A subarray-level LFM signal MIMO radar partial correlation waveform design method

Abstract

The application discloses a kind of subarray level LFM signal MIMO radar partial correlation waveform design methods, comprising: based on the initial phase and bandwidth of each transmitting subarray and the center frequency difference between adjacent two transmitting subarrays, the LFM signal waveform of each transmitting subarray is obtained;The LFM signal waveform of each transmitting subarray is processed to obtain the pulse synthesis result;Based on the sidelobe amplitude of the pulse synthesis result obtained by the LFM signal waveform, the initial phase and bandwidth of each transmitting subarray and the center frequency difference between adjacent transmitting subarrays, a cost function is constructed;The LFM signal waveform is optimized using the cost function, to obtain the optimized LFM signal waveform.The application adds the optimization of the center frequency difference between adjacent subarrays in the design of cost function, improves the degree of freedom of waveform design, further reduces the sidelobe peak value of the pulse synthesis result in each angle in the desired direction, and the main lobe is not widened.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar, and particularly relates to a subarray-level LFM signal MIMO radar partial correlation waveform design method. BACKGROUND

[0002] With the continuous development of electronic technology, MIMO (Multiple Input Multiple Output) radar system emerges as the times require. MIMO radar can be divided into distributed MIMO radar and centralized MIMO radar according to the distribution of array elements. Among them, the array element distribution of the centralized MIMO radar is similar to that of the phased array radar. The MIMO radar described below is a centralized MIMO radar. MIMO radar has a very high waveform design freedom, and its performance in parameter discrimination and anti-interception is also stronger than that of phased array radar.

[0003] MIMO radar waveform design is one of the keys to the successful application of MIMO radar. MIMO radar transmit waveforms can be classified into fully correlated waveforms, orthogonal waveforms, and partially correlated waveforms according to the correlation of the waveforms. Among them, the partially correlated waveforms are between the fully correlated waveforms and the orthogonal waveforms, and have a higher degree of freedom in design, which can concentrate the transmit energy in the area to be observed. Compared with the orthogonal waveforms, the energy utilization rate of the radar and the signal-to-noise ratio of the return signal are improved, which is beneficial to the detection and parameter estimation of the target. The transmit waveform of the MIMO radar can be selected from phase-coded signals and LFM (Linear Frequency Modulation) signals, wherein the LFM signal is less affected by the Doppler effect, and has a wider application scenario compared with the phase-coded waveform. Therefore, the design method of the partially correlated LFM waveform has been one of the important research directions of MIMO radar waveform design.

[0004] However, the optimization effect of the existing method can be further increased. SUMMARY

[0005] In order to solve the above problems existing in the prior art, the application provides a subarray-level LFM signal MIMO radar partial correlation waveform design method. The technical problem to be solved by the application is solved by the following technical scheme:

[0006] A subarray-level LFM signal MIMO radar partial correlation waveform design method, the design method comprising:

[0007] Step 1, establishing a MIMO radar model; wherein the MIMO radar model comprises M1 transmitting subarrays, and the number of array elements of each transmitting subarray is M2;

[0008] Step 2: Based on the initial phase and bandwidth of the transmitting subarray and the center frequency difference between two adjacent transmitting subarrays, obtain the LFM signal waveform of each transmitting subarray;

[0009] Step 3: Process the LFM signal waveform of each of the transmitting subarrays to obtain the pulse synthesis result;

[0010] Step 4: Based on the sidelobe amplitude of the pulse synthesis result obtained from the LFM signal waveform, the initial phase and bandwidth of each of the transmitting subarrays, and the center frequency difference between adjacent transmitting subarrays, construct a cost function;

[0011] Step 5: Optimize the LFM signal waveform using the cost function to obtain the optimized LFM signal waveform.

[0012] In one embodiment of the present invention, step 2 includes:

[0013] Step 2.1: Obtain the frequency modulation slope of each of the transmitting subarrays based on the bandwidth of each of the transmitting subarrays and the pulse width of a single transmitted signal;

[0014] Step 2.2: Obtain the center frequency f of each of the transmitting subarrays based on the center frequency difference between the transmitting subarrays and the carrier frequency. k , where f k This represents the center frequency of the k-th subarray, where k = 1, 2, 3, ..., M1;

[0015] Step 2.3: Obtain the LFM signal waveform based on the center frequency, the frequency modulation slope, and the initial phase.

[0016] In one embodiment of the present invention, when k = 1, the center frequency f1 = f0, where f0 represents the carrier frequency;

[0017] When k = 2, 3, ..., M1, the center frequency f k Represented as:

[0018] in, This represents the center frequency difference between the LFM signal waveform of the (n+1)th transmitting subarray and the LFM signal waveform of the nth transmitting subarray, where n = 1, 2, 3, ..., M1-1. M1-1 values ​​are randomly generated within the range, and each is assigned a center frequency difference. Indicates center frequency difference The upper limit, Indicates center frequency difference The lower limit;

[0019] In one embodiment of the present invention, the center frequency difference lower limit Represented as:

[0020]

[0021] Where f represents the frequency variable, T e σ represents the pulse width of the radar transmitted signal, and σ represents the maximum correlation coefficient of the LFM signal waveform between adjacent transmitting subarrays, where 0 < σ ≤ 1.

[0022] In one embodiment of the present invention, the LFM signal waveform is represented as follows:

[0023]

[0024] Among them, s k This represents the LFM signal waveform of the k-th transmitting subarray, where k = 1, 2, 3, ..., M1, and t represents 0 to T. e Sampling time within T e f represents the pulse width of a single transmitted signal. k μ represents the center frequency of the LFM signal waveform of the k-th transmitting subarray. k This represents the frequency modulation slope of the LFM signal waveform of the k-th transmitting subarray. This represents the initial phase of the LFM signal waveform of the k-th transmitting subarray.

[0025] In one embodiment of the present invention, step 3 includes:

[0026] Step 3.1: Process the LFM signal waveform of each of the transmitting subarrays to obtain the pulse synthesis result;

[0027] Step 3.2: Construct a cost function based on the sidelobe amplitude of the pulse synthesis result, the initial phase and bandwidth of each of the transmitter subarrays, and the center frequency difference between adjacent transmitter subarrays.

[0028] In one embodiment of the present invention, the cost function is expressed as:

[0029]

[0030] stB min ≤B k ≤B max

[0031]

[0032]

[0033] Where J represents the cost function, B k B represents the signal bandwidth of the LFM signal waveform of the k-th transmitting subarray. min and B max They represent B respectively k The lower and upper limits, This represents the initial phase of the LFM signal waveform of the k-th transmitting subarray. This represents the signal bandwidth of the LFM signal waveform of the M1th transmitting subarray. This represents the initial phase of the LFM signal waveform of the M1th transmitting subarray. This represents the center frequency difference of the LFM signal waveform of the M1th transmitting subarray.

[0034] In one embodiment of the present invention, step 5 includes:

[0035] Step 5.1: Optimize the signal bandwidth, initial phase, and center frequency difference of the LFM signal waveform between adjacent transmitting subarrays using the cost function to obtain the optimized signal bandwidth, optimized initial phase, and optimized center frequency difference.

[0036] Step 5.2: After obtaining the optimized frequency modulation slope based on the optimized signal bandwidth, μ′ k =B′ k / T e , μ′ k B′ represents the optimized frequency modulation slope of the k-th transmitting subarray. k The optimized signal bandwidth represents the LFM signal waveform of the k-th transmitting subarray.

[0037] Step 5.3: Obtain the optimized center frequency based on the optimized center frequency difference; where, when k = 1, f1′ = f0, f1′ represents the optimized center frequency of the LFM signal waveform of the first transmitting subarray, and when k = 2, 3, ..., M1, ... f′ k This represents the optimized center frequency of the LFM signal waveform of the k-th transmitting subarray. This represents the optimized center frequency difference;

[0038] Step 5.4: Obtain the final subarray LFM signal waveform based on the optimized frequency modulation slope, the optimized initial phase, and the optimized center frequency. The final subarray LFM signal waveform is expressed as follows:

[0039]

[0040] Among them, s′ kThis represents the final LFM signal waveform of the k-th transmitting subarray, where k = 1, 2, 3, ..., M1, and t represents 0 to T. e Sampling time within T e This represents the pulse width of a single signal. This represents the optimized initial phase of the LFM signal waveform of the k-th transmitting subarray.

[0041] In one embodiment of the present invention, step 5.1 includes:

[0042] Step 5.11, move M1 B min M1 zeros and M1-1 zeros Form the first column vector, and combine M1 Bs max M1 2π units and M1-1 units Form the second column vector;

[0043] Step 5.12: Based on the cost function, the signal bandwidth of the LFM signal waveform of the transmitting subarray, the initial phase of the LFM signal waveform of the transmitting subarray, the first column vector, and the second column vector, the fminimax function is used to optimize the signal bandwidth, initial phase, and center frequency difference of the LFM signal waveform to obtain the optimized signal bandwidth, optimized initial phase, and optimized center frequency difference.

[0044] The beneficial effects of this invention are:

[0045] This invention incorporates optimization of the center frequency difference between adjacent subarrays in the cost function design, increasing the freedom of waveform design and further reducing the sidelobe peak value of the pulse synthesis result at each angle within the desired direction, without broadening the main lobe. Simultaneously, by limiting the optimization range of the center frequency difference between adjacent subarrays, this invention ensures the orthogonality between the subarrays, making the emission energy coverage pattern design effect consistent with existing technologies. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating a method for designing the relevant waveforms of a subarray-level LFM signal MIMO radar section, as provided in an embodiment of the present invention.

[0047] Figure 2 This is a comparison diagram of waveform emission energy coverage designed by existing methods one and two and the method proposed in this invention under simulation conditions, provided by an embodiment of the present invention.

[0048] Figure 3 This is a pulse synthesis comparison diagram of the waveforms of existing methods 1 and 2 and the method proposed in this invention at -5° under simulation conditions, provided by the embodiments of this invention.

[0049] Figure 4 This is a pulse synthesis comparison diagram of the waveforms of existing methods 1 and 2 and the method proposed in this invention at 0° under simulation conditions, provided by an embodiment of the present invention.

[0050] Figure 5 This is a pulse synthesis comparison diagram of the waveforms of existing methods 1 and 2 and the method proposed in this invention at 5° under simulation conditions, provided by an embodiment of the present invention.

[0051] Figure 6 This is a comparison diagram of waveform emission energy coverage between the existing method 1 and the method proposed in this invention under simulation condition 2, provided by an embodiment of the present invention.

[0052] Figure 7 This is a pulse synthesis comparison diagram of the waveforms of the existing method one and the method proposed in this invention at 20° under simulation condition two, provided by an embodiment of this invention. Detailed Implementation

[0053] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0054] Example 1

[0055] Please see Figure 1 , Figure 1 This is a flowchart illustrating a method for designing the correlation waveform of a subarray-level LFM signal MIMO radar section according to an embodiment of the present invention. The present invention provides a method for designing the correlation waveform of a subarray-level LFM signal MIMO radar section, the method comprising:

[0056] Step 1: Establish a MIMO radar model; the MIMO radar model includes M1 transmitting subarrays, and each transmitting subarray has M2 array elements.

[0057] Specifically, the MIMO radar model is set to include M1 transmitting subarrays. The number of elements in each transmitting subarray is determined to be M2 based on the -3dB width of the desired transmitting energy coverage map. Then the total number of elements in the transmitting array is M, and M = M1M2.

[0058] M array elements are arranged in a straight line with equal spacing between them to form the transmitting array of a MIMO radar. All array elements in the transmitting subarray transmit the same LFM signal, and the beam pointing (i.e., the center pointing of the transmitted energy coverage map) can be controlled by changing the initial phase of each LFM signal in the transmitting subarray. The transmitted signals of each transmitting subarray are orthogonal to each other.

[0059] Initialize the parameters of the radar model and set the pulse width of the radar transmitted signal to T. e L is 0 to T e Total number of sampling times within the period.

[0060] Set the center frequency difference between the (n+1)th and nth transmitting subarrays to be... And determine the center frequency difference The upper limit is Then, the center frequency difference is determined based on the orthogonality between the transmitting subarrays. lower limit Lower limit of the center frequency difference between adjacent transmitter subarrays for:

[0061]

[0062] in, express The lower limit value, f represents the frequency variable, σ represents the maximum correlation coefficient of LFM signal waveforms between adjacent transmitter subarrays, 0≤σ≤1. M1-1 values ​​are randomly generated within the range, and assigned to the corresponding values ​​respectively. Where n = 1, 2, 3, ..., M1-1.

[0063] The center frequency of the LFM signal waveform of the k-th transmitting subarray is f. k When k = 1, f1 = f0; when k = 2, 3, ..., M1, ... Where f0 is the carrier frequency, and simultaneously represents the initial phase of the LFM signal waveform of the k-th transmitting subarray. Let it be a random value in the range [0, 2π).

[0064] The signal bandwidth of the LFM signal waveform of the k-th transmitting subarray is set to B. k And determine B k The upper limit is B max Then, the lower limit B is determined based on the results of the signal Doppler sensitivity at different bandwidth lower limits. min ; in [B min B max M1 values ​​are randomly generated within the range of ], and each is assigned to the corresponding B. k , k = 1, 2, 3, ..., M1.

[0065] Step 2: Based on the initial phase and bandwidth of the transmitting subarray and the center frequency difference between two adjacent transmitting subarrays, obtain the LFM signal waveform of each transmitting subarray.

[0066] In one specific embodiment, step 2 includes:

[0067] Step 2.1: Obtain the frequency modulation slope based on the signal bandwidth and the pulse width of a single transmitted signal. The frequency modulation slope is expressed as:

[0068] μ k=B k / T e

[0069] Where, μ k This represents the frequency modulation slope of the LFM signal waveform of the k-th transmitting subarray.

[0070] Step 2.2: Obtain the center frequency f of each of the transmitting subarrays based on the center frequency difference between the transmitting subarrays and the carrier frequency. k , where f k Let M1 represent the center frequency of the k-th subarray, where k = 1, 2, 3, ..., M1.

[0071] Here, when k = 1, the center frequency f1 = f0, where f0 represents the carrier frequency; when k = 2, 3, ..., M1, the center frequency f k Represented as:

[0072] Step 2.3: Based on the center frequency, the frequency modulation slope, and the initial phase, the LFM signal waveform is represented as follows:

[0073]

[0074] Among them, s k This represents the LFM signal waveform of the k-th transmitting subarray, where k = 1, 2, 3, ..., M1, and t represents 0 to T. e Sampling time within.

[0075] Step 3: Process the LFM signal waveform of each transmitter subarray to obtain the pulse synthesis result.

[0076] In one specific embodiment, step 3 includes:

[0077] Step 3.1: Convert the LFM signal waveforms s of each transmitter subarray. k The LFM signal waveform matrix S that makes up each transmitting subarray k =[s k ;…;s k ], where S k Including M2 s k .

[0078] Step 3.2: Convert the LFM signal waveform matrix S of each transmitting subarray. k The total LFM signal waveform matrix that makes up the entire transmitting array is S = [S1; S2; ...; S...]. M1 ].

[0079] Step 3.3: Process the total LFM signal waveform matrix S to obtain the pulse synthesis result.

[0080] Step 3.31: Take P sampling angles discretely and uniformly within the -3dB range of the desired emission energy coverage map, and calculate the steering vector for each sampling angle.

[0081] Specifically, P sampling angles are discretely and uniformly selected within the -3dB range of the desired emission energy coverage map, and arranged in ascending order as [θ1, θ2, ..., θ]. p Based on the distance d between the transmitting array elements and the wavelength λ of the radar transmitted signal, the sampling angle θ is obtained. p The guide vector,

[0082] a(θ p )=[1,exp(j2πdsinθ p / λ),…,exp(j2π(M-1)dsinθ p / λ)] T

[0083] Where a(θ) p ) represents the sampling angle θ p The guiding vector, p = 1, 2, ..., P, and the sampling angle θ p Satisfying θ1<θ2<…<θ p M represents the total number of elements in the transmitting array, d represents the spacing between the transmitting elements, and λ represents the wavelength of the radar transmitted signal. T This indicates the transpose operation.

[0084] Step 3.32: Obtain the echo signal based on the guide vector of the sampling angle and the total LFM signal waveform matrix.

[0085] Specifically, the echo signal S r The expression is S r =a(θ) p ) T S represents the total LFM signal waveform matrix.

[0086] Step 3.33: Perform pulse synthesis processing on the echo signal to obtain the pulse synthesis result.

[0087] Specifically, the pulse synthesis result y(θ) p The expression for ,l) is:

[0088] y(θ p ,l)=xcorr(S r )=xcorr(a(θ p ) T S)

[0089] Where l represents -T e ~T e The sampling time is 2L-1 points within the range, where L represents 0 to T. eThe total number of sampling times within the range, xcorr(·) represents the autocorrelation operation.

[0090] Step 4: Construct a cost function based on the sidelobe amplitude of the pulse synthesis result obtained from the LFM signal waveform, the initial phase and bandwidth of each transmitter subarray, and the center frequency difference between adjacent transmitter subarrays.

[0091] Specifically, based on the signal y(θ) after pulse synthesis processing p The following cost function model is established:

[0092]

[0093] stB min ≤B k ≤B max

[0094]

[0095]

[0096] Where J represents the cost function, This represents the signal bandwidth of the LFM signal waveform of the M1th transmitting subarray. This represents the initial phase of the LFM signal waveform of the M1th transmitting subarray. This represents the center frequency difference of the LFM signal waveform of the M1th transmitting subarray.

[0097] Step 5: Optimize the LFM signal waveform using the cost function to obtain the optimized LFM signal waveform.

[0098] In one specific embodiment, step 5 includes:

[0099] Step 5.1: Optimize the signal bandwidth, initial phase, and center frequency difference of the LFM signal waveform between adjacent transmitter subarrays using the cost function to obtain the optimized signal bandwidth, optimized initial phase, and optimized center frequency difference.

[0100] Step 5.11, move M1 B min M1 zeros and M1-1 zeros Form the first column vector, and combine M1 Bs max M1 2π units and M1-1 units This forms the second column vector.

[0101] Specifically, M1 B min and M1 zeros and M1-1 zeros The first column vector b1 is formed, and its expression is: At the same time, M1 B max and M1 2π and M1-1 The second column vector b2 is formed, and its expression is:

[0102] Step 5.12: Based on the cost function, the signal bandwidth of the LFM signal waveform of the transmitting subarray, and the initial phase, first column vector, and second column vector of the LFM signal waveform of the transmitting subarray, the fminimax function is used to optimize the signal bandwidth, initial phase, and center frequency difference of the LFM signal waveform to obtain the optimized signal bandwidth, optimized initial phase, and optimized center frequency difference.

[0103] Specifically, the fminimax function is introduced, with the cost function J serving as the function of fminimax, and the signal bandwidth B of the LFM signal waveform of the transmitting subarray is calculated. k The initial phase of the LFM signal waveform of the transmitting subarray and the center frequency difference between adjacent transmitting subarrays As input variables for the fminimax function, the first column vector b1 is used as the lower limit of the input variables for the fminimax function, and the second column vector b2 is used as the upper limit of the input variables for the fminimax function; thus, the mathematical model of the cost function J is converted into a form that fminimax can call.

[0104] The `fminimax` function is called to optimize the signal bandwidth, initial phase, and center frequency difference between adjacent transmitter subarrays of the LFM signal waveform for each subarray, resulting in the optimized signal bandwidth B′. k Optimized initial phase and the optimized center frequency difference between adjacent subarrays

[0105] Step 5.2: After obtaining the optimized frequency modulation slope based on the optimized signal bandwidth, μ′ k =B′ k / T,μ′ k B′ represents the optimized frequency modulation slope of the k-th transmitting subarray. k The optimized signal bandwidth represents the LFM signal waveform of the k-th transmitting subarray.

[0106] Step 5.3: Obtain the optimized center frequency based on the optimized center frequency difference; where, when k = 1, f1′ = f0, f1′ represents the optimized center frequency of the LFM signal waveform of the first transmitting subarray, and when k = 2, 3, ..., M1, ... f′ k This represents the optimized center frequency of the LFM signal waveform of the k-th transmitting subarray. This represents the optimized center frequency difference.

[0107] Step 5.4: Based on the optimized frequency modulation slope, optimized initial phase, and optimized center frequency, obtain the final subarray LFM signal waveform, which is expressed as follows:

[0108]

[0109] Among them, s′ k This represents the final LFM signal waveform of the k-th transmitting subarray, where k = 1, 2, 3, ..., M1, and t represents 0 to T. e Sampling time within T e This represents the pulse width of a single signal. This represents the optimized initial phase of the LFM signal waveform of the k-th transmitting subarray.

[0110] On the one hand, in order to illustrate the correlation between the signal pulse synthesis result and the center frequency difference between the signals, the present invention will explain the following:

[0111] First, the transmitted and received signals are sampled in time. Assume the MIMO radar has M transmitting elements and N receiving elements, with both transmitting and receiving elements sharing the same array (M = N). The element spacing is d, the wavelength of the transmitted signal is λ, and the time width and bandwidth of each of the M transmitted signals are T and B respectively. s s m (l) represents the l-th sample of the signal transmitted by the m-th transmitting element, x n (l) represents the l-th sample of the signal received by the n-th receiving array element, where l = 1, 2, 3...L, and L is the number of discrete sampling points of the transmitted signal. The discretized transmitted signal matrix and received signal matrix can then be expressed as:

[0112] S(l)=[s1(l),s2(l),…s m (l)…s M (l)] T

[0113] X(l)=[x1(l),x2(l),…x n (l)…x N (l)] T

[0114] Suppose that the radar forms a receiving beam in a certain airspace direction, and this direction is denoted as θ. r Then the weighting coefficients of the receiving filter are related to θ r Receiver steering vector b(θ) in the direction rConsistent with the output z(l) of the DBF receiver, it can be expressed as:

[0115] z(l)=b H (θ r )X(l)

[0116] Where, b(θ) r ) is θ r The receiving guidance vector in the direction can be expanded as follows:

[0117]

[0118] In order to be with θ r The echoes in the direction are matched to maximize the gain of the pulse synthesis result. The matched filter coefficient h(l) of the pulse synthesis result should be the transmitted signal at θ. r The conjugate reversal in the direction effectively performs the emission DBF. h(l) can be expressed as:

[0119] h(l)=a T (θ r )S c (Ll)

[0120] in,[·] c This represents the conjugate operation, a(θ) r ) is θ r The emission steering vector in the direction can be expanded as follows:

[0121]

[0122] Finally, pulse synthesis is performed on the output of the received DBF, and the final pulse synthesis result is u(θ). r ,l) is:

[0123]

[0124] Here, * represents the convolution operation.

[0125] As can be seen from the above formula, the pulse synthesis result is actually the sum of the correlation functions of the waveforms of each array element after being weighted by the corresponding steering vector. The steering vector is an inherent property of the array and cannot be changed, so the pulse synthesis result is determined by the correlation function between the waveforms of each array element.

[0126] The correlation function C′ between the i-th and j-th transmitted signals ij (τ) can be expressed as:

[0127]

[0128] β ij =f i -f j+μτ

[0129] Among them, s i (t) represents the transmitted signal of the i-th transmitting element, s j (t) represents the transmitted signal of the j-th transmitting element, f i f is the center frequency of the transmitted signal of the i-th transmitting element. j Let μ be the center frequency of the transmitted signal of the j-th transmitting element, and μ be the frequency modulation slope, μ = B. s / T, where τ is the signal delay. Let be the initial phase of the transmitted signal of the i-th transmitting element. Let be the initial phase of the transmitted signal of the j-th transmitting element.

[0130] Suppose that when τ takes a certain value, C′ ij The modulus of (τ) |C′ ij (τ)| reaches its maximum value, at which point the value of τ is denoted by τ0. Through simple analysis, it can be seen that when β... ij When |C′ = 0, ij (τ)| reaches its maximum value, at which point τ0 is represented as,

[0131]

[0132] At this time, |C′ ij The maximum value of (τ)| is |C′ ij (τ0)| can be expressed as:

[0133]

[0134] Analysis of the above formula shows that as |f i -f j |Continuously increasing,|C′ ij (τ0)| gradually decreases, and in |f i -f j |=B s At that time, |C′ ij (τ0)| reaches its minimum value, at which point |C′| ij (τ0)|=0.

[0135] Since the signal pulse synthesis result is the sum of the phase-modulated superposition of the correlation functions between signals, and the function values ​​of the correlation functions are all complex numbers, the magnitude of the pulse synthesis result must be less than the sum of the magnitudes of the correlation functions. Therefore, when |f i -f j As the voltage increases, the sidelobe peak value of the pulse synthesis result tends to decrease. In summary, the signal pulse synthesis result is closely related to the center frequency difference between the signals.

[0136] On the other hand, according to the definition of LFM waveform, the correlation coefficient r between the i-th and j-th transmitted signals is... ij It can be represented as:

[0137]

[0138] Where T is the duration of the transmitted signal, s i (t) represents the transmitted signal of the i-th transmitting element, s j (t) represents the transmitted signal of the j-th transmitting element.

[0139] Analyzing the above formula, we can obtain that when f i -f j =q / T, where q is any integer, r ij =0, at this time the i-th and j-th transmitted signals are orthogonal to each other, and the transmitted signals are orthogonal LFM signals.

[0140] Furthermore, observing the above formula, it can be found that the correlation coefficient r between the i-th and j-th transmitted signals is... ij The value of is related to sinc[π(f)] i -f j The maximum value of the sinc function is 1, but the sinc function decays rapidly when |f... i -f j When |T>2.7, the value of the sinc function is already less than 0.1. Therefore, when the frequency difference between signals is greater than a certain value, it is not necessary to strictly adhere to the rule that the frequency difference is an integer multiple of 1 / T to achieve an approximately orthogonal effect.

[0141] Therefore, based on the above two proofs, we can draw the following conclusion:

[0142] 1. For LFM signals, the fact that the center frequency difference between the transmitted signals of adjacent array elements is an integer multiple of 1 / T is only a sufficient but not necessary condition for the transmitted signals of adjacent array elements to be orthogonal to each other. When the center frequency difference between the transmitted signals of adjacent array elements is greater than a certain value, the transmitted signals of adjacent array elements can always remain approximately orthogonal.

[0143] 2. For LFM-based MIMO radar waveform design, the center frequency difference between array elements will significantly affect the radar pulse synthesis result. Optimizing the center frequency difference is an important part of MIMO radar waveform design. In this method, the optimization of the center frequency difference between adjacent subarrays will significantly improve the degree of freedom of waveform design, thereby reducing the sidelobes of the pulse synthesis result and improving the radar's target detection capability.

[0144] The beneficial effects of the present invention are further described below through simulation experiments.

[0145] One existing method is a partial correlation waveform design method for MIMO radar based on subarray orthogonal LFM signals. This method is a subarray-level waveform design approach. It optimizes the transmit energy coverage of the waveform by designing the number of subarray elements and optimizes the pulse synthesis performance of the waveform by adjusting the bandwidth and initial phase of the subarray. The orthogonality between subarrays ensures that the two optimization methods do not interfere with each other. This method achieves transmit energy coverage design for a single beam, but the sidelobe peak value of the pulse synthesis is still relatively high. However, this method places too much emphasis on the orthogonality between subarrays, thus fixing the center frequency of the subarrays. This results in insufficient waveform optimization, reducing the degree of freedom in waveform design, which in turn limits the pulse synthesis performance of the waveform design. The pulse synthesis sidelobe peak value of this method can be further reduced.

[0146] Existing Method Two is a partial correlation waveform design method for MIMO radar based on LFM signals. This method is an array element-level waveform design method that simultaneously optimizes the pulse synthesis result and transmit energy coverage map of the waveform by using the center frequency difference and initial phase of the array elements. In practice, the two optimization objectives interfere with each other, resulting in excessively high sidelobe peaks in both the transmit energy coverage map and the pulse synthesis. Therefore, Existing Method Two is inferior to Existing Method One in both transmit energy coverage map and pulse synthesis performance.

[0147] Simulation condition one:

[0148] The MIMO radar's transmitting array is a uniform linear array with 20 transmitting elements (M=20), an element spacing of half a wavelength, and a signal duration T. e =100μs, total transmitted signal bandwidth B = 8MHz, desired transmit energy coverage beamwidth of 20°, beam pointing θ0 = 0°. For this invention, to ensure consistent simulation conditions, the number of transmit array elements M = 20, of which the number of subarrays M1 = 4, the number of array elements in each subarray M2 = 5, and the upper limit of signal bandwidth B max =8MHz, the maximum correlation coefficient σ of the LFM signal waveform between adjacent transmitter subarrays is 0.1.

[0149] Simulation condition two:

[0150] The MIMO radar's transmitting array is a uniform linear array with 20 transmitting elements (M=20), an element spacing of half a wavelength, and a signal duration T. e =100μs, total transmitted signal bandwidth B = 8MHz, desired transmit energy coverage beamwidth of 20°, beam pointing θ0 = 20°. For this invention, to ensure consistent simulation conditions, the number of transmit array elements M = 20, of which the number of subarrays M1 = 4, the number of array elements in each subarray M2 = 5, and the upper limit of signal bandwidth B max =8MHz, the maximum correlation coefficient σ of the LFM signal waveform between adjacent transmitter subarrays is 0.1.

[0151] Simulation Experiment 1:

[0152] Under simulation conditions, the LFM signal partial correlation waveforms were designed using the method of this invention, existing method one, and existing method two, respectively. The transmit energy coverage diagrams of these three methods were then compared. (See [link to relevant documentation]). Figure 2 , Figure 2 This is a comparison diagram of the waveform emission energy coverage designed by existing methods one and two and the method proposed in this invention under simulation conditions, provided by an embodiment of the present invention. Figure 2 The horizontal axis represents angles in degrees, and the vertical axis represents normalized amplitude in dB.

[0153] Depend on Figure 2 It is known that the sidelobes of the transmit energy coverage pattern designed by the existing Method 1 are approximately -9dB, while the sidelobes of the transmit energy distribution patterns designed by the existing Method 2 and this method are approximately -13dB, which is much lower than that of the existing Method 1. Although this method incorporates optimization of the center frequency difference between adjacent subarrays, the orthogonality between subarrays is still guaranteed because the magnitude of the center frequency difference between adjacent subarrays is limited during optimization. Therefore, the design capability of the transmit energy coverage pattern of this method is essentially no different from that of the existing Method 1.

[0154] A lower sidelobe in the transmit energy coverage pattern means that the radar's transmit energy is more concentrated within the desired transmit energy coverage area. Under the same radar transmit power, using a waveform with a lower sidelobe in the transmit energy coverage pattern can improve the radar's signal-to-noise ratio, thereby further improving the radar's target detection performance and parameter estimation performance.

[0155] Simulation Experiment 2:

[0156] Under simulation conditions, the LFM signal partial correlation waveforms were designed using the method of this invention, existing method one, and existing method two, respectively. The synthesized signal pulse results of the two methods in the -5°, 0°, and 5° spatial domains were compared. (See [link to relevant documentation]). Figures 3-5 , Figure 3 This is a pulse synthesis comparison diagram of the waveforms of existing methods 1 and 2 and the method proposed in this invention at -5° under simulation conditions, provided by the embodiments of this invention. Figure 4 This is a pulse synthesis comparison diagram of the waveforms of existing methods 1 and 2 and the method proposed in this invention at 0° under simulation conditions, provided by an embodiment of the present invention. Figure 5 This is a pulse synthesis comparison diagram of the waveforms of existing methods one and two and the method proposed in this invention at 5° under simulation conditions, provided by an embodiment of the present invention; wherein, Figure 3 , Figure 4 and Figure 5 The horizontal axis represents time, in μs, and the vertical axis represents normalized amplitude, in dB.

[0157] Depend on Figure 3 , Figure 4 and Figure 5 It can be seen that the pulse synthesis result of the present invention has lower side lobes at each angle than the existing method one, and the main lobe width is much smaller than that of the existing method two.

[0158] As is well known, excessively wide main lobes and excessively high side lobes in radar pulse synthesis can lead to large targets obscuring smaller targets, and also increase the radar's false alarm probability. These are problems that radar waveform design must avoid. Figure 3 , Figure 4 and Figure 5 It can be seen that, using the waveform designed by this invention, the sidelobe peak value of the pulse synthesis result is smaller than that of the existing method 2 in all directions within the desired angle range, and the main lobe width is also smaller than that of the existing method 1. Overall, the effect is better than that of the existing method 1 and the existing method 2.

[0159] In addition, to further demonstrate the beneficial effects of the present invention, simulation experiments 3 and 4 are conducted to demonstrate the performance of the present invention relative to the existing method 1.

[0160] Simulation Experiment 3:

[0161] Under simulation condition two, the LFM signal partial correlation waveforms were designed using both the method of this invention and the existing method one, and the transmit energy coverage diagrams of the two methods were compared. Please refer to [link to relevant documentation]. Figure 6 , Figure 6 This is a comparison diagram of the waveform emission energy coverage designed by the existing method one and the method proposed in this invention under simulation condition two, provided by an embodiment of the present invention. Figure 6 The horizontal axis represents angles in degrees, and the vertical axis represents normalized amplitude in dB.

[0162] Depend on Figure 6 It is understood that the method of the present invention can change the center direction of the emission energy coverage map. When the center direction is in other directions, the present invention can still maintain the matching degree with the desired emission energy coverage map and has similar performance to the existing method.

[0163] Simulation Experiment 4:

[0164] Under simulation condition two, the LFM signal partial correlation waveforms were designed using both the method of this invention and the existing method one, and the pulse compression results of the synthesized signal in the 20° spatial domain were compared between the two methods. Please refer to [link to relevant documentation]. Figure 7 , Figure 7 This is a pulse synthesis comparison diagram of the waveforms of the existing method one and the method proposed in this invention at 20° under simulation condition two, provided by an embodiment of the present invention; wherein, Figure 7 The horizontal axis represents time in μs, and the vertical axis represents the normalized amplitude in dB.

[0165] Depend on Figure 7 It can be seen that when the center of the emission energy coverage map points to 20°, the pulse comprehensive performance of the present invention is still better than that of the existing method one.

[0166] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0167] Although this application has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the accompanying drawings, disclosure, and appended claims, will understand and implement other variations of the disclosed embodiments in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0168] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for designing the correlation waveform of a subarray-level LFM signal MIMO radar section, characterized in that, The design method includes: Step 1: Establish a MIMO radar model; the MIMO radar model includes M1 transmitting subarrays, and each transmitting subarray has M2 array elements; Step 2: Based on the initial phase and bandwidth of each of the transmitting subarrays and the center frequency difference between two adjacent transmitting subarrays, obtain the LFM signal waveform of each transmitting subarray; Step 3: Process the LFM signal waveform of each of the transmitting subarrays to obtain the pulse synthesis result; Step 4: Based on the sidelobe amplitude of the pulse synthesis result obtained from the LFM signal waveform, the initial phase and bandwidth of each of the transmitting subarrays, and the center frequency difference between adjacent transmitting subarrays, construct a cost function; Step 5: Optimize the LFM signal waveform using the cost function to obtain the optimized LFM signal waveform.

2. The method for designing the correlation waveform of the subarray-level LFM signal MIMO radar section according to claim 1, characterized in that, Step 2 includes: Step 2.1: Obtain the frequency modulation slope of each of the transmitting subarrays based on the bandwidth of each of the transmitting subarrays and the pulse width of a single transmitted signal; Step 2.2: Obtain the center frequency f of each of the transmitting subarrays based on the center frequency difference between the transmitting subarrays and the carrier frequency. k , where f k Let M1 represent the center frequency of the k-th subarray, where k = 1, 2, 3, ..., M1; Step 2.3: Obtain the LFM signal waveform based on the center frequency, the frequency modulation slope, and the initial phase.

3. The method for designing the correlation waveform of the subarray-level LFM signal MIMO radar section according to claim 2, characterized in that, When k = 1, the center frequency f1 = f0, where f0 represents the carrier frequency; When k = 2, 3, ..., M1, the center frequency f k Represented as: Among them, the center frequency difference This represents the center frequency difference between the LFM signal waveform of the (n+1)th transmitting subarray and the LFM signal waveform of the nth transmitting subarray, where n = 1, 2, 3, ..., M1-1. M1-1 values ​​are randomly generated within the range, and each is assigned a center frequency difference. Indicates the center frequency difference The upper limit, Indicates the center frequency difference The lower limit.

4. The method for designing the correlation waveform of the subarray-level LFM signal MIMO radar section according to claim 3, characterized in that, The center frequency difference lower limit Represented as: Where f represents the frequency variable, T e σ represents the pulse width of the radar transmitted signal, and σ represents the maximum correlation coefficient of the LFM signal waveform between adjacent transmitting subarrays, where 0 < σ ≤ 1.

5. The method for designing the correlation waveform of the subarray-level LFM signal MIMO radar section according to claim 4, characterized in that, The LFM signal waveform is represented as follows: Among them, s k This represents the LFM signal waveform of the k-th transmitting subarray, where k = 1, 2, 3, ..., M1, and t represents 0 to T. e Sampling time within T e f represents the pulse width of a single transmitted signal. k μ represents the center frequency of the LFM signal waveform of the k-th transmitting subarray. k This represents the frequency modulation slope of the LFM signal waveform of the k-th transmitting subarray. This represents the initial phase of the LFM signal waveform of the k-th transmitting subarray.

6. The method for designing the correlation waveform of the subarray-level LFM signal MIMO radar section according to claim 3, characterized in that, Step 3 includes: Step 3.1: Process the LFM signal waveform of each of the transmitting subarrays to obtain the pulse synthesis result; Step 3.2: Construct a cost function based on the sidelobe amplitude of the pulse synthesis result, the initial phase and bandwidth of each of the transmitter subarrays, and the center frequency difference between adjacent transmitter subarrays.

7. The method for designing the correlation waveform of the subarray-level LFM signal MIMO radar section according to claim 6, characterized in that, The cost function is expressed as: Where J represents the cost function, and B = [B1, B2, ... B M1 ], B k B represents the signal bandwidth of the LFM signal waveform of the k-th transmitting subarray. min and B max They represent B respectively k The lower limit and upper limit, This represents the initial phase of the LFM signal waveform of the k-th transmitting subarray. This represents the signal bandwidth of the LFM signal waveform of the M1th transmitting subarray. This represents the initial phase of the LFM signal waveform of the M1th transmitting subarray. This represents the center frequency difference of the LFM signal waveform of the M1th transmitting subarray.

8. The method for designing the correlation waveform of the subarray-level LFM signal MIMO radar section according to claim 7, characterized in that, Step 5 includes: Step 5.1: Optimize the signal bandwidth, initial phase, and center frequency difference of the LFM signal waveform between adjacent transmitting subarrays using the cost function to obtain the optimized signal bandwidth, optimized initial phase, and optimized center frequency difference. Step 5.2: After obtaining the optimized frequency modulation slope based on the optimized signal bandwidth, μ k ′=B k ′ / T e μ k ′ represents the optimized frequency modulation slope of the k-th transmitting subarray, B k ′ represents the optimized signal bandwidth of the LFM signal waveform of the k-th transmitting subarray; Step 5.3: Obtain the optimized center frequency based on the optimized center frequency difference; where, when k = 1, f1′ = f0, f1′ represents the optimized center frequency of the LFM signal waveform of the first transmitting subarray, and when k = 2, 3, ..., M1, ... f k ′ represents the optimized center frequency of the LFM signal waveform of the k-th transmitting subarray. This represents the optimized center frequency difference; Step 5.4: Obtain the final subarray LFM signal waveform based on the optimized frequency modulation slope, the optimized initial phase, and the optimized center frequency. The final subarray LFM signal waveform is expressed as follows: Among them, s′ k This represents the final LFM signal waveform of the k-th transmitting subarray, where k = 1, 2, 3, ..., M1, and t represents 0 to T. e Sampling time within T e This represents the pulse width of a single signal. This represents the optimized initial phase of the LFM signal waveform of the k-th transmitting subarray.

9. The method for designing the correlation waveform of the subarray-level LFM signal MIMO radar section according to claim 8, characterized in that, Step 5.1 includes: Step 5.11, move M1 B min M1 zeros and M1-1 zeros Form the first column vector, and combine M1 Bs max M1 2π units and M1-1 units Form the second column vector; Step 5.12: Based on the cost function, the signal bandwidth of the LFM signal waveform of the transmitting subarray, the initial phase of the LFM signal waveform of the transmitting subarray, the first column vector, and the second column vector, the fminimax function is used to optimize the signal bandwidth, initial phase, and center frequency difference of the LFM signal waveform to obtain the optimized signal bandwidth, optimized initial phase, and optimized center frequency difference.

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