A radar cancellation angle error analysis method and a semi-physical verification system

Abstract

The application belongs to the technical field of radio navigation, and specifically discloses a radar cancellation angle measurement error analysis method and a semi-physical verification system. The method comprises the following steps: based on the radar array structure parameters and the spatial radiation signal characteristics, a monopulse angle measurement model based on sum channels and difference channels is constructed; receiving signals generated after the radar array receives spatial radiation signals are acquired; initial difference channel signals are multiplexed to perform signal cancellation processing, the sum pattern is updated under the condition of maintaining the difference pattern of the difference channel unchanged, and the sum channel signal after cancellation and the difference channel signal after cancellation are output; based on the relative characteristic parameters of the sum channel signal after cancellation and the difference channel signal after cancellation, the mapping relationship in the monopulse angle measurement model is called, and the radar pointing angle corresponding to the receiving signal is calculated; the radar pointing angle is compared with the real angle of the target, and the angle measurement error corresponding to the receiving signal is acquired. Through the application, a stable and reliable cancellation angle measurement error analysis link is constructed.

Description

Technical Field

[0001] This application belongs to the field of radio navigation technology, specifically to the field of radar signal processing technology, and more specifically, to a radar cancellation angle measurement error analysis method and a semi-physical verification system. Background Technology

[0002] Radar angle measurement technology is one of the important technologies used in radar systems to obtain target spatial position information. Monopulse phased array radars based on sum and difference beams are widely used in phased array radar systems due to their high angle measurement accuracy and good real-time performance. However, in the complex electromagnetic battlefield environment, radar systems often face the influence of external signal interference. To effectively suppress the impact of interference signals on radar performance, interference cancellation has been used to process the radar received signal. This method can effectively reduce the impact of interference signals on radar detection performance. However, the cancellation process may also change the signal characteristics of the sum and difference channels of the phased array radar, thus affecting its angle measurement results.

[0003] However, existing technologies for interference cancellation often focus on the interference suppression capability of the cancellation algorithm and the improvement effect on the signal-to-interference-plus-noise ratio (SINR). In practical engineering, it has been found that the angle measurement accuracy of radar signals after interference cancellation often exhibits unexplained degradation or systematic deviations. This is particularly true for monopulse radar systems without dedicated cancellation channels (such as differential channels), where the error coupling mechanism between cancellation and angle measurement processing is highly complex. Existing performance evaluation methods struggle to accurately quantify the angle measurement error patterns introduced by this cancellation operation; furthermore, there is a lack of effective means to verify these error phenomena in conjunction with actual hardware conditions. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this application is to provide a radar cancellation angle measurement error analysis method and a semi-physical verification system. This aims to solve the technical problem that existing monopulse phased array radars, especially those without dedicated cancellation channels, have difficulty in accurately quantifying and evaluating the degradation of angle measurement accuracy after interference suppression, and lack effective hardware verification methods.

[0005] The first aspect of this application relates to a radar cancellation angle measurement error analysis method, comprising: constructing a single-pulse angle measurement model based on sum and difference channels according to radar array structural parameters and spatial radiation signal characteristics, to establish a mapping relationship between relative characteristic parameters and radar indication angle; acquiring the received signal generated by the radar array after receiving spatial radiation signals, the received signal including an initial sum channel signal synthesized by sum beams and an initial difference channel signal synthesized by difference beams; performing signal cancellation processing by multiplexing the initial difference channel signal, updating the sum pattern while maintaining the difference pattern of the difference channel unchanged, and outputting the cancelled sum channel signal and the cancelled difference channel signal; calculating the radar indication angle corresponding to the received signal by invoking the mapping relationship in the single-pulse angle measurement model based on the relative characteristic parameters of the cancelled sum channel signal and the cancelled difference channel signal; comparing the radar indication angle with the true angle of the target to obtain the angle measurement error corresponding to the received signal.

[0006] This application constructs a cancellation angle measurement error analysis link based on difference channel multiplexing by reusing the initial difference channel signal as an interference reference and updating the sum and difference radiation patterns while maintaining the difference radiation pattern unchanged. This solves the error coupling problem between the interference cancellation process and the angle measurement processing. In particular, it is suitable for radar systems that do not have a dedicated cancellation channel (such as a difference-to-difference channel) and is applicable to hardware conditions without an independent reference channel. It provides an analytical basis for evaluating the angle measurement performance of radar systems in complex interference environments.

[0007] In some implementations, the multiplexing of the initial difference channel signal to perform signal cancellation processing, updating the sum pattern while maintaining the difference pattern of the difference channel unchanged, and outputting the cancelled sum channel signal and the cancelled difference channel signal, includes: multiplexing the initial difference channel signal as an interference reference signal, calculating the optimal cancellation weights in combination with the initial sum channel signal; using the optimal cancellation weights to perform interference suppression processing on the initial sum channel signal to generate the cancelled sum channel signal after updating the sum pattern; and directly extracting the initial difference channel signal as the cancelled difference channel signal to maintain the difference pattern of the difference channel unchanged before and after cancellation.

[0008] This scheme extracts the initial difference channel signal directly into the canceled difference channel signal, ensuring that the difference radiation pattern remains unchanged before and after cancellation. It also adaptively updates the sum radiation pattern, thus facilitating the analysis of the impact of sum channel changes on angle measurement results and reducing the interference of difference channel changes on error analysis.

[0009] In some embodiments, the step of multiplexing the initial difference channel signal as an interference reference signal and calculating the optimal cancellation weights by combining the initial sum channel signal includes: calculating the autocorrelation matrix of the initial difference channel signal to characterize the spatial energy distribution characteristics of the interference reference signal; calculating the cross-correlation matrix of the initial sum channel signal and the initial difference channel signal to characterize the interference coupling characteristics between the initial sum channel signal and the interference reference signal; calculating the product of the inverse of the autocorrelation matrix and the cross-correlation matrix, and outputting the optimal cancellation weights for reconstructing the interference compensation component; and using the optimal cancellation weights to perform interference suppression processing on the initial sum channel signal to generate the cancelled sum channel signal with updated sum pattern, including: multiplying the optimal cancellation weights with the initial difference channel signal to obtain the interference compensation component; subtracting the interference compensation component from the initial sum channel signal, and outputting the cancelled sum channel signal.

[0010] This scheme solves for the optimal cancellation weights by jointly operating the autocorrelation matrix and the cross-correlation matrix, which characterizes the spatial energy distribution of the interference reference signal and its coupling relationship with the signal in the channel. This enables the generated interference compensation component to be used to suppress interference components in the channel and helps to reduce the impact of interference on subsequent angle measurement calculations.

[0011] In some implementations, the step of constructing a single-pulse angle measurement model based on sum and difference channels, based on radar array structural parameters and spatial radiation signal characteristics, to establish the mapping relationship between relative characteristic parameters and radar indication angle, includes: dividing the radar array into multiple subarrays; calculating the progressive phase of each subarray by combining the element spacing parameter in the radar array structural parameters, and generating a composite radiation pattern for each subarray; performing superposition and subtraction operations on the composite radiation patterns of each subarray to obtain a sum radiation pattern and a difference radiation pattern based on the global array, respectively; and fitting a single-pulse slope based on the relative characteristic parameters of the difference radiation pattern and the sum radiation pattern at different target angles to construct the mapping relationship between the relative characteristic parameters and the radar indication angle.

[0012] This scheme constructs a sum-difference direction pattern by dividing the subarray and calculating the phase gradient, and fits the single pulse slope based on the relative characteristic parameters under different target angles, establishing a complete mapping model from signal characteristics to angle indication. This enables the angle measurement model to accurately reflect the influence of array geometry and beamforming characteristics on the angle measurement results, providing a benchmark for error analysis under subsequent cancellation conditions.

[0013] In some embodiments, the step of superimposing and subtracting the composite radiation patterns of each of the subarrays to obtain a sum radiation pattern and a difference radiation pattern based on the global array includes: obtaining the amplitude fluctuation error and phase fluctuation error of the radar receiving channel; using the amplitude fluctuation error and the phase fluctuation error to modulate the composite radiation pattern of the corresponding subarray to generate a distorted composite radiation pattern containing the non-ideal characteristics of the channel; and performing superposition and subtraction operations on each of the distorted composite radiation patterns to obtain the sum radiation pattern and the difference radiation pattern.

[0014] This scheme modulates the amplitude and phase fluctuation errors in the subarray synthesis pattern, incorporating the unavoidable non-ideal characteristics of the channel in actual hardware into the angle measurement model. This makes the constructed sum and difference pattern closer to the real physical response, thereby enabling the analysis of the coupling effect of channel amplitude and phase inconsistency and interference cancellation during the error analysis stage, making the analysis results closer to engineering conditions.

[0015] In some implementations, comparing the radar indication angle with the target's true angle to obtain the angle measurement error corresponding to the received signal includes: when the radar is in the search and scanning phase and no point convergence processing is performed, extracting the relative angle between the azimuth of the interference source and the center of the radar beam in the spatial radiation signal under different beam directions; calculating the difference between the radar indication angle and the target's true angle within different offset intervals of the relative angle, and determining the angle measurement error of a single observation.

[0016] This scheme, by dividing the angle measurement error into zones according to the relative angle between the interference source and the beam center under the condition that point convergence is not performed during the search and scanning phase, can be used to analyze the change of angle measurement deviation introduced by cancellation processing under a single beam action with spatial position, and provides fine-grained data support for the radar to evaluate instantaneous angle measurement performance, optimize beam dwell strategy and interference suppression parameters in search mode.

[0017] In some embodiments, the method further includes: when the radar is in the search and scan phase and point convergence processing is performed, performing point convergence calculation on the radar indication angle for multiple consecutive scan cycles to obtain the converged target angle; comparing the converged target angle with the true target angle to determine the distribution range of the angle measurement error and the target angle trace expansion characteristics under multiple observation accumulation conditions.

[0018] This scheme simulates the angle measurement performance of radar after multi-frame data fusion in actual search mode by performing point-track convergence calculation on radar indication angles of multiple consecutive scanning cycles. It can be used to analyze the impact of multiple observation accumulation on the distribution range of angle measurement error and the target angle track extension characteristics, and provides a reference for the angle measurement performance evaluation in the radar search phase.

[0019] In some implementations, comparing the radar indication angle with the target's true angle to obtain the angle measurement error corresponding to the received signal includes: when the radar is in the target tracking phase, extracting the radar indication angle under different angular offset positions of the interference source in the spatial radiation signal within the main lobe of the beam; calculating the difference distribution between the radar indication angle and the target's true angle, and determining the angle measurement error introduced by the cancellation process in the target tracking phase.

[0020] This scheme extracts the radar indication angle of the interference source at different offset positions within the main lobe during the target tracking phase and calculates the difference distribution. It can be used to analyze the angle measurement error under different main lobe interference angle offset conditions during the target tracking phase, providing a reference for interference suppression and angle measurement performance evaluation in tracking mode.

[0021] The second aspect of this application relates to a hardware-in-the-loop verification system, comprising: a hardware transceiver subsystem including a radar receiving antenna array, a signal transceiver connected to the radar receiving antenna array, and a synchronization control device connected to the signal transceiver; the radar receiving antenna array receives spatial radiated signals and generates received signals through the signal transceiver under the constraint of the synchronization control device, the received signals including an initial sum channel signal synthesized by sum beamforming and an initial difference channel signal synthesized by difference beamforming; a computational verification subsystem including a processor and a memory interconnected thereto, the signal transceiver being connected to the processor; the signal transceiver transmitting the generated received signals to the processor, the processor executing a computer program stored in the memory to implement the radar cancellation angle measurement error analysis method using the received signals, calculating and outputting the angle measurement error corresponding to the received signals.

[0022] This scheme generates the received signal of the real physical environment through the hardware transceiver subsystem under synchronous control, and the aforementioned analysis method is executed by the calculation and verification subsystem. This realizes the comparison and verification between the theoretical model and the actual hardware response. It can combine the actual hardware response verification to eliminate the angle measurement error analysis results and supplement the problem that pure software simulation is insufficient in reflecting some non-ideal characteristics of hardware.

[0023] In some embodiments, the system further includes an anechoic chamber turntable arranged in an anechoic chamber environment, and a target signal radiation source and an interference signal radiation source respectively disposed in the anechoic chamber environment; the target signal radiation source and the interference signal radiation source are used to transmit the spatial radiation signal; the processor is also connected to the anechoic chamber turntable and is used to change the spatial pointing angle between the target signal radiation source and the interference signal radiation source relative to the radar receiving antenna array by adjusting the offset angle of the anechoic chamber turntable, so as to verify the angle measurement error under different spatial angle conditions.

[0024] This scheme uses a turntable in an anechoic chamber to adjust the spatial pointing angle between the target and the interference radiation source relative to the receiving array, reproducing various interference incident conditions in a controllable electromagnetic environment. This enables the system to automatically traverse and verify the angle measurement error under different spatial angles, which is beneficial to improving the coverage and repeatability of the verification scenario and providing controllable test conditions for the performance evaluation of radar angle measurement algorithms.

[0025] Thirdly, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation thereof.

[0026] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0027] Fifthly, this application provides a computer program product that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0028] It is understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0029] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: (1) This application constructs a stable and reliable cancellation angle measurement error analysis link by reusing the initial difference channel signal as an interference reference and updating the sum pattern while maintaining the difference pattern unchanged. This enables the calculation of angle measurement error to reflect the real changes of the sum channel signal after cancellation processing, avoiding analysis bias introduced by the distortion of the difference channel. This scheme is not only applicable to conventional monopulse radar, but also eliminates the dependence on dedicated auxiliary channels (such as difference-to-difference channels), and can be used to evaluate the angle measurement error of radars without reserved dedicated channels under cancellation conditions.

[0030] (2) This application introduces channel amplitude fluctuation error and phase fluctuation error into the angle measurement model, and combines various working modes such as search scanning, point convergence and target tracking to conduct scene error analysis. It can be used to analyze the changes in angle measurement error under the coupling effect of interference cancellation and hardware non-ideal factors, so that the analysis results not only cover ideal conditions, but also reflect the real performance boundary of the radar system in the actual engineering environment.

[0031] (3) This application constructs a semi-physical verification system that includes a hardware transceiver subsystem and an anechoic chamber turntable. It realizes closed-loop verification of the angle measurement error analysis method in a controllable electromagnetic environment, closely combining theoretical derivation with real hardware response. This can supplement the problem that pure digital simulation is insufficient in reflecting the physical effects of non-ideal characteristics of devices and channel mismatch, and provide a reference for analysis conclusions and system design. Attached Figure Description

[0032] Figure 1 This is a flowchart of the radar cancellation angle measurement error analysis method provided in the embodiments of this application; Figure 2 This is a schematic diagram of the processing flow of a single-pulse phased array radar receiver provided in an embodiment of this application; Figure 3 This is a schematic diagram of the two-dimensional array plane partitioning provided in an embodiment of this application; Figure 4 This is a schematic diagram of beam division provided in an embodiment of this application; Figure 5 This is a schematic diagram of the cancellation principle of multiplexed differential beam sampling provided in the embodiments of this application; Figure 6 This is a schematic diagram of the hardware-in-the-loop verification system provided in the embodiments of this application; Figure 7 This is a block diagram of the software radio platform system architecture provided in the embodiments of this application; Figure 8 This is a schematic diagram of the physical prototype of the semi-physical verification system provided in the embodiments of this application. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0034] The embodiments of this application are described below with reference to the accompanying drawings. Figure 1 and Figure 2 As shown, this embodiment provides a radar cancellation angle measurement error analysis method, which is applicable to single-pulse phased array radar systems performing interference suppression. In a typical and advantageous application scenario, this method is particularly suitable for radar systems that do not have a dedicated cancellation channel (such as a differential channel), aiming to solve the problem that angle measurement errors are difficult to accurately quantify due to pattern distortion when the radar uses a differential channel for interference cancellation. The method includes the following steps 110-150.

[0035] Step 110: Based on the radar array structure parameters and spatial radiation signal characteristics, construct a single-pulse angle measurement model based on the sum and difference channels to establish the mapping relationship between relative characteristic parameters and radar indication angle.

[0036] Specifically, radar array structural parameters include, but are not limited to, physical attributes such as element spacing, subarray division method, element feed amplitude, and array geometric arrangement; spatial radiation signal characteristics encompass electromagnetic features such as the incident angle, frequency, and polarization of target echoes and interference signals. The monopulse angle measurement model is an abstract representation of the mathematical relationship between the aforementioned physical attributes and electromagnetic characteristics, used to describe the spatial response of the sum and difference beams under ideal or specific non-ideal conditions. The relative characteristic parameter refers to the amplitude ratio or phase difference between the difference channel signal and the sum channel signal; this parameter exhibits a monotonically changing characteristic with the angle of the target's deviation from the beam center. The mapping relationship is usually represented by a monopulse slope curve or lookup table, its function being to convert the measured signal characteristic parameters into corresponding angle estimates. The purpose of this step is to establish a stable angle measurement reference ruler, which remains unchanged as a reference system for evaluating angle measurement accuracy regardless of subsequent signal processing changes.

[0037] Step 120: Obtain the received signal generated after the radar array receives the spatial radiation signal. The received signal includes the initial sum channel signal synthesized by sum beam and the initial difference channel signal synthesized by difference beam.

[0038] Specifically, the radar array senses electromagnetic waves in space through its antenna array. After down-conversion, sampling, and digital beamforming processing by the radio frequency front-end, multiple digital baseband signals are generated. The initial and channel signals are formed by the in-phase superposition of signals from all array elements or subarrays, primarily carrying target energy information and detection capabilities. The initial differential channel signals are formed by the out-of-phase superposition of signals from array elements or subarrays in different regions, primarily carrying target angular deviation information. The initial state here refers to the fact that these signals have not yet undergone any interference cancellation or adaptive filtering, retaining the most original environmental information and hardware channel characteristics. In actual engineering implementation, the received signals can be acquired by real-time acquisition of radar front-end data or by reading pre-stored simulation data or anechoic chamber test data; this embodiment does not impose any limitations on this.

[0039] Step 130: Perform signal cancellation processing using the initial difference channel signal. Update the sum pattern while keeping the difference pattern of the difference channel unchanged. Output the canceled sum channel signal and the canceled difference channel signal.

[0040] Specifically, multiplexing the initial difference channel signal means directly using the difference channel signal originally used for angle measurement as a reference signal source for interference cancellation, without the need for additional dedicated auxiliary channels or difference-to-difference channels. In this process, the initial difference channel signal is given a dual function: on the one hand, it retains the original angle deviation information for subsequent angle measurement; on the other hand, it directly serves as the reference input for the adaptive filter. This multiplexing strategy eliminates the dependence on dedicated auxiliary channel hardware, reducing system complexity; even if the radar system is not configured with an independent difference-to-difference channel, it can still effectively acquire interference reference sources, breaking the constraints of the hardware architecture.

[0041] Maintaining the difference pattern of the difference channel unchanged means that no adaptive weighting coefficients or filtering are applied to the difference channel signal during the cancellation operation; the difference channel signal is directly transmitted. In contrast, updating the sum pattern involves using optimal weights to perform weighted subtraction operations on the initial sum channel signal to cancel out the interference components it contains, resulting in an adaptive change in the spatial response of the sum channel. This asymmetric approach confines the impact of interference cancellation on the angle measurement system to the sum channel dimension, avoiding angle measurement reference drift caused by difference channel distortion, thus providing relatively stable conditions for subsequent analysis of angle measurement errors introduced by the cancellation.

[0042] Step 140: Based on the relative characteristic parameters of the canceled sum channel signal and the canceled difference channel signal, the mapping relationship in the single-pulse angle measurement model is called to calculate the radar indication angle of the corresponding received signal.

[0043] Specifically, after completing the cancellation process in step 130, the current relative characteristic parameters (such as difference and ratio) are extracted from the output canceled sum channel signal and the canceled difference channel signal. Since the difference pattern remains unchanged, the change in this characteristic parameter mainly reflects the change in signal purity after interference suppression in the sum channel and its impact on the angle measurement result. Subsequently, the extracted characteristic parameters are substituted into the single-pulse angle measurement model constructed in step 110, and the current radar indication angle is obtained by looking up a table or formula.

[0044] Step 150: Compare the radar indication angle with the target's true angle to obtain the angle measurement error of the corresponding received signal.

[0045] Specifically, the true angle of the target refers to the actual spatial orientation of the target under ideal conditions without interference or cancellation effects, or calibrated by a high-precision external measuring device. The angle measurement error is the difference between the radar indication angle and the true angle of the target. This error includes not only the inherent thermal noise error and hardware mismatch error of the radar system, but more importantly, the systematic deviation introduced by the cancellation process itself in step 130. Statistical analysis of this error can quantitatively assess the impact of the multiplexed difference channel cancellation algorithm on angle measurement accuracy under different operating conditions, thereby verifying the effectiveness of the algorithm or guiding the optimization and adjustment of algorithm parameters. For example, if the angle measurement error exceeds a preset threshold, it indicates that although the current cancellation strategy suppresses interference, it severely damages the angle measurement performance, requiring a redesign of the weight solution strategy or adjustment of the cancellation depth.

[0046] Through steps 110-150 above, this embodiment constructs a complete radar cancellation angle measurement error analysis process. This process, by reusing the initial difference channel and locking the difference pattern, analyzes the change in the angle measurement reference under cancellation conditions for radars without dedicated difference channels. This ensures that the angle measurement error analysis results reflect the impact of cancellation processing on the angle measurement results, rather than being mixed with uncontrollable factors such as channel distortion, thus providing support for the anti-jamming design and performance evaluation of this type of radar system.

[0047] Based on the above embodiments, this embodiment provides a detailed explanation of the construction process of the single-pulse angle measurement model in step 110 and the introduction of non-ideal characteristics.

[0048] Specifically, dividing the radar array into multiple subarrays is a fundamental step in constructing sum and difference beams. For a regular two-dimensional planar array, the mathematical expressions for its array and radiation pattern are: ; in, Indicates the array at the pitch angle and azimuth Complex response of composite pattern in the direction; and These represent the total number of array elements along the X and Y axes, respectively. and The first one in the X-axis direction Each element and the Y-axis direction The feed amplitude of each element is used to control the sidelobe level and beam shape of the radiation pattern; and These are the spatial frequency variables along the X and Y axes, respectively, reflecting the phase difference between the signal incident direction and the beam direction; and These are the element spacings along the X and Y axes, respectively; and These are the preset beam pointing elevation angle and azimuth angle, respectively; The unit is the imaginary unit. This formula describes the radiative synthesis characteristics of a regular two-dimensional planar array in various directions in space, and is the mathematical basis for subsequent subarray division and sum-difference beam construction.

[0049] like Figure 3 and Figure 4 As shown, for regular two-dimensional planar arrays, a four-quadrant partitioning strategy is typically adopted. This involves dividing the entire antenna array along the centerlines of the azimuth and elevation directions into four independent subarray regions, denoted as subarray D1, subarray D2, subarray D3, and subarray D4, respectively. This partitioning method utilizes the symmetry or antisymmetry between subarrays to directly form sum and difference beams through simple addition and subtraction operations. It should be understood that although this embodiment uses a four-quadrant partitioning approach, in other implementations, a larger number of subarrays (such as eight-subarrays or sixteen-subarrays) or asymmetric partitioning methods can be used depending on the array size, as long as independent output of the sum and difference channels can be achieved through subarray combinations.

[0050] After completing the subarray division, the element spacing parameter in the radar array structural parameters needs to be combined to calculate the progressive phase of each subarray and generate the composite radiation pattern of each subarray. The mathematical representation of the composite pattern of a subarray composed of n array elements is as follows: ; in, Complex response of the composite pattern of the reference subarray (first subarray); , , These are the complex response patterns of the composite radiation patterns of the second, third, and fourth subarrays, respectively. and These represent the number of array elements in the subarray along the X and Y axes, respectively. and These are the element index numbers in the X and Y axes, respectively; and These are the spatial frequency variables in the X and Y axes, respectively; and These are the element spacings along the X and Y axes, respectively; The operating wavelength of the radar; The unit is the imaginary unit. This set of formulas describes the spatial phase delay relationship of each subarray relative to the reference subarray D1, and forms the mathematical basis for the subsequent synthesis of the global radiation pattern.

[0051] Furthermore, spatial frequency variables and Taking into account the phase relationship between the signal incident direction and the beam pointing direction, its expression is: ; in, and These are the spatial frequency variables in the X and Y axes, respectively; For wave number, and ; and These are the element spacings along the X and Y axes, respectively; and These are the incident angle components of the signal in the X and Y axes, respectively; and The linear arrays arranged along the X and Y axes have uniformly varied phases to control the beam's scanning direction in space. When a signal is incident on the array from a certain direction, the phase difference between adjacent elements due to the path difference, minus the compensation phase preset to achieve beam pointing, is the spatial frequency variable. This variable determines the shape and pointing characteristics of the array pattern in space.

[0052] Beam pointing , The expression for the corresponding phase change of adjacent array elements is: ; in, and The phases are uniformly varied by linear arrays arranged along the X and Y axes, respectively. For wave number, and ; and These are the preset beam pointing elevation and azimuth angles, respectively. Meanwhile, to avoid grating lobe interference during array scanning, the element spacing... and The following constraints must be met: ; in, represent or , This is the maximum scan angle. This constraint ensures the uniqueness of the array pattern within the effective scan range, avoiding angle measurement ambiguity caused by insufficient spatial sampling.

[0053] After completing the subarray pattern modeling and signal model construction, it is necessary to further define the sum and difference patterns based on the two-dimensional subarrays. The four subarrays are combined through addition and subtraction to form sum and difference beams, and their sum and difference patterns are defined as follows: ; in, It is a global beam pattern, formed by the in-phase superposition of four sub-array beam patterns, with a maximum value at the beam center, and is mainly used for target detection and energy reception. This is a pitch difference pattern, used to extract pitch angle deviation information of the target; This is an azimuth difference pattern, used to extract the azimuth angle deviation information of the target.

[0054] The formula for the joint subarray pattern and the definition of the sum and difference pattern, representing each subarray pattern using a reference subarray D1, yields a unified expression for the sum and difference pattern based on 4 subarrays: ; in, The composite pattern of the reference subarray (first subarray); and These represent the number of array elements in the subarray along the X and Y axes, respectively. and These are the element spacings along the X and Y axes, respectively; and These are the spatial frequency variables in the X and Y axes, respectively; The wavelength is the operating wavelength of the radar. This expression unifies the sum and difference beam pattern as the product of the reference subarray D1 and the exponential phase factor, revealing the decisive influence of the spatial phase delay between subarrays on the shape of the sum and difference beam.

[0055] After constructing the antenna array model, a radar signal model needs to be further established to describe the superposition characteristics of the target echo signal and the interference signal in each radar channel. Noise frequency modulation (FM) suppression jamming is a typical form of radar jamming. Assuming the amplitude ratio of the interference source signal arriving at the radar antenna array to the target echo signal is... The incident angle of the interference signal is The incident angle of the target echo signal is Then the signal models of the interference source signal and the radar echo signal reaching the radar and the channel are: ; in, For discrete-time signals received by the radar and the channel; For the radiation pattern in the incident direction of the interference source The response value at the location; It is a Gaussian white noise signal, which characterizes the random modulation properties of the interference signal; To the direction of the target echo incidence pattern The response value at the location; The amplitude ratio coefficient of the target echo signal relative to the interference signal; Let be the target echo signal received by the phased array radar antenna. This formula shows that the received signal in the and channels is a linear superposition of the interference signal weighted by and patterns and the target echo weighted by and patterns.

[0056] The interference-to-signal ratio reaching the radar antenna array is: ; in, The jamming-to-signal ratio (MTR) characterizes the ratio of the power of the interfering signal to the power of the target echo signal. This is the amplitude ratio coefficient of the target echo signal relative to the interference signal. The interference-to-signal ratio is a key indicator for measuring the intensity of interference; the larger the value, the stronger the interference signal is relative to the target echo, and the more significant its impact on radar angle measurement performance.

[0057] Similarly, the signal model for the interference signal and the target echo signal arriving at the radar differential channel is as follows: ; in, This refers to the discrete-time signal received by the radar differential channel; For difference radiation patterns (including azimuth difference radiation patterns or elevation difference radiation patterns) in the incident direction of the interference source The response value at the location; The difference pattern is in the direction of the target echo incidence. The response value at the specified location. The structure of the difference channel signal model is similar to that of the sum channel, but because the difference pattern has a null characteristic near the beam center, the amplitude of the corresponding signal in the difference channel will be significantly attenuated when the interference source or target approaches the beam center. The sum channel signal model and the difference channel signal model together constitute the radar signal model, which is used to describe the superposition characteristics of the target echo signal and the interference signal in each radar channel.

[0058] To more realistically reflect the actual engineering environment, this embodiment explicitly introduces channel non-ideal characteristics during the modeling stage. Specifically, the amplitude and phase fluctuation errors of the radar receiving channel are acquired, and these errors are used to modulate the corresponding subarray composite radiation patterns to generate distorted composite radiation patterns that incorporate channel non-ideal characteristics. The purpose of this step is to decouple inherent hardware defects from errors introduced by subsequent cancellation algorithms during the theoretical analysis stage. If the analysis is based solely on an ideal model, the resulting angle measurement error conclusions are often overly optimistic and cannot guide the tolerance design of actual systems; however, by introducing amplitude and phase error modulation, the impact boundary of hardware consistency level on the final angle measurement performance can be quantitatively evaluated.

[0059] Assuming there is amplitude-phase inconsistency among the subarrays, a relative amplitude-phase error factor is defined. for: ; in, This represents the amplitude fluctuation error coefficient, reflecting the degree to which the gain of each channel deviates from the ideal value; This represents the phase fluctuation error, reflecting the random deviation in the phase response of each channel. After modulating the subarray pattern using this error factor, the resulting expression for the distortion and difference pattern becomes: ; in, Represents the global and directional patterns that include non-ideal characteristics; and The figures represent the pitch difference and azimuth difference radiation patterns, respectively, which contain non-ideal characteristics. It can be seen that the amplitude and phase errors, in the form of a product, disrupt the ideal symmetrical superposition relationship between the subarrays, causing distortion in the synthesized sum and difference radiation patterns, which in turn leads to nonlinear changes in the single-pulse slope.

[0060] Finally, superposition and subtraction operations are performed on each distorted synthetic radiation pattern to obtain the final sum and difference radiation patterns, respectively. Based on the relative characteristic parameters of the difference and sum radiation patterns at different target angles, a single pulse slope is fitted to construct the mapping relationship between the relative characteristic parameters and the radar indication angle.

[0061] Specifically, this mapping relationship is usually achieved through... The ratio curve is obtained by linear or polynomial fitting. Since the model already includes the distortion effect caused by amplitude and phase errors, the mapping relationship established based on the model can characterize the initial angle measurement characteristics of the radar system before cancellation processing under the condition of amplitude and phase errors, providing a physical basis for subsequent evaluation of the additional errors introduced by the cancellation algorithm.

[0062] Based on the above embodiments, this embodiment provides a detailed description of the specific implementation method of performing signal cancellation processing on the multiplexed initial difference channel signal in step 130. For example... Figure 5 As shown, this processing method aims to solve the problem of radar systems that do not reserve a dedicated differential channel lacking an independent reference source when canceling interference. Through specific signal flow and operation logic, the angle measurement reference characteristics of the differential channel are strictly maintained while suppressing channel interference.

[0063] Specifically, step 130 includes sub-step 131, which multiplexes the initial difference channel signal as an interference reference signal and calculates the optimal cancellation weights by combining the initial and channel signals. During this process, the initial difference channel signal... It is given a dual function: on the one hand, it retains the original angle deviation information for subsequent angle measurement; on the other hand, it is directly used as the reference input of the adaptive filter to estimate the interference components in the channel. This multiplexing strategy avoids adding additional hardware channels or complex RF network modifications, significantly reducing system complexity. The solution for the optimal cancellation weights is not a simple adjustment of the scaling factor, but rather a complex weight vector that minimizes the output interference power of the channel after cancellation, based on statistical signal processing theory and matrix operations.

[0064] Furthermore, in order to more accurately characterize the spatial characteristics and coupling relationship of the interference signal, sub-step 131 specifically includes the following matrix operation process: First, calculate the autocorrelation matrix of the initial difference channel signal. The autocorrelation matrix characterizes the spatial energy distribution of the interfering reference signal. It reflects the correlation strength between the difference channel signals at different times or between different array elements. Its main diagonal elements represent the average power level of the interfering signal in the difference channel, while the off-diagonal elements reveal the coherent structure of the interfering signal in the spatial dimension. Since the difference beam itself has a specific spatial directivity (usually with a null point at the beam center), this autocorrelation matrix actually encodes the spatial location information of the interfering source relative to the difference beam null point, forming the basis for constructing the interfering subspace.

[0065] Secondly, calculate the cross-correlation matrix between the initial sum channel signal and the initial difference channel signal. The cross-correlation matrix characterizes the interference coupling properties between the initial and channel signals and the interfering reference signal. It quantifies the similarity between the interfering components in the sum channel and the reference signal in the difference channel. Ideally, if the interfering source is located at the difference beam null, the cross-correlation should be zero; however, in practical engineering, due to the interfering source potentially deviating from the null or having sidelobes entering, a definite linear coupling relationship exists between the two. This matrix provides the transfer function information needed to reconstruct the interfering components from the difference channel.

[0066] Subsequently, the product of the inverse of the autocorrelation matrix and the cross-correlation matrix is ​​calculated, and the optimal cancellation weights for reconstructing the interference compensation components are output. The calculation process can be represented by the following formula: ; in, It is the optimal cancellation weight vector in the azimuth dimension, used to cancel interference components in the azimuth difference channel signal; The optimal cancellation weight vector for the pitch dimension is used to cancel interference components in the pitch difference channel signal. The weight vector for using the difference channel signal to cancel the interference components in the azimuth difference channel; The weight vector is used to eliminate interference components in the pitch difference channel using the difference channel signal. This represents the inverse matrix of the azimuth difference channel signal autocorrelation matrix. Its function is to whiten the reference signal and eliminate the influence of the reference signal's own correlation on the weight estimation. The cross-correlation matrix between the sum channel signal and the azimuth difference channel signal; The matrix representing the inverse of the autocorrelation matrix of the pitch difference channel signal; The cross-correlation matrix between the sum channel signal and the pitch difference channel signal; This represents the inverse matrix of the autocorrelation matrix of the differential channel signal; This is the cross-correlation matrix between the azimuth difference channel signal and the difference channel signal; This represents the cross-correlation matrix between the elevation difference channel signal and the differential difference channel signal. The four weighting formulas above are all based on Wiener filtering theory. Their physical meaning is to solve for the optimal complex weight vector that minimizes the output interference power after cancellation, using the autocorrelation matrix of each reference channel and the cross-correlation matrix of the main channel and the reference channel, under the minimum mean square error criterion. For radar systems without a pre-reserved differential difference channel, and It cannot be calculated; the interference signal in the differential channel cannot be removed by cancellation. In this case, only [the following method can be used]. and The channels are then canceled out.

[0067] As an alternative implementation, in scenarios with high real-time requirements or limited computing resources, a simplified scalar weight calculation formula can also be used, the complete expression of which is: ; in, , , , These are simplified scalar forms of azimuth cancellation weights, pitch cancellation weights, azimuth difference-difference channel cancellation weights, and pitch difference-difference channel cancellation weights, respectively. To and the radiation pattern in the direction of the interference source The response value at the location; The azimuth difference pattern is shown in the direction of the interference source. The response value at the location; The pitch difference pattern is shown in the direction of the interference source. The response value at the location; The difference pattern is shown in the direction of the interference source. The simplified form utilizes prior knowledge of the antenna pattern, approximating the matrix inversion operation with the ratio of the pattern's response at the direction of the interference source. It is suitable for situations where the location of the interference source is known or changes slowly, and can significantly reduce computational complexity.

[0068] After completing the weight calculation, sub-step 132 is executed to perform interference suppression processing on the initial and channel signals using the optimal cancellation weights, generating the updated and patterned cancelled and channel signals. Specifically, this includes: multiplying the optimal cancellation weights with the initial differential channel signal to obtain the interference compensation component; subtracting the interference compensation component from the initial and channel signals to output the cancelled and channel signals. For radar systems without a pre-reserved differential channel, the cancelled and channel signals can be represented as: ; in, For the canceled and channel signals; For initial and channel signals; For directional cancellation weights; This is the azimuth difference channel signal; To cancel out the pitch weights; This is the pitch difference channel signal. The subtraction operation essentially removes the interference components reconstructed from the difference channel from the sum channel, significantly improving the signal-to-interference-plus-noise ratio (SNR) of the target echo in the sum channel signal after cancellation. Since the weights are adaptively calculated based on statistical characteristics, the updated sum pattern automatically forms nulls in the direction of interference, achieving dynamic reshaping of the sum pattern.

[0069] Simultaneously, sub-step 133 is executed, directly extracting the initial difference channel signal into the canceled difference channel signal to maintain the difference pattern of the difference channel before and after cancellation. The canceled difference channel signal undergoes no adaptive weighting processing and is completely equivalent to the original initial difference channel signal (or in some implementations, it only undergoes a fixed normalized gain, without changing the shape of the pattern). Considering that the accuracy of single-pulse angle measurement is highly dependent on the monotonicity and stability of the difference and ratio, if the difference channel also participates in adaptive cancellation, its pattern will be dynamically distorted with the interference environment, leading to nonlinearity of the angle measurement curve or even the appearance of a blind zone, causing the error analysis to lose its reference. By locking the difference channel, this application strictly limits the variables introduced by cancellation to the sum channel side, ensuring the rigidity of the angle measurement reference ruler, so that the mapping relationship called in the subsequent step 140 remains valid, thereby ensuring the accuracy and attributability of the angle measurement error analysis results from a mathematical perspective.

[0070] After the cancellation process is completed, the single-pulse slope under different conditions needs to be calculated based on the single-pulse angle measurement model to obtain the radar indication angle. The single-pulse slope is the ratio of the difference channel signal to the sum channel signal, and there is a definite mapping relationship between it and the radar indication angle. Depending on the different operating conditions, the calculation of the single-pulse slope is divided into the following three cases: Under ideal conditions, i.e., without considering the amplitude-phase difference of the phased array antenna channel, the formula for calculating the single-pulse slope of the elevation angle is: ; in, The slope of a single pulse under ideal conditions; The pitch difference pattern response under ideal conditions; This represents the sum and pattern response under ideal conditions. This ratio changes approximately linearly near the beam center, and its slope determines the angle measurement sensitivity.

[0071] Under non-ideal hardware channel conditions, i.e., considering amplitude-phase inconsistency in the receiving channel, the formula for calculating the single-pulse slope of the elevation angle is: ; in, The slope of a single pulse under non-ideal conditions; The pitch difference pattern response includes channel amplitude and phase errors; The sum and pattern response include channel amplitude and phase errors. Because amplitude and phase errors disrupt the ideal symmetrical superposition relationship between subarrays, the single-pulse slope curve under non-ideal conditions will be distorted, manifesting as increased nonlinearity and zero-point shift.

[0072] After cancellation, the difference radiation pattern remains unchanged while the sum radiation pattern has been updated. The formula for calculating the single-pulse slope of the pitch angle is as follows: ; in, The slope of the single pulse after cancellation; The pitch difference pattern response after cancellation remains unchanged since the difference channel does not participate in the cancellation. This represents the updated sum and radiation pattern response after cancellation. The cancellation process alters the spatial response characteristics of the sum and radiation channels, causing a change in the single-pulse slope after cancellation compared to before cancellation. This change is the mathematical root cause of the angle measurement error introduced by cancellation. By comparing and analyzing the single-pulse slopes under the above three scenarios, the impact of cancellation processing and channel non-ideals on radar angle measurement accuracy can be quantitatively assessed.

[0073] Based on the above embodiments, this embodiment refines the process of comparing the radar indication angle with the target's true angle in step 150 to obtain the angle measurement error. Given that radar faces various operating conditions in practice, a single error evaluation index is insufficient to fully reflect system performance. Therefore, this embodiment provides a multi-condition angle measurement error analysis strategy for different operating modes.

[0074] Specifically, when the radar is in the search and scanning phase and point convergence processing is not performed, the relative angle between the azimuth of the interference source and the center of the radar beam in the spatial radiation signal under different beam directions is extracted. Here, the relative angle refers to the instantaneous spatial angle difference between the direction of the interference source and the direction of the maximum value of the radar received beam at the current moment; it is a key geometric variable affecting cancellation performance and angle measurement accuracy. Subsequently, the difference between the output radar indication angle and the target's true angle is calculated within different offset intervals of the relative angle to determine the angle measurement error of a single observation. The offset interval is a quantification method that divides continuous relative angles into several discrete statistical windows; for example, each interval can be divided into 0.5° or 1° to observe the local characteristics of the error changing with the angle. Through this partitioned statistical method, the angle measurement deviation introduced by the cancellation algorithm under a single beam illumination can be accurately characterized. Based on experimental verification data, when the receiving channel exhibits 2dB amplitude inconsistency and 10° phase inconsistency, the cancellation analysis method proposed in this application reduces the sensitivity of the angle measurement error to amplitude-phase inconsistency by an order of magnitude compared to traditional methods, indicating that the analysis strategy has good robustness. Further statistical analysis shows that the angle measurement error of a single observation exhibits a significant trend of being large at both ends and small in the middle as the relative angle changes: when the beam points towards the target (i.e., the relative angle is close to zero), the angle measurement error introduced by cancellation is minimal; as the beam gradually deviates from the target or the interference source deviates from the beam center, the angle measurement error gradually increases; when the target coincides with the interference source and the beam direction deviates from the maximum angle of the interference source within the main lobe, the angle measurement error introduced by cancellation reaches its extreme value and then decreases. This analysis reveals the spatial distribution characteristics of instantaneous angle measurement performance in the search mode, providing fine-grained data support for optimizing beam dwell time and interference suppression parameters.

[0075] As another implementation method, when the radar is in the search and scanning phase and point convergence processing is performed, point convergence calculation is performed on the radar indication angles of multiple consecutive scanning cycles. Point convergence calculation is an algorithmic process in radar data processing that associates and fuses multiple discrete points belonging to the same target into a stable track point. Essentially, it involves weighted averaging or filtering and smoothing the measurement data in the time dimension. The converged target angle is compared with the true target angle to determine the distribution range of the angle measurement error and the target angle track expansion characteristics under the condition of multiple observation accumulation. Because cancellation processing alters the statistical characteristics of the signal, the error distribution after convergence is often different from the simple superposition of single observation errors. Experimental data shows that after point convergence, compared with the target angle track obtained before cancellation, the target angle track after cancellation has expanded to a certain extent, and its angle measurement error is mainly distributed in the range of -1° to 2°. This result indicates that although cancellation processing effectively suppresses interference energy, it may introduce specific systematic biases or variance changes during multi-frame data fusion, leading to changes in the accuracy boundary at the beginning of the track. By analyzing the distribution range and track extension characteristics, the performance of the radar in the actual search and tracking handover process can be evaluated more accurately, providing a direct basis for setting the track association threshold and optimizing the parameters of the tracking filter.

[0076] As another implementation method, when the radar is in the target tracking phase, the radar indication angle is extracted from the spatial radiation signal under different angular offset positions of the interference source within the main lobe of the beam. The target tracking phase typically means that the radar beam is precisely aligned with the target. If the interference source enters the main lobe at this time, its offset from the beam center is usually small, but its impact on angle measurement accuracy is most sensitive. The difference distribution between the radar indication angle and the target's true angle is calculated to determine the angle measurement error introduced by the cancellation process during the target tracking phase. This difference distribution reflects the response capability and stability of the cancellation algorithm to weak angular deviations in a precise tracking scenario. Experimental verification shows that under main lobe interference conditions, when the interference source is located at typical offset positions such as -1°, 0°, or 1° from the beam center, the radar angle measurement error introduced after cancellation processing remains at an extremely low level, specifically less than 0.1°. This high-precision conclusion proves that the multiplexed difference channel cancellation strategy proposed in this application can effectively avoid the destruction of the precise angle measurement reference during the cancellation process while maintaining the difference pattern unchanged, ensuring that the radar still has reliable target tracking capability in a strong main lobe interference environment. The analysis results provide key criteria for determining whether a radar meets the requirements for high-precision guidance or fire control, and also verify the effectiveness of the lock-on differential channel design concept in the aforementioned embodiments in engineering applications.

[0077] like Figures 6-8As shown, this embodiment provides a hardware-in-the-loop (HIL) verification system for verifying the effectiveness of the aforementioned radar angle measurement error analysis method in a near-real electromagnetic environment. The HIL includes a hardware transceiver subsystem and a computational verification subsystem.

[0078] The hardware transceiver subsystem includes a radar receiving antenna array, signal transceiver equipment connected to the radar receiving antenna array, and synchronization control equipment connected to the signal transceiver equipment. Specifically, the radar receiving antenna array is the physical entry point for space-radiated signals, and its structural parameters (such as element spacing and subarray division) directly determine the initial sum and difference beamforming characteristics. In practical deployments, the radar receiving antenna array can be a 4×4 planar array, or it can be replaced with other sizes of linear or planar arrays depending on verification requirements. The signal transceiver equipment is the hub connecting the analog radio frequency domain and the digital baseband domain. It is responsible for down-converting and sampling the radio frequency signals sensed by the antenna into digital baseband signals, and also for up-converting the digital baseband test signals and transmitting them into space.

[0079] like Figure 7 As shown, in this embodiment, the signal transceiver preferably employs a software-defined radio platform that supports multi-channel phase synchronization. This platform has four independent transceiver channels, a maximum receiving bandwidth of 200MHz, and a sampling rate of 245.76MHz, which can meet the high-fidelity acquisition requirements of broadband radar signals. In other embodiments, the signal transceiver can also be a dedicated radar RF front-end component or a vector signal analyzer, as long as it has multi-channel synchronous transceiver capability.

[0080] Synchronization control equipment ensures strict consistency in time, frequency, and phase of multi-channel signals by providing a unified reference clock and trigger signal to the signal transceiver equipment. Specifically, since the core of the method in this application lies in multiplexing the initial difference channel signal for cancellation, this requires that a definite phase relationship must be maintained between the synchronous and differential channels. Without high-precision synchronization control, random phase drift between channels will be misjudged as interference signals or target angle deviations, leading to the failure of the cancellation algorithm or distortion of the angle measurement error analysis results. In one specific implementation, the synchronization control equipment can be integrated into the signal transceiver equipment, distributing the reference clock through an onboard clock buffer; or it can be used as an independent external instrument, broadcasting synchronization signals to multiple distributed transceiver nodes via cables.

[0081] The radar receiving antenna array receives space-radiated signals and generates received signals through signal transceivers constrained by synchronization control equipment. The received signals include an initial sum channel signal synthesized from sum beams and an initial difference channel signal synthesized from difference beams. This generation process involves both the physical induction of space electromagnetic waves by the antenna array surface and the analog or digital beamforming processing within the signal transceivers. For example, analog sum and difference signals can be directly output from the radio frequency end via a sum-difference network and then digitized by the signal transceivers; alternatively, the signal transceivers can acquire the raw data from each array element and then synthesize the sum and difference channels through digital computation.

[0082] The computational verification subsystem includes interconnected processors and memory, with signal transceivers connected to the processors. Specifically, the processor can be a general-purpose computer's central processing unit (CPU), graphics processing unit (GPU), or a dedicated processing chip in an embedded system. The memory stores a computer program that implements the radar cancellation angle measurement error analysis method. When the processor executes this program, it can convert the digital baseband data transmitted by the signal transceivers into specific analysis results. This hardware-software co-design allows theoretical algorithms to run based on real hardware responses, thereby exposing nonlinear effects, quantization noise, and channel mismatch that cannot be predicted by pure mathematical simulations.

[0083] The signal transceiver transmits the generated received signal to the processor. The processor executes a computer program stored in memory to implement the radar cancellation angle measurement error analysis method described in the previous embodiment using the received signal, calculating and outputting the angle measurement error of the corresponding received signal. In specific implementation, the processor first loads the single-pulse angle measurement model parameters and cancellation weight calculation algorithm from memory; reads the initial sum and difference channel data collected by the signal transceiver in real time or offline; executes multiplexed difference channel cancellation, radiation pattern update, and indicator angle calculation according to predetermined logic; compares the calculated radar indicator angle with the preset target true angle (which can be set by turntable feedback or simulation) to generate an angle measurement error statistical report. Through the above closed-loop verification process, the semi-physical verification system provided in this embodiment not only reproduces the complete signal processing link of radar cancellation angle measurement, but more importantly, introduces the non-ideal characteristics of real physical devices, making the analysis conclusions have extremely high engineering confidence.

[0084] In some embodiments, to verify the effectiveness of the aforementioned radar angle measurement error analysis method in a near-real physical environment, this application also provides a specific anechoic chamber verification implementation scheme. This scheme includes an anechoic chamber turntable arranged in the anechoic chamber environment, and a target signal radiation source and an interfering signal radiation source respectively disposed in the anechoic chamber environment; the target signal radiation source and the interfering signal radiation source are used to transmit spatial radiation signals; a processor is also connected to the anechoic chamber turntable and is used to change the spatial pointing angle between the target signal radiation source and the interfering signal radiation source relative to the radar receiving antenna array by adjusting the offset angle of the anechoic chamber turntable, in order to verify the angle measurement error under different spatial angle conditions.

[0085] Specifically, the construction of a darkroom environment is the physical basis for ensuring the credibility of verification results. For example... Figure 6 As shown, the verification site is a shielded microwave anechoic chamber, whose inner walls are fully covered with high-performance absorbing material to maximize the absorption of electromagnetic wave reflections, simulate free-space propagation conditions, and avoid interference from multipath effects on angle measurement accuracy. In the anechoic chamber's internal layout, both the target signal radiation source and the interference signal radiation source are mounted on a high-precision turntable, with their vertical distance from the radar receiving antenna array set, for example, to 3.9m. To achieve dynamic adjustment of the spatial angle, the radar receiving antenna array is mounted on the anechoic chamber turntable. In another optional embodiment, the target signal radiation source and the interference signal radiation source can also be mounted together on the high-precision anechoic chamber turntable. To ensure the consistency of transmission characteristics and eliminate additional error variables introduced by individual antenna differences, the target signal radiation source and the interference signal radiation source preferably use identical horn antennas.

[0086] In terms of signal flow and control of the verification system, such as Figure 8 As shown, the entire verification process forms a complete closed loop of "computer-software radio platform-anechoic chamber-computer". The computer, acting as the host computer, is responsible for generating baseband waveform data of the target signal and interference signal, and sending it to the software radio platform. The software radio platform up-converts the digital signal into a radio frequency signal, which is then fed to the transmitting antenna in the anechoic chamber via a coaxial cable for radiation. After the radar receiving antenna array senses the spatially synthesized signal in the anechoic chamber, it is down-converted and sampled by the software radio platform, and the digital baseband data is transmitted back to the computer in real time. The computer runs the algorithm program stored in its memory, performing the cancellation processing and angle calculation described in the previous embodiment on the received signal. Simultaneously, the computer sends control commands to the anechoic chamber turntable, driving it to rotate to change the mechanical angle between the antenna array beam pointing and the radiation source, and compares the calculated radar indication angle with the actual mechanical angle fed back by the anechoic chamber turntable. In this process, the software radio platform not only undertakes signal transmission and reception tasks but also ensures the phase coherence of multi-channel signals through its internal synchronization module.

[0087] In the specific verification and execution phase, system calibration is required first. With the beam pointing at 0°, the receiving channel parameters are adjusted to ensure that the amplitude ratio of the received signals from the sum and difference channels is 1 and the phase difference is 0°, thus establishing a standard angle measurement reference. Subsequently, the anechoic chamber turntable is controlled to traverse different angular positions at preset step sizes, recording and analyzing the angle measurement errors. Experimental results show that, without interference cancellation processing, the angle measurement results based on the sum and difference channels exhibit significant deviations throughout the entire test angle range. The consistency between the angle measurement curve and the actual angle change trend is poor, and the angle measurement results are significantly affected by noise and interference. As the interference signal strength increases, the radar angle measurement error shows a significant increasing trend, verifying the severe destructive effect of external interference on the performance of single-pulse angle measurement.

[0088] In contrast, the interference signal's influence on angle measurement is effectively suppressed after processing using the multiplexed difference channel cancellation method proposed in this application. Experimental data show that the angle measurement error is significantly reduced after cancellation, and the consistency between the angle measurement curve and the actual angle change trend is greatly improved. Especially under main lobe interference conditions, the cancellation process does not introduce additional nonlinear distortion. Furthermore, since the sum-difference angle measurement algorithm mainly relies on phase difference information in this scenario, and the amplitude difference between channels is extremely small, the stability of the phase relationship after cancellation becomes a key factor determining the angle measurement accuracy. The experimental results confirm that after cancellation processing, the smoothness and linearity of the phase difference curve are better than the uncancelled state, thus significantly optimizing the angle measurement accuracy and stability. These experimental data from a real hardware environment not only intuitively demonstrate the beneficial effects of this solution but also complete the entire closed loop from theoretical derivation, simulation analysis to engineering verification, fully proving the effectiveness and robustness of the radar cancellation angle measurement error analysis method proposed in this application in practical applications.

[0089] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0090] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A radar cancellation angle measurement error analysis method, characterized in that, include: Based on radar array structural parameters and spatial radiation signal characteristics, a single-pulse angle measurement model based on sum and difference channels is constructed to establish the mapping relationship between relative characteristic parameters and radar indication angle. The received signal generated after the radar array receives the spatial radiation signal includes an initial sum channel signal synthesized by sum beams and an initial difference channel signal synthesized by difference beams. The initial difference channel signal is reused to perform signal cancellation processing. The sum pattern is updated while maintaining the difference pattern of the difference channel unchanged. The canceled sum channel signal and the canceled difference channel signal are output. Based on the relative characteristic parameters of the canceled sum channel signal and the canceled difference channel signal, the mapping relationship in the single-pulse angle measurement model is invoked to calculate the radar indication angle corresponding to the received signal; The radar indication angle is compared with the target's true angle to obtain the angle measurement error corresponding to the received signal.

2. The method according to claim 1, characterized in that, The process of multiplexing the initial difference channel signal to perform signal cancellation processing, updating the sum pattern while maintaining the difference pattern of the difference channel unchanged, and outputting the cancelled sum channel signal and the cancelled difference channel signal includes: The initial difference channel signal is multiplexed into an interference reference signal, and the optimal cancellation weight is obtained by combining the initial and channel signals. The initial and channel signals are subjected to interference suppression processing using the optimal cancellation weights to generate the cancelled and channel signals with updated and patterned signals. The initial difference channel signal is directly extracted into the canceled difference channel signal to maintain the difference pattern of the difference channel before and after cancellation.

3. The method according to claim 2, characterized in that, The step of multiplexing the initial difference channel signal into an interference reference signal and calculating the optimal cancellation weights by combining the initial and channel signals includes: Calculate the autocorrelation matrix of the initial difference channel signal to characterize the spatial energy distribution characteristics of the interference reference signal; Calculate the cross-correlation matrix between the initial sum channel signal and the initial difference channel signal to characterize the interference coupling characteristics between the initial sum channel signal and the interference reference signal; Calculate the product of the inverse of the autocorrelation matrix and the cross-correlation matrix, and output the optimal cancellation weights used to reconstruct the interference compensation components; The step of using the optimal cancellation weights to perform interference suppression processing on the initial and channel signals to generate the updated and channel signals with updated patterns includes: The optimal cancellation weight is multiplied by the initial difference channel signal to obtain the interference compensation component; the interference compensation component is subtracted from the initial sum channel signal to output the cancelled sum channel signal.

4. The method according to claim 1, characterized in that, Based on radar array structure parameters and spatial radiation signal characteristics, a single-pulse angle measurement model based on sum and difference channels is constructed to establish the mapping relationship between relative characteristic parameters and radar indication angle, including: The radar array is divided into multiple subarrays; By combining the element spacing parameter in the radar array structure parameters, the progressive phase of each subarray is calculated to generate the composite radiation pattern of each subarray; The composite radiation patterns of each subarray are superimposed and subtracted to obtain the sum radiation pattern and difference radiation pattern based on the global array, respectively. Based on the relative characteristic parameters of the difference radiation pattern and the sum radiation pattern under different target angles, a single pulse slope is fitted to construct a linear mapping relationship between the relative characteristic parameters and the radar indication angle.

5. The method according to claim 4, characterized in that, The superposition and subtraction operations on the composite radiation patterns of each of the subarrays to obtain the sum radiation pattern and difference radiation pattern based on the global array, respectively, include: Obtain the amplitude fluctuation error and phase fluctuation error of the radar receiving channel; Using the amplitude fluctuation error and the phase fluctuation error, the synthetic pattern of the corresponding subarray is modulated to generate a distorted synthetic pattern containing channel non-ideal characteristics; The superposition and subtraction operations are performed on each of the distortion synthesis patterns to obtain the sum pattern and the difference pattern, respectively.

6. The method according to any one of claims 1 to 5, characterized in that, The step of comparing the radar indication angle with the target's true angle to obtain the angle measurement error corresponding to the received signal includes: When the radar is in the search and scanning phase and no point aggregation processing is performed, the relative angle between the azimuth of the interference source and the center of the radar beam is extracted in the spatial radiation signal under different beam directions. For different offset ranges of the relative angle, the difference between the radar indication angle and the target's true angle is statistically analyzed to determine the angle measurement error of a single observation.

7. The method according to claim 6, characterized in that, The method further includes: When the radar is in the search and scanning phase and is performing point convergence processing, point convergence calculation is performed on the radar indication angle for multiple consecutive scanning cycles to obtain the converged target angle. By comparing the condensed target angle with the true target angle, the distribution range of the angle measurement error and the target angle trace expansion characteristics under the condition of multiple observation accumulation are determined.

8. The method according to any one of claims 1 to 5, characterized in that, The step of comparing the radar indication angle with the target's true angle to obtain the angle measurement error corresponding to the received signal includes: When the radar is in the target tracking phase, the radar indication angle is extracted from the spatial radiation signal under the condition that the interference source is located at different angular offset positions within the main lobe of the beam. Calculate the distribution of the difference between the radar indication angle and the target's true angle to determine the angle measurement error introduced by the cancellation process during the target tracking phase.

9. A semi-physical verification system, characterized in that, include: The hardware transceiver subsystem includes a radar receiving antenna array, a signal transceiver device connected to the radar receiving antenna array, and a synchronization control device connected to the signal transceiver device. The radar receiving antenna array receives spatial radiation signals. Under the control of the synchronization control device, the signal transceiver generates a received signal based on the spatial radiation signals received by the radar receiving antenna array. The received signal includes an initial sum channel signal synthesized by sum beams and an initial difference channel signal synthesized by difference beams. The computational verification subsystem includes a processor and a memory interconnected, and the signal transceiver is connected to the processor. The signal transceiver device transmits the generated received signal to the processor, and the processor executes a computer program stored in the memory to implement the radar cancellation angle measurement error analysis method as described in any one of claims 1 to 8 using the received signal, and calculates and outputs the angle measurement error corresponding to the received signal.

10. The system according to claim 9, characterized in that, It also includes a darkroom turntable arranged in the darkroom environment, and a target signal radiation source and an interference signal radiation source respectively arranged in the darkroom environment; The target signal radiation source and the interference signal radiation source are used to emit the space radiation signal; The anechoic chamber turntable is used to support the radar receiving antenna array, or to support the target signal radiation source and the interference signal radiation source; The processor is also connected to the anechoic chamber turntable and is used to drive the radar receiving antenna array to rotate relative to the radiation source by adjusting the offset angle of the anechoic chamber turntable, so as to change the spatial pointing angle between the target signal radiation source and the interference signal radiation source relative to the radar receiving antenna array, thereby verifying the angle measurement error under different spatial angle conditions.

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