and the second signal sub-tensor are obtained by performing tensor decomposition on the signal tensor.

[0086] Based on this, this embodiment alternately fixes the first parameter item and the second parameter item to solve the model, and the process may be, but is not limited to, steps S61 to S610 as shown below.

[0087] S61. Obtain the first parameter item and the second parameter item at the nth iteration, wherein when n is 1, the first parameter item and the second parameter item at the nth iteration are initial values.

[0088] After obtaining the first parameter item and the second parameter item at the nth iteration, the kernel width at the nth iteration can be determined, and the process is shown in the following step S62.

[0089] S62 determines the kernel width at the nth iteration; in specific applications, this embodiment adopts an adaptive kernel width selection strategy to improve the performance and convergence speed of the algorithm; specifically, the kernel width at the nth iteration is calculated as follows: (26) In the above formula (26), represents the kernel width at the nth iteration, represents the kernel width control coefficient, represents the lower bound of the kernel width; at the same time, Represents the third intermediate parameter.

[0090] in, , where , represents the first reconstructed sub-signal tensor and the second reconstructed sub-signal tensor obtained by the n-1th iteration, real represents the real part, and imag represents the imaginary part; at the same time, Indicates the value at the 1 / 4 position and the value at the 3 / 4 position in the length of the third intermediate parameter.

[0091] In this way, after calculating the kernel width at the nth iteration, the kernel width, the first parameter, and the second parameter at the nth iteration can be substituted into the complex conjugate gradient signal model to obtain the conjugate model at the nth iteration. The process is shown in the following step S63.

[0092] S63. Substitute the kernel width, the first parameter term, and the second parameter term at the nth iteration into the complex conjugate gradient signal model to obtain a conjugate model at the nth iteration.

[0093] After obtaining the conjugate model at the nth iteration, the model residual of the conjugate model can be calculated so as to determine whether the iteration stop condition is met based on the model residual. The model residual calculation process is shown in the following step S64.

[0094] S64. Calculate the model residual of the conjugate model at the nth iteration. In a specific implementation, the calculation formula for the model residual of the conjugate model at the nth iteration is: (27) In formula (27), represents the residual of the conjugate model at the nth iteration, and The first reconstructed sub-signal tensor and the second reconstructed sub-signal tensor obtained by the n-th iteration are represented in sequence. and ( ) obtained by inverse Fourier transform; It represents the second intermediate tensor at the nth iteration. Its calculation method can be found in the aforementioned formula (23). It is only necessary to replace the first signal sub-tensor and the second signal sub-tensor in formula (23) with the first reconstructed sub-signal tensor and the second reconstructed sub-signal tensor at the nth iteration.

[0095] After the model residual at the nth iteration is calculated, the iteration stopping condition can be determined, and the process is shown in the following step S65.

[0096] S65. Determine whether an iteration stopping condition is met, wherein the iteration stopping condition is that a relative error between the model residual at the nth iteration and the model residual at the (n-1)th iteration is less than a preset threshold.

[0097] In this embodiment, the relative error between model residuals is defined as: ; Among them, when the relative error is greater than or equal to the preset threshold, an iterative solution is required, that is, an alternating solution is performed, and the process is shown in the following steps S66 to S610.

[0098] If not, fix the second parameter term in the conjugate model at the nth iteration, and update the first parameter term in the conjugate model at the nth iteration to obtain the first parameter term at the (n+1)th iteration. In a specific implementation, the first parameter term update process may be, but is not limited to, as shown in the following steps S66a to S66e.

[0099] S66a. After fixing the second parameter term in the conjugate model at the nth iteration, calculate the first partial derivative of the conjugate model at the nth iteration with respect to the first parameter term at the nth iteration; in specific applications, first fix , and then use Wirtinger differentiation to deal with the conjugate model; where, let ,So, about The first partial derivative of is: (28) In formula (28), represents the first partial derivative with respect to the first parameter, It represents the fixed second parameter term in the conjugate model at the nth iteration, represents the gradient parameter, represents the conjugate transpose, where , Represents the Fourier transform of the kth forward facet of the signal tensor.

[0100] In this way, after obtaining the first partial derivative of the conjugate model at the nth iteration with respect to the first parameter term at the nth iteration, the conjugate direction coefficient at the nth iteration can be calculated, and the process is shown in the following step S66b.

[0101] S66b. Obtain a second partial derivative of the conjugate model at the n-1th iteration with respect to the first parameter term at the n-1th iteration, and calculate a conjugate directional coefficient at the nth iteration based on the second partial derivative and the first partial derivative.

[0102] In specific implementation, the calculation formula of the conjugate direction coefficient at the nth iteration is: (29) In the above formula (29), represents the conjugate direction coefficient at the nth iteration, represents the second partial derivative.

[0103] Thus, based on the aforementioned formula (29), after the conjugate direction coefficient at the nth iteration is calculated, the conjugate direction at the current iteration can be calculated in combination with the first partial derivative, as shown in the following step S66c.

[0104] S66c. Based on the first partial derivative and the conjugate direction coefficient, the conjugate direction at the nth iteration is calculated. In a specific implementation, the calculation formula for the conjugate direction at the nth iteration is: (30) In the above formula (30), represents the conjugate direction at the nth iteration, represents the conjugate direction at the n-1th iteration.

[0105] After obtaining the conjugate direction at the nth iteration, the update step length of the first parameter item, that is, the following optimal step length, can be determined. The determination process is shown in the following step S66d.

[0106] S66d. Determine the optimal step size of the first parameter item of the nth iteration.

[0107] In specific implementation, the optimal step length can be obtained by solving the following minimization problem: (30) In formula (30), represents the optimal step size, represents the first parameter item at the nth iteration, Represents the second parameter term at the nth iteration.

[0108] At the same time, using the properties between the Frobenius norm and the matrix trace, let , then the above formula (30) can be transformed into: (31) In formula (31), represents the operation of taking the real part of a complex number, Represents the operation of taking the trace of a matrix.

[0109] Thus, after calculating the update step size of the first parameter term based on formula (31), the first parameter term can be updated in combination with the aforementioned conjugate direction to obtain the first parameter term at the (n+1)th iteration. The process is shown in the following step S66e.

[0110] S66e. Using the conjugate direction and the optimal step size at the nth iteration, update the first parameter item at the nth iteration to obtain the first parameter item at the (n+1)th iteration.

[0111] In a specific implementation, the update formula of the first parameter item at the nth iteration is: (32) In the above formula (32), Represents the first parameter item at the n+1th iteration.

[0112] Therefore, through the aforementioned steps S66a to S66e, the update of the first parameter item can be completed, and then the first parameter item at the n+1th iteration can be used to update the model, so that the first parameter item in the updated model can be fixed to update the second parameter item at the nth iteration. The process is shown in the following steps S67 and S68.

[0113] S67. Using the first parameter item at the n+1th iteration, the conjugate model is updated to obtain an updated conjugate model. In this embodiment, this is equivalent to updating the first parameter item at the nth iteration in the conjugate model at the nth iteration to the first parameter item at the n+1th iteration, while the second parameter item in the conjugate model at the nth iteration remains unchanged. At this time, the updated conjugate model can be obtained. Thereafter, the first parameter item in the updated conjugate model can be fixed, and the second parameter item can be updated. The process is shown in the following step S68.

[0114] S68. Fix the first parameter term in the updated conjugate model, and update the second parameter term in the updated conjugate model to obtain the second parameter term at the n+1th iteration; in specific implementation, the updating process of the second parameter term is the same as that of the first parameter term, and both are to first calculate the partial derivative of the conjugate model with respect to the second parameter term, and then obtain the partial derivative of the model with respect to the second parameter term at the previous iteration, and based on the two, calculate the conjugate direction coefficient of the second parameter term at the nth iteration; then, calculate its conjugate direction at the nth iteration based on the partial derivative of the model with respect to the second parameter term and the conjugate direction coefficient of the second parameter term at the nth iteration; then, calculate the optimal step size of the second parameter term; finally, based on the optimal step size and conjugate direction of the second parameter term, obtain the second parameter term at the n+1th iteration; wherein, the aforementioned updating process can be referred to the aforementioned steps S66a to S66e, which will not be repeated here.

[0115] After completing the update of the first parameter term and the second parameter term at the nth iteration, they can be substituted back into the complex conjugate gradient signal model, and then the model residual is calculated to obtain the model residual at the next iteration; then, it is determined again whether the iteration stop condition is met, and the iteration can be terminated until the iteration stop condition is met; wherein, the iterative solution process is shown in the following step S69.

[0116] S69. Increment n by 1 and re-obtain the first parameter term and the second parameter term at the nth iteration until the iteration stopping condition is met, thereby obtaining the optimal Fourier transform term of the forward surface of the first signal sub-tensor and the optimal Fourier transform term of the forward surface of the second signal sub-tensor.

[0117] Through the aforementioned steps S61 to S69, the complex conjugate gradient signal model is solved, and after obtaining the optimal Fourier transform term of the forward plane of the first signal sub-tensor and the optimal Fourier transform term of the forward plane of the second signal sub-tensor, an inverse Fourier transform is performed on the two, and a tensor t-product is performed to obtain the reconstructed signal tensor. The process is shown in the following step S610.

[0118] S610. Perform inverse Fourier transform processing and tensor t-product processing on the optimal Fourier transform terms of the forward planes of the first signal sub-tensor and the second signal sub-tensor in sequence, so as to obtain the reconstructed signal tensor after the tensor t-product processing.

[0119] Thus, through the aforementioned steps S61 to S610 , a reconstructed signal tensor can be obtained, and then, based on the reconstructed signal tensor, a reconstructed radar signal can be generated.

[0120] Also, see Figures 2 to 4 As shown, this embodiment provides a schematic diagram of the original signal, a schematic diagram of the signal contaminated by an outlier, and a schematic diagram of the radar signal reconstructed using the method provided by this embodiment. By comparison Figure 2 , Figure 3 and Figure 4 It can be seen that the radar signal reconstructed by this embodiment has removed the influence of outliers and is highly consistent with the original signal; therefore, it is proved that the method provided by this embodiment can achieve the reconstruction and recovery of radar signals contaminated by outliers.

[0121] Therefore, through the radar signal reconstruction method based on maximum complex correlation entropy described in detail in the aforementioned steps S1 to S6, the present invention realizes the reconstruction and recovery of radar signals contaminated by outliers, solves the current problem of poor performance of radar signal reconstruction caused by the influence of outliers, and improves the signal processing capability of the system in complex electromagnetic environments.

[0122] like Figure 5As shown, the second aspect of this embodiment provides a hardware device for implementing the radar signal reconstruction method based on maximum complex correlation entropy described in the first aspect of the embodiment, including: The baseband signal generation unit is used to establish a baseband signal model of the radar signal received by the UAV.

[0123] The tensor unit is used to perform sampling processing on the baseband signal model to obtain sampling data, and use the sampling data to construct a signal tensor corresponding to the baseband signal model.

[0124] The signal reconstruction unit is used to establish a radar signal reconstruction model with maximum complex correlation entropy as an error function based on the signal tensor.

[0125] A signal reconstruction unit is used to convert the radar signal reconstruction model into a weighted signal reconstruction model by using a semi-quadratic optimization algorithm, wherein the weighted signal reconstruction model is a convex model.

[0126] The signal reconstruction unit is used to construct a complex conjugate gradient signal model based on the weighted signal reconstruction model.

[0127] The signal reconstruction unit is further configured to solve the complex conjugate gradient signal model using an alternating complex conjugate gradient optimization algorithm to obtain a reconstructed signal tensor after the solution, and generate a reconstructed radar signal based on the reconstructed signal tensor.

[0128] The working process, working details and technical effects of the device provided in this embodiment can be found in the first aspect of the embodiment and will not be described in detail here.

[0129] A third aspect of this embodiment provides another radar signal reconstruction device based on maximum complex correlation entropy. Taking the device as an electronic device as an example, the device includes: a memory, a processor, and a transceiver that are communicatively connected in sequence, wherein the memory is used to store computer programs, the transceiver is used to send and receive messages, and the processor is used to read the computer program and execute the radar signal reconstruction method based on maximum complex correlation entropy as described in the first aspect of the embodiment.

[0130] The working process, working details and technical effects of the electronic device provided in this embodiment can be found in the first aspect of the embodiment and will not be described in detail here.

[0131] A fourth aspect of this embodiment provides a storage medium storing instructions for the radar signal reconstruction method based on maximum complex correlation entropy as described in the first aspect of the embodiment, that is, the storage medium stores instructions that, when executed on a computer, execute the radar signal reconstruction method based on maximum complex correlation entropy as described in the first aspect of the embodiment.

[0132] The storage medium refers to a carrier for storing data, which may include but is not limited to a floppy disk, an optical disk, a hard disk, a flash memory, a USB flash drive and / or a memory stick, and the computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device.

[0133] The working process, working details and technical effects of the storage medium provided in this embodiment can be found in the first aspect of the embodiment and will not be described in detail here.

[0134] A fifth aspect of this embodiment provides a computer program product comprising instructions. When the instructions are executed on a computer, the computer is caused to perform the radar signal reconstruction method based on maximum complex correlation entropy as described in the first aspect of the embodiment. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device.

[0135] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A radar signal reconstruction method based on maximum complex correlation entropy, characterized in that: include: Establish a baseband signal model for the radar signal received by the UAV; Sampling the baseband signal model to obtain sampled data, and constructing a signal tensor corresponding to the baseband signal model using the sampled data; Based on the signal tensor, a radar signal reconstruction model is established with maximum complex correlation entropy as an error function; Using a semi-quadratic optimization algorithm, the radar signal reconstruction model is converted into a weighted signal reconstruction model, wherein the weighted signal reconstruction model is a convex model; Based on the weighted signal reconstruction model, a complex conjugate gradient signal model is constructed; The complex conjugate gradient signal model is solved by using an alternating complex conjugate gradient optimization algorithm to obtain a reconstructed signal tensor after the solution, and a reconstructed radar signal is generated based on the reconstructed signal tensor.

2. The method according to claim 1, characterized in that The radar signal received by the UAV contains multiple signal sequences, where each signal sequence contains several baseband signals. The total number of signal sequences is equal to the number of exposures of the phased array radar scanning the UAV. The total number of baseband signals in any signal sequence is equal to the number of pulse signals emitted by the phased array radar to each beam under one exposure, and one baseband signal corresponds to one pulse signal emitted by the phased array radar. Among them, the baseband signal model of the radar signal received by the UAV is established, including: Generate a baseband signal corresponding to each pulse signal emitted by the phased array radar received by the UAV under each illumination, and use the baseband signal corresponding to each pulse signal under each illumination to form the baseband signal model; Among them, under the illumination of the phased array radar, the baseband signal corresponding to the mth pulse signal received by the drone is: Where, represents the baseband signal corresponding to the mth pulse signal under one illumination, represents the mth pulse signal emitted by the phased array radar, represents the delay of the mth pulse signal, represents the center frequency, represents the baseband noise signal, Indicates the signal amplification factor of the receiver on the drone, is an imaginary unit, where ,and Indicates the number of pulse signals emitted to each wave velocity under one irradiation.

3. The method according to claim 2, characterized in that Sampling the baseband signal model to obtain sampled data, and constructing a signal tensor corresponding to the baseband signal model using the sampled data, including: Performing Nyquist sampling on each baseband signal in the baseband signal model to obtain sampling data of each baseband signal; Based on the sampling data of each baseband signal, and according to the number of irradiation times and slow time sampling points of the phased array radar, the signal tensor is constructed, wherein the signal tensor , represents the number of sampled data of each baseband signal, the number of slow-time sampling points, and the number of irradiations of the phased array radar in sequence. The number of slow-time sampling points is the number of pulse signals emitted by the phased array radar to each wave velocity under one irradiation. represents the kth irradiation The pulse signal corresponds to the i-th sampling data in the baseband signal, represents the complex field, ,and A pointer to an entry representing a signal tensor.

4. The method according to claim 1, wherein Based on the signal tensor, a radar signal reconstruction model is established with maximum complex correlation entropy as an error function, including: Performing tensor decomposition on the signal tensor to obtain a decomposition tensor, wherein the decomposition tensor includes a first signal sub-tensor and a second signal sub-tensor; Calculating the maximum complex correlation entropy between the signal tensor and the decomposition tensor; Based on the maximum complex correlation entropy, a radar signal reconstruction model is constructed with the maximum complex correlation entropy as an error function.

5. The method according to claim 4, characterized in that The signal tensor is constructed by sampling each baseband signal in the baseband signal model and using the sampled data. Each baseband signal in the baseband signal model belongs to a different signal sequence. The total number of signal sequences is the number of irradiations of the phased array radar of the scanning drone. The dimension of the signal tensor is , It represents the number of sampled data of each baseband signal, the number of pulse signals transmitted by the phased array radar each time it is illuminated, and the number of illuminations, and one pulse signal corresponds to one baseband signal; Accordingly, based on the maximum complex correlation entropy, a radar signal reconstruction model is constructed with the maximum complex correlation entropy as the error function, which includes: According to the following formula, the radar signal reconstruction model is constructed; Where, represents the radar signal reconstruction model, Indicates the indicated parameter, represents the first signal subtensor, represents the second signal subtensor, represents the maximum complex correlation entropy, represents the kernel width of the kernel function, represents the intermediate parameters, express conjugation of; in, , where Indicates that the j-th pulse signal in the k-th forward plane in the signal tensor corresponds to the i-th sampled data of the baseband signal. The k-th forward plane is the forward plane formed by the tensor consisting of the sampled data of all baseband signals received by the UAV under the k-th illumination of the phased array radar. and , where A pointer to an entry representing a signal tensor.

6. The method according to claim 5, characterized in that The radar signal reconstruction model is converted into a weighted signal reconstruction model using a semi-quadratic optimization algorithm, including: Construct the conjugate function; The conjugate function is used to perform model conversion processing on the radar signal reconstruction model, so as to obtain the weighted signal reconstruction model after the model conversion processing.

7. The method according to claim 6, characterized in that The conjugate function is used to perform a model conversion process on the radar signal reconstruction model to obtain the weighted signal reconstruction model after the model conversion process, including: According to the following formula, the radar signal reconstruction model is converted to obtain a weighted signal reconstruction model; Where, represents the first intermediate tensor, represents the conjugate function, and ; in, .

8. The method according to claim 7, characterized in that Based on the weighted signal reconstruction model, a complex conjugate gradient signal model is constructed, including: Performing model simplification processing on the weighted signal reconstruction model to obtain a simplified signal reconstruction model; Performing equivalent transformation on the simplified signal reconstruction model to obtain a complex conjugate gradient signal model after the equivalent transformation; Among them, the simplified signal reconstruction model is: Where, represents the second intermediate tensor, represents the indicator tensor, represents the signal tensor, represents the Vandermonde product, represents the Frobenius norm; and , where Represents the value of the jth row and ith column in the kth forward face in the second intermediate tensor; Correspondingly, the complex conjugate gradient signal model is: Where, represents the Fourier transform of the k-th forward face in the second intermediate tensor, represents the Fourier transform of the indicated tensor, represents the Fourier transform of the kth forward face in the signal tensor, represents the Fourier transform of the kth forward face in the first signal subtensor, represents the Fourier transform of the kth forward facet in the second signal subtensor.

9. The method according to claim 1, characterized in that The complex conjugate gradient signal model includes a first parameter term, a second parameter term, and a kernel width, wherein the first parameter term is a Fourier transform term of a forward plane of the first signal subtensor, the second parameter term is a Fourier transform term of a forward plane of the first signal subtensor, and the first signal subtensor and the second signal subtensor are obtained by performing tensor decomposition on the signal tensor; The alternating complex conjugate gradient optimization algorithm is used to solve the complex conjugate gradient signal model, so as to obtain a reconstructed signal tensor after solving the problem, including: Obtaining the first parameter item and the second parameter item at the nth iteration, wherein when n is 1, the first parameter item and the second parameter item at the nth iteration are initial values; Determine the kernel width at the nth iteration; Substituting the kernel width, the first parameter term, and the second parameter term at the nth iteration into the complex conjugate gradient signal model to obtain a conjugate model at the nth iteration; Calculate the model residual of the conjugate model at the nth iteration; Determine whether an iteration stopping condition is met, wherein the iteration stopping condition is that the relative error between the model residual at the nth iteration and the model residual at the (n-1)th iteration is less than a preset threshold; If not, the second parameter term in the conjugate model at the nth iteration is fixed, and the first parameter term in the conjugate model at the nth iteration is updated to obtain the first parameter term at the (n+1)th iteration; Using the first parameter term at the (n+1)th iteration, the conjugate model is updated to obtain an updated conjugate model; Fixing the first parameter term in the updated conjugate model, and updating the second parameter term in the updated conjugate model to obtain the second parameter term at the (n+1)th iteration; Increment n by 1, and re-obtain the first parameter term and the second parameter term at the nth iteration until the iteration stop condition is met, thereby obtaining the optimal Fourier transform term of the forward surface of the first signal subtensor and the optimal Fourier transform term of the forward surface of the second signal subtensor; The optimal Fourier transform items of the forward plane of the first signal sub-tensor and the second signal sub-tensor are sequentially subjected to inverse Fourier transform processing and tensor t-product processing, so as to obtain the reconstructed signal tensor after the tensor t-product processing.

10. The method according to claim 9, characterized in that The first parameter term in the conjugate model at the nth iteration is updated to obtain the first parameter term at the (n+1)th iteration, including: After fixing the second parameter term in the conjugate model at the nth iteration, calculating the first partial derivative of the conjugate model at the nth iteration with respect to the first parameter term at the nth iteration; Obtaining a second partial derivative of the conjugate model at the n-1th iteration with respect to the first parameter term at the n-1th iteration, and calculating a conjugate directional coefficient at the nth iteration based on the second partial derivative and the first partial derivative; Calculating the conjugate direction at the nth iteration based on the first partial derivative and the conjugate direction coefficient; Determine the optimal step size of the first parameter term of the nth iteration; The first parameter item at the nth iteration is updated using the conjugate direction at the nth iteration and the optimal step size to obtain the first parameter item at the (n+1)th iteration.

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