Fast design method of low-integration sidelobe non-contiguous spectrum signal for MIMO radar

Abstract

The application discloses a kind of MIMO radar low integration side lobe non-continuous spectrum signal fast design method, belongs to radar waveform design field.The application is aimed at the problem that the design of existing MIMO radar non-continuous spectrum signal does not consider spectrum time variation, so that signal adaptability is weak.The application is designed according to spectrum environment time variation in real time, considers the overall performance in accumulation time, defines average autocorrelation function, and takes average autocorrelation integration side lobe and cross-correlation integration side lobe weighting as objective function, comprehensively considers the trade-off between single-element performance and orthogonality of each element;Meanwhile, constant modulus constraint and stopband energy constraint are added, a new optimization problem is constructed;Then ADMM method is used for iteration solution, and conjugate gradient method is used for fast solution when solving subproblem, and the calculation efficiency is higher.Simulation results show that the signal designed by the method has good orthogonality between each element, and the average autocorrelation performance of single element is better than single autocorrelation, which shows the effectiveness of the method.

Description

TECHNICAL FIELD

[0001] The present application relates to a fast design method of MIMO radar low-integration sidelobe non-continuous spectrum signal, and belongs to the field of radar waveform design. BACKGROUND

[0002] Multiple Input Multiple Output (MIMO) radar is a new type of radar, which is flexible in operation and has high degree of freedom at the transmitting end. It can transmit completely orthogonal waveforms to realize full-space scanning at the transmitting end, or transmit partially correlated waveforms to realize wide-space scanning. Because MIMO radar has high degree of freedom in transmitting waveforms, designing MIMO radar transmitting waveforms to detect target space and obtain better signal performance has become a hot research topic for scholars.

[0003] In addition, in recent years, the number of radio systems has increased explosively. In order to better improve the quality of signal and information transmission, the demand for working bandwidth of radio systems also continues to grow. Radar is one of the common radio users, and with the improvement and innovation of radar theory and technology, modern radar has been widely used in various fields of military and civilian use, so 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 problem of communication radar spectrum coexistence has become increasingly urgent. In addition to civilian radio equipment, the level of enemy electronic countermeasures and radar countermeasures faced by modern radar in combat is rapidly improving, so there are a large number of same-frequency interferences in the electromagnetic environment in which modern high-frequency radars exist, and the electromagnetic environment is complex and harsh, so how to improve the working performance of radar systems in complex electromagnetic spectrum environment has also become a big problem that radar workers need to solve.

[0004] Modern scholars consider means of waveform design to set notches at unusable frequency bands to avoid other interferences, and control the omnidirectional scanning / directing of MIMO radar beams to fixed directions to meet the performance requirements of radars. However, the autocorrelation function is the inverse Fourier transform of the power spectral density, and setting notches at interference frequency bands will affect the autocorrelation function of the signal. Specifically, it will raise the autocorrelation sidelobes of the signal, causing weak target shadowing effect, so the autocorrelation sidelobe performance of the non-continuous spectrum signal needs to be optimized.

[0005] In actual radar signal processing, two-dimensional processing is often needed, that is, fast-time matched filtering and slow-time correlation processing to improve the received signal-to-noise ratio. However, due to the uncertainty of the working time of the civil radio system and the complex and variable local enemy interference, the spectrum environment of the radar is not constant during the entire correlation accumulation time. Therefore, the signal needs to be designed according to the real-time changes of the spectrum to reduce the influence caused by the time-varying spectrum. Meanwhile, the MIMO beam pattern design is considered.

[0006] In the existing design, only the MIMO beam pattern design problem is considered, but the influence of the time-varying spectrum is not considered when the spectrum is discontinuous. Therefore, when the spectrum environment is time-varying, there are still some problems in the design of the MIMO radar non-continuous spectrum signal, which makes the signal weak in adaptability. SUMMARY

[0007] In view of the problem that the existing design of the MIMO radar non-continuous spectrum signal does not consider the time-varying spectrum, which makes the signal weak in adaptability, the present application provides a kind of MIMO radar low integration sidelobe non-continuous spectrum signal fast design method.

[0008] The MIMO radar low integration sidelobe non-continuous spectrum signal fast design method provided by the present application designs the transmitting signal of the M elements of the MIMO radar array in a pulse group diversity manner, which includes,

[0009] Step one: set a signal processing period of each element to contain G groups of pulse signals, the time length of each group of pulse signals corresponds to the time-varying period of the change of the external spectrum environment, and each group of pulse signals contains L pulses;

[0010] An expression of the mth element gth group of pulse transmitting signal is established, and a relationship formula between the transmitting signal and the power spectrum is established to calculate the autocorrelation expression of the mth element gth group of pulse transmitting signal; m=1, 2, 3, …, M, g=1, 2, 3, 4, …, G;

[0011] Step two: calculate the average autocorrelation function of the mth element gth group of pulse transmitting signal, and further obtain the average autocorrelation function integration sidelobe level of the mth element gth group of pulse transmitting signal; the average autocorrelation function integration sidelobe level of the mth element gth group of pulse transmitting signal is expressed in the form of power spectrum;

[0012] Meanwhile, the cross-correlation integration sidelobe level of the gth group of pulse transmitting signal of the M elements is obtained from the sum of the autocorrelation integration sidelobe level of the gth group of pulse transmitting signal of the M elements and the cross-correlation integration sidelobe level of the gth group of pulse transmitting signal of the M elements;

[0013] Step three: constructing a target function from the power spectrum expression of the average autocorrelation function integral sidelobe level of the gth group of pulse emission signals of the mth array element and the cross-correlation integral sidelobe level of the gth group of pulse emission signals of the M array elements; then combining the spectral stopband energy constraint and the constant modulus constraint to describe the optimization problem;

[0014] Step four: solving the optimization problem by using the ADMM method to obtain the final optimization result, and realizing the design of the emission signal.

[0015] According to the MIMO radar low-integral sidelobe non-continuous spectrum signal fast design method, in step one, the expression of the gth group of pulse emission signals of the mth array element is:

[0016]

[0017] In the formula, s m,g is the gth group of pulse emission signals of the mth array element, s m,g,N is the value of the gth group of pulse emission signals of the mth array element at the Nth point, and N is the phase coding length of the pulse emission signal.

[0018] is the phase of s m,g,N , is the phase of s m,g :

[0019]

[0020] The method for establishing the relationship between the emission signal and the power spectrum is:

[0021] The 2N-point spectrum f m,g of s m,g is expressed by using a discrete Fourier transform:

[0022]

[0023] In the formula, f m,g,2N-1 is the value of the 2Nth point of the spectrum f m,g , is the zero-padded form of the emission signal s m,g :

[0024]

[0025] In the formula, f is the value of the 2Nth point of the spectrum f ;

[0026] In the formula, f is the value of the 2Nth point of the spectrum f ;

[0027] is a 2N*2N DFT transform matrix:

[0028]

[0029] the (l1+1)th row and (l2+1)th column element of F;

[0030] the mth array element gth group of pulse emission signal s m,g and the power spectrum p m,g is expressed as:

[0031]

[0032] where p m,g,2N-1 is the value of the power spectrum p m,g at the 2N point, and ⊙ represents the Hadamard product;

[0033] the autocorrelation r m,g of the mth array element gth group of pulse emission signal is:

[0034] r m,g = [r m,g,1-N ,...,r m,g,-1 ,r m,g,0 ,r m,g,1 ,...,r m,g,N-1 ],

[0035] where r m,g,N-1 is the value of the autocorrelation r m,g at the 2N point:

[0036]

[0037] According to the Wiener-Sinai theorem, the power spectrum p m,g of the mth array element gth group of pulse emission signal and the autocorrelation r m,g are a pair of Fourier transform, and the autocorrelation r m,g is transformed to obtain the expression of the autocorrelation :

[0038]

[0039] where is the 2N value of the autocorrelation .

[0040] According to the MIMO radar low-integration sidelobe non-continuous spectrum signal fast design method of the application, in step two, the average autocorrelation function of the mth array element gth group of pulse emission signal is:

[0041]

[0042] The average autocorrelation function integration sidelobe level of the mth array element gth group of pulse emission signal is defined as ISLm,g :

[0043]

[0044] According to formula (6), we have

[0045] FF H = 2N·I 2N , (12)

[0046] In the formula, I 2N is a 2N row and 2N column unit matrix;

[0047] Thus, the average autocorrelation function integral sidelobe level of the mth array element gth group pulse emission signal is expressed as the form of power spectrum:

[0048]

[0049] According to the MIMO radar low-integral sidelobe non-continuous spectrum signal fast design method of the present application, in step two, the sum of the autocorrelation integral sidelobe level of the M array element gth group pulse emission signal and the cross-correlation integral sidelobe level of the M array element gth group pulse emission signal is expressed as ξ:

[0050]

[0051] In the formula, the nth value of the cross-correlation function between the mth array element and the m1th array element gth group pulse emission signal is

[0052] In the formula, S g is the M array element gth group pulse emission signal matrix:

[0053]

[0054] A k is the intermediate operation matrix:

[0055]

[0056] In which Thus, we have:

[0057]

[0058] Then The formula (14) is transformed as:

[0059]

[0060] The autocorrelation integral sidelobe level ISL mm,g of the mth array element gth group pulse emission signal is expressed as:

[0061] ​

[0062] Thus, the correlation integration sidelobe level ISL of the gth group of pulse emission signals of the M array elements is obtained h,g :

[0063]

[0064] According to the MIMO radar low-integration sidelobe non-continuous spectrum signal fast design method of the application, in step three, the objective function f is constructed:

[0065]

[0066] In the formula, λ represents the autocorrelation integration sidelobe level weight coefficient;

[0067] The frequency spectrum stopband energy constraint of the gth group of pulse emission signals of the mth array element is:

[0068]

[0069] In the formula, Ω y represents the stopband position, Ω y ∈Ω=[Ω1,...,Ω Y ], Ω represents the stopband position set, y=1, 2, 3, …, Y; represents the upper limit of the stopband energy;

[0070] The constant modulus constraint is:

[0071] |s m,g,n |=1; (23)

[0072] Thus, the optimization problem of the gth group of pulse emission signals of the mth array element is converted into:

[0073]

[0074] According to the MIMO radar low-integration sidelobe non-continuous spectrum signal fast design method of the application, formula (24) is deformed, and the optimization problem is rewritten as being related to the phase:

[0075] According to the signal constant modulus constraint, the following is obtained: According to the Parseval theorem, the following relationship is obtained:

[0076]

[0077] Then,

[0078] The ISL h,g in formula (20) is expressed as:

[0079]

[0080] The constant modulus constraint is represented as The objective function f is represented as a function of phase The optimization problem of rewriting formula (24) is obtained:

[0081]

[0082] According to the MIMO radar low-integration sidelobe non-continuous spectrum signal fast design method of the application, in step four, the ADMM method is used to solve the optimization problem, which includes:

[0083] The auxiliary variable is introduced to rewrite formula (28) as:

[0084]

[0085] In the formula, x is an auxiliary variable; The augmented Lagrangian function is constructed

[0086]

[0087] In the formula, ρ is a penalty parameter,

[0088] is a dual variable;

[0089] The ADMM method is used to solve the augmented Lagrangian function iteratively, and on the basis of the first q optimization, the q+1 iteration optimization process includes:

[0090] 1) solving the phase The corresponding optimization problem is:

[0091]

[0092] Formula (31) is an unconstrained optimization problem, and the conjugate gradient method is used to solve it;

[0093] 2) solving the auxiliary variable

[0094]

[0095] In the formula, x is a known constant, and formula (32) is solved to obtain:

[0096] 2) solving the dual variable

[0097]

[0098] ​​

[0099] The method of the present application considers the case that the spectrum environment changes in a single accumulation period. It is designed in real time according to the time-varying spectrum environment, considers the overall autocorrelation function performance in the accumulation time, defines the average autocorrelation function, and takes the average autocorrelation integral sidelobe and the cross-correlation integral sidelobe as the objective function, comprehensively considers the trade-off between the single-array element performance and the orthogonality of each array element. At the same time, a new optimization problem is constructed by adding constant modulus constraint and stopband energy constraint. The present application uses ADMM method to solve iteratively, and uses conjugate gradient method when solving the sub-problem and deduces a fast solution method for calculating the gradient, which has high calculation efficiency. The simulation results show that the orthogonality between each array element is good, and the average autocorrelation performance of single-array element is better than that of single autocorrelation, which shows the effectiveness and reliability of the method of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0100] Figure 1 is the schematic diagram of the pulse component signal of the MIMO radar low-integral sidelobe non-continuous spectrum signal fast design method described in the present application;

[0101] Figure 2 is the cross-correlation schematic diagram between the first group of pulse arrays of the first and second array elements in the specific embodiment;

[0102] Figure 3 is the cross-correlation schematic diagram between the first group of pulse arrays of the first and third array elements in the specific embodiment;

[0103] Figure 4 is the cross-correlation schematic diagram between the first group of pulse arrays of the second and third array elements in the specific embodiment;

[0104] Figure 5 is the cross-correlation schematic diagram between the second group of pulse arrays of the first and second array elements in the specific embodiment;

[0105] Figure 6 is the cross-correlation schematic diagram between the second group of pulse arrays of the first and third array elements in the specific embodiment;

[0106] Figure 7 is the cross-correlation schematic diagram between the second group of pulse arrays of the second and third array elements in the specific embodiment;

[0107] Figure 8 is the autocorrelation comparison diagram of each group of pulse signals of the first array element in the specific embodiment;

[0108] Figure 9 is the autocorrelation comparison diagram of each group of pulse signals of the second array element in the specific embodiment;

[0109] Figure 10 is the autocorrelation comparison diagram of each group of pulse signals of the third array element in the specific embodiment;

[0110] Figure 11 is a comparison chart of power spectrum of each group of pulse signals of the first array element in the specific embodiment;

[0111] Figure 12 is a comparison chart of power spectrum of each group of pulse signals of the second array element in the specific embodiment;

[0112] Figure 13 is a comparison chart of power spectrum of each group of pulse signals of the third array element in the specific embodiment. DETAILED DESCRIPTION

[0113] 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 skilled in the art without creative work fall within the scope of protection of the present application.

[0114] 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.

[0115] The present application will be further described below with reference to the drawings and specific embodiments, but is not limited to the present application.

[0116] DETAILED DESCRIPTION Figure 1 As shown in the specific embodiment, the present application provides a fast design method of MIMO radar low-integration sidelobe non-continuous spectrum signal, which adopts pulse group diversity to design the transmitting signal of M array elements of the MIMO radar, including,

[0117] Step one: set a signal processing period of each array element to contain G groups of pulse signals, the time length of each group of pulse signals corresponds to the time-varying period of the change of external spectrum environment, and each group of pulse signals contains L pulses;

[0118] An expression of the gth group of pulse transmitting signals of the mth array element is established, and a relationship formula between the transmitting signals and the power spectrum is established, and the autocorrelation expression of the gth group of pulse transmitting signals of the mth array element is calculated; m=1, 2, 3, …, M, g=1, 2, 3, 4, …, G;

[0119] Step two: the average autocorrelation function of the gth group of pulse transmitting signals of the mth array element is calculated, and the average autocorrelation function integration sidelobe level of the gth group of pulse transmitting signals of the mth array element is further obtained; the average autocorrelation function integration sidelobe level of the gth group of pulse transmitting signals of the mth array element is expressed in the form of power spectrum;

[0120] The sum of the autocorrelation integration sidelobe level of the gth group of pulse transmission signals of the M array elements and the cross-correlation integration sidelobe level of the gth group of pulse transmission signals of the M array elements and the autocorrelation integration sidelobe level of the gth group of pulse transmission signals of the M array elements is used to obtain the cross-correlation integration sidelobe level of the gth group of pulse transmission signals of the M array elements;

[0121] Step three: constructing a target function from the power spectrum form expression of the average autocorrelation function integration sidelobe level of the gth group of pulse transmission signals of the mth array element and the cross-correlation integration sidelobe level of the gth group of pulse transmission signals of the M array elements; and combining the spectral stopband energy constraint and the constant modulus constraint to describe the optimization problem;

[0122] Step four: solving the optimization problem by using the ADMM method to obtain the final optimization result, and realizing the design of the transmission signal.

[0123] In this embodiment, for the M array elements of the MIMO radar array, in order to cope with the problem of spectrum environment change, the pulse group diversity method is used to design the transmission signal, and the phase coding form is used for a single pulse. According to the feedback of the frequency monitoring device, the change of the external spectrum environment can be obtained, and GL pulses are contained in one signal processing period; in this embodiment, the next group of pulses is designed adaptively according to the spectrum environment change after every L pulse period, so as to achieve the time-varying effect. The non-continuous spectrum signal diagram under this design mode is shown in FIG. 1. As shown in FIG. 1, the spectrum environment does not change within L pulses, and the time-varying design is performed every L pulse. The L pulses transmit the same signal. Next, the signal modeling is performed. Figure 1 Figure 1 As can be seen from FIG. 1, the spectrum environment does not change within L pulses, and the time-varying design is performed every L pulse. The L pulses transmit the same signal. Next, the signal modeling is performed.

[0124] Further, in order to facilitate problem modeling and waveform optimization, the discrete digital waveform after uniform sampling is usually considered. At the same time, in order to maximize the radar transmission power, the radar waveform is required to have the constant modulus characteristic. Therefore, in step one, the expression of the gth group of pulse transmission signals of the mth array element is:

[0125]

[0126] In the formula, s m,g is the gth group of pulse transmission signals of the mth array element, s m,g,N is the value of the gth group of pulse transmission signals of the mth array element at the Nth point, and N is the phase coding length of the pulse transmission signal;

[0127] is the phase of s m,g,N is the phase of s m,g

[0128]

[0129] ​​​The method for establishing the relationship between the transmitted signal and the power spectrum is as follows:

[0130] s m,g 2N-point spectrum f m,g Represented using the Discrete Fourier Transform (DFT):

[0131]

[0132] In the formula f m,g,2N-1 For the spectrum f m,g The value at point 2N, For transmitting signal s m,g Zero-padding form:

[0133]

[0134] In the formula for The value at point 2N;

[0135] in

[0136] The DFT transformation matrix is ​​2N×2N:

[0137]

[0138] This is the element in the (l1+1)th row and (l2+1)th column of F;

[0139] The pulse transmission signal s of the m-th array element in the g-th group will be transmitted. m,g With power spectrum p m,g The relationship is represented as:

[0140]

[0141] In the formula p m,g,2N-1 For power spectrum p m,g The value at point 2N, ⊙ represents the Hadamard product;

[0142] Then the autocorrelation r of the pulse transmission signal of the m-th array element in the g-th group m,g for:

[0143] r m,g =[r m,g,1-N ,...,r m,g,-1 ,r m,g,0 ,r m,g,1 ,...,r m,g,N-1 ],

[0144] In the formula r m,g,N-1 For autocorrelation rm,g the 2Nth value of the autocorrelation r

[0145]

[0146] According to the Wiener-sinc theorem, the power spectrum p m,g of the mth array element gth pulse emission signal is m,g and the autocorrelation r m,g is transformed to obtain the autocorrelation The expression of r

[0147]

[0148] In the formula, r is the autocorrelation of the 2Nth value.

[0149] According to formulas (1) and (8), r m,g,0 = N.

[0150] Next, the optimization problem is constructed:

[0151] The optimization problem needs to consider the influence of the sidelobe performance reduction of the autocorrelation function of each array element of the signal on the weak target, consider the cross-correlation function between the array elements to ensure the orthogonality between the array elements to realize omnidirectional scanning, and consider the spectrum compatibility to reduce the influence of the same frequency interference. When optimizing the autocorrelation sidelobe performance of the single array element emission waveform, the embodiment considers the integral sidelobe level.

[0152] However, since the spectrum environment is time-varying in an accumulation period, the GL pulses in the accumulation period cannot be designed and processed as a whole, so when designing the gth pulse, the average autocorrelation function and the average integral sidelobe level of the gth group are considered on the basis of the design of the first g-1 pulses.

[0153] In step two, first define the average autocorrelation function of the first g-1 pulse emission signals of the mth array element as:

[0154]

[0155] The average autocorrelation function integral sidelobe level of the first g-1 pulse emission signals of the mth array element is defined as ISL m,g :

[0156]

[0157] When designing the gth pulse code, the first g-1 pulses have been designed. According to formula (6), we have:

[0158] FF H = 2N·I 2N , (12)

[0159] where I 2N is a 2N-by-2N identity matrix;

[0160] According to formula (9), the autocorrelation function and the signal power spectrum are Fourier transform pairs, and thus the average autocorrelation function integral sidelobe level of the gth group of pulse emission signals of the mth array element represented by formula (11) can be expressed in the form of a power spectrum:

[0161]

[0162] Next, the cross-correlation level between the M array elements is considered, and the cross-correlation integral sidelobe level is considered in this embodiment.

[0163] In step two, the sum of the autocorrelation integral sidelobe level of the gth group of pulse emission signals of the M array elements and the cross-correlation integral sidelobe level of the gth group of pulse emission signals of the M array elements is represented as ξ:

[0164]

[0165] where is the nth value of the cross-correlation function between the gth group of pulse emission signals of the mth array element and the m1th array element;

[0166] For the convenience of subsequent optimization problem representation, the signal is represented by a spectrum. In formula (13), S g is the gth group of pulse emission signals matrix of the M array elements:

[0167]

[0168] A k is an intermediate operation matrix:

[0169]

[0170] where Thus, we obtain:

[0171]

[0172] Then Formula (14) is transformed as:

[0173]

[0174] The autocorrelation integral sidelobe level ISL of the gth group of pulse emission signals of the mth array element is represented as: mm,g

[0175]

[0176] ​Thus, the correlation integration sidelobe level ISL of the gth group of pulse emission signals of the M array elements is obtained h,g :

[0177]

[0178] Further, since the autocorrelation integration sidelobe level and the cross-correlation integration sidelobe level are contradictory to each other, a trade-off between the two is required, and thus in step three, a target function f is constructed:

[0179]

[0180] where λ represents a weight coefficient of the autocorrelation integration sidelobe level;

[0181] In addition, the signal needs to be constrained, first, a spectrum stopband energy constraint, the spectrum stopband energy constraint of the gth group of pulse emission signals of the mth array element is:

[0182]

[0183] where Ω y represents a stopband position, Ω y ∈Ω=[Ω1,...,Ω Y ], Ω represents a set of stopband positions, y=1, 2, 3, …, Y; represents an upper limit of stopband energy;

[0184] At the same time, the constant modulus constraint is:

[0185] |s m,g,n |=1; (23)

[0186] Thus, the optimization problem of the gth group of pulse emission signals of the mth array element is converted to:

[0187]

[0188] The optimization problem is rewritten as being related to the phase by transforming formula (24):

[0189] According to the constant modulus constraint of the signal, it is obtained that According to the Parseval theorem, the following relationship is obtained:

[0190]

[0191] Then

[0192] ISL h,g in formula (20) is expressed as:

[0193]

[0194] The constant modulus constraint can be expressed as The objective function f can be expressed as a function of phase The constant modulus constraint can be omitted, and the optimization problem of rewriting formula (24) is obtained:

[0195]

[0196] Further, in step four, the ADMM method is used to solve the optimization problem, including:

[0197] The ADMM method can be used to solve the constrained optimization problem, which converts the equality constraint into a penalty term by constructing an augmented Lagrangian function, and introduces a dual variable and an auxiliary variable. By optimizing the variables one by one, the final optimization problem is solved. Using the ADMM method, first introduce the auxiliary variable to rewrite formula (28) as:

[0198]

[0199] In the formula is an auxiliary variable;

[0200] The augmented Lagrangian function is constructed as

[0201]

[0202] In the formula, ρ is the penalty parameter, is a dual variable;

[0203] The augmented Lagrangian function is solved by iteration. Based on the completion of the first q optimization, the q+1 iteration optimization process includes:

[0204] 1) Solve the phase The corresponding optimization problem is:

[0205]

[0206] Formula (31) is an unconstrained optimization problem, which is solved by the conjugate gradient method;

[0207] 2) Solve the auxiliary variable The optimization problem can be expressed as:

[0208]

[0209] In the formula is a known constant, and formula (32) is solved to obtain:

[0210]

[0211] 2) Solve the dual variable

[0212]

[0213] In this embodiment, the method of solving the optimization problem (31) using the conjugate gradient method is presented. The conjugate gradient method is often used to solve unconstrained optimization problems. It has small storage requirements, fast convergence, and is suitable for solving large-scale optimization problems. The method of this invention uses the conjugate gradient method to solve the optimization problem represented by equation (31).

[0214] Phase is solved using the conjugate gradient method. The method is as follows:

[0215] Simplifying formula (31) by removing the superscript q representing the iteration number, we get:

[0216]

[0217] Solving for phase The optimal solution:

[0218] Assuming phase The initial value of the vector is The initial iteration pointer t = 0; The phase of the t-th iteration is

[0219] 1) Calculate the phase Corresponding objective function and gradient

[0220] (ii) Calculate the search direction d t :

[0221]

[0222] In the formula γ t The rotation factor;

[0223] (iii) Determine the adjustment step size η through linear search. t ,make Reaching the minimum value;

[0224] (iv) Update And set the iteration pointer t = t + 1;

[0225] (v) Repeat steps one through four until the specified termination condition is met, and then... Update result as phase The optimal solution.

[0226] Table 1 shows the steps of the gradient descent method:

[0227] Table 1 Gradient descent method operation steps

[0228]

[0229] In ii) of the present embodiment, the rotation factor γ t is determined by the following method:

[0230]

[0231] wherein is the conjugate factor of the rotation factor γ t , In order to ensure the search direction:

[0232]

[0233] In iii), the step size is adjusted using the inexact line search method; in v), the termination condition satisfies the strong Wolfe criterion, which is defined as:

[0234]

[0235] wherein c1 and c2 are both constants, and 0 < c1 < c2 < 1.

[0236] Further, as can be seen from Table 1, when the gradient descent method is used 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.

[0237] The function f is decomposed into three parts, and the gradient is calculated respectively:

[0238] The first part is defined as f1 = f (s

[0239] The second part is defined as f2 = f (s

[0240] The third part is defined as f3 = ISL h,g ;

[0241] First, the partial derivative of f2 with respect to then'th phase of the m'th element of the g'th group of pulse emission signals s m',g is calculated:

[0242] wherein n' = 1, 2, 3,..., N: m' = 1, 2, 3,..., M;

[0243] Let a m',g,k = [a m',g,1 ,...,a m',g,2N ] T ,​​

[0244] Then:

[0245] where is an intermediate variable, let and have:

[0246]

[0247] Let Then

[0248] Thus:

[0249] Solve for

[0250]

[0251] where Re(·) represents taking the real part and Im(·) represents taking the imaginary part;

[0252] Then formula (42) is expressed as:

[0253]

[0254] Thus:

[0255] Solve for m',g the nth phase of the gth group of pulse transmission signals s of the mth element:

[0256]

[0257] Let:

[0258] Thus:

[0259]

[0260] Then:

[0261]

[0262] Solve for m',g the nth phase of the gth group of pulse transmission signals s of the mth element:

[0263]

[0264] Let: Then:

[0265]

[0266] Therefore:

[0267]

[0268] Finally, we get:

[0269]

[0270] As can be seen from equations (45), (49) and (52), 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 by fast Fourier transform, so the calculation time can be greatly shortened and the algorithm running speed can be improved.

[0271] Through the above derivation and the steps of Table 1, the optimization problem represented by equation (31) can be solved, so that the original optimization problem can be solved according to the ADMM method. Specific embodiments:

[0273] The beneficial effects of the method of the application are verified by the following specific embodiments:

[0274] The following simulation parameters are set: the number of array elements M = 3, the code length of a single pulse N = 128, the weighting value λ = 0.9, the spectrum environment change period is 3 pulses, that is, L = 3, and the inter-pulse time-varying 2 can reach a coherent accumulation period, that is, G = 2. When g = 1, the normalized spectrum stop band position Ω out = [0.078, 0.098] U [0.3125, 0.3516], and when g = 2, the normalized spectrum stop band 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. The algorithm optimization result is calculated by the method of the application, and the average autocorrelation and the single autocorrelation in the optimization result are compared, as well as the average power spectrum and the single power spectrum.

[0275] First, the cross-correlation between the arrays is given, Figure 2 The cross-correlation between element 1 and element 2 when designing the first group of pulses is given, Figure 3 The cross-correlation between element 1 and element 3 when designing the first group of pulses is given, Figure 4 The cross-correlation between element 2 and element 3 when designing the first group of pulses is given; Figure 5 The cross-correlation between element 1 and element 2 when designing the second group of pulses is given, Figure 6 The cross-correlation between element 1 and element 3 when designing the second group of pulses is given, Figure 7The cross-correlation between element 2 and element 3 when the second group of pulses is designed is given, and it can be seen that the cross-correlation is less than -15dB, and the orthogonality between the signals of each element is good.

[0276] Next, the autocorrelation and average autocorrelation of the first group and the second group of pulses of the three elements are given, Figure 8 The comparison of the first group autocorrelation function, the second group autocorrelation function and the average autocorrelation function of element 1 is given, Figure 9 and Figure 10 The results of element 2 and element 3 are given respectively. Figure 11 The comparison of the first group power spectrum, the second group power spectrum and the average power spectrum of element 1 is given, Figure 12 and Figure 13 The results of element 2 and element 3 are given respectively. From Figures 8 to 10 it can be seen that the average autocorrelation function side lobe of the three elements is lower than the autocorrelation function side lobe of each element, which can verify the effectiveness and reliability of the method of the application. From Figures 11 to 13 it can be seen that in the design of the pulse group diversity signal, the power spectrum has a 50dB or more notch at the unusable frequency band, and due to the effect of energy compensation, the average power spectrum is relatively flat compared to the power spectrum of each pulse group, so from the Fourier transform principle, the average autocorrelation side lobe is lower than the autocorrelation function side lobe of each pulse group, which is consistent with the simulation result.

[0277] Although the application is described herein with reference to particular embodiments, it should be understood that these examples are merely set forth for purposes of example and illustration. As such, many modifications and variations will be apparent to those skilled in the art, and it is contemplated to be within the scope of the claimed application to employ both currently known alternatives and future equivalents. It is therefore intended that the claimed application not be limited to the described embodiments, but that it include all modifications and alternatives within the scope of the claimed application. It is further intended that claims that include dependent clauses, can be drafted to include alternatives to the dependent clauses and equivalents thereto. It is intended, therefore, to discover all such modifications and alternatives as a result of the application of the scope of the claimed application, in its broadest form.

Claims

1. A fast design method for low-integral-sidelobe discontinuous spectrum signals of MIMO radar, wherein the transmitted signal is designed for the M elements of the MIMO radar array using pulse component diversity, characterized in that... Comprising, Step one: set a signal processing period of each array element to contain G groups of pulse signals, the time length of each group of pulse signals corresponds to the time-varying period of the change of external frequency spectrum environment, and each group of pulse signals contains L pulses; An expression of the mth array element gth group of pulse transmission signals is established, a relationship between the transmission signals and the power spectrum is established, and the autocorrelation expression of the mth array element gth group of pulse transmission signals is calculated; m=1, 2, 3, …, M, g=1, 2, 3, 4, …, G; Step two: the average autocorrelation function of the mth array element gth group of pulse transmission signals is calculated, and the average autocorrelation function integral sidelobe level of the mth array element gth group of pulse transmission signals is further obtained; the average autocorrelation function integral sidelobe level of the mth array element gth group of pulse transmission signals is expressed in the form of power spectrum; At the same time, the cross-correlation integral sidelobe level of the M array element gth group of pulse transmission signals is obtained from the sum of the autocorrelation integral sidelobe level of the M array element gth group of pulse transmission signals and the cross-correlation integral sidelobe level of the M array element gth group of pulse transmission signals; Step three: the objective function is constructed from the power spectrum form expression of the average autocorrelation function integral sidelobe level of the mth array element gth group of pulse transmission signals and the cross-correlation integral sidelobe level of the M array element gth group of pulse transmission signals; and the optimization problem is described in combination with the spectrum stopband energy constraint and the constant modulus constraint; Step four: the ADMM method is used to solve the optimization problem to obtain the final optimization result, and the design of the transmission signal is realized.

2. The MIMO radar low-integral sidelobe non-continuous spectrum signal fast design method according to claim 1, characterized in that, In step one, the expression of the mth array element gth group of pulse transmission signals is: In the formula, s m,g is the gth group of pulse emission signals of the mth array element, s m,g,N is the value of the Nth point of the gth group of pulse emission signals of the mth array element, N is the phase encoding length of the pulse emission signals; s m,g,N the phase of s s m,g the phase of s The method for establishing the relationship between the transmission signals and the power spectrum is: s m,g f m,g is expressed using a discrete Fourier transform as: In the formula f m,g,2N-1 For the spectrum f m,g The value at point 2N, For transmitting signal s m,g Zero-padding form: In the formula is the value of the 2Nth point; wherein is a DFT transform matrix of 2Nx2N: the element in the (11+1)th row and the (12+1)th column of F; The pulse transmission signal s of the m-th array element in the g-th group will be transmitted. m,g With power spectrum p m,g The relationship is represented as: where p m,g,2N-1 is the power spectrum p m,g the value of the 2Nth point, and denotes the Hadamard product; The autocorrelation r of the mth array element gth group of pulse emission signal is m,g is: r m,g ＝[r m,g,1-N ,...,r m,g,-1 ,r m,g,0 ,r m,g,1 ,...,r m,g,N-1 ]， where r m,g,N-1 is the autocorrelation r m,g of the 2Nth point of the sequence According to the Wiener-sinc theorem, the power spectrum p m,g with the autocorrelation r m,g for a pair of Fourier transform pairs, the autocorrelation r m,g is transformed to the autocorrelation with the expression: In the formula is the autocorrelation of the 2Nth value.

3. The method of claim 2, wherein, In step two, the average autocorrelation function of the mth array element gth group of pulse transmission signals is: The average autocorrelation function integral sidelobe level of the gth group of pulse emission signals of the mth array element is defined as ISL m,g : According to formula (6), the average autocorrelation function integral sidelobe level of the mth array element gth group of pulse transmission signals is expressed in the form of power spectrum: FF H = 2N I 2N , (12) wherein I 2N is a 2N by 2N identity matrix; In step two, the sum of the autocorrelation integral sidelobe level of the M array element gth group of pulse transmission signals and the cross-correlation integral sidelobe level of the M array element gth group of pulse transmission signals is expressed as ξ:

4. The method of claim 3, wherein, In step three, the objective function f is constructed: In the formula is the nth value of the cross-correlation function between the gth group of pulse emission signals of the mth array element and the m1th array element. In the formula, S g is the gth group of pulse emission signal matrix of M elements A k is the intermediate operation matrix: wherein Thus, it is obtained: Then Rewriting equation (14) as The self-correlation integration sidelobe level ISL of the mth array element gth group of pulse emission signals mm,g is represented as: Thus, the correlation integration sidelobe level ISL of the gth group of pulse emission signals of the M array elements is obtained h,g :

5. The method of claim 4, wherein, Wherein λ represents the autocorrelation integral sidelobe level weight coefficient; The spectrum stopband energy constraint of the mth array element gth group of pulse transmission signals is: The constant modulus constraint is: where Ω y denotes the stopband position, Ω y ∈ Ω = [Ω1,..., Ω Y ], Ω denotes the set of stopband positions, y = 1, 2, 3, …, Y; denotes the upper stopband energy limit; Therefore, the optimization problem of the mth array element gth group of pulse transmission signals is transformed into: |s m,g,n |＝1；(23) Formula (24) is transformed, and the optimization problem is rewritten as phase related:

6. The method of claim 5, wherein, In step four, the ADMM method is used to solve the optimization problem, which includes: According to the signal constant modulus constraint, we have According to the Parseval theorem, we have the following relation: then ISL in equation (20) is expressed as: h,g is expressed as: The constant modulus constraint is then expressed as The objective function f is then expressed as a function of the phase and the optimization problem is rewritten as 7. The method of claim 6, wherein, An auxiliary variable is introduced to rewrite formula (28) as: Formula (31) is an unconstrained optimization problem, which is solved by using the conjugate gradient method; In the formulae are auxiliary variables; Constructing augmented lagrangian function where p is a penalty parameter, is a dual variable; The augmented Lagrangian function is solved by ADMM method The iteration is solved, and on the basis of the first q optimization, the q+1 iteration optimization process includes: 1) Solving the phase The corresponding optimization problem is: Formula (31) is simplified to remove the upper index q representing the number of iterations, and the following formula is obtained: 2) Solve for the auxiliary variables wherein is a known constant, and solving equation (32) gives: 2) Solving for dual variables 8. The method of claim 7, wherein, Phase is solved using the conjugate gradient method. The method is as follows: In five), the termination condition satisfies the strong Wolfe criterion, which is defined as: Solving for phase Optimal solution for phase Assume phase of the vector is Start iteration pointer t = 0; The tth iteration phase of the vector is i) calculating the phase the corresponding objective function and the gradient ii) computing a search direction d t : wherein γ t is a rotation factor; iii) determining the adjustment step size η by linear search t such that reaches a minimum; iv) update and set iteration pointer t = t + 1; V) repeat one to four until the specified termination condition is met, and the final update result as the optimal solution of the phase .

9. The method of claim 8, wherein, In the case of ii), the rotation factor γ t is determined as follows: In the formula is the rotation factor γ t the conjugate factor: Wherein c1 and c2 are both constants, and 0 ​ 10. The method of claim 9, wherein, The function is decomposed into three parts: The first part of the definition is The second part is defined as The third part is defined as f3 = ISL h,g ; First, f2 is applied to the m'th element, the g'th group of pulse emission signals s m',g of then'th phase Partial derivative: where n' = 1, 2, 3,..., N; m' = 1, 2, 3,..., M; Let a m',g,k = [a m',g,1 ,...,a m',g,2N ] T , then: wherein is an intermediate variable, let and has: Let Then Thus: re-solve where Re(·) represents taking real part, and Im(·) represents taking imaginary part; Thus, formula (42) is expressed as: Thus: f1 is applied to the m'th element of the g'th group of pulse emission signals s m',g then'th phase of f1 partial derivative: Let: Therefore, Thus, we have Finally, f3 is the m'th element of the g'th group of pulse emission signals s m',g of then'th phase Partial derivatives are found: Let: Then: Therefore, Finally, we have

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