A method for designing random frequency-modulated waveforms that suppress range sidelobes and range ambiguities

Abstract

This invention provides a method for designing stochastic frequency-modulated waveforms to suppress range sidelobes and range ambiguity. The method includes: Step 1: Initialization, inputting the center frequency f of the waveform. c The first step is to determine the bandwidth B and pulse width T; the second step is to determine the instantaneous frequency f of the RFM waveform based on the random Fourier coefficients. t The variance Var(f) t The third step: design N and D; after determining N, use Var(f) to define the range of N and D. t The range of D can be calculated from the range of ), and the largest possible D is selected within this range to obtain a narrower main lobe width; the fourth step: generate random Fourier coefficients; the fifth step: obtain the output RFM waveform. This invention can generate a large-capacity waveform set with low sidelobes, good quasi-orthogonality, high spectral compactness, and constant amplitude. At the same time, by increasing the number of waveforms, sidelobes can be effectively reduced and the maximum unambiguous distance can be extended.

Description

Technical Field

[0001] This invention relates to the field of radar detection and imaging, specifically to a method for designing stochastic frequency modulated waveforms to suppress range sidelobes and range ambiguity. Background Technology

[0002] Suppressing range sidelobes and range ambiguity is crucial for improving radar system performance. Linear frequency modulated waveforms exhibit a high sidelob of -13.26 dB after pulse compression, which can lead to target masking. Range ambiguity, on the other hand, limits the detection swath width and restricts the radar's dynamic range in the presence of nearby land / sea clutter. With the increasing demand for accurate detection, high-quality imaging, and wide-swath remote sensing, suppressing range sidelobes and range ambiguity becomes even more critical.

[0003] Traditional methods for reducing range sidelobes include using window functions, but windowing introduces a loss in signal-to-noise ratio (SNR). On the other hand, a direct way to suppress range ambiguity is to set a lower pulse repetition frequency. However, a low pulse repetition frequency leads to Doppler ambiguity. Furthermore, constructing multiple channels to mitigate range ambiguity inevitably increases system complexity. In recent years, waveform design has received increasing attention due to its ability to improve radar system performance. Low-sidelobe quasi-orthogonal radar waveforms can suppress sidelobes without sacrificing SNR, and when combined with pulse-agile transmission methods, range ambiguity can be reduced. Therefore, many researchers have begun to study the design of low-sidelobe quasi-orthogonal radar waveforms.

[0004] For the design of low-sidelobe quasi-orthogonal radar waveforms, scholars have proposed various waveform models, which can be broadly classified into two categories. The first category employs deterministic modulation, including phase-coded waveforms, waveforms based on positive and negative linear frequency modulation (LFM), orthogonal frequency division multiplexing-linear frequency modulation (OFDM-LFM), piecewise nonlinear frequency modulation (FFM), and nonlinear frequency modulation (FFM) waveforms based on Fourier series. Deterministic modulation means that the parameters in these waveform models are determined by optimization. Therefore, their low sidelobe and quasi-orthogonal characteristics are determined by the optimized waveform parameters and are also closely related to the selected waveform model and optimization algorithm. For designing a large set of waveforms that simultaneously possess low autocorrelation function (ACF) and low cross-correlation function (CCF), diverse waveform models and effective optimization algorithms are crucial. Mittermayer et al. (MITTERMAYER J, MARTíNEZ J M. Analysis of range ambiguity suppression in SAR by up and downchirp modulation for point and distributed targets[C]. IGARSS 2003,6:4077-4079.) provided a derivation based on positive and negative linear frequency modulation waveforms, but only two waveforms were used. To expand the number of waveforms, Wang (WANG WQ. MIMO SAR OFDM chirp waveform diversity design with random matrix modulation[J]. IEEE Transactions on Geoscience and Remote Sensing,2014,53(3):1615-1625.) proposed an orthogonal frequency division multiplexing-linear frequency modulation waveform based on random matrix modulation. To achieve lower ACF and CCF, Li et al. (LI H, ZHAO Y, CHENG Z, et al. OFDM chirp waveform diversity design with correlation interference suppression for MIMO radar[J].IEEE Geoscience and Remote Sensing Letters, 2017, 14(7): 1032-1036.) used sequential quadratic programming to design an orthogonal frequency division multiplexing-linear frequency modulation waveform with variable sub-time width and sub-bandwidth.In addition, Gao et al. (GAO C, TEH KC, LIU A. Piecewise nonlinear frequency modulation waveform for MIMO radar[J]. IEEE Journal of Selected Topics in Signal Processing, 2016, 11(2):379-390.) used a genetic algorithm to optimize piecewise nonlinear frequency modulation waveforms. However, these works using deterministic modulation all involve a trade-off between low sidelobes and quasi-orthogonality of the waveforms. The reason is that the optimized low-sidelobe waveforms generally have an S-shaped time-frequency relationship, so they are similar in the time-frequency domain. However, in order to improve the quasi-orthogonality between waveforms, it is necessary to obtain different time-frequency relationships as much as possible, which weakens the low-sidelobe performance to some extent.

[0005] The second type of waveform model employing random modulation does not face this trade-off because it does not require low sidelobe characteristics for individual waveforms. Its sidelobe suppression is achieved through coherent accumulation of pulse compression results from multiple randomly modulated waveforms, while quasi-orthogonality is guaranteed by its random time-frequency relationship. Waveforms employing random modulation include chaotic FM waveforms and random FM waveforms. Wu et al. (WU Y, FU K, DIAO W, et al. Range Sidelobe Suppression Approach for SAR Images Using Chaotic FM Signals[J]. IEEE Transactions on Geoscience and Remote Sensing, 2021, 60: 1-15.) studied the design of chaotic FM waveforms but did not provide numerical results to quantify the spectral compactness of their waveforms. Blunt et al. (JAKABOSKY J, BLUNT SD, HIMED B. Spectral-shape optimized FM noise radar for pulse agility[C] / / Spectral-shape optimized FM noise radar for pulse agility. 2016 IEEE Radar Conference (RadarConf). IEEE: 1-6.) proposed a stochastic frequency-modulated waveform with a Gaussian spectral shape and used an alternating projection method for waveform optimization. However, this iterative method may be inefficient in generating waveforms with large time-bandwidth products. Summary of the Invention

[0006] This invention addresses the need for low range sidelobes and wide mapping bands in systems such as Synthetic Aperture Radar (SAR). It proposes a random frequency modulation (RFM) waveform design method to suppress range sidelobes and range ambiguity. The method is based on the random Fourier coefficients of the RFM waveform design and can generate a large-capacity waveform set with both low sidelobes and quasi-orthogonal characteristics. Furthermore, by transmitting the pulse-agile RFM waveform, the range sidelobes and range ambiguity can be further effectively suppressed.

[0007] According to one aspect of the present invention, a method for designing stochastic frequency-modulated waveforms to suppress range sidelobes and range ambiguity is proposed, comprising the following steps:

[0008] Step 1: Initialization, input the center frequency f of the waveform c Bandwidth B and pulse width T;

[0009] Step 2: Determine the instantaneous frequency f of the RFM waveform based on the random Fourier coefficients. t The variance Var(f) t ) range;

[0010] Step 3: Design N and D, where N is the number of random Fourier coefficients and D represents the interval of uniform distribution; after determining N, use Var(f t The range of D can be calculated from the range of ), and the largest possible D within this range can be selected to obtain a narrower main lobe width;

[0011] Step 4: Generate random Fourier coefficients; After designing the parameters N and D, randomly generate Fourier coefficients K1, K2, ..., K within (-D, D). N To generate W RFM waveforms, W sets of Fourier coefficients need to be generated independently.

[0012] Step 5: Output the RFM waveform and convert the generated Fourier coefficients K1, K2, ..., K N Substituting parameters N and D into the phase of the transmitted and transmitted RFM waveforms of the random Fourier coefficients yields the output RFM waveform.

[0013] Furthermore, in the second step, according to the 3σ criterion of the normal distribution, the probabilities of the RFM waveform spectrum distribution being located at σ, 2σ, and 3σ are 68.3%, 95.5%, and 99.7%, respectively. Determine Var(f) based on requirements. t The range of ) is used to obtain a compact spectrum.

[0014] Furthermore, in the third step, a larger number of random Fourier coefficients N implies faster frequency modulation, thereby enhancing the randomness and low interception of the RFM waveform; N is determined by the required frequency change rate in practice; after determining N, it is used through Var(f t The range of D can be calculated from the range of ), and the largest possible D can be selected within this range to obtain a narrower main lobe width.

[0015] Furthermore, in the fifth step, the transmitted waveform s(t) of the RFM waveform can be expressed as:

[0016]

[0017] Where T is the pulse width φ(t) represents the phase.

[0018] Furthermore, in the fifth step, the phase φ(t) of the RFM waveform based on random Fourier coefficients is as follows:

[0019]

[0020] Among them, f c B represents the center frequency, and K represents the bandwidth. n Here, K1, K2, ..., K is the nth randomly generated Fourier coefficient, and N is the number of random Fourier coefficients; we assume K1, K2, ..., K N Let K1,…,K be independent and uniformly distributed random variables. N ~U(-D,D), where D represents a uniformly distributed interval.

[0021] Furthermore, by taking the phase derivative of equation (2), the instantaneous frequency of the RFM waveform based on the random Fourier coefficients is expressed as:

[0022]

[0023] To characterize the spectral distribution of the RFM waveform, f is then calculated. t The mean and variance of K1,…,K N The mean of all values ​​is 0, therefore f t The mean is:

[0024] E(f t )=f c (4)

[0025] According to the definition of variance, Var(f) t )=E{[f t -E(f t )] 2}, combined with K1, K2, ..., K N The independence of f can be obtainedt The variance is:

[0026]

[0027]

[0028] Furthermore, when N is large, the first term within the curly braces in formula (5) is much larger than the product of the trigonometric functions in the second term, therefore Var(f t It can be approximated as:

[0029]

[0030] According to the central limit theorem, when N is large, when N is greater than 30, f t It approximately follows a normal distribution, that is...

[0031] The 3σ criterion of normal distribution is used to design N and D of RFM waveform based on random Fourier coefficients, thereby limiting its spectrum.

[0032] Furthermore, range sidelobes can be suppressed by transmitting pulse-agile RFM waveforms. Since the time-frequency relationship of the RFM waveform at each pulse repetition interval PRI is random, the sidelobes of its autocorrelation function ACF are also random. The position of the main lobe of the ACF is determined by the distance between the target and the radar. Range sidelobes can be reduced by complex summation of multiple ACFs.

[0033] By transmitting W pulse-agile RFM waveforms, the maximum unambiguous distance R can be increased. max Expanding by W times, as shown in the following formula:

[0034]

[0035] Where c represents the speed of light, and PRI is the interval between each pulse repetition.

[0036] Furthermore, assuming that W pulse-agile RFM waveforms are transmitted, the order of the RFM waveform sequences of the radar echoes received from target 1 and target 2 in the same time period is different. Due to the non-repetitiveness and quasi-orthogonality of the RFM waveforms, filter bank 1 and filter bank 2 can be used to separate the echoes of target 1 and target 2 respectively, thereby achieving range ambiguity suppression.

[0037] The advantages of this invention over the prior art are:

[0038] (1) An RFM waveform model based on random Fourier coefficients was established, and an RFM waveform design method was proposed based on the theoretical analysis of its spectrum distribution.

[0039] (2) The proposed RFM waveform design method based on random Fourier coefficients does not require a cumbersome iterative process and is highly efficient. This method can generate a large-capacity waveform set with low sidelobes, good quasi-orthogonality, high spectral compactness, and constant amplitude.

[0040] (3) A method is proposed to simultaneously achieve range sidelobe suppression and range ambiguity suppression by transmitting pulse-agile RFM waveforms. Furthermore, by increasing the number of waveforms, the sidelobe can be effectively reduced and the maximum unambiguous distance can be extended.

[0041] To meet practical application needs, the parameters in this waveform design method can be adjusted to obtain an RFM waveform set with suitable spectral compactness, main lobe width, and side lobe performance under different pulse widths and bandwidths. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are only used to illustrate preferred embodiments and are not considered as limiting the present invention. Moreover, the same reference numerals are used to denote the same parts throughout the drawings. In the drawings:

[0043] Figure 1 This is a schematic diagram of the frequency-time curve of an RFM waveform based on random Fourier coefficients.

[0044] Figure 2 A flowchart for RFM waveform design based on random Fourier coefficients;

[0045] Figure 3 This is a schematic diagram of range sidelobe suppression achieved through inter-pulse agile RFM waveform;

[0046] Figure 4 A schematic diagram of the ACF of a single RFM waveform and the complex summation of the ACF of W RFM waveforms (N=30, D=0.1118);

[0047] Figure 5 A schematic diagram of the ACF of a single RFM waveform and the complex summation of the ACF of W RFM waveforms (N=100, D=0.0408);

[0048] Figure 6 This is a schematic diagram illustrating distance ambiguity suppression achieved through inter-pulse agile RFM waveform. Detailed Implementation

[0049] The present invention will be further described below with reference to the accompanying drawings.

[0050] This invention proposes a random frequency modulation (RFM) waveform design method to suppress range sidelobes and range ambiguity. Based on the design of RFM waveforms with random Fourier coefficients, and utilizing the good quasi-orthogonality of RFM waveforms, different filter banks can be used at the receiver to separate echoes from different ranges, thereby reducing range ambiguity. The waveform design method is as follows:

[0051] (1) RFM waveform design

[0052] The emitted waveform s(t) with constant envelope can be expressed as:

[0053]

[0054] Where T is the pulse width σ(t) represents the phase. The phase φ(t) of the RFM waveform based on the random Fourier coefficients is shown in the following equation:

[0055]

[0056] Among them, f c B represents the center frequency, and K represents the bandwidth. n Here, K1, K2, ..., K is the nth randomly generated Fourier coefficient, and N is the number of random Fourier coefficients. Let K1, K2, ..., K be the coefficients generated randomly. N Let K1,…,K be independent and uniformly distributed random variables. N ~U(-D,D). D represents a uniformly distributed interval. Therefore, for a given bandwidth B and pulse width T, the two key design parameters for the RFM waveform based on random Fourier coefficients are N and D. When N = 30, D = 0.1, B = 100MHz, and T = 10μs, the frequency-time curve of the RFM waveform based on random Fourier coefficients is as follows: Figure 1 As shown, the generated RFM has a random time-frequency relationship.

[0057] By differentiating the phase of equation (2), the instantaneous frequency of the RFM waveform based on the random Fourier coefficients can be expressed as:

[0058]

[0059] To characterize the spectral distribution of the RFM waveform, f is then calculated. t The mean and variance. Since K1,…,K N The mean of all values ​​is 0, therefore f t Mean:

[0060] E(f t )=f c (4)

[0061] According to the definition of variance, Var(f)t )=E{[f t -E(f t )] 2}, combined with K1, K2, ..., K N The independence of f can be obtained t variance:

[0062]

[0063]

[0064] When N is large, the first term within the curly braces in (5) is much larger than the product of the trigonometric functions of the second term, therefore Var(f t It can be approximated as:

[0065]

[0066] Furthermore, according to the central limit theorem, when N is large (usually greater than 30), f t It approximately follows a normal distribution, that is... Therefore, the 3σ criterion of normal distribution can be used to design N and D of RFM waveform based on random Fourier coefficients, thereby limiting its spectrum.

[0067] Figure 2 As shown, through the derivation of the RFM waveform spectral distribution based on random Fourier coefficients, its waveform design process mainly includes five steps:

[0068] Step 1: Initialization. Input waveform center frequency f c , bandwidth B and pulse width T.

[0069] Step 2: Determine Var(f) t The range of ) is defined. According to the 3σ criterion of the normal distribution, the probabilities of the RFM waveform spectrum distribution falling within σ, 2σ, and 3σ are 68.3%, 95.5%, and 95.5%, respectively. In practice, Var(f) needs to be determined based on requirements. t The range of ) is selected to obtain suitable spectral compactness. A 2σ constraint is chosen, i.e. That is, D is required 2 N≤0.375. Similarly, choosing a 3σ constraint requires D 2 N≤0.167.

[0070] Step 3: Design N and D. A larger number of random Fourier coefficients N means faster frequency modulation, thus enhancing the randomness and low interception of the RFM waveform. Therefore, N is determined by the required frequency change rate in practice. Here, N=30 and N=100 are selected as two examples. After determining N, the values ​​are calculated using Var(f tThe range of D can be calculated from the range of ), and the largest possible D can be selected within this range to obtain a narrower main lobe width.

[0071] Step 4: Generate random Fourier coefficients. After designing the parameters N and D, randomly generate Fourier coefficients K1, K2, ..., K within the range (-D, D). N To generate W RFM waveforms, W sets of Fourier coefficients need to be generated independently.

[0072] Step 5: Output the RFM waveform. The generated Fourier coefficients K1, K2, ..., K... N Substituting parameters N and D into formulas (2) and (1), the output RFM waveform is obtained.

[0073] Here, 2σ and 3σ constraints are selected to verify the performance of the RFM waveform. The bandwidth B and pulse width T of the RFM waveform are 100MHz and 10μs, respectively, and N is set to 30 and 100, respectively. The parameters and performance evaluation of the RFM waveforms for the four corresponding cases are shown in Table 1, and the performance index values ​​are the average results of 100 RFM waveforms. Among them, the indexes for measuring the autocorrelation sidelobes of the RFM waveform are the peak-to-sidelobe level ratio (PSLR) and the integrated sidelobe level ratio (ISLR), the index for measuring cross-correlation is the cross-correlation peak (CCP), the index for measuring the main lobe width is the normalized 3dB impulse response width (IRW), and the index for measuring spectral compactness is the percentage η of the waveform power spectrum within the bandwidth. It can be seen that in all four cases, the RFM waveform based on the random Fourier coefficients has low sidelobes and low cross-correlation, and the value of η is also consistent with the 3σ criterion of the normal distribution. Compared to 2σ constraint, 3σ constraint achieves higher spectral compactness, but also widens the main lobe.

[0074] Table 1. Parameters and performance evaluation of RFM waveforms based on random Fourier coefficients.

[0075]

[0076] (2) RFM waveform of inter-pulse agility

[0077] Distance sidelobe suppression

[0078] like Figure 3As shown, range sidelobes can be suppressed by transmitting inter-pulse agile RFM waveforms. Since the time-frequency relationship of the RFM waveform in each pulse repetition interval (PRI) is random, its ACF sidelobes are also random, while the main lobe position of the ACF is determined by the distance between the target and the radar. Therefore, range sidelobes can be reduced by complex summing multiple ACFs; W ACFs can achieve 10log... 10 Sidelobe suppression at WdB. Table 2 and Figure 3 Simulation results of sidelobe suppression achieved through complex summation of multiple ACFs are presented for two cases: N=30, D=0.1118, and N=100, D=0.0408. The pulse width T and bandwidth B of the RFM waveform are set to 10μs and 100MHz, respectively. In both cases, as the number of waveforms W increases by a factor of 10, both PSLR and ISLR decrease by approximately 10dB. Other combinations of parameters N and D also produce RFM waveforms with considerable sidelobe suppression effects, basically conforming to 10log 10 Sidelobe suppression in WdB. However, it can be seen that the suppression of PSLR and ISLR with 3σ constraint N=100, D=0.0408 is slightly worse than that with 2σ constraint N=30, D=0.1118. This is because the stricter spectral constraint will reduce the randomness of the RFM waveform to some extent.

[0079] Furthermore, it can be observed that this method of reducing sidelobes by using multiple inter-pulse agile RFM waveforms does not involve the trade-off between low sidelobes and narrow IRW found in the design problem of a single low-sidelobe waveform. For example... Figure 4 and Figure 5 As shown, the IRW remains constant as W increases, which means that PSLR and ISLR can be reduced while preserving the narrow main lobe.

[0080] Table 2. Sidelobe suppression results of inter-pulse agile RFM waveforms under different waveform counts (N=30, D=0.1118)

[0081] W PSLR (dB) ISLR (dB) IRW 1 -18.5 -0.3 1.1 10 -29.8 -9.8 1.1 100 -39.8 -19.4 1.1 1000 -48.3 -27.0 1.1

[0082] Table 3. Sidelobe suppression results of inter-pulse agile RFM waveforms under different waveform counts (N=100, D=0.0408)

[0083]

[0084]

[0085] Distance blur suppression

[0086] In traditional radar systems, the waveforms transmitted under different PRI (Radar Imaging Parameters) are identical, leading to range ambiguity. This study utilizes the good quasi-orthogonality between RFM waveforms to alleviate range ambiguity. Figure 6 The diagram illustrates a simple radar scenario consisting of two point targets, Target 1 and Target 2, located within range range 1 and range range 2, respectively. Assuming W pulse-agile RFM waveforms are transmitted, the order of the RFM waveform sequences received from the radar echoes of Target 1 and Target 2 within the same time period will differ. Due to the non-repetitiveness and quasi-orthogonality of the RFM waveforms, filter bank 1 and filter bank 2 can be used to separate the echoes of Target 1 and Target 2, respectively, thereby suppressing range ambiguity. Transmitting W pulse-agile RFM waveforms can maximize the unambiguous range R. max Expanded by W times, as shown in the following formula:

[0087]

[0088] Where c represents the speed of light, and PRI represents the interval between each pulse repetition.

[0089] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing stochastic frequency-modulated waveforms to suppress range sidelobes and range ambiguity, characterized in that, Includes the following steps: Step 1: Initialization, input the center frequency of the waveform ,bandwidth And pulse width ; Step 2: Determine the instantaneous frequency of the RFM waveform based on the random Fourier coefficients. Scope; Step 3: Design and ,in It is the number of random Fourier coefficients. Represents a uniformly distributed interval; determine Afterwards, through The range can be calculated Within the range, select the largest possible value within that range. To achieve a narrower main lobe width; Step 4: Generate random Fourier coefficients, after designing the parameters. and Afterwards, Fourier coefficients are generated randomly within the inner quadrant. To generate Each RFM waveform needs to be generated independently. Group Fourier coefficients; Step 5: Calculate the generated Fourier coefficients and parameters and Substituting the phase of the transmitted RFM waveform into the random Fourier coefficients, we obtain the output RFM waveform. In the second step, based on the normal distribution 3 Criteria: RFM waveform spectral distribution is located in , , The probabilities are 68.3%, 95.5%, and 99.7%, respectively. Determine based on needs The range is used to obtain a compact spectrum; In the third step, a larger number of random Fourier coefficients are used. This means faster frequency modulation, which enhances the randomness and low interceptivity of the RFM waveform; The frequency change rate is determined by the actual required rate of change; Afterwards, through The range can be calculated Within the range, select the largest possible value within that range. To achieve a narrower main lobe width; In the fifth step, the transmitted waveform of the RFM waveform It can be represented as: (1) in, The pulse width. , For phase; In the fifth step, The phase of the RFM waveform based on random Fourier coefficients As shown in the following formula: (2) in Represents the center frequency. It's bandwidth. It is the first Fourier coefficients generated randomly It is the number of random Fourier coefficients; here we assume Let them be independent and uniformly distributed random variables, i.e. , This represents an interval with a uniform distribution.

2. The stochastic frequency-modulated waveform design method for suppressing range sidelobes and range ambiguity according to claim 1, characterized in that, By differentiating the phase of equation (2), the instantaneous frequency of the RFM waveform based on the random Fourier coefficients is expressed as: (3)。 3. The random frequency modulated waveform design method for suppressing range sidelobes and range ambiguity according to claim 2, characterized in that, To characterize the spectral distribution of the RFM waveform, the following calculations are performed. The mean and variance, due to The mean of all values ​​is 0, therefore The mean is: (4)。 4. The random frequency modulated waveform design method for suppressing range sidelobes and range ambiguity according to claim 3, characterized in that, According to the definition of variance , combined The independence of can be obtained The variance is: (5)。 5. The stochastic frequency-modulated waveform design method for suppressing range sidelobes and range ambiguity according to claim 4, characterized in that, when When the value is large, the first term within the curly braces in formula (5) is much larger than the product of the trigonometric functions in the second term, therefore It can be approximated as: (6)。 6. The stochastic frequency modulated waveform design method for suppressing range sidelobes and range ambiguity according to claim 5, characterized in that, According to the central limit theorem, when When N is large, when N is greater than 30, It approximately follows a normal distribution, that is... .

7. The stochastic frequency modulated waveform design method for suppressing range sidelobes and range ambiguity according to claim 1, characterized in that, Using a normal distribution 3 Criteria for designing RFM waveforms based on random Fourier coefficients and This limits its spectrum.

8. The random frequency modulated waveform design method for suppressing range sidelobes and range ambiguity according to claim 1, characterized in that, Range sidelobes can be suppressed by transmitting pulse-agile RFM waveforms. Since the time-frequency relationship of the RFM waveform at each pulse repetition interval PRI is random, the sidelobes of its autocorrelation function ACF are also random. The position of the main lobe of the ACF is determined by the distance between the target and the radar. Range sidelobes can be reduced by complex summation of multiple ACFs.

9. The random frequency-modulated waveform design method for suppressing range sidelobes and range ambiguity according to claim 8, characterized in that, By launch Inter-pulse agile RFM waveforms can achieve the maximum unambiguous distance. Extend The multiple is shown in the following formula: (7) in, Represents the speed of light, and PRI is the interval between each pulse repetition.

10. The method for designing stochastic frequency-modulated waveforms to suppress range sidelobes and range ambiguity according to claim 9, characterized in that, Assuming it was launched For pulse-to-pulse agile RFM waveforms, the order of the RFM waveform sequences of radar echoes received from target 1 and target 2 in the same time period is different. Due to the non-repetitiveness and quasi-orthogonality of RFM waveforms, filter bank 1 and filter bank 2 can be used to separate the echoes of target 1 and target 2 respectively, thereby achieving range ambiguity suppression.

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