Design method of MIMO radar amplitude-phase response optimization waveform

Abstract

The invention relates to the technical field of radars, in particular to an MIMO radar amplitude-phase response optimization waveform design method, which comprises the steps of obtaining a waveform coding matrix based on waveform codes of a plurality of transmitting channels of an initialized MIMO radar; constructing a comprehensive optimization objective function based on the waveform coding matrix; based on the comprehensive optimization objective function, performing iterative traversal optimization on each waveform code of the plurality of transmitting channels, and gradually updating each waveform code in each iteration so as to reduce the function value of the comprehensive optimization objective function; and when the optimization process meets a preset convergence condition, stopping iteration, and determining the current optimized waveform code as the transmitted waveform of the MIMO radar. According to the method, the high-resolution spectrum estimation performance and the anti-interference capability of the MIMO radar on the target can be remarkably improved.

Description

Technical Field

[0001] The embodiments of this application relate to the field of radar technology, and in particular to a design method for optimizing the amplitude and phase response waveform of MIMO radar. Background Technology

[0002] Multiple-input multiple-output (MIMO) radar, as a new generation of array radar technology with highly customizable transmitter signals, allows its transmitting elements to transmit waveforms relatively independently. By transmitting orthogonal signals and operating in multiple-input multiple-output mode, MIMO radar can obtain a larger virtual aperture to improve angular resolution, thereby achieving high-resolution target estimation performance and possessing stronger anti-jamming and low-interception characteristics. Simultaneously, MIMO radar is backward compatible with existing phased array radar systems, transmitting fully coherent signals.

[0003] However, due to the constant mode constraint of radar signals, the orthogonal waveforms used by MIMO radars in the same frequency band have poor performance, and the high sidelobes generated by their autocorrelation and cross-correlation functions will seriously affect the accuracy of target estimation.

[0004] Therefore, how to design high-performance MIMO radar waveforms to improve the high-resolution spectral estimation performance and anti-jamming capability of MIMO radar for targets is a technical problem that urgently needs to be solved. Summary of the Invention

[0005] To address the aforementioned technical problems, embodiments of this application propose a design method for optimized waveforms of MIMO radar amplitude and phase response. This method aims to overcome the defect of reduced target estimation accuracy caused by high correlation sidelobes in existing MIMO radar orthogonal waveforms. By optimizing the sidelobe amplitude in traditional waveform design, the method introduces optimization of the correlation phase response characteristics between waveforms. By jointly optimizing the amplitude and phase response of the waveforms, the waveform performance approaches that of ideal orthogonal waveforms, thereby significantly improving the high-resolution spectral estimation performance and anti-jamming capability of MIMO radar for targets.

[0006] To achieve the above objectives, embodiments of this application propose a method for designing an optimized waveform for the amplitude and phase response of a MIMO radar, the method comprising: Based on the waveform encoding of multiple transmission channels of the MIMO radar after initialization, a waveform encoding matrix is ​​obtained; Based on the waveform coding matrix, a comprehensive optimization objective function is constructed; wherein, the comprehensive optimization objective function includes a first term for optimizing the amplitude response of waveform-related sidelobes and a second term for optimizing the similarity of waveform-related sidelobe phase responses; Based on the comprehensive optimization objective function, the waveform codes of multiple transmission channels are iteratively optimized. In each iteration, the waveform codes are gradually updated to reduce the function value of the comprehensive optimization objective function. When the optimization process meets the preset convergence condition, the iteration stops, and the current optimized waveform is encoded and determined as the transmission waveform of the MIMO radar.

[0007] To achieve the above objectives, embodiments of this application also propose a design system for optimizing the amplitude and phase response waveform of a MIMO radar, the system comprising: The matrix determination module is used to obtain the waveform encoding matrix based on the waveform encoding of multiple transmission channels of the MIMO radar after initialization. The function construction module is used to construct a comprehensive optimization objective function based on the waveform encoding matrix; wherein, the comprehensive optimization objective function includes a first term for optimizing the amplitude response of the waveform-related sidelobes and a second term for optimizing the similarity of the phase response of the waveform-related sidelobes; The iterative optimization module is used to iteratively optimize the waveform codes of multiple transmission channels based on the comprehensive optimization objective function. In each iteration, the waveform codes are gradually updated to reduce the function value of the comprehensive optimization objective function. The waveform determination module is used to stop the iteration when the optimization process meets the preset convergence condition, and to encode and determine the current optimized waveform as the transmission waveform of the MIMO radar.

[0008] To achieve the above objectives, embodiments of this application also propose an electronic device, including a processor and a memory, wherein the memory stores instructions executable by the processor, and the processor is configured to execute the instructions such that the electronic device can implement a design method for optimizing the amplitude and phase response waveform of a MIMO radar as described above.

[0009] To achieve the above objectives, embodiments of this application also propose a computer-readable storage medium storing a computer program that, when executed by a processor, enables the implementation of a design method for optimizing the amplitude and phase response waveform of a MIMO radar as described above.

[0010] This application proposes a method for designing waveforms to optimize the amplitude and phase response of a MIMO radar. Based on the waveform encoding of multiple transmission channels of the initialized MIMO radar, a waveform encoding matrix is ​​obtained. Based on the waveform encoding matrix, a comprehensive optimization objective function is constructed. This objective function includes a first term for optimizing the amplitude response of the waveform-related sidelobes and a second term for optimizing the similarity of the phase response of the waveform-related sidelobes. Based on the comprehensive optimization objective function, the waveform encodings of each transmission channel are iteratively optimized. In each iteration, the waveform encodings are gradually updated to reduce the function value of the comprehensive optimization objective function. When the optimization process meets a preset convergence condition, the iteration stops, and the currently optimized waveform encoding is determined as the transmitted waveform of the MIMO radar. This scheme, by introducing optimization of the correlation phase response characteristics between waveforms on the basis of traditional waveform design optimization of sidelobe amplitude, and by jointly optimizing the amplitude and phase response of the waveforms, makes the waveform performance approach that of an ideal orthogonal waveform. This overcomes the technical problem of decreased target estimation accuracy caused by high correlation sidelobes in existing MIMO radar orthogonal waveforms, thereby significantly improving the high-resolution spectrum estimation performance and anti-jamming capability of the MIMO radar.

[0011] Optionally, based on the waveform encoding matrix, a comprehensive optimization objective function is constructed, including: obtaining an integral sidelobe scaling function characterizing the amplitude level of the correlated sidelobe based on the covariance matrix of the waveform encoding matrix under different time delays; obtaining a scaling function characterizing the similarity of the correlated phase response based on the correlation matrix of the waveform encoding matrix under different time delays; and obtaining the comprehensive optimization objective function based on the integral sidelobe scaling function characterizing the amplitude level of the correlated sidelobe and the scaling function characterizing the similarity of the correlated phase response.

[0012] Optionally, based on the correlation matrices of the waveform encoding matrix at different time delays, a scaling function characterizing the similarity of the correlated phase responses is obtained, including: calculating the correlation matrix at each time delay based on the waveform encoding matrix; extracting the phase of each element from the correlation matrix to construct a phase response matrix; extracting the autocorrelation phase response vector and the cross-correlation phase response vector from the phase response matrix; calculating the autocorrelation phase response similarity term based on the autocorrelation phase response vector, and simultaneously calculating the cross-correlation phase response similarity term based on the cross-correlation phase response vector; and performing a weighted summation of the autocorrelation phase response similarity term and the cross-correlation phase response similarity term to obtain the scaling function characterizing the similarity of the correlated phase responses.

[0013] Optionally, based on the covariance matrix of the waveform encoding matrix under different time delays, an integral sidelobe scaling function characterizing the amplitude level of the relevant sidelobe is obtained, including: calculating the covariance matrix under different time delays based on the waveform encoding matrix; and obtaining the integral sidelobe scaling function by summing the difference norms of the covariance matrix and the ideal diagonal matrix.

[0014] Optionally, based on the comprehensive optimization objective function, the waveform codes of multiple transmission channels are iteratively optimized. In each iteration, each waveform code is gradually updated to reduce the function value of the comprehensive optimization objective function. This includes: using the coordinate descent method for iterative optimization, and fixing all codes in the waveform coding matrix except for one specific code in each iteration; in the current iteration, by adjusting the value of the specific code and calculating the current function value of the comprehensive optimization objective function, the code value at which the function value of the comprehensive optimization objective function is minimized is obtained, and the specific code is updated based on this code value; traversing and updating each code in the waveform coding matrix to complete the current iteration.

[0015] Optionally, the objective function can be comprehensively optimized. The expression is: ; in, , and Represents a weighting coefficient, a positive real number used to balance the importance of different optimization terms in the objective function; This represents the integral sidelobe level scaling function. This represents the scaling function used to characterize the similarity of related phase responses; Indicates a delay index; This indicates the number of phase codes for each transmitted waveform; This indicates the number of waveforms, i.e., the number of transmission channels in a MIMO radar system; express An identity matrix of 3D; Represents the unit impulse function, and when hour ,otherwise ; Indicates time delay The covariance matrix at the location; Indicates delay The autocorrelation phase response vector at the location; Represents a constant matrix; Indicates time delay Place, No. The cross-correlation phase response vectors of the waveforms; The optimization problem of the comprehensive optimization objective function is expressed as follows: ; in, Indicates the first The first waveform One code, This indicates a constant modulus constraint on the waveform.

[0016] Optionally, the preset convergence condition is that the norm of the difference between the waveform encoding matrices obtained in two adjacent iterations is less than a preset threshold. That is, satisfying: ; in, and They represent the first Second and third The waveform encoding matrix after each iteration. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies of this application will be briefly introduced below. Obviously, the following drawings are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. The drawings described herein are only used to explain this application and are not intended to limit this application.

[0018] Figure 1 This is a flowchart of a method for designing an optimized waveform for the amplitude and phase response of a MIMO radar, provided in one embodiment of this application. Figure 2 This is a schematic diagram comparing the correlation phase response angle difference between a traditional orthogonal waveform and a phase response optimized waveform provided in one embodiment of this application; Figure 3 This is a schematic diagram of the correlated phase response angle difference of a phase response consistent waveform provided in one embodiment of this application; Figure 4 This is a schematic diagram of the target Capon spectrum estimation result when using a traditional orthogonal waveform, provided in one embodiment of this application; Figure 5 This is a schematic diagram of the target Capon spectrum estimation result when using amplitude and phase response to optimize the waveform, provided in one embodiment of this application; Figure 6 This is an example of an embodiment of the present application showing the output signal-to-interference-plus-noise ratio curves of a MIMO radar resisting main lobe deception interference under different waveform conditions; Figure 7 This is a schematic diagram of the structure of a design system for optimizing the amplitude and phase response waveform of a MIMO radar, provided in another embodiment of this application; Figure 8 This is a schematic diagram of the structure of an electronic device provided in another embodiment of this application. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. Those skilled in the art will understand that many technical details have been presented in the embodiments of this application to facilitate better understanding. However, the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of this application. The following embodiments can be combined with and referenced by each other without contradiction.

[0020] Multiple-input multiple-output (MIMO) radar, as a new generation of array radar technology with highly customizable transmitter signals, allows its transmitting elements to transmit waveforms relatively independently. By transmitting orthogonal signals and operating in multiple-input multiple-output mode, MIMO radar can obtain a larger virtual aperture to improve angular resolution, thereby achieving high-resolution target estimation performance and possessing stronger anti-jamming and low-interception characteristics. Simultaneously, MIMO radar is backward compatible with existing phased array radar systems, transmitting fully coherent signals.

[0021] However, due to the constant mode constraint of radar signals, the orthogonal waveforms used by MIMO radars in the same frequency band have poor performance, and the high sidelobes generated by their autocorrelation and cross-correlation functions will seriously affect the accuracy of target estimation.

[0022] Therefore, how to design high-performance MIMO radar waveforms to improve the high-resolution spectral estimation performance and anti-jamming capability of MIMO radar for targets is a technical problem that urgently needs to be solved.

[0023] In view of this, embodiments of this application provide a design method for optimizing the amplitude and phase response waveform of MIMO radar, which aims to overcome the defect of reduced target estimation accuracy caused by high correlation sidelobes in existing MIMO radar orthogonal waveforms. By optimizing the sidelobe amplitude in traditional waveform design, the method introduces optimization of the correlation phase response characteristics between waveforms. By jointly optimizing the amplitude and phase response of the waveform, the waveform performance is made close to the ideal orthogonal waveform, thereby significantly improving the high-resolution spectrum estimation performance and anti-jamming capability of MIMO radar for targets.

[0024] Specifically, the embodiments of this application provide a method that proposes the concept of waveform pulse compression phase response optimization in radar waveform design. The waveform phase response optimization is based on the traditional orthogonal waveform design, which considers minimizing the amplitude of autocorrelation and cross-correlation sidelobes. It focuses on optimizing the characteristics of the correlation phase response between different waveforms to reduce the influence of autocorrelation and cross-correlation sidelobe components in the receiver data in conventional orthogonal MIMO waveform design, thereby improving the high-resolution spectrum estimation performance of MIMO radar targets.

[0025] One embodiment of this application proposes a design method for optimizing the amplitude and phase response waveform of MIMO radar, applied to an electronic device, wherein the electronic device can be a terminal or a server. This embodiment and the following embodiments will use a server as an example for description. The implementation details of the design method for optimizing the amplitude and phase response waveform of MIMO radar proposed in this embodiment will be described in detail below. The following implementation details are provided for ease of understanding and are not necessary for implementing this solution.

[0026] The core of the method provided in the embodiments of this application lies in introducing optimization constraints on the consistency of autocorrelation and cross-correlation sidelobe phase responses, based on the traditional method of only optimizing the amplitude of waveform-related sidelobes. By constructing a comprehensive amplitude and phase response optimization objective function and solving it using an iterative algorithm, an orthogonal waveform with low sidelobe amplitude and consistent phase response characteristics is designed to improve the high-resolution spectral estimation and anti-jamming performance of MIMO radar.

[0027] The specific process of the MIMO radar amplitude and phase response optimization waveform design method proposed in this embodiment can be described as follows: Figure 1 As shown, it includes: Step 101: Based on the waveform encoding of multiple transmission channels of the initialized MIMO radar, obtain the waveform encoding matrix.

[0028] For example, the number of transmission channels in a MIMO radar (i.e., a MIMO radar system) can represent the number of waveforms.

[0029] For example, the number of transmission channels of the MIMO radar can first be determined as follows: and the phase encoding length of each transmitted waveform. Initialize the iteration counter. Subsequently, for The waveforms of each transmission channel generate the initial phase code.

[0030] For example, random phase coding can be used as the initialization method, that is, each coded phase is... The data is generated uniformly and randomly within the interval. Let the i-th... The waveform encoding (i.e., the encoded waveform to be optimized) for each transmission channel is as follows: ; in, For the first A vector expression for a coded waveform to be optimized, where the elements are phase codes; Indicates the first The first waveform The phase of each symbol; All The coded waveform vectors are arranged column-wise to form a waveform coding matrix. Specifically, it is expressed as follows: ; It is understandable that this waveform encoding matrix This can serve as the starting point for subsequent optimization processes. In practical implementation, the number of transmission channels... and the phase encoding length of each transmitted waveform It can be configured according to system requirements; for example, , .

[0031] Step 102: Construct a comprehensive optimization objective function based on the waveform encoding matrix.

[0032] The comprehensive optimization objective function includes a first term for optimizing the amplitude response of waveform-related sidelobes and a second term for optimizing the similarity of waveform-related sidelobe phase responses.

[0033] Understandably, by constructing a comprehensive optimization objective function that can simultaneously measure the similarity of waveform correlation sidelobe amplitude level and phase response, and then using it as a guide for the subsequent optimization process, the smaller the value, the closer the waveform performance is to the ideal fuzzy function.

[0034] For example, the second term for optimizing the waveform correlation sidelobe phase response similarity may include an autocorrelation phase response similarity term and a cross-correlation phase response similarity term.

[0035] Specifically, the first term used to optimize the waveform-correlated sidelobe amplitude response can be used as an integral sidelobe scaling function characterizing the amplitude level of the correlated sidelobes. The second term used to optimize the similarity of the waveform-correlated sidelobe phase response can be used as a scaling function characterizing the similarity of the correlated phase response.

[0036] In one possible embodiment, step 102 includes: obtaining an integral sidelobe scaling function characterizing the amplitude level of the correlated sidelobe based on the covariance matrix of the waveform encoding matrix under different time delays; obtaining a scaling function characterizing the similarity of the correlated phase response based on the correlation matrix of the waveform encoding matrix under different time delays; and obtaining a comprehensive optimization objective function based on the integral sidelobe scaling function characterizing the amplitude level of the correlated sidelobe and the scaling function characterizing the similarity of the correlated phase response.

[0037] In one possible embodiment, an integral sidelobe scaling function characterizing the amplitude level of the relevant sidelobe is obtained based on the covariance matrix of the waveform encoding matrix under different time delays, including: calculating the covariance matrix under different time delays based on the waveform encoding matrix; and obtaining the integral sidelobe scaling function by summing the difference norm between the covariance matrix and the ideal diagonal matrix.

[0038] In one possible embodiment, a scaling function characterizing the similarity of correlated phase responses is obtained based on the correlation matrices of the waveform encoding matrix at different time delays. This includes: calculating the correlation matrix at each time delay based on the waveform encoding matrix; extracting the phase of each element from the correlation matrix to construct a phase response matrix; extracting autocorrelation phase response vectors and cross-correlation phase response vectors from the phase response matrix; calculating an autocorrelation phase response similarity term based on the autocorrelation phase response vectors, and simultaneously calculating a cross-correlation phase response similarity term based on the cross-correlation phase response vectors; and performing a weighted summation of the autocorrelation phase response similarity term and the cross-correlation phase response similarity term to obtain the scaling function characterizing the similarity of correlated phase responses.

[0039] For example, to comprehensively optimize the objective function It can be composed of a weighted sum of three parts: The first term is the integral sidelobe level term (ISL), which is the integral sidelobe scaling function that characterizes the amplitude level of the correlated sidelobe and is used to optimize the amplitude response of the correlated sidelobe of the waveform.

[0040] This project aims to suppress all latency. The total energy of the side lobes of the autocorrelation and crosscorrelation.

[0041] First, calculate the time delay. covariance matrix at , ; in, The displacement matrix can be represented as follows: ; in, Represent a A matrix of all zeros; Represent a The identity matrix; The ISL term is defined as the sum of squares of the Frobenius norm of all non-zero time delay covariance matrices: ; in, express An identity matrix of 3D; Represents the unit impulse function, and when hour ,otherwise ; Indicates time delay The covariance matrix at that location.

[0042] The unit impact function can be expressed as follows: ; It is understandable that the better the orthogonality between waveforms, the lower the sidelobe amplitude.

[0043] The second term is the autocorrelation phase response similarity term.

[0044] Understandably, the autocorrelation phase response similarity term aims to make the autocorrelation sidelobes of different waveforms (i.e., main diagonal element , The phase response of the phase response should be as consistent as possible.

[0045] Take the covariance matrix The phases of the elements in the matrix form a matrix called the correlation delay. Phase response matrix at It can be represented as follows: ; in, for phase, The elements on the main diagonal are the phase terms of the autocorrelation function, and the other terms are the phase terms of the cross-correlation function. The elements on the main diagonal are constructed into a vector, defined as the autocorrelation phase response vector, which can be represented as follows: ; Therefore, through a fixed difference matrix Acting on Construct the target item: The autocorrelation phase response similarity term, i.e., the objective function for autocorrelation phase response similarity, can be expressed as: ; in, It is a constant matrix used to calculate vectors. The pairwise differences between all elements in the set can be represented as follows: ; in, It is the first A unit column vector with each term being 1. The operation represents the transformation of the autocorrelation phase response vector. Combine all elements in pairs and subtract them, then construct a vector from all the resulting differences.

[0046] Understandably, the smaller this value, the more similar the autocorrelation sidelobe phases of all waveforms become under the same time delay. For example... Figure 2 As shown, Figure 2 The angle difference between the phase responses of traditional orthogonal waveforms and waveforms based on phase response similarity constraints is shown. Because the design of traditional waveforms does not consider phase response optimization, the phase responses between different waveforms are random and chaotic, with the angle difference between the phase responses being basically uniformly distributed between -180° and 180°. However, Figure 3 This indicates a waveform with consistent phase response; the phase responses of its different waveforms are almost identical, and the corresponding phase response angle differences are basically distributed around 0°.

[0047] The third term is the cross-correlation phase response similarity term.

[0048] Understandably, the cross-correlation phase response similarity term aims to minimize the cross-correlation sidelobes (i.e., ...) generated by the same waveform after passing through different matched filters. Non-diagonal elements, such as the first The waveform and the first Cross-correlation of matched filters The phase response of the phase response should be as consistent as possible.

[0049] The autocorrelation phase response vector is then used again. Reconstructing all elements into a diagonal matrix can be represented as follows: ; Then the relevant phase response matrix The cross-correlation function term within can be represented as follows: ; Understandable, In each row of the algorithm, the elements need to be paired to calculate the phase difference between each pair of elements. In other words, the elements in the first row... Line, i.e., the first The waveform passes through The cross-correlation function term formed after path matched filtering is analogous to the autocorrelation phase response vector. ; can be a matrix The The row is defined as the first The cross-correlation phase response vector of each waveform Its expression is as follows: ; Similarly, following the expression for the autocorrelation phase response objective function, the cross-correlation phase response similarity objective function can also be expressed using a matrix. With each cross-correlated phase response vector Obtained through calculation.

[0050] It should be noted that, There exists a zero element in the matrix such that the matrix... In the calculation, non-zero elements are combined with zero elements to form differences. Therefore, the objective function for cross-correlation phase response similarity should subtract this combination difference. Its expression is as follows:

[0051] in, Let the objective function be the cross-correlation phase response similarity. As the objective function of the optimization problem, the constant term can be discarded. Then, the cross-correlation phase response similarity objective function can be simplified to: ; Combining the above objective functions for autocorrelation and cross-correlation phase response similarity, the scaling function characterizing the similarity of correlated phase responses can be expressed as follows: ; Therefore, in one possible embodiment, the objective function is comprehensively optimized. The expression is: ; in, , , and Represents a weighting coefficient, a positive real number used to balance the importance of different optimization terms in the objective function; This represents the integral sidelobe level scaling function. This represents the scaling function used to characterize the similarity of related phase responses; This indicates a delay index.

[0052] Step 103: Based on the comprehensive optimization objective function, iteratively traverse and optimize the waveform codes of multiple transmission channels. In each iteration, the waveform codes are gradually updated to reduce the function value of the comprehensive optimization objective function.

[0053] In one possible embodiment, step 103 includes: performing iterative traversal optimization using the coordinate descent method, and fixing all codes in the waveform coding matrix except for one specific code in each iteration; in the current iteration, adjusting the value of the specific code and calculating the current function value of the comprehensive optimization objective function to obtain the code value when the function value of the comprehensive optimization objective function is minimized, and updating the specific code based on the code value; traversing and updating each code in the waveform coding matrix to complete the current iteration.

[0054] In one possible embodiment, the optimization problem of the comprehensive optimization objective function is expressed as follows: ; in, Indicates the first The first waveform One code, This indicates a constant modulus constraint on the waveform.

[0055] Understandably, this is to minimize the constant modulus constraint (i.e., the amplitude of each code is always 1, only the phase is variable). This embodiment employs a coordinate descent method for iterative optimization. This method decomposes the high-dimensional optimization problem into a series of one-dimensional sub-problems, and optimizes the waveform encoding matrix sequentially. Each phase element in .

[0056] That is, in each iteration, only the optimal value of one code in the encoding matrix is ​​searched. Therefore, for the encoding matrix... One iteration of optimization can be decomposed into There are one-dimensional sub-optimization problems, which can be represented as follows: ; Specifically, the optimization process can be described as follows: In the In the next iteration ( Fixed waveform encoding matrix (i.e., the first) The waveform encoding matrix obtained after the iteration, excluding a specific phase All other phases outside of this. At this time, It can be viewed as only about the variable A one-dimensional periodic function. Through a one-dimensional phase space. Perform precise or intensive searches within to find what enables The optimal phase with the smallest value .

[0057] Then, update the current iteration number. The first waveform Encode ; and substitute the updated value into Then, in a predetermined order (e.g., from arrive , From 1 to Iterate through each phase element in the waveform encoding matrix to complete one global iteration.

[0058] Step 104: When the optimization process meets the preset convergence condition, stop the iteration and encode the current optimized waveform as the transmission waveform of the MIMO radar.

[0059] For example, the iterative optimization process continues. The convergence condition can be set as one or a combination of the following two: First, the waveform encoding change threshold: when the norm of the difference between the waveform encoding matrices obtained from two adjacent iterations (e.g., the Frobenius norm difference) is less than a very small positive number, such as a preset threshold. The waveform is considered to have converged, as shown below: ; in, and They represent the first Second and third The waveform encoding matrix after each iteration; It can be .

[0060] Second, the threshold for changes in the objective function value: when the objective function value changes between two consecutive iterations... and When the absolute difference is less than a very small positive number, the waveform is considered to have converged.

[0061] Third, reach the maximum number of iterations: Set a maximum number of iterations. ,For example When the number of iterations reaches this upper limit, the iteration stops regardless of whether it has fully converged to prevent infinite loops.

[0062] The iteration terminates when any stopping condition is met. The waveform encoding matrix obtained from the last iteration is output as the final MIMO radar transmit waveform.

[0063] It is understood that the waveforms designed through the embodiments of this application not only have low amplitude related sidelobes, but also exhibit highly consistent phase response. For example... Figure 4 As shown, Figure 4 For target Capon spectrum estimation under traditional orthogonal waveform conditions, it can be seen that the target power is dispersed throughout the entire transmission space dimension, and the target main lobe peak is almost submerged in the side lobes. However, as... Figure 5 As shown, Figure 5 Target Capon spectrum estimation is performed under optimized waveform conditions for amplitude and phase response, while the autocorrelation and cross-correlation sidelobe powers can be effectively focused at the corresponding transmission spatial frequencies. Figure 2 The sidelobe effects are effectively suppressed. Furthermore, the cross-correlation sidelobe components are focused at the zero-emission RF point; this power distribution pattern can be effectively suppressed using beamforming. In addition, such as Figure 6 As shown, Figure 6Output signal-to-interference-plus-noise ratio (SNR) curves for MIMO radar under anti-main-lobe deception interference conditions are presented. The red curve represents the amplitude and phase response optimized waveform proposed in this application, while the other waveforms represent those obtained using traditional optimization methods. Therefore, under anti-main-lobe deception interference scenarios, the waveform designed by this method (red curve in the figure) can achieve an output SNR improvement of approximately 8 dB compared to various traditional optimized waveforms, demonstrating its significant effect in improving the performance of MIMO radar systems.

[0064] This application proposes a method for designing waveforms to optimize the amplitude and phase response of a MIMO radar. Based on the waveform encoding of multiple transmission channels of the initialized MIMO radar, a waveform encoding matrix is ​​obtained. Based on the waveform encoding matrix, a comprehensive optimization objective function is constructed. This objective function includes a first term for optimizing the amplitude response of the waveform-related sidelobes and a second term for optimizing the similarity of the phase response of the waveform-related sidelobes. Based on the comprehensive optimization objective function, the waveform encodings of each transmission channel are iteratively optimized. In each iteration, the waveform encodings are gradually updated to reduce the function value of the comprehensive optimization objective function. When the optimization process meets a preset convergence condition, the iteration stops, and the currently optimized waveform encoding is determined as the transmitted waveform of the MIMO radar. This scheme, by introducing optimization of the correlation phase response characteristics between waveforms on the basis of traditional waveform design optimization of sidelobe amplitude, and by jointly optimizing the amplitude and phase response of the waveforms, makes the waveform performance approach that of an ideal orthogonal waveform. This overcomes the technical problem of decreased target estimation accuracy caused by high correlation sidelobes in existing MIMO radar orthogonal waveforms, thereby significantly improving the high-resolution spectrum estimation performance and anti-jamming capability of the MIMO radar.

[0065] The steps described above are for clarity only. In implementation, they can be combined into one step, or some steps can be broken down into multiple steps, as long as they involve the same logical relationship, they are all within the scope of protection of this application. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, without changing the core design of the algorithm and process, are also within the scope of protection of this application.

[0066] Another embodiment of this application proposes a design system for optimizing the amplitude and phase response waveform of MIMO radar. The details of this design system are described below. The following implementation details are provided for ease of understanding and are not essential for implementing this example. Figure 7 This is a schematic diagram of the design system for optimizing the amplitude and phase response waveform of a MIMO radar proposed in this embodiment, including: The matrix determination module 210 is used to obtain a waveform encoding matrix based on the waveform encoding of multiple transmission channels of the MIMO radar after initialization. The function construction module 220 is used to construct a comprehensive optimization objective function based on the waveform encoding matrix; wherein, the comprehensive optimization objective function includes a first term for optimizing the amplitude response of the waveform-related sidelobes and a second term for optimizing the similarity of the phase response of the waveform-related sidelobes. The iterative optimization module 230 is used to iteratively optimize the waveform codes of multiple transmission channels based on the comprehensive optimization objective function, and gradually update each waveform code in each iteration to reduce the function value of the comprehensive optimization objective function. The waveform determination module 240 is used to stop the iteration when the optimization process meets the preset convergence condition, and to encode the currently optimized waveform as the transmission waveform of the MIMO radar.

[0067] It is not difficult to see that this embodiment is a system embodiment corresponding to the above method embodiments, and this embodiment can be implemented in conjunction with the above method embodiments. The relevant technical details and technical effects mentioned in the above method embodiments are still valid in this embodiment, and will not be repeated here to reduce repetition. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above method embodiments.

[0068] It is worth mentioning that all modules and units involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed in this application; however, this does not mean that other units do not exist in this embodiment.

[0069] Another embodiment of this application provides an electronic device, such as Figure 8 As shown, it includes a processor 31 and a memory 32. The memory 32 stores instructions that the processor 31 can execute. When the processor 31 is configured to execute the instructions, the electronic device can implement a design method for optimizing the amplitude and phase response waveform of a MIMO radar as described in the above method embodiment.

[0070] The memory and processor are connected via a bus, which includes any number of interconnecting buses and bridges, connecting various circuits of one or more processors and the memory. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0071] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0072] Another embodiment of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, enables the design method for optimizing the amplitude and phase response waveform of a MIMO radar as described in the above method embodiments.

[0073] That is, those skilled in the art will understand that all or part of the steps in the above method embodiments can be implemented by a program instructing related hardware. The program is stored in a storage medium and includes several instructions to cause a device (such as a microcontroller, chip, etc.) or processor to execute all or part of the steps of the method described in the method embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory, random access memory, magnetic disks, or optical disks.

[0074] Those skilled in the art will understand that the above embodiments are specific implementations of this application, and in practical applications, various changes can be made in form and detail without departing from the spirit and scope of this application. For those skilled in the art, several improvements and modifications can be made without departing from the principles of this application, and these improvements and modifications are also considered to be within the scope of protection of this application.

Claims

1. A method for designing optimized waveforms for the amplitude and phase response of a MIMO radar, characterized in that, The method includes: Based on the waveform encoding of multiple transmission channels of the MIMO radar after initialization, a waveform encoding matrix is ​​obtained; Based on the waveform coding matrix, a comprehensive optimization objective function is constructed; wherein, the comprehensive optimization objective function includes a first term for optimizing the amplitude response of waveform-related sidelobes and a second term for optimizing the similarity of waveform-related sidelobe phase responses; Based on the comprehensive optimization objective function, the waveform codes of multiple transmission channels are iteratively optimized. In each iteration, the waveform codes are gradually updated to reduce the function value of the comprehensive optimization objective function. When the optimization process meets the preset convergence condition, the iteration stops, and the current optimized waveform is encoded and determined as the transmission waveform of the MIMO radar.

2. The method according to claim 1, characterized in that, The construction of the comprehensive optimization objective function based on the waveform coding matrix includes: Based on the covariance matrix of the waveform coding matrix under different time delays, an integral sidelobe scaling function characterizing the amplitude level of the relevant sidelobe is obtained. Based on the correlation matrix of the waveform coding matrix under different time delays, a scaling function characterizing the similarity of the correlated phase response is obtained; Based on the integral sidelobe scaling function characterizing the amplitude level of the relevant sidelobe and the scaling function characterizing the similarity of the relevant phase response, a comprehensive optimization objective function is obtained.

3. The method according to claim 2, characterized in that, The scaling function characterizing the similarity of the correlated phase response is obtained based on the correlation matrix of the waveform encoding matrix under different time delays, including: Calculate the correlation matrix at each time delay based on the waveform encoding matrix; Extract the phase of each element from the correlation matrix to construct the phase response matrix; Extract the autocorrelation phase response vector and the cross-correlation phase response vector from the phase response matrix, respectively; Based on the autocorrelation phase response vector, the autocorrelation phase response similarity term is calculated, and simultaneously based on the cross-correlation phase response vector, the cross-correlation phase response similarity term is calculated. The weighted summation of the autocorrelation phase response similarity term and the cross-correlation phase response similarity term yields a scaling function characterizing the similarity of the correlated phase responses.

4. The method according to claim 2, characterized in that, The integral sidelobe scaling function, which characterizes the amplitude level of the relevant sidelobe, is obtained based on the covariance matrix of the waveform encoding matrix under different time delays, including: Calculate the covariance matrix under different time delays based on the waveform encoding matrix; The integral sidelobe scaling function is obtained by summing the difference norms of the covariance matrix and the ideal diagonal matrix.

5. The method according to claim 1, characterized in that, The method involves iteratively optimizing the waveform codes of multiple transmission channels based on a comprehensive optimization objective function. In each iteration, the waveform codes are gradually updated to reduce the value of the comprehensive optimization objective function. This includes: The coordinate descent method is used for iterative traversal optimization, and in each iteration, all codes in the waveform coding matrix except for one specific code are fixed. In the current iteration, by adjusting the value of a specific code and calculating the current function value of the comprehensive optimization objective function, the code value at which the function value of the comprehensive optimization objective function is minimized is obtained, and the specific code is updated based on this code value. Iterate through and update each code in the waveform coding matrix to complete the current iteration.

6. The method according to any one of claims 1 to 5, characterized in that, Comprehensive optimization objective function The expression is: ； in, , and Represents a weighting coefficient, a positive real number used to balance the importance of different optimization terms in the objective function; This represents the integral sidelobe level scaling function. This represents the scaling function used to characterize the similarity of related phase responses; Indicates a delay index; This indicates the number of phase codes for each transmitted waveform; This indicates the number of waveforms, i.e., the number of transmission channels in a MIMO radar system; express An identity matrix of 3D; Represents the unit impulse function, and when hour ,otherwise ; Indicates time delay The covariance matrix at the location; Indicates delay The autocorrelation phase response vector at the location; Represents a constant matrix; Indicates time delay Place, No. The cross-correlation phase response vectors of the waveforms; The optimization problem of the comprehensive optimization objective function is expressed as follows: ； in, Indicates the first The first waveform One code, This indicates a constant modulus constraint on the waveform.

7. The method according to any one of claims 1 to 5, characterized in that, The preset convergence condition includes that the norm of the difference between the waveform encoding matrices obtained in two consecutive iterations is less than a preset threshold. That is, satisfying: ； in, and They represent the first Second and third The waveform encoding matrix after each iteration.

8. A design system for optimizing the amplitude and phase response waveform of a MIMO radar, characterized in that, The system includes: The matrix determination module is used to obtain the waveform encoding matrix based on the waveform encoding of multiple transmission channels of the MIMO radar after initialization. The function construction module is used to construct a comprehensive optimization objective function based on the waveform encoding matrix; wherein, the comprehensive optimization objective function includes a first term for optimizing the amplitude response of the waveform-related sidelobes and a second term for optimizing the similarity of the phase response of the waveform-related sidelobes; The iterative optimization module is used to iteratively optimize the waveform codes of multiple transmission channels based on the comprehensive optimization objective function. In each iteration, the waveform codes are gradually updated to reduce the function value of the comprehensive optimization objective function. The waveform determination module is used to stop the iteration when the optimization process meets the preset convergence condition, and to encode and determine the current optimized waveform as the transmission waveform of the MIMO radar.

9. An electronic device, characterized in that, include: A processor and a memory, wherein the memory stores instructions that the processor can execute, and the processor is configured to, when executing the instructions, enable the electronic device to implement a design method for an optimized waveform for the amplitude and phase response of a MIMO radar as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it can implement a design method for optimizing the amplitude and phase response waveform of a MIMO radar as described in any one of claims 1 to 7.

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