Inter-pulse time-varying intra-pulse coded non-continuous spectrum signal design method

Abstract

The application discloses a design method of intra-pulse coding non-continuous spectrum signal considering inter-pulse time-varying, and belongs to the field of radar waveform design. The application aims at the problem that the change of spectrum environment in accumulation time is not considered in the existing non-continuous spectrum signal design, and the signal adaptability is weak. The application comprises the following steps: a power spectrum of a discrete transmission signal vector of each pulse is used to represent a transmission signal, and a self-correlation expression of the transmission signal of each pulse is obtained; a mean self-correlation function of the transmission signal of the mth group of pulses and a mean self-correlation sidelobe level of the mth group of pulses are further obtained; the mean self-correlation function of the transmission signal of the first m groups of pulses and the mean self-correlation sidelobe level of the first m groups of pulses are calculated; the mean self-correlation sidelobe level of the first m groups of pulses is expressed in the form of a power spectrum, and a target function is established by balancing the energy of the transmission signal of the mth group of L pulses at the unusable frequency band; and the gradient descent method is used to optimize and solve the target function to obtain an optimization result. The application is used for the design of non-continuous spectrum signals.

Description

TECHNICAL FIELD

[0001] The present application relates to an intra-pulse coding non-continuous spectrum signal design method considering inter-pulse time variation, and belongs to the field of radar waveform design. BACKGROUND

[0002] With the development and progress of electronic technology in recent years and the rapid development of 5G technology, the number of radio systems has increased explosively. In order to better improve the signal and information transmission quality, the demand for the width of the working frequency band of the radio system also continues to grow.

[0003] As one of the common main radio users, with the improvement and innovation of radar theory and technology, modern radar is also widely used in various fields of military and civilian, such as strategic early warning, enemy target locking, and climate monitoring, etc. Therefore, the demand for spectrum resources of radar is also increasing. However, spectrum resources are a kind of limited natural resources, and with the increasing demand for working bandwidth of modern radar, communication systems, etc., the spectrum congestion problem becomes increasingly acute. At this time, the spectrum coexistence problem between radar systems and communication systems has attracted widespread attention. In addition to civilian radio equipment, the level of enemy electronic countermeasures and radar countermeasures faced by modern radar in combat are rapidly improving, so there are a large number of same-frequency interferences in the electromagnetic environment in which the modern high-frequency radar is located. Due to the complex and harsh electromagnetic environment, how to improve the working performance of the radar system in the complex electromagnetic spectrum environment has become a big problem that radar workers need to solve. In addition to considering the distance resolution of the radar itself, when selecting the working frequency band and bandwidth, it is also necessary to reduce the interference of other same-frequency users to the radar as much as possible. Considering the means of waveform design, that is, using multiple non-continuous silent frequency bands to synthesize a large bandwidth to achieve high range resolution, and setting notches at unusable frequency bands to avoid other interferences, has become an important way to solve this problem.

[0004] However, the autocorrelation function is the inverse Fourier transform of the power spectral density, and setting notches in the interference frequency band will affect the autocorrelation function of the signal, which specifically manifests as raising the autocorrelation sidelobes of the signal, causing a weak target masking effect, so the autocorrelation sidelobe performance of the non-continuous spectrum signal needs to be optimized. The autocorrelation sidelobe of the transmitted signal can be measured by the integral sidelobe and the peak sidelobe. The integral sidelobe level is the two-norm of the autocorrelation function of the waveform in the sidelobe region, which measures the average level of the radar waveform in the entire sidelobe region, and is suitable for the scene where the clutter is uniformly distributed. The methods for optimizing the integral sidelobe in the prior art include two categories of random evolution algorithm and greedy descent algorithm, wherein the random evolution algorithm includes genetic algorithm and simulated annealing algorithm, and the greedy descent algorithm includes MM method, etc.

[0005] In addition, in the signal processing at the receiving end, the modern radar usually adopts fast time matching filtering and slow time coherent accumulation to improve the signal-to-noise ratio, and the coherent accumulation time is multiple of the single pulse time. However, due to the uncertainty of the working time of the radio system, the spectrum environment in which the radar is located may change in the entire coherent accumulation time. The signal is designed according to the real-time change of the spectrum, so as to reduce the influence caused by the time-varying spectrum. In addition, it is also necessary to consider that the autocorrelation performance of different pulses is excellent as a whole. However, the existing technology assumes that the spectrum environment does not change in the accumulation time, and the non-continuous spectrum signal designed by the foregoing method has the problem of weak adaptability. SUMMARY

[0006] In view of the problem that the change of the spectrum environment in the accumulation time is not considered in the design of the existing non-continuous spectrum signal, thereby the adaptability of the signal is weak, the present application provides a non-continuous spectrum signal design method considering inter-pulse time-varying intra-pulse coding.

[0007] The non-continuous spectrum signal design method considering inter-pulse time-varying intra-pulse coding provided by the present application is used for the design of the transmitting signal in which the inter-pulse time-varying and different phase codes are transmitted in a group of pulses, and the method comprises the following steps.

[0008] Step one: in the transmitting signal of the L pulses in the mth group, the power spectrum of the transmitting signal is represented based on the discrete transmitting signal vector of each pulse, and then the autocorrelation expression of the transmitting signal of each pulse is obtained based on the power spectrum;

[0009] Step two: the mean autocorrelation function of the transmitting signal of the mth group of pulses is obtained according to the autocorrelation expression of the transmitting signal of each pulse, and then the mean autocorrelation sidelobe level of the mth group of pulses is obtained based on the mean autocorrelation function;

[0010] Step three: the mean autocorrelation function of the transmitting signal of the first m group of pulses is obtained based on the optimization result of the transmitting signal of the first m-1 group of pulses and the transmitting signal of the mth group of pulses, and then the mean autocorrelation sidelobe level of the first m group of pulses is obtained according to the mean autocorrelation function of the transmitting signal of the first m group of pulses;

[0011] Step four: the mean autocorrelation sidelobe level of the first m group of pulses is expressed in the form of the power spectrum, and a target function is established by balancing the energy of the L pulses in the mth group at the unusable frequency band;

[0012] Step five: the gradient descent method is used to optimize and solve the target function, so as to obtain the final optimization result and realize the design of the inter-pulse time-varying intra-pulse coding non-continuous spectrum transmitting signal.

[0013] According to the non-continuous spectrum signal design method considering inter-pulse time-varying intra-pulse coding provided by the present application, in step one, the method for obtaining the power spectrum expression comprises the following steps.

[0014] the m-th group of the l-th pulse m,l is denoted as

[0015]

[0016] where m = 1, 2, 3, …, M; l = 1, 2, 3, …, L; s m,l,N denotes the value of the N-th point of s m,l ; N is the phase encoding length of s m,l denotes the phase of s m,l denotes the value of the N-th point of s m,l,N ;

[0017]

[0018] the spectrum f m,l of the discrete emission signal vector s m,l is denoted as

[0019]

[0020] where f m,l,2N is the spectrum f m,l of the value of the 2N-th point, is the zero-padded form of the discrete emission signal vector s m,l

[0021]

[0022] where is the value of the 2N-th point of f ;

[0023] where:

[0024] is a 2N x 2N discrete Fourier transform matrix, the element of the l1+1-th row and the l2+1-th column of the discrete Fourier transform matrix F is:

[0025]

[0026] then the power spectrum p m,l is denoted as m,l is:

[0027]

[0028] where p m,l,2N-1 is the power spectrum p m,l of the value of the 2N-th point.

[0029] ​​​According to the pulse-intra coding non-continuous spectrum signal design method considering pulse-to-pulse time variation of the present application, in step one, the method for obtaining the autocorrelation expression of the transmitting signal of each pulse comprises:

[0030] The autocorrelation r m,l of the discrete transmitting signal vector s m,l is expressed as:

[0031] r m,l = [r m,l,1-N ,...,r m,l,-1 ,r m,l,0 ,r m,l,1 ,...,r m,l,N-1 ],

[0032] wherein r m,l,N-1 is the value of the 2Nth element of r m,l .

[0033] The element r m,l of the autocorrelation r m,l,l3 is expressed as:

[0034]

[0035] According to the Wiener-Sin theorem, the power spectrum of the signal and the autocorrelation are a pair of Fourier transform, the autocorrelation r m,l is transformed to obtain the autocorrelation

[0036]

[0037] wherein r is the value of the 2Nth element of the autocorrelation r .

[0038] According to the formula (1) and (8), r m,l,0 =N.

[0039] According to the pulse-intra coding non-continuous spectrum signal design method considering pulse-to-pulse time variation of the present application, in step two, the mean autocorrelation function of the transmitting signal of the mth group of pulses is:

[0040]

[0041] wherein r is the value of the 2Nth element of the mean autocorrelation function of the transmitting signal .

[0042] Then the mean autocorrelation integral sidelobe level ISL m of the mth group of pulses is:

[0043]

[0044] According to the pulse-intra coding non-continuous spectrum signal design method considering pulse-to-pulse time variation of the present application, in step three, the mean autocorrelation function R m is:

[0045]

[0046] The mean autocorrelation integral sidelobe level ISLL of the first m pulses is: m is:

[0047]

[0048] where R m,n is the mean autocorrelation function R m of the transmitted signal.

[0049] According to the pulse-intra coding non-continuous spectrum signal design method considering pulse-to-pulse time variation of the present application, in step four, the method for representing the mean autocorrelation integral sidelobe level ISLL of the first m pulses in the form of power spectrum includes:

[0050] According to formula (6), we have:

[0051] FF H = 2N·I 2N , (14)

[0052] where I 2N is a 2N by 2N unit matrix.

[0053] According to formula (9), the mean autocorrelation integral sidelobe level ISLL of the first m pulses represented by formula (13) is: m represented in the form of power spectrum as:

[0054]

[0055] where p m,'l',k is the value of the power spectrum p m,l' at the kth point.

[0056] According to the pulse-intra coding non-continuous spectrum signal design method considering pulse-to-pulse time variation of the present application, in step four, the method for establishing the objective function includes:

[0057] The stopband energy of the transmitted signal of the lth pulse in the mth group is:

[0058]

[0059] where w m,l,k is the kth weighted value of the power spectrum of the lth pulse in the mth group.

[0060]

[0061] wherein is the energy weight of the unusable frequency band, Ω m,j represents the jth value of the interference frequency band Ω m in the mth group of pulses:

[0062] Ω m = [Ω m,1 ,..., Ω m,J ],

[0063] J is the total number of points of the interference frequency band in the mth group of pulses;

[0064] then the total energy E out of the L pulse signals in the mth group is:

[0065]

[0066] the objective function of the mth group of pulses is established

[0067]

[0068] wherein λ is a weighting value;

[0069] the specific expression of the objective function is obtained according to formula (15) and formula (18).

[0070] The present application has the beneficial effects that the present application proposes a fast design method of the non-continuous spectrum signal of the inter-pulse time-varying-intra-pulse coding, and considers optimizing the integral sidelobe. The present application designs the intra-pulse coding according to the spectrum environment variation, and in order to ensure the autocorrelation function performance in the coherent integration time, the mean autocorrelation and the mean power spectrum in the coherent integration time are defined, and the mean autocorrelation function integral sidelobe and the unusable frequency band energy weighted minimum are taken as the objective function to perform the signal optimization design. When the gradient descent method is adopted, the fast calculation method of the target gradient is obtained through the objective function derivation, and the calculation efficiency is greatly improved; and the obtained transmission signal has stronger adaptivity.

[0071] Through the experiment verification, the average autocorrelation integral sidelobe performance of the non-continuous spectrum signal designed by the present application is better than that of a single autocorrelation, which indicates the advancement and effectiveness of the present application method. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 is the coding signal schematic diagram of the non-continuous spectrum signal design method considering the inter-pulse time-varying intra-pulse coding of the present application;

[0073] Figure 2 is the schematic diagram of the inter-pulse time-varying and the same phase coding signal transmission in a group of pulses, which is a special case of Figure 1 .

[0074] Figure 3 is a power spectrum density graph in the first transmission mode in the specific embodiment;

[0075] Figure 4 is a self-correlation function graph in the first transmission mode in the specific embodiment;

[0076] Figure 5 is a first group of power spectrum graphs in the second transmission mode in the specific embodiment;

[0077] Figure 6 is a first group of self-correlation function graphs in the second transmission mode in the specific embodiment;

[0078] Figure 7 is a second group of power spectrum graphs in the second transmission mode in the specific embodiment;

[0079] Figure 8 is a second group of self-correlation function graphs in the second transmission mode in the specific embodiment;

[0080] Figure 9 is a comparison of two groups of power spectrum graphs in the second transmission mode in the specific embodiment;

[0081] Figure 10 is a comparison of two groups of self-correlation function graphs in the second transmission mode in the specific embodiment. DETAILED DESCRIPTION

[0082] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0083] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0084] The present application will be further described below with reference to the drawings and specific embodiments, but is not limited by the present application.

[0085] Specific embodiment one, combination Figure 1 and Figure 2 As shown in the specific embodiment, the present application provides a pulse-intra coding non-continuous spectrum signal design method considering inter-pulse time variation, which is used for inter-pulse time variation and a group of different phase coding in a group of pulses, and includes the following steps:

[0086] Step one: based on the discrete transmission signal vector of each pulse, express the power spectrum of the transmission signal, and then obtain the autocorrelation expression of each pulse based on the power spectrum;

[0087] Step two: obtain the mean autocorrelation function of the transmission signal of the mth group of pulses according to the autocorrelation expression of each pulse, and obtain the mean autocorrelation integral sidelobe level of the mth group of pulses based on the mean autocorrelation function;

[0088] Step three: obtain the mean autocorrelation function of the transmission signal of the first m groups of pulses based on the transmission signal optimization results of the first m-1 groups of pulses and the transmission signal of the mth group of pulses, and obtain the mean autocorrelation integral sidelobe level of the first m groups of pulses according to the mean autocorrelation function of the transmission signal of the first m groups of pulses;

[0089] Step four: express the mean autocorrelation integral sidelobe level of the first m groups of pulses in the form of power spectrum, and establish a target function by balancing the energy of the mth group of L pulses at the unavailable frequency band;

[0090] Step five: use gradient descent method to optimize and solve the target function to obtain the final optimization result, and realize the design of the inter-pulse time-varying intra-pulse coded non-continuous spectrum transmission signal.

[0091] In order to solve the problem of spectrum environment change, the embodiment adopts the inter-pulse time-varying mode to design the transmission signal, and the single pulse adopts the phase coding form. According to the frequency monitoring device, the period of external environment change can be obtained. Assuming that the time-varying period is L pulse duration, a signal processing period contains M groups, that is, ML pulses; then the embodiment adaptively designs the next group of pulses according to the spectrum environment change after every L pulse period to achieve the time-varying effect. The non-continuous spectrum signal diagram under this design mode is shown in Figure 1 and Figure 2 .

[0092] As can be seen from Figure 1 and Figure 2 , the spectrum environment does not change within L pulses, and the time-varying design is performed on every L pulses. This design mode can be divided into two kinds, the first kind of transmission mode is inter-pulse time-varying and the same phase coding signal is transmitted within a group of pulses; the second kind of transmission mode is inter-pulse time-varying and different phase coding signals are transmitted within a group of pulses. Since the first kind is a special case of the second kind, the embodiment models the signal based on the second design model.

[0093] Further, in step one, the method for obtaining the power spectrum expression includes:

[0094] For convenience of problem modeling and waveform optimization, the discrete digital waveform after uniform sampling is usually considered, and the signal form is phase-coded signal. Meanwhile, in order to maximize the radar transmitting power, the radar waveform is required to have constant modulus characteristic. Therefore, the discrete transmitting signal vector s m,l is expressed as:

[0095]

[0096] wherein m = 1, 2, 3, …, M; l = 1, 2, 3, …, L; s m,l,N represents the value of the Nth point of s m,l , N is the phase-coded length of s m,l , represents the phase of s m,l , the value of the Nth point of s m,l,N ;

[0097]

[0098] The spectrum f m,l of the discrete transmitting signal vector s m,l is expressed by Discrete Fourier Transform (DFT) as:

[0099]

[0100] wherein f m,l,2N is the value of the 2Nth point of the spectrum f m,l , is the zero-padded form of the discrete transmitting signal vector s m,l :

[0101]

[0102] wherein is the value of the 2Nth point of s ;

[0103] wherein:

[0104] is the Discrete Fourier Transform matrix of 2N x 2N, the element of the l1+1th row and the l2+1th column of the Discrete Fourier Transform matrix F is:

[0105]

[0106] then the power spectrum p m,l based on the discrete transmitting signal vector s m,l is expressed as:

[0107] ​

[0108] where p m,l,2N-1 is the power spectrum p m,l of the signal s m,l . The value of the 2Nth element of r m,l is denoted by r m,l .

[0109] In the present embodiment, when the waveform design mode is the first mode, the following relationship exists:

[0110]

[0111] In step one of the present embodiment, the method for obtaining the autocorrelation expression of the transmission signal of each pulse comprises:

[0112] The autocorrelation r m,l of the discrete transmission signal vector s m,l is expressed as:

[0113] r m,l = [r m,l,1-N ,...,r m,l,-1 ,r m,l,0 ,r m,l,1 ,...,r m,l,N-1 ],

[0114] where r m,l,N-1 is the value of the 2Nth element of r m,l ;

[0115] The element r m,l of the autocorrelation r m,l is expressed as:

[0116]

[0117] According to the Wiener-Chintin theorem, the power spectrum and the autocorrelation of a signal are a pair of Fourier transform, and the autocorrelation r m,l is transformed to obtain the autocorrelation r m,l :

[0118]

[0119] where p is the value of the 2Nth element of the autocorrelation r ;

[0120] According to formulas (1) and (8), r m,l,0 = N.

[0121] The optimization problem is constructed as follows:

[0122] The optimization problem considers the sidelobe performance of the autocorrelation function and the spectrum compatibility performance. In optimizing the sidelobe performance of the autocorrelation of the transmitted waveform, the integral sidelobe level is considered. However, since the spectrum environment is time-varying in an accumulation period, the transmitted signal is designed to be time-varying between pulses, and therefore the embodiment defines the mean autocorrelation function and the mean autocorrelation integral sidelobe to balance the autocorrelation integral sidelobe performance of different pulses of the transmitted signal. In step two, the mean autocorrelation function Rm of the transmitted signal of the mth group of pulses is m is:

[0123]

[0124] wherein is the mean autocorrelation function of the transmitted signal is the value of the nth point.

[0125] The mean autocorrelation integral sidelobe level ISLm of the mth group of pulses is m is:

[0126]

[0127] Since the external spectrum environment changes without a stable rule and cannot be predicted, the ML pulses in the accumulation period cannot be designed and processed as a whole, and the mean autocorrelation performance is considered. In the design of the lth group of pulses, the mean autocorrelation function and the mean integral sidelobe level of the mth group are considered on the basis of the design of the first m-1 groups of pulses.

[0128] In step three, the mean autocorrelation function Rm of the transmitted signal of the first m groups of pulses is m is:

[0129]

[0130] The mean autocorrelation integral sidelobe level ISLLm of the first m groups of pulses is m is:

[0131]

[0132] wherein Rm is the mean autocorrelation function of the transmitted signal m,n is the mean autocorrelation function of the transmitted signal m is the value of the nth point.

[0133] Since the first m-1 groups of pulses have been designed when designing the mth group of pulse codes, r1,..., rm-1 in formula (13) are distinguished from rm. m-1 and rm. m

[0134] Further, in step four, the method for expressing the mean autocorrelation integral sidelobe level of the first m groups of pulses as the form of the power spectrum includes:

[0135] ​According to formula (6), we have

[0136] FF H = 2N I 2N , (14)

[0137] where I 2N is a 2N by 2N identity matrix;

[0138] According to formula (9), the mean autocorrelation sidelobe level ISLL m of the first m groups of pulses represented by formula (13) is expressed as:

[0139]

[0140] where p m,'l',k is the value of the power spectrum p m,l' at the kth point.

[0141] In step four of the embodiment, the method for establishing the objective function includes:

[0142] For the spectral compatibility performance of the non-continuous spectrum signal, the embodiment uses the stopband energy as the spectral compatibility performance index. Since the spectral environment is time-varying, only the stopband energy of the designed mth group needs to be considered. The stopband energy of the lth pulse emission signal of the mth group is

[0143]

[0144] where w m,l,k is the kth weighted value of the lth pulse power spectrum of the mth group;

[0145]

[0146] where is the unusable frequency band energy weight, Ω m,j represents the jth value of the interference frequency band Ω m in the mth group of pulses:

[0147] Ω m = [Ω m,1 ,..., Ω m,J ],

[0148] J is the total number of points of the interference frequency band in the mth group of pulses;

[0149] The total energy E out of the L pulse emission signals of the mth group is:

[0150]

[0151] In order to comprehensively consider the mean autocorrelation performance and the spectrum compatibility performance of the signal, a trade-off objective function of the mth group of pulses is established

[0152]

[0153] In the formula, λ is a weighted value;

[0154] According to the formula (15) and the formula (18), the specific expression of the objective function is obtained.

[0155] The optimization problem is solved below, and the gradient descent method is used to solve the proposed optimization problem.

[0156] The gradient descent method is commonly used to solve the unconstrained optimization problem, and it has small storage requirement, fast convergence, and is suitable for solving large-scale optimization problems. In the embodiment, the gradient descent method is used to solve the objective function represented by the formula (19). Meanwhile, in order to find a better convergence direction and accelerate the convergence speed, a rotation factor is introduced.

[0157] In step five, the conjugate gradient descent method is used to optimize and solve the optimal phase angle of the objective function

[0158] The phase vector is:

[0159]

[0160] Suppose that the initial value of is The starting iteration pointer t=0; The tth iteration phase of

[0161] I. Calculate the objective function of and the gradient

[0162] II. Calculate the search direction d t :

[0163]

[0164] In the formula, γ t is a rotation factor;

[0165] III. Adjust t to make reach the minimum value according to the adjustment step size η ;

[0166] IV. Update and set the iteration pointer t=t+1; ​​​

[0167] V. Repeat I to IV until the specified termination condition is met.

[0168] In step V.2, γ t d t-1 In order to make the convergence direction more optimal and faster, a rotation factor is introduced. A reset mechanism is introduced, and the rotation factor is defined as:

[0169]

[0170] The intermediate variable is:

[0171]

[0172] In step V.3, the step size will be adjusted using the inexact line search method, and in step V.5, the termination condition of the search is to meet the strong Wolfe criterion, which is defined as:

[0173]

[0174] Where c1 and c2 are constants, and 0 < c1 < c2 < 1.

[0175] From the solving process of the optimal phase angle, it can be seen that when using gradient descent method for optimization, the calculation amount of the algorithm is mainly concentrated in the calculation of the objective function and its gradient. In order to reduce the calculation time of the algorithm, the gradient of the objective function is derived, and a method for quickly calculating the gradient is found.

[0176] In this embodiment, the objective function ISLL m and E out are divided into two parts, and first, ISLL m The gradient of the nth' phase m,l of the discrete emission signal vector s is calculated, n' = 1, 2, 3, …, N:

[0177]

[0178] Let: At the same time, Bring equation (24) into (23) to get:

[0179]

[0180] Next, solve

[0181]

[0182] Similarly, we get: Therefore:

[0183]

[0184] Then, equation (25) is rewritten as:

[0185]

[0186] where is the matrix F * all elements of the nth row;

[0187] Therefore is rewritten as:

[0188]

[0189] where is the matrix F * all elements of the first to Nth rows;

[0190] Again, take the gradient of :

[0191]

[0192] According to equation (27), equation (30) is rewritten as:

[0193]

[0194] where w m,l = [w m,l,1 ,...,w m,l,2N ] T ;

[0195] Therefore is expressed as:

[0196]

[0197] Therefore, the objective function is: m,l the first-order derivative of the phase of the transmitted signal s :

[0198]

[0199] According to equation (33), calculate in turn

[0200] From the expressions of and , it can be seen that the main calculation of the gradient is concentrated in the matrix multiplication operation containing the Fourier transform matrix F, and this matrix operation can be realized through the fast Fourier transform, so the calculation time can be greatly shortened and the algorithm running speed can be improved. Embodiments

[0202] The following simulation parameters are set: single pulse intra-pulse code length N = 128, weighting value λ = 0.01, spectrum environment change period is 3 pulses, i.e. L = 3, and inter-pulse time-varying 2 can reach a coherent accumulation period, i.e. L = 2. When l = 1, the normalized spectrum stopband position Ω out = [0.078, 0.098] U [0.3125, 0.3516], when l = 2, the normalized spectrum stopband position is Ω out = [0.273, 0.293] U [0.508, 0.527] U [0.801, 0.820], and a random phase sequence is used for initialization. This embodiment gives the optimization results of the algorithm, and compares the mean autocorrelation and single autocorrelation, the mean power spectrum and single power spectrum in the optimization results.

[0203] First, the first transmission mode is used, i.e. inter-pulse time-varying design and the same phase encoding for a group of 3 pulses, Figure 3 The comparison of the power spectrum of each group of pulses and the mean power spectrum is given, Figure 4 The comparison of the autocorrelation of each group of pulses and the mean autocorrelation is given, and the autocorrelation sidelobe and the mean autocorrelation sidelobe of each are calculated as shown in Table 1. From Figure 3 It can be seen that the power spectrum of the first group and the second group is set to a deep spectrum notch at the corresponding unusable frequency band position, which well suppresses the spectrum interference, Figure 4 It can be seen that the integral sidelobe level of the mean autocorrelation is lower than that of the autocorrelation sidelobe of the first group and the second group. This phenomenon can be explained from the power spectrum. Since the Fourier transform relationship between the power spectrum and the autocorrelation, the mean power spectrum can fill the energy defect at the unusable frequency band of the first group by the spectrum energy of the second group, so that the mean power spectrum becomes flat. When the power spectrum energy is uniformly distributed in the frequency band, the integral sidelobe is the smallest. Therefore, the flatter the power spectrum is, the smaller the integral sidelobe is.

[0204] Table 1 Integral sidelobe level of different group autocorrelation functions

[0205]

[0206] Next, the second transmission mode is used. That is, the inter-pulse time-varying design and the different encoding for a group of 3 pulses; the single pulse code length, the spectrum notch position, M, L are not changed, the weighting value λ = 0.2, and a random phase sequence is used for initialization. This embodiment gives the optimization results of the algorithm, and compares the mean autocorrelation and single autocorrelation of each group in the optimization results, the mean power spectrum and single power spectrum, and the overall mean autocorrelation and mean power spectrum.

[0207] Figure 5The first group of power spectrum for the second transmission mode, Figure 6 The first group of power spectrum for the second transmission mode is shown, and Table 2 gives the respective integral sidelobes of the first group and the mean autocorrelation of the first group. Figure 7 The second group of power spectrum for the second transmission mode, Figure 8 The second group of autocorrelation for the second transmission mode is shown. Table 3 gives the respective integral sidelobes of the second group and the mean autocorrelation of the second group. It can be seen that the mean autocorrelation integral sidelobes of the three pulse codes are much lower than the respective autocorrelation integral sidelobes when the pulse codes are different, achieving the desired optimization effect of the present application.

[0208] Table 2 Integral sidelobe level of the first group of autocorrelation functions

[0209]

[0210] Table 3 Integral sidelobe level of the second group of autocorrelation functions

[0211]

[0212] Finally Figure 9 The comparison of the mean power spectrum of the first group, the mean power spectrum of the second group and the total mean power spectrum is given, Figure 10 The comparison of the mean autocorrelation of the first group, the mean autocorrelation of the second group and the total mean autocorrelation is given, and the comparison of the mean autocorrelation integral sidelobe level is given in Table 4. It can be found that the total mean autocorrelation integral sidelobe is much lower than the respective mean autocorrelation integral sidelobes of the first two groups, which shows the effectiveness of the present application.

[0213] Table 4 Integral sidelobe level of the autocorrelation functions of different groups

[0214]

[0215] The present application can also be used for other various data and scenarios. Those skilled in the art can process different data in different scenarios according to the present application without departing from the spirit and essence of the present application, but these should all belong to the protection scope of the appended claims of the present application.

Claims

1. A method for designing intra-pulse encoded discontinuous spectrum signals considering inter-pulse time-varying characteristics, characterized in that... Design of transmit signals for pulse-to-pulse time-varying transmissions with different phase codes emitted within a set of pulses, including: Step 1: Within the L pulse transmission signals of the m-th group, the power spectrum of the transmission signal is represented by the discrete transmission signal vector of each pulse, and then the autocorrelation expression of the transmission signal of each pulse is obtained based on the power spectrum; Step 2: Obtain the mean autocorrelation function of the transmitted signal of the m-th group of pulses based on the autocorrelation expression of the transmitted signal of each pulse; obtain the mean autocorrelation integral sidelobe level of the m-th group of pulses based on the mean autocorrelation function; Step 3: Based on the optimization results of the transmitted signals of the first m-1 groups of pulses and the transmitted signal of the mth group of pulses, obtain the mean autocorrelation function of the transmitted signals of the first m groups of pulses, and obtain the mean autocorrelation integral sidelobe level of the first m groups of pulses according to the mean autocorrelation function of the transmitted signals of the first m groups of pulses. Step 4: Express the mean value of the first m groups of pulses in the form of the autocorrelation integral sidelobe level as a power spectrum, and establish an objective function by weighing the energy of the L pulses transmitted in the m-th group in the unusable frequency band; Step 5: Use the gradient descent method to optimize and solve the objective function, obtain the final optimization result, and realize the design of the inter-pulse time-varying-intra-pulse coded discontinuous spectrum transmission signal.

2. The method for designing intra-pulse encoded discontinuous spectrum signals considering inter-pulse time-varying characteristics according to claim 1, characterized in that, In step one, the methods for obtaining the power spectrum expression include: The discrete transmitted signal vector s of the l-th pulse in the m-th group m,l Represented as: Where m = 1, 2, 3, ..., M; l = 1, 2, 3, ..., L; s m,l,N s m,l The value of the Nth point; N is s m,l Phase encoding length, s m,l phase The value at point N corresponds to s m,l,N ; Discrete transmitted signal vector s m,l The spectrum f m,l Expressed by the Discrete Fourier Transform: In the formula f m,l,2N For the spectrum f m,l The value at point 2N, For discrete transmitted signal vectors s m,l Zero-padding form: In the formula for The value at point 2N; in: Let F be a 2N×2N discrete Fourier transform matrix. The element in the (l1+1)th row and (l2+1)th column of the discrete Fourier transform matrix F... for: Based on the discrete transmitted signal vector s m,l Indicates power spectrum p m,l for: In the formula p m,l,2N-1 For power spectrum p m,l The value at point 2N.

3. The method for designing intra-pulse encoded discontinuous spectrum signals considering inter-pulse time-varying characteristics according to claim 2, characterized in that, In step one, the methods for obtaining the autocorrelation expression of the transmitted signal for each pulse include: Discrete transmitted signal vector s m,l autocorrelation r m,l Represented as: r m,l ＝[r m,l,1-N ,...,r m,l,-1 ,r m,l,0 ,r m,l,1 ,...,r m,l,N-1 ]， In the formula r m,l,N-1 For r m,l The value of the element at point 2N; Autocorrelation r m,l elements Represented as: According to the Wiener-Khinchin theorem, the power spectrum and autocorrelation of a signal form a Fourier transform pair. For the autocorrelation r... m,l Deformation yields autocorrelation In the formula For autocorrelation The value of the 2Nth point; According to formulas (1) and (8), we obtain r m,l,0 =N.

4. The method for designing intra-pulse encoded discontinuous spectrum signals considering inter-pulse time-varying characteristics according to claim 3, is characterized in that, In step two, the mean autocorrelation function of the transmitted signal of the m-th pulse group... for: In the formula The mean autocorrelation function of the transmitted signal The value at point 2N; Then the mean autocorrelation integral sidelobe level of the m-th pulse group is... m for:

5. The method for designing intra-pulse encoded discontinuous spectrum signals considering inter-pulse time-varying characteristics according to claim 4, characterized in that, In step three, the mean autocorrelation function R of the transmitted signals of the first m groups of pulses is... m for: The mean autocorrelation integral sidelobe level of the first m pulse groups m for: In the formula R m,n R is the mean autocorrelation function of the transmitted signal. m The value at point n.

6. The method for designing intra-pulse encoded discontinuous spectrum signals considering inter-pulse time-varying characteristics according to claim 5, is characterized in that, In step four, the method for expressing the mean autocorrelation integral sidelobe level of the first m pulse groups in the form of a power spectrum includes: According to formula (6): FF H =2N·I 2N (14) In the formula I 2N It is a 2N-row, 2N-column identity matrix; Then, according to formula (9), the mean value of the first m groups of pulses represented by formula (13) is obtained from the correlation integral sidelobe level ISLL. m Represented in the form of power spectrum: In the formula p m,'l',k For power spectrum p m,l' The value at point k.

7. The method for designing intra-pulse encoded discontinuous spectrum signals considering inter-pulse time-varying characteristics according to claim 6, characterized in that, In step four, the methods for establishing the objective function include: The stopband energy of the l-th pulse transmitted in the m-th group is In the formula w m,l,k It is the k-th weighted value of the power spectrum of the l-th pulse in the m-th group; In the formula For unavailable frequency band energy weighting, Ω m,j Ω represents the interference frequency band in the m-th pulse group. m The j-th value: Oh m =[Ω m,1 ,...,Oh m,J ], J represents the total number of interference frequency bands in the m-th pulse group; Then the total energy E of the L pulse transmission signals in the m-th group out for: Establish the objective function for the m-th group of pulses In the formula, λ is the weighting value; The objective function is obtained from formulas (15) and (18). The specific expression.

8. The method for designing intra-pulse encoded discontinuous spectrum signals considering inter-pulse time-varying characteristics according to claim 7, characterized in that, In step five, the gradient descent method is used to optimize and solve the objective function. Optimal phase angle: Phase vector for: Assumption The initial value is The initial iteration pointer t = 0; The phase of the t-th iteration is I. Calculation objective function and gradient II. Calculate the search direction d t : In the formula γ t It is the rotation factor; III. Adjusting step size η t Adjustment make Reaching the minimum value; IV. Update And set the iteration pointer t = t + 1; 5. Repeat steps 1 to 4 until the specified termination condition is met.

9. The method for designing intra-pulse encoded discontinuous spectrum signals considering inter-pulse time variation according to claim 8, characterized in that, In step five, section two, the method for determining the rotation factor is as follows: As an intermediate variable: In step five, the termination condition is that the Strong Wolf criterion is satisfied, defined as: Where c1 and c2 are both constants, and 0 < c1 < c2 < 1.

10. The method for designing intra-pulse encoded discontinuous spectrum signals considering inter-pulse time-varying characteristics according to claim 9, characterized in that, The objective function Divided into ISLL m With E out Two parts, firstly regarding ISLL m Regarding the discrete transmitted signal vector s m,l The n'th phase Find the gradient, n' = 1, 2, 3, ..., N: make:, Simultaneously Substituting equation (24) into equation (23), we get: Solve Similarly, we get: therefore: Equation (25) can be rewritten as: In the formula Let matrix F * All elements in the n'th row; therefore Rewritten as: In the formula Let matrix F * All elements in rows 1 to N; Again Find the gradient: Based on equation (27), equation (30) can be rewritten as: In the formula w m,l =[w m,l,1 ,...,w m,l,2N ] T ; therefore Represented as: Therefore, for the objective function Regarding the transmitted signal s m,l phase The first derivative is: According to equation (33), calculate sequentially. Thus obtain

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