Airborne radar variable scale mutual exclusion waveform subset design method

Abstract

The invention discloses an airborne radar variable scale mutual exclusion waveform subset design method, and belongs to the field of airborne fire control radar systems, and the method comprises the steps: initializing airborne radar waveform parameters and performance indexes; designing waveform parameters and mutual exclusion performance indexes to generate a variable-scale mutual exclusion subset; and performing mutual exclusion waveform screening according to the non-fuzzy distance and the non-fuzzy speed index. According to the method, an airborne radar confrontation waveform variable scale mutual exclusion subset is optimally designed, so that waveform agility in a single task period of the radar is not repeated, and the problem that an existing airborne radar waveform is easy to intercept and sort is solved; the method can be suitable for an existing airborne radar system, can generate a mutual exclusion waveform set meeting different detection capability requirements under the condition that hardware can be realized, expands the waveform complexity and the frequency spectrum utilization rate, and improves the radar search efficiency; the problem that an existing airborne radar is fixed in waveform and easy to detect and sort can be solved, and the detectability of the airborne radar in a complex confrontation environment is improved.

Description

Technical Field

[0001] This invention belongs to the field of airborne fire control radar systems and relates to a method for optimizing and designing variable-scale mutually exclusive waveform subsets for airborne radar. Background Technology

[0002] As future combat systems continue to evolve, the intensity of battlefield electromagnetic warfare is constantly increasing, and the battlefield situation is changing rapidly. Airborne platforms are increasingly demanding rapid, low-intercept situational awareness capabilities from their radars. Looking at the radar capabilities of advanced foreign military aircraft, the system design, detection mode design, and detection waveform design of airborne radars are all continuously developing in multiple directions towards the low-intercept domain to ensure the platform's survivability and combat effectiveness in highly contested environments.

[0003] As a carrier of interaction with targets, the environment, and jammers, radar transmitted waveforms possess inherent advantages in countering jammers. Therefore, breakthroughs can be sought at the radar transmitter to gain the initiative in electronic warfare. For example, given the time required for coherent copying and forwarding of digital radio frequency memory (RFMemory), the transmitter can utilize waveform diversity and agility to alter one or more parameters of the transmitted signal in both the fast and slow time domains. This makes the transmitted signal random and exhibits low inter-pulse correlation, preventing the jamming signal from gaining sufficient coherence gain at the radar receiver and thus successfully suppressing it. Furthermore, radar jamming presupposes that the radar signal is intercepted by enemy electronic warfare equipment. The interception process involves measuring, sorting, and identifying parameters such as the radar signal's carrier frequency, bandwidth, duration, pulse repetition period, and modulation method. Therefore, using transmitted waveforms with large bandwidth-time product, complex signal forms, and agile parameters significantly increases the difficulty of measurement and sorting for the enemy receiver, reduces the probability of radar signal interception, and ultimately prevents effective coherent jamming.

[0004] Existing research shows that using parameter-agile waveforms can effectively reduce the probability of radar interception, improve countermeasure capabilities, and expand the unambiguous detection range. However, currently, airborne radar parameter-agile waveforms still have the following problems: 1) Airborne radar waveform libraries are relatively fixed, limiting their application scenarios and resulting in low search efficiency; 2) Most waveform optimization algorithms require offline processing, and the waveform optimization speed cannot meet the real-time processing requirements of hardware; 3) The waveform complexity and spectral efficiency are not high enough to meet the application requirements in complex electromagnetic warfare environments; 4) Most anti-warfare waveform design techniques are still in the theoretical stage and have insufficient correlation with actual combat performance indicators. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention aims to provide a method for designing variable-scale mutually exclusive waveform subsets for airborne radar.

[0006] The technical solution of this invention is as follows: This invention proposes a method for designing variable-scale mutually exclusive waveform subsets for airborne radar, with the following specific steps: Step 1: Initialize airborne radar waveform parameters and performance indicators From the radar equation:

[0007] in, The minimum energy required for a radar to detect a target; This refers to the radar's transmitted signal power. Antenna gain; The target's reflective cross-sectional area; The wavelength. Due to the receiver input noise power. , Boltzmann's constant, Standard room temperature, Given the receiver bandwidth, the input signal power is:

[0008] If the radar's detection threshold is set to the minimum output signal-to-noise ratio Then the minimum detectable signal power can be expressed as

[0009] At this point, a new radar equation can be obtained:

[0010] Modern radar uses statistical decision methods based on statistical detection theory to detect signals. The minimum output signal-to-noise ratio required to detect a target signal is also known as the detection factor. ,Right now . This refers to the minimum signal-to-noise ratio (SNR) that a single pulse at the detector input must achieve to meet the required detection performance; it is also often expressed as... Generally, bandwidth is approximated as the derivative of time width, i.e. Then energy signals can be introduced. Replace pulse power Using detection factors replace And considering the receiver bandwidth ratio When the bandwidth is large, a bandwidth correction factor is added to the radar equation. This is understandable. Substituting into the radar equation, we get:

[0011] Using detection factors and energy The radar equations can be expressed in a way that facilitates subsequent pulse compression and coherent accumulation. We now assume that other parameters remain constant. Then the original expression is:

[0012] Variations in radar waveform parameters are constrained by radar performance and, in turn, affect waveform characteristics. Based on this, a corresponding scaling factor, its constraints, and range are designed by analyzing radar performance.

[0013] a) Duty cycle For pulse train signals, the duty cycle not only relates to the signal energy and affects the signal processing effect after receiving the echo, but it is also one of the important characteristics of the signal. In order to better control it, a pulse width scaling factor is set here. and PRI scaling factor Their relationship with their respective parameters is as follows: ; ,in and Let PRI and pulse width be the maximum configurable signal values. The energy of a single pulse signal controlled by the scaling factor can be expressed as: ,in for and The corresponding signal energy.

[0014] b) Pulse pressure The output of the matched filter for a linear frequency modulated signal is a Sinc function with a time width of . According to the law of conservation of energy ,have The peak power of the output pulse is greater than that of the peak power of the input pulse. This means that the peak amplitude of the received signal after pulse compression is 1 / 3 of the original peak amplitude of the transmitted signal. The bandwidth correction factor is multiplied by 10 times. ,but ,in This is the bandwidth scaling factor.

[0015] c) Coherent accumulation improvement factor Since single pulses have limited energy, radar typically does not use a single received pulse for detection and decision-making. Before decision-making, multiple pulses of a single pulse position are coherently or incoherently accumulated. Coherent accumulation is performed before envelope detection; by utilizing the phase relationship between the received pulses, the superposition of signal amplitudes can be obtained. Theoretically, the signal-to-noise ratio (SNR) of coherent accumulation is equal to the SNR of a single pulse multiplied by the number of pulse trains. Here, we define a coherent accumulation improvement factor. Then there is Therefore, the formula for radar detection range after signal processing can be obtained:

[0016] To maintain the original distance equation, the following must be satisfied:

[0017] To ensure that changes in the mutual exclusion factor do not affect the detection range, the following conditions must be met:

[0018] d) Distance fuzzy criterion The unambiguous distance corresponding to a fixed PRI pulse train is When the fuzzy distance is not less than At that time, the pulse repetition period must satisfy .

[0019] e) Velocity fuzzy criterion The formula for calculating Doppler frequency shift is: ,in The upper limit of the set carrier frequency, The radial velocity of the target relative to the radar. The carrier frequency scale factor is . The unambiguous Doppler frequency corresponding to the fixed PRI of the radar is . When the required frequency offset is less than When, then it must meet the following conditions. .

[0020] f) Near-field occlusion criteria To achieve optimal radar range resolution and reduce near-range obstruction, pulse radar is not allowed to receive any signals during each transmitted pulse until the pulse has been fully transmitted. This limits the radar's minimum effective range. ,therefore Must meet: .

[0021] g) Coherent accumulation quantity criterion When performing coherent accumulation processing on a signal, there is an upper limit to the coherent accumulation time; coherent accumulation can only be performed on target echo signals within the same gate. Let the coherent accumulation time be... Then the number of coherent pulses needs to satisfy .

[0022] Based on the above analysis, we can draw the following conclusions regarding the scaling factor. The set of mutually exclusive waveform subsets is as follows:

[0023] Variable-scale mutually exclusive waveforms are obtained through a scale factor. The random combination forms a waveform set. Assume the radar has the following quantities for each scale factor: Then the number of waveforms that can be constructed is:

[0024] The waveform set is divided into several categories based on the previously derived criteria. A subset of waveform parameters If a subset of waveform parameters is formed, then there is a corresponding mutual exclusion factor. The corresponding waveforms are:

[0025] in , For specific waveforms, the following analysis and design will focus on point frequency, linear frequency modulation, and Barker code signals. The corresponding waveforms are... This represents the maximum value of each parameter that meets the conditions.

[0026] Mutually exclusive waveforms have the same detection capability, but they differ in waveform details by creating parameter differences. For the same parameter, the greater the difference, the better the mutual exclusion of the waveforms. When multiple different parameters differ, the mutual exclusion effect is weighted and superimposed to achieve the desired mutual exclusion effect.

[0027] Step 2: Design waveform parameters and mutual exclusion performance indices to generate variable-scale mutually exclusive subsets. After determining the upper and lower bounds of each factor according to the radar detection criteria ( ), and divide each factor into ranges There are discrete points. The value of each factor at each discrete point is... Given the initial radar detection capability, according to the formula... Select all combinations that satisfy this formula to form a new subset of scaled waveforms:

[0028] in This indicates the scale factor index of the current waveform. The detection power coefficient corresponding to the waveform generated by the scale factor is set to...

[0029] The corresponding radar power measurement coefficient can then be set as follows:

[0030] in As a reference element, For other elements in the subset that meet the requirements, set the allowable fluctuation range of power. Within 5%. Then the set condition. It can be written quantitatively as: Since the scale factor combination distribution is mainly in the lower-middle range of radar power, in order to divide the total combination set into multiple combination subsets with similar radar power and mutually exclusive parameters, we set a mutual exclusion value to measure the waveform mutual exclusion performance of the four scale factor combinations. First, we construct a 4-dimensional vector about the scale factors. Then the mutual exclusion value between two mutually exclusive waveforms is:

[0031] This represents the mutual exclusion difference between the subsequent waveform and the current waveform. After obtaining a set of waveforms with similar radar power, it is necessary to further divide the elements within them to meet practical applications. After initially dividing the entire set by radar detection power to obtain a set of radars with the same power, the mutual exclusion coefficient of each combination element is calculated according to the above formula. Based on the coefficient differences, the set is further divided into subsets with mutual exclusion differences. The method is as follows: Figure 1 As shown.

[0032] After obtaining the waveform set that satisfies the radar power requirement, a series of mutual exclusion coefficients are set. The scaling factor of the current waveform is substituted into the formula to filter the set. After calculating mutually exclusive values, the scaling factors of the waveforms in the set fall within a certain coefficient range. It is assumed that the combined elements within this range (subset) have similar and non-exclusive radar power, while combined elements in different ranges (subsets) have the same but mutually exclusive radar power. The new mutually exclusive waveform subset is represented as follows:

[0033] After separating the signals into different power sets, K-means multidimensional clustering algorithm is used within each set to cluster the mutual exclusivity of the signals, generating corresponding mutually exclusive subsets. Based on this, a variable-scale mutual exclusive waveform parameter selection method is proposed to improve the performance of mutual exclusive waveforms in practical applications.

[0034] Furthermore, different combinations, due to their varying parameters, will cause fluctuations in the duration of each frame's signal. Therefore, to better statistically analyze and utilize the combined elements within a subset, a mutual exclusion factor is set to determine the duration of the combined elements. After each frame of signal action ends, the system switches to other combined elements in the subset to achieve similar effects and mutually exclusive characteristics. Analysis reveals... The scaling factor, determined by the pulse accumulation time and pulse repetition interval, is expressed as follows: .

[0035] Step 3: Perform mutually exclusive waveform filtering based on unambiguous distance and unambiguous speed indices. Based on the generated mutually exclusive waveform subsets, a two-step screening method is used to divide the subsets. The complete set of scale factor combinations is divided into different scale waveform sets according to the differences in radar power. Then, mutual exclusion is performed within these sets to generate mutually exclusive subsets, resulting in a final set of multiple variable-scale mutually exclusive waveform subsets.

[0036] This invention optimizes the design of variable-scale mutually exclusive subsets of airborne radar countermeasure waveforms from multiple parameter dimensions such as space, time, frequency, phase, and power. This ensures that the waveforms change rapidly and do not repeat within a single radar mission cycle, thus improving the problem that existing airborne radar waveforms are easily intercepted and sorted. The optimized design of radar waveform parameters focuses on improving radar detection performance and expanding the application scope and strategies of agile waveforms in electromagnetic countermeasures environments.

[0037] The technical effects of this invention are as follows: This invention is applicable to existing airborne radar systems and can generate mutually exclusive waveform sets that meet different detection capability requirements under hardware-featured conditions, thereby expanding waveform complexity and spectrum utilization and improving radar search efficiency. It can solve the problem of fixed waveforms in current airborne radar systems, which are easily detected and sorted, and improve the detection capability of airborne radar in complex combat environments. Attached Figure Description

[0038] Figure 1 This is a flowchart for generating mutually exclusive waveform subsets. Figure 2 This is a flowchart of the generation of three sets of repetition frequency signals. Figure 3 This is a flowchart of the generation of three sets of repetition frequency signals. Figure 4 This is a radar power distribution map based on a combination of global search scale factors. Figure 5 The number of elements in each waveform set Figure 6 It is an unambiguous distance statistics chart of triple frequency combination. Figure 7 It is an unambiguous distance statistics chart of a five-frequency combination. Figure 8 It is an unambiguous distance statistics chart of a seven-frequency combination. Figure 9 It is an unambiguous velocity probability statistical graph of mutually exclusive waveform combinations. Detailed Implementation The present invention will be further described below through specific embodiments.

[0039] Reference Figure 1 As shown, after initially dividing the entire set into sets with the same radar power by radar detection power, the mutual exclusion coefficients of each combination element are calculated according to the above formula. Based on the coefficient differences, the set is further divided into subsets with mutual exclusion differences, generating a flowchart of mutually exclusive waveform subsets.

[0040] Reference Figure 2 As shown, after initially dividing the entire set into sets with the same radar power by radar detection power, the mutual exclusion coefficients of each combination element are calculated according to the above formula. Based on the coefficient differences, the set is further divided into subsets with mutual exclusion differences, generating a flowchart of mutually exclusive waveform subsets.

[0041] Reference Figure 3 As shown, after initially dividing the entire set into sets with the same radar power by radar detection power, the mutual exclusion coefficients of each combination element are calculated according to the above formula. Based on the coefficient differences, the set is further divided into subsets with mutual exclusion differences, generating three sets of repetition frequency signal generation flowcharts.

[0042] Reference Figure 4 As shown, after initially dividing the entire set into sets with the same radar power by radar detection power, the mutual exclusion coefficients of each combination element are calculated according to the above formula. Based on the coefficient differences, the set is further divided into subsets with mutual exclusion differences, generating a radar power distribution map of global search scale factor combinations.

[0043] Reference Figure 5-8 As shown, based on the radar detection equation, waveform parameters and performance indicators are initialized. The given pulse width parameter has a lower limit of 0.5 μs, a parameter interval of 0.04 μs, and an upper limit of 4 μs. The PRI parameter has a lower limit of 1 μs, a parameter interval of 0.25 μs, and an upper limit of 20 μs. The bandwidth parameter has a lower limit of 2 MHz, a parameter interval of 0.1 MHz, and an upper limit of 20 MHz. The coherent pulse number has a lower limit of 64, a parameter interval of 8, and an upper limit of 256. The carrier frequency parameter has a lower limit of 8 GHz, a parameter interval of 0.01 GHz, and an upper limit of 12 GHz. Based on parameter pairings, a total of 9.5 billion parameter combinations can be obtained. According to the radar power distribution rules, 20 waveform sets with different radar powers were successfully identified. Figure 4 The distribution of radar power across all scale factors is given after a global search.

[0044] Reference Figure 9 As shown, the same test was conducted by extracting 1000 times from the mutually exclusive subset to perform speed deblurring experiments. The experimental data were statistically analyzed, and the unblurred speed showed very good performance on the repetition frequency signals of the three groups.

[0045] (1) Step 1: Based on the radar detection equation, waveform parameters and performance indicators were initialized. The pulse width parameter had a lower limit of 0.5 μs, a parameter interval of 0.04 μs, and an upper limit of 4 μs. The PRI parameter had a lower limit of 1 μs, a parameter interval of 0.25 μs, and an upper limit of 20 μs. The bandwidth parameter had a lower limit of 2 MHz, a parameter interval of 0.1 MHz, and an upper limit of 20 MHz. The coherent pulse number had a lower limit of 64, a parameter interval of 8, and an upper limit of 256. The carrier frequency parameter had a lower limit of 8 GHz, a parameter interval of 0.01 GHz, and an upper limit of 12 GHz. Based on parameter pairings, a total of 9.5 billion parameter combinations were obtained. According to the radar power distribution rules, 20 waveform sets with different radar powers were successfully identified. Figure 4 The distribution of radar power across all scale factors is given after a global search. Figure 5 Provide the number of elements in each waveform set curve.

[0046] (2) Step 2: After separating the signals into different power sets, the K-means multidimensional clustering algorithm is used within each set to cluster the mutually exclusive signals, generating corresponding mutually exclusive subsets. The basic idea is to iteratively find a partitioning scheme of K clusters that minimizes the loss function corresponding to the clustering result. The loss function can be defined as the sum of squared errors between each sample and its cluster center.

[0047]

[0048] in To represent the first One sample, yes The cluster to which it belongs The center point corresponding to the cluster. Let be the total number of samples. Based on the above formula, 80 mutually exclusive subsets are finally divided into the Power set.

[0049] (3) Step 3: A two-step selection method is used to divide the subsets. Based on the differences in radar power, the complete set of scale factor combinations is divided into different scale waveform sets. Then, mutual exclusion is performed within these sets to generate mutually exclusive subsets, resulting in a final subset of mutually exclusive waveforms with multiple variable scales.

[0050] After obtaining 20 sets of powerful waveforms and their corresponding mutually exclusive subsets through experiments using the above method, a required number of mutually exclusive subsets (using 3, 5, and 7 repetition frequency signals as experimental objects) were randomly selected. One combination element was then randomly extracted from these subsets as the repetition frequency signal for experimentation. The unambiguous distance and unambiguous velocity of the signal groups after deambiguation were statistically tested 1000 times each to analyze their feasibility. For combinations with mediocre performance, targeted extraction procedures were designed to improve the results. Specific simulation experiments are as follows: a) Unambiguous distance For the 3rd, 5th, and 7th frequency repetition signals, a distance deblurring experiment was conducted 1000 times using mutually exclusive subsets. The experimental statistical results are shown below. Figure 6 , Figure 7 , Figure 8 As shown, the proportions of unambiguous distances exceeding 200 km for each frequency repetition frequency are 60.5%, 95.2%, and 99.5%, respectively. In the experiment, the compliance rate of mutually exclusive combinations extracted from 5 frequencies well meets the actual detection requirements. However, the compliance rate for 3 frequencies is relatively low. Therefore, after generating subsets, elements from the three mutually exclusive subsets cannot be arbitrarily combined; a screening step is required to select from elements that meet the coprime condition. For combinations of 5 or more frequency repetition frequencies, since the coprime rate of random combinations is high, they can be directly extracted and used. Only a simple identification of their unambiguous distance is needed. Even if the unambiguous distance of the selected combination is short, it can be extracted again without affecting the actual waveform generation efficiency.

[0051] b) Unambiguous speed Similarly, 1000 speed unambiguity experiments were conducted using a mutually exclusive subset, and the experimental data were statistically analyzed. The unambiguous speed demonstrated excellent performance on the repetition frequency signals of the three groups. The statistical results of these 1000 experiments are as follows: Figure 9 As shown in the figure, the number of samples with unambiguous speeds greater than 2 km / s in the experiment was 999, and the minimum value of 1875 m / s also meets the requirements for practical use. Based on the simulation experiment, it can be concluded that mutually exclusive waveform subsets have great potential and good feasibility in practical applications. For combinations of more than 5 repetition frequencies, the pass rate for unambiguous distances exceeding 200 km can exceed 95%. Even with 3 repetition frequencies, the predetermined indicators can be achieved and the pass rate improved by adding a screening step during the selection of mutually exclusive elements, demonstrating very high practical value.

Claims

1. A method for designing variable-scale mutually exclusive waveform subsets for airborne radar, the specific steps of which are as follows: Step 1: Initialize airborne radar waveform parameters and performance indicators; Step 2: Design waveform parameters and mutual exclusion performance indicators to generate variable-scale mutually exclusive subsets; Step 3: Perform mutually exclusive waveform filtering based on unambiguous distance and unambiguous speed indicators.

2. The method according to claim 1, characterized in that, Step 1: Initialize airborne radar waveform parameters and performance indicators Modern radar uses statistical decision methods based on statistical detection theory to detect signals. The minimum output signal-to-noise ratio required to detect a target signal is also known as the detection factor. ,Right now And considering the receiver bandwidth ratio When the bandwidth is large, a bandwidth correction factor is added to the radar equation. This is understandable. Using detection factors and energy The radar equations can be expressed in a way that facilitates subsequent pulse compression and coherent accumulation. We now assume that other parameters remain constant. Variations in radar waveform parameters are constrained by radar performance and also affect waveform characteristics. By analyzing radar performance, the corresponding scale factor and its constraints and ranges can be designed.

3. The method according to claim 1, characterized in that, In step two, designing waveform parameters and mutually exclusive performance indices to generate variable-scale mutually exclusive subsets refers to determining the upper and lower bounds of each factor according to radar detection criteria. ), and divide each factor into ranges There are discrete points, and the value of each factor at each discrete point is... Given the initial radar detection capability, according to the formula... Select all combinations that satisfy this formula to form a new subset of scaled waveforms: in This indicates the scale factor index of the current waveform. The detection power coefficient corresponding to the waveform generated by the scale factor is set to... The corresponding radar power measurement coefficient can then be set as follows: in As a reference element, For other elements in the subset that meet the requirements, set the allowable fluctuation range of power. If it is within 5%, then the set condition is... It can be written quantitatively as: Since the distribution of scale factor combinations is mainly in the lower-middle position of radar power, in order to divide the entire combination set into multiple combination subsets with similar radar power and mutually exclusive parameters, a mutual exclusion value is set to measure the waveform mutual exclusion performance of the combination of four scale factors.

4. The method according to claim 3, characterized in that, To measure the waveform mutual exclusion performance of the combination of four scale factors, a mutual exclusion value is first constructed. Then the mutual exclusion value between two mutually exclusive waveforms is: It represents the mutual exclusion difference between the subsequent waveform and the current waveform. After obtaining a set of scale waveforms with similar radar power, it is necessary to further divide the elements to meet practical applications. After initially dividing the entire set by radar detection power to obtain a set of radar power with the same power, the mutual exclusion coefficient of each combination element is calculated according to the above formula. Based on the difference in coefficients, the set is further divided into subsets with mutual exclusion differences.

5. The method according to claim 4, characterized in that, After obtaining the waveform set that satisfies the radar power requirement, a series of mutual exclusion coefficients are set. The scaling factor of the current waveform is substituted into the formula to filter the set. After calculating the mutual exclusion value, the scaling factors of the waveforms in the set are within the coefficient interval. It is assumed that the radar power of the combined elements in this interval (subset) is similar and not mutually exclusive, while the radar power of the combined elements in different intervals (subsets) is the same but mutually exclusive. The new mutually exclusive waveform subset is represented as follows. After separating the different power sets, the K-means multidimensional clustering algorithm is used within each set to cluster the mutual exclusivity of the signals and generate corresponding mutually exclusive subsets.

6. The method according to claim 4 or 5, characterized in that, Set the duration of the combination of mutually exclusive factors. After each frame of signal ends, the system switches to other combined elements in the subset to achieve similar effects and mutually exclusive features. Analysis revealed... The scaling factor, determined by the pulse accumulation time and pulse repetition interval, is expressed as follows: .

7. The method according to claim 1, characterized in that, Step 3 involves filtering mutually exclusive waveforms based on unambiguous distance and unambiguous speed indices. A two-step filtering method is used to divide the subsets based on the generated mutually exclusive waveform subsets.

8. The method according to claim 7, characterized in that, The two-step screening method divides the complete set of scale factors into different scale waveform sets based on the differences in radar power, and then performs mutual exclusion distinctions in the sets to generate mutually exclusive subsets, thus obtaining the final set of mutually exclusive waveform subsets with multiple variable scales.

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