CN106646420A - Method for designing MIMO (Multiple-input multiple-output) radar transmitting direction diagram based on LFM (Linear Frequency Modulation) signals - Google Patents

Abstract

The invention discloses a method for designing an MIMO (Multiple-input multiple-output) radar transmitting direction diagram based on LFM (Linear Frequency Modulation) signals. The main idea comprises the steps of determining an MIMO radar and an expected transmitting direction diagram of the MIMO radar, wherein the MIMO radar comprises N' transmitting array elements, each array element transmits linear frequency modulation signals, the expected transmitting direction diagram of the MIMO radar comprises I transmitting wave beams; calculating a calculation formula of the expected transmitting direction diagram of the MIMO radar; respectively determining the number N of linear frequency modulation LFM signals transmitted by the MIMO radar, the total bandwidth B of the MIMO radar and the transmitting pulse time-width T' of the MIMO radar, respectively calculating an initial frequency interval vector delta(f0) of the N linear frequency modulation LFM signals and an initial phase vector delta(phi0) of the N linear frequency modulation LFM signals, and thus calculating N final linear frequency modulation LFM signals S transmitted by the MIMO radar; and sequentially calculating a covariance correlation matrix of the N final linear frequency modulation LFM signals transmitted by the MIMO radar and a transmitting direction diagram of the N final linear frequency modulation LFM signals transmitted by the MIMO radar according to the final linear frequency modulation LFM signals S.

Description

Method for designing MIMO radar emission pattern based on LFM signal

Technical Field

The invention belongs to the technical field of MIMO radars, and particularly relates to a method for designing an emission directional diagram of an MIMO radar based on an LFM signal, namely a method for designing an emission directional diagram of a multi-input multi-output (MIMO) radar based on a Linear Frequency Modulation (LFM) signal, which is suitable for designing an emission energy diagram of the MIMO radar and reasonably distributing the emission energy of the MIMO radar.

Background

The concept of the MIMO radar is a new system radar which is proposed in recent years, and the MIMO radar becomes a research hotspot in the radar field at home and abroad at present. In the definition of MIMO radar, multiple input refers to simultaneous transmission of multiple radar signal waveforms, and multiple output refers to simultaneous reception by multiple antennas to obtain multi-channel spatial sampling signals. In the MIMO radar, the transmitting signal of each transmitting array element can be independently controlled, so that the MIMO radar has the advantage of waveform diversity. According to the correlation among the MIMO radar transmitting waveforms, the MIMO radar transmitting waveforms are divided into orthogonal waveforms and partial correlation waveforms; all the orthogonal emission waveforms are orthogonal to each other, so that the MIMO radar can be ensured to perform uniform energy irradiation on the whole space; and for partial correlation waveforms, each waveform has correlation, and the correlation between each transmitting waveform is adjusted, so that the transmitting energy of the MIMO radar can be concentrated in a specific space region, the energy utilization rate of the system is improved, and the flexibility of energy distribution of the MIMO radar is improved. Peter Stoica and Li Jian et al in the literature "wave form synthesis for diversity-based transmit antenna design, IEEE Transactions on Signal Processing,2008,56, (6), pp.2593-2598" provide a method for designing a multi-phase code-based MIMO radar transmission pattern, which obtains a plurality of code signals satisfying desired transmission energy characteristics by adjusting the phase of each transmission array element transmission Signal, but the Waveform designed by using the method is sensitive to doppler frequency, and when the doppler frequency of a target echo is large, the plurality of code signals decrease the target gain, which seriously affects target detection.

Disclosure of Invention

In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for designing an LFM signal-based MIMO radar transmission pattern, which can improve the sensitivity of a transmission waveform to a target doppler frequency.

In order to achieve the purpose, the invention is realized by adopting the following technical scheme.

A method for designing an emission directional diagram of an MIMO radar based on an LFM signal comprises the following steps:

step 1, respectively determining an MIMO radar and an expected emission directional diagram of the MIMO radar, wherein the MIMO radar comprises N' emission array elements, and each array element emits a linear frequency modulation signal; the desired transmission pattern of the MIMO radar comprises IA transmission beam, and the central direction of the ith transmission beam is recorded as psi_iLet the beam width of the ith transmit beam be pi_iI ∈ {1,2, …, I }, and further obtains a calculation formula P of a desired emission pattern of the MIMO radar_d(θ); wherein theta represents the space domain angle of the MIMO radar; n' and I are natural numbers respectively;

step 2, respectively determining N, MIMO total bandwidths B of the MIMO radar and T' of the MIMO radar, and calculating the bandwidth B of each linear frequency modulation LFM signal_sAn initial frequency interval △ f between the nth 'chirp LFM signal and the nth' +1 chirp LFM signal_0n', and the initial phase of the nth chirp LFM signalThereby obtaining initial frequency interval vectors △ f of N linear frequency modulation LFM signals₀And the initial phase vectors of the N chirped LFM signalsN '∈ {1,2, …, N-1}, N ∈ {1,2, …, N }, where N is N', and N is a natural number;

step 3, according to the bandwidth B of each linear frequency modulation signal_sN chirp LFM signal initial frequency spacing vector △ f₀And the initial phase vectors of the N chirped LFM signalsRespectively calculating final frequency interval vector △ f of MIMO radar transmitting chirp LFM signal and final initial phase vector of MIMO radar transmitting chirp LFM signal

Step 4, according to the bandwidth B of each linear frequency modulation signal_sAnd the final frequency interval vector △ f of the LFM signal transmitted by the MIMO radar is calculated in sequence to obtain the transmission of the MIMO radarFinal center frequency f of nth chirp LFM signal_nAnd the nth final chirp LFM signal s transmitted by the MIMO radar_nSequentially taking 1 to N from N to obtain N final chirp LFM signals S transmitted by the MIMO radar, N ∈ {1,2, …, N };

and 5, calculating a covariance correlation matrix R of the N final linear frequency modulation LFM signals transmitted by the MIMO radar according to the N final linear frequency modulation LFM signals S transmitted by the MIMO radar, and further calculating a transmission directional diagram P (theta) of the N final linear frequency modulation LFM signals transmitted by the MIMO radar.

Compared with the prior art, the invention has the following advantages:

according to the invention, the linear frequency modulation LFM signal is utilized to design the transmitting signal of the MIMO radar, and the transmitting signal designed by the method is insensitive to the target Doppler frequency due to the good Doppler tolerance characteristic of the linear frequency modulation LFM signal, and meanwhile, the transmitting directional diagram corresponding to the transmitting waveform designed by the method can be better matched with an expected transmitting energy diagram.

Compared with the prior art, the designed waveform has better Doppler tolerance characteristic, and the energy distribution diagram corresponding to the transmitted waveform can be better matched with an expected transmitting directional diagram.

The invention utilizes the characteristic that the linear frequency modulation LFM signal is insensitive to Doppler frequency, and adjusts the correlation among all the transmitting signals by adjusting the frequency interval and the initial phase of the linear frequency modulation LFM signal transmitted by the MIMO radar, so that the transmitting signals of the MIMO radar have better Doppler sensitivity, and simultaneously, the transmitting directional diagram can be ensured to be as close to an expected transmitting directional diagram as possible.

Drawings

The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.

FIG. 1 is a flow chart of a method for designing an emission pattern of an MIMO radar based on LFM signals according to the present invention;

FIG. 2 is a diagram of a MIMO radar transmitting directional diagram obtained by using the method of the present invention and the existing method respectively when a single desired transmitting beam is obtained;

FIG. 3 is a diagram of MIMO radar transmission patterns obtained by using the method of the present invention and the prior art method, respectively, when multiple desired transmission beams are obtained;

FIG. 4 is a comparison graph of Doppler tolerance of MIMO radar obtained by using the method of the present invention and the existing method respectively when a single desired transmission beam is obtained;

fig. 5 is a comparison graph of doppler tolerance of MIMO radar obtained by using the method of the present invention and the existing method respectively when there are multiple desired transmission beams.

Detailed Description

Referring to fig. 1, it is a flowchart of a method for designing an emission pattern of an MIMO radar based on LFM signals according to the present invention; the method for designing the transmitting directional diagram of the MIMO radar based on the LFM signal comprises the following steps:

step 1, respectively determining an MIMO radar and an expected emission directional diagram of the MIMO radar, wherein the MIMO radar comprises N' emission array elements, and each array element emits a linear frequency modulation signal; the expected emission pattern of the MIMO radar comprises I emission beams, and the central direction of the ith emission beam is recorded as psi_iLet the beam width of the ith transmit beam be pi_iI ∈ {1,2, …, I }, and further obtains a calculation formula P of a desired emission pattern of the MIMO radar_d(θ); where θ represents the spatial angle of the MIMO radar, and N' and I are natural numbers, respectively.

Specifically, an expected emission directional diagram of an MIMO radar and an MIMO radar are respectively determined, wherein the MIMO radar comprises N' emission array elements, and each array element emits a chirp signal; the expected emission pattern of the MIMO radar comprises I emission beams, and the central direction of the ith emission beam is recorded as psi_iLet the beam width of the ith transmit beam be pi_iAnd pointing according to the center of the ith transmission beam psi_iAnd beam width pi of ith transmission beam_iCalculating formula P for obtaining expected emission directional diagram of MIMO radar_d(θ), expressed as:

wherein theta represents the space domain angle of the MIMO radar, and theta_idDenotes the lower spatial angle limit, theta, of the ith transmit beam_iuDenotes the upper spatial angle limit, theta, of the ith transmit beam_id＝ψ_i-Π_i/2，θ_iu＝ψ_i+Π_i/2，ψ_iIndicating the central pointing direction, Π, of the ith transmit beam_iThe beam width of the ith transmitting beam is shown, I represents the number of the transmitting beams contained in the expected transmitting directional diagram of the MIMO radar, and N' and I are natural numbers respectively.

Step 2, respectively determining N, MIMO total bandwidths B of the MIMO radar and T' of the MIMO radar, and calculating the bandwidth B of each linear frequency modulation LFM signal_sAn initial frequency interval △ f between the nth 'chirp LFM signal and the nth' +1 chirp LFM signal_0n', and the initial phase of the nth chirp LFM signalThereby obtaining initial frequency interval vectors △ f of N linear frequency modulation LFM signals₀And the initial phase vectors of the N chirped LFM signals

N 'is set to {1,2, …, N-1}, N is set to {1,2, …, N }, N is set to N', and N is a natural number.

Specifically, the transmitting arrays of the MIMO radar are respectively determinedThe number of elements N, the total bandwidth B of the MIMO radar, and the transmit pulse time width T' of the MIMO radar, thereby calculating the bandwidth B of each chirp LFM signal_s，B_sInitial frequency interval △ f between the nth 'chirp LFM signal and the nth' +1 chirp LFM signal_0n'，△f_0n'＝B_sN, N' ∈ {1,2, …, N-1}, and the initial phase of the nth chirp LFM signal

N ∈ {1,2, …, N }, andat [0,2 π]Making N' take 1 to N-1 respectively to obtain initial frequency interval vector △ f of N linear frequency modulation LFM signals₀，△f₀＝[△f₀₁,…,△f_0n',…,△f_0(N-1)]^T(ii) a N is respectively 1 to N to obtain initial phase vectors of N linear frequency modulation LFM signals The superscript T denotes transpose, N ═ N', and N is a natural number.

Step 3, according to the bandwidth B of each linear frequency modulation LFM signal_sN chirp LFM signal initial frequency spacing vector △ f₀And the initial phase vectors of the N chirped LFM signalsRespectively calculating final frequency interval vector △ f of MIMO radar transmitting chirp LFM signal and final initial phase vector of MIMO radar transmitting chirp LFM signal

(3a) According to the bandwidth B of each chirp LFM signal_sCalculating the chirp rate mu, mu-B of each chirp LFM signal_sa,/T', wherein B_sRepresenting the bandwidth of each chirp LFM signal.

(3b) Initialization: let K ∈ {0,1, …, K-1}, where K denotes the kth iteration, K has an initial value of 0, and K denotes the preset maximum number of iterations.

(3c) Using the bandwidth B of each chirp LFM signal_sAn initial frequency interval △ f between the nth '+1 chirp LFM signal and the nth' + chirp LFM signal after the kth iteration_kn' calculating the center frequency f of the nth chirp signal after the kth iteration_kn，Wherein N ∈ {1,2, …, N }, N represents the number of linear frequency modulation signals transmitted by the MIMO radar, and f₀Represents the carrier frequency of the MIMO radar transmitting the chirp signal,

n'∈{1,2,…,N-1}，△f_0n'representing the initial frequency separation between the nth 'chirp LFM signal and the nth' +1 chirp LFM signal.

(3d) According to the central frequency f of the nth chirp signal after the kth iteration_knAnd the FM slope mu of each linear FM LFM signal, and the nth linear FM signal s after the kth iteration is obtained by calculation_kn，

Wherein f is_knRepresents the center frequency of the nth chirp signal after the kth iteration, N ∈ {1,2, …, N }, wherein N represents the number of the transmitting array elements of the MIMO radar, T is the sampling time within 0-T',indicating the nth chirp after the kth iterationThe phase of the signal, T', represents the transmit pulse duration of the MIMO radar.

(3e) N is sequentially selected from 1 to N to respectively obtain the 1 st linear frequency modulation signal s after the kth iteration_k1Up to the nth chirp signal s after the kth iteration_kNAnd the 1 st chirp signal s after the kth iteration is processed_k1Up to the nth chirp signal s after the kth iteration_kNAs N chirp signals S after the kth iteration_k，

S_k＝[s_k1,…,s_kn,…,s_kN]^TThe superscript T represents transposition, and the covariance correlation matrix R of the N linear frequency modulation signals after the kth iteration is obtained through calculation_k，The superscript H represents the conjugate transpose, and then the covariance matrix R of the N linear frequency modulation signals after the kth iteration is obtained_kCalculating emission directional diagram of N linear frequency modulation signals after the k time of iterationThe expression is as follows:

wherein a (theta) represents a transmit array steering vector of the MIMO radar at an angle theta,

a(θ)＝[1,…,e^j(n-1)α,…,e^j(N-1)α]^Tα ═ 2 π dsin θ/λ, λ denotes the wavelength of the chirp LFM signal transmitted by the MIMO radar, d denotes the spacing between the transmitting elements of the MIMO radar, θ denotes the spatial angle of the MIMO radar, △ f_kRepresenting the frequency interval vector of the N chirp LFM signals after the kth iteration,indicating N chirps LF after kth iterationThe initial phase vector of the M signal is marked with a mark to represent conjugate, N ∈ {1,2, …, N }, and N represents the number of transmitting array elements of the MIMO radar.

(3f) According to the expected emission pattern P of the MIMO radar_d(theta) and emission pattern of N chirps after kth iterationCalculating to obtain a target function after the kth iterationThe expression is as follows:

wherein | · | purple sweet₂Denotes a 2 norm, △ f_kRepresenting the frequency interval vector of the N chirp LFM signals after the kth iteration,representing the initial phase vector of the N chirped LFM signals after the kth iteration, and μ represents the chirp rate of each chirped LFM signal.

(3h) For the target function after the k iterationOptimizing, namely:

wherein,representation by constraint △ f_kAndso that the minimum operator is taken and the subject to represents the constraint condition symbol △ f_kn'indicating the frequency interval between the nth' chirp LFM signal and the nth '+1 chirp LFM signal after the kth iteration, and making N' take 1,2, …, N-1 in sequence to obtain the frequency interval vector △ f of the N chirp LFM signals after the kth iteration_k，

△f_k＝[△f_k1,…,△f_kn',…,△f_k(N-1)]^T；Representing the phase of the nth linear frequency modulation LFM signal after the kth iteration, and enabling N to sequentially take 1,2, … and N to obtain the phase vector of the N linear frequency modulation LFM signals after the kth iteration

Solving the optimization problem by using a nonlinear programming method to respectively obtain frequency interval vectors △ f of the N linear frequency modulation LFM signals after the (k + 1) th iteration_k+1，△f_k+1＝[△f_k+1,1,…,△f_k+1,n',…,△f_k+1,(N-1)]^TAnd the initial phase vector of the N chirped LFM signals after the (k + 1) th iteration △f_k+1,n'Representing the frequency separation between the nth '+1 chirp LFM signal and the nth' +1 chirp LFM signal after the (k + 1) th iteration,the initial phase of the nth chirp LFM signal after the (k + 1) th iteration is shown, with the superscript T indicating the transposition.

(3i) Adding K to 1, and repeatedly executing the substeps (3c) to (3h) until obtaining a vector △ f of frequency intervals of the N chirp LFM signals after the Kth iteration_KAnd the initial phase vector of the N chirped LFM signals after the Kth iteration

(3j) The frequency interval vector △ f of the N chirp LFM signals after the Kth iteration_KAs a final frequency interval vector △ f of the MIMO radar transmitted chirp LFM signals, the initial phase vectors of the N chirp LFM signals after the Kth iterationAs final initial phase vector for MIMO radar transmitting chirp LFM signal△f＝△f_K＝[△f₁,…,△f_n',…,△f_(N-1)]^T，△f_n'Representing the final frequency separation between the n 'th chirp LFM signal and the n' +1 th chirp LFM signal transmitted by the MIMO radar,representing the final initial phase of the nth chirp LFM signal transmitted by the MIMO radar.

Step 4, according to the bandwidth B of each linear frequency modulation LFM signal_sAnd the final frequency interval vector △ f of the LFM signal transmitted by the MIMO radar, and the final central frequency f of the nth chirp LFM signal transmitted by the MIMO radar is obtained by calculation in sequence_nAnd the nth final chirp LFM signal s transmitted by the MIMO radar_nSequentially taking N from 1 to N to obtain N final chirp LFM signals S transmitted by the MIMO radar, N ∈ {1,2, …,N}。

(4a) Using the bandwidth B of each chirp LFM signal_sAnd the final frequency interval △ f of the linear frequency modulation LFM signal transmitted by the MIMO radar is calculated to obtain the final central frequency f of the nth linear frequency modulation LFM signal transmitted by the MIMO radar_n，N represents the number of chirp signals transmitted by the MIMO radar,

q∈{1,2,…,n-1}，△f_qrepresenting the final frequency separation, f, between the q-th and q + 1-th chirp LFM signals transmitted by the MIMO radar₀Representing the carrier frequency of the chirp signal transmitted by the MIMO radar.

(4b) Transmitting a final center frequency f of an nth chirp LFM signal using a MIMO radar_nAnd calculating the frequency modulation slope mu of each linear frequency modulation LFM signal to obtain the nth final linear frequency modulation LFM signal s transmitted by the MIMO radar_nSequentially taking 1 to N from N to obtain N final linear frequency modulation LFM signals S transmitted by the MIMO radar,

S＝[s₁,…,s_n,…,s_N]^T，

wherein T is a sampling time within 0 to T', f_nRepresenting the final center frequency of the nth chirp LFM signal transmitted by the MIMO radar,the final initial phase of the N-th chirp LFM signal transmitted by the MIMO radar is represented, T' represents the pulse transmission time width of the MIMO radar, exp represents an exponential function, N represents the number of chirp signals transmitted by the MIMO radar, and superscript T represents transposition.

And 5, calculating a covariance correlation matrix R of the N final linear frequency modulation LFM signals transmitted by the MIMO radar according to the N final linear frequency modulation LFM signals S transmitted by the MIMO radar, and further calculating a transmission directional diagram P (theta) of the N final linear frequency modulation LFM signals transmitted by the MIMO radar.

Specifically, a covariance correlation matrix R, R ═ SS of N final chirp LFM signals transmitted by the MIMO radar is calculated according to the N final chirp LFM signals S transmitted by the MIMO radar^HThe superscript H represents the conjugate transpose, and then the emission pattern P (θ) of the N final chirp LFM signals emitted by the MIMO radar is calculated, and the expression is:

P(θ)＝a^T(θ)Ra^*(θ)

where the superscript T denotes transpose, a (θ) denotes the transmit array steering vector of the MIMO radar at angle θ, and a (θ) [1, …, e ]^j(n-1)α,…,e^j(N-1)α]^Tα is 2 pi dsin theta/lambda, lambda represents the wavelength of the chirp LFM signal transmitted by the MIMO radar, d represents the transmission array element spacing of the MIMO radar, theta represents the space domain angle of the MIMO radar, superscript is a conjugate, N ∈ {1,2, …, N } represents the number of chirp signals transmitted by the MIMO radar.

The effect of the present invention is further verified and explained by the following simulation experiment.

Simulation conditions

Setting a transmitting array of the MIMO radar as an equidistant linear array formed by 16 array elements, namely N' is 16; the distance d between the transmitting array elements of the MIMO radar is half wavelength, and the carrier frequency f of the transmitting linear frequency modulation LFM signal of the MIMO radar₀450MHz, the time width T' of each linear frequency modulation LFM signal transmitted by the MIMO radar is 600 mus, and the total bandwidth B of the MIMO radar is 1 MHz; in this simulation, the maximum number of iterations K is set to 100.

(II) simulation content

Simulation 1, first, simulation analysis is performed on a case where a single beam is included in a desired transmission pattern. Setting an expected emission directional diagram of the MIMO radar as a rectangular wide beam with 0 degree as a center and 60 degrees as a width, and respectively adopting the method and the existing method to carry out emission waveform design so as to match the expected emission directional diagram to obtain a design result as shown in FIG. 2, wherein the MIMO radar emission directional diagram is obtained by respectively adopting the method and the existing method when the single expected emission beam is shown in FIG. 2; the prior art method is a method for designing a multi-phase code-based MIMO radar emission pattern, which is proposed by Peter Stoica and Li Jian et al in the documents "wave synthesis for diversity-based transmit beam pattern design, IEEE Transactions on Signal Processing,2008,56, (6), pp.2593-2598.

As can be seen from fig. 2, the transmission patterns of the waveforms designed by the method of the present invention and the existing method can be well matched with the desired transmission direction.

Simulation 2, this experiment is used to perform simulation analysis on the situation when a desired transmission pattern contains a plurality of beams. Setting an expected emission directional diagram of the MIMO radar system to comprise two rectangular wave beams, wherein the two wave beams respectively take-30 degrees and 30 degrees as centers, the widths of the two wave beams are both 10 degrees, then respectively adopting the method of the invention and the existing method to carry out emission waveform design so as to match the expected emission directional diagram, and obtaining a design result as shown in figure 3, and when the figure 3 shows that the wave beams are expected to be emitted, respectively adopting the method of the invention and the existing method to obtain the MIMO radar emission directional diagram.

As can be seen from fig. 3, when the desired transmission pattern includes a plurality of transmission beams, the transmission patterns of the waveforms designed by the method of the present invention and the existing method can be well matched with the desired transmission direction.

Simulation 3, comparing the doppler tolerance of the transmission waveforms designed in simulation 1 and simulation 2, wherein the simulation results are respectively shown in fig. 4 and fig. 5, and fig. 4 is a comparison graph of the doppler tolerance of the MIMO radar obtained by using the method of the present invention and the existing method when a single transmission beam is expected; fig. 5 is a comparison graph of doppler tolerance of MIMO radar obtained by using the method of the present invention and the existing method respectively when multiple desired transmission beams are obtained.

As can be seen from fig. 4 and 5, because the waveform design is performed by using the polyphase code in the prior art, the designed waveform is very sensitive to the doppler frequency of the target, and because the waveform designed by the method of the present invention uses a set of chirped LFM signals, the designed result has very strong doppler tolerance, and has little loss in some doppler ranges, and basically does not affect the detection of the target.

In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the method.

It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention; thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (6)

1. A method for designing an emission directional diagram of an MIMO radar based on an LFM signal is characterized by comprising the following steps:

step 1, respectively determining an MIMO radar and an expected emission directional diagram of the MIMO radar, wherein the MIMO radar comprises N' emission array elements, and each array element emits a linear frequency modulation signal; the expected emission pattern of the MIMO radar comprises I emission beams, and the central direction of the ith emission beam is recorded as psi_iLet the beam width of the ith transmit beam be pi_iI ∈ {1,2, …, I }, and further obtains the expected transmission of the MIMO radarFormula P for calculating emission pattern_d(θ); wherein theta represents the space domain angle of the MIMO radar; n' and I are natural numbers respectively;

step 2, respectively determining N, MIMO total bandwidths B of the MIMO radar and T' of the MIMO radar, and calculating the bandwidth B of each chirp signal_sAn initial frequency interval Δ f between the nth 'chirp signal and the nth' +1 chirp signal_0n'And the initial phase of the nth chirp signalFurther, the initial frequency interval vectors delta f of the N linear frequency modulation signals are obtained respectively₀And the initial phase vectors of the N chirp signalsN '∈ {1,2, …, N-1}, N ∈ {1,2, …, N }, where N is N', and N is a natural number;

step 3, according to the bandwidth B of each linear frequency modulation signal_sN chirp signal initial frequency spacing vector Δ f₀And the initial phase vectors of the N chirp signalsRespectively calculating a final frequency interval vector delta f of the linear frequency modulation signal transmitted by the MIMO radar and a final initial phase vector of the linear frequency modulation signal transmitted by the MIMO radar

Step 4, according to the bandwidth B of each linear frequency modulation signal_sAnd calculating the final frequency interval vector delta f of the MIMO radar transmitting signal in sequence to obtain the final central frequency f of the nth chirp signal transmitted by the MIMO radar_nAnd the nth final chirp signal s transmitted by the MIMO radar_nSequentially taking 1 to N from N to obtain N final linear frequency modulation signals S transmitted by the MIMO radar;

and 5, calculating a covariance correlation matrix R of the N final linear frequency modulation signals transmitted by the MIMO radar according to the N final linear frequency modulation signals S transmitted by the MIMO radar, and further calculating a transmission directional diagram P (theta) of the N final linear frequency modulation signals transmitted by the MIMO radar.

2. The method as claimed in claim 1, wherein in step 1, the calculation formula P of the expected transmission pattern of the MIMO radar is calculated_d(θ), expressed as:

$P_d\left(\mathrm{\θ}\right)=\left\{\begin{array}{cc}1& \mathrm{\θ}\∈\[{\mathrm{\θ}}_{id},{\mathrm{\θ}}_{iu}\],i=1,2...I\\ 0& \mathrm{\θ}\∉\[{\mathrm{\θ}}_{id},{\mathrm{\θ}}_{iu}\],i=1,2...I\end{array}\right.$

wherein theta represents the space domain angle of the MIMO radar, and theta_idDenotes the lower spatial angle limit, theta, of the ith transmit beam_iuDenotes the upper spatial angle limit, theta, of the ith transmit beam_id＝ψ_i-Π_i/2，θ_iu＝ψ_i+Π_i/2，ψ_iIndicating the central pointing direction, Π, of the ith transmit beam_iThe beam width of the ith transmission beam is shown, and I represents the number of transmission beams contained in a desired transmission pattern of the MIMO radar.

3. The method as claimed in claim 1, wherein in step 2, the bandwidth B of each chirp signal is defined as_sAn initial frequency interval Δ f between the nth 'chirp signal and the nth' +1 chirp signal_0n'Obtaining initial frequency interval vectors delta f of the N linear frequency modulation signals₀And the initial phase vectors of the N chirp signalsThe expressions are respectively:

B_s＝B/N，Δf_0n'＝B_s/N，

Δf₀＝[Δf₀₁,…,Δf_0n',…,Δf_0(N-1)]^T，

where the superscript T denotes transpose.

4. The method as claimed in claim 1, wherein the step 3 comprises the sub-steps of:

(3a) according to the bandwidth B of each chirp signal_sCalculating the chirp rate mu, mu-B of each chirp signal_sa,/T', wherein B_sRepresenting the bandwidth of each chirp signal;

(3b) initialization: let K belong to {0,1, …, K-1}, where K represents the kth iteration, the initial value of K is 0, and K represents the preset maximum iteration number;

(3c) using the bandwidth B of each chirp signal_sAfter the kth iteration, an initial frequency interval Δ f between the nth 'chirp signal and the nth' +1 chirp signal_kn'Calculating the center frequency f of the nth chirp signal after the kth iteration_kn，Wherein N ∈ {1,2, …, N }, N represents the number of linear frequency modulation signals transmitted by the MIMO radar, and f₀Represents the carrier frequency of the linear frequency modulation signal transmitted by the MIMO radar, N' ∈ {1,2, …, N-1}, delta f_0n'Representing an initial frequency interval between the nth 'chirp signal and the nth' +1 chirp signal;

(3d) according to the central frequency f of the nth chirp signal after the kth iteration_knAnd the frequency modulation slope mu of each linear frequency modulation signal, and the nth linear frequency modulation signal s after the kth iteration is obtained through calculation_kn，

Wherein T is a sampling time within 0 to T',the phase of the nth linear frequency modulation signal after the kth iteration is represented, and T' represents the time width of the transmission pulse of the MIMO radar;

(3e) n is sequentially selected from 1 to N to respectively obtain the 1 st linear frequency modulation signal s after the kth iteration_k1Up to the nth chirp signal s after the kth iteration_kNAnd the 1 st chirp signal s after the kth iteration is processed_k1Up to the nth chirp signal s after the kth iteration_kNAs N chirp signals S after the kth iteration_k，

S_k＝[s_k1,…,s_kn,…,s_kN]^TThe superscript T represents transposition, and the covariance correlation matrix R of the N linear frequency modulation signals after the kth iteration is obtained through calculation_k，The superscript H represents the conjugate transpose, and then the covariance matrix R of the N linear frequency modulation signals after the kth iteration is obtained_kCalculating emission directional diagram of N linear frequency modulation signals after the k time of iterationThe expression is as follows:

wherein a (theta) represents a transmit array steering vector of the MIMO radar at an angle theta,

a(θ)＝[1,…,e^j(n-1)α,…,e^j(N-1)α]^Tα ═ 2 π dsin θ/λ, λ denotes the wavelength of the chirp signal transmitted by the MIMO radar, d denotes the spacing between the transmitting elements of the MIMO radar, θ denotes the spatial angle of the MIMO radar, Δ f denotes the spatial angle of the MIMO radar, and_krepresenting the vector of frequency intervals of the N chirp signals after the kth iteration,representing the initial phase vectors of the N linear frequency modulation signals after the k iteration, and the superscript indicates conjugation;

(3f) according to the expected emission pattern P of the MIMO radar_d(theta) and emission pattern of N chirps after kth iterationCalculating to obtain a target function after the kth iterationThe expression is as follows:

wherein | · | purple sweet₂Denotes a 2 norm,. DELTA.f_kRepresenting the vector of frequency intervals of the N chirp signals after the kth iteration,representing the initial phase vectors of the N linear frequency modulation signals after the kth iteration, and mu represents the frequency modulation slope of each linear frequency modulation signal;

(3h) for the target function after the k iterationOptimizing, wherein the optimization expression is as follows:

wherein,by constraining Δ f_kAndmake · get the minimum operand, subject to represents the constraint condition symbol; Δ f_kn'Representing the frequency interval between the nth ' chirp signal and the nth ' +1 chirp signal after the kth iteration, and enabling N ' to sequentially take 1,2, … and N-1 to obtain the frequency interval vector delta f of the N chirp signals after the kth iteration_k，

Δf_k＝[Δf_k1,…,Δf_kn',…,Δf_k(N-1)]^T；The phase of the nth linear frequency modulation signal after the kth iteration is shown, N is made to sequentially take 1,2, … and N to obtain the phase vector of the N linear frequency modulation signals after the kth iteration

Solving the optimization problem by using a nonlinear programming method to respectively obtain frequency interval vectors delta f of the N linear frequency modulation signals after the k +1 th iteration_k+1，

Δf_k+1＝[Δf_k+1,1,…,Δf_k+1,n',…,Δf_k+1,(N-1)]^TAnd the initial phase vector of the N chirps after the (k + 1) th iteration Δf_k+1,n'Representing the frequency separation between the nth 'chirp signal and the nth' +1 chirp signal after the (k + 1) th iteration,representing the initial phase of the nth chirp signal after the (k + 1) th iteration, and the superscript T representing the transposition;

(3i) adding 1 to K, and repeatedly executing the substeps (3c) to (3h) until obtaining a frequency interval vector delta f of the N linear frequency modulation signals after the Kth iteration_KAnd the initial phase vectors of the N chirps after the Kth iteration

(3j) The frequency interval vector delta f of the N linear frequency modulation signals after the Kth iteration_KAs a final frequency interval vector delta f of the linear frequency modulation signals transmitted by the MIMO radar, the initial phase vectors of the N linear frequency modulation signals after the Kth iterationAs final initial phase vector of MIMO radar transmitting chirp signal

Δf＝Δf_K＝[Δf₁,…,Δf_n',…,Δf_(N-1)]^T，Δf_n'Representing the final frequency separation between the nth 'chirp signal and the nth' +1 chirp signal transmitted by the MIMO radar,representing the final initial phase of the nth chirp signal transmitted by the MIMO radar.

5. The method as claimed in claim 1, wherein the step 4 comprises the sub-steps of:

(4a) using the bandwidth B of each chirp signal_sAnd the final frequency interval delta f of the linear frequency modulation signals transmitted by the MIMO radar is calculated to obtain the final central frequency f of the nth linear frequency modulation signal transmitted by the MIMO radar_n，

N represents the number of chirp signals transmitted by the MIMO radar,

q∈{1,2,…,n-1}，Δf_qrepresenting the final frequency interval, f, between the q-th and the q + 1-th chirp signal transmitted by the MIMO radar₀Representing the carrier frequency of the chirp signal transmitted by the MIMO radar.

(4b) Transmitting the final center frequency f of the nth chirp signal by using a MIMO radar_nAnd calculating the frequency modulation slope mu of each linear frequency modulation signal to obtain the nth final linear frequency modulation signal s transmitted by the MIMO radar_nSequentially taking 1 to N from N to obtain N final chirp signals S transmitted by the MIMO radar,

S＝[s₁,…,s_n,…,s_N]^T，

wherein T is a sampling time within 0 to T', f_nRepresenting the final center frequency of the nth chirp signal transmitted by the MIMO radar,the final initial phase of the N-th chirp signal transmitted by the MIMO radar is represented, T' represents the pulse time width transmitted by the MIMO radar, exp represents an exponential function, N ∈ {1,2, …, N }, N represents the number of the chirp signals transmitted by the MIMO radar, and superscript T represents transposition.

6. The method as claimed in claim 1, wherein in step 5, the covariance correlation matrix R of the N final chirps transmitted by the MIMO radar and the transmission pattern P (θ) of the N final chirps transmitted by the MIMO radar are respectively expressed as:

R＝SS^H，P(θ)＝a^T(θ)Ra^*(θ)

where the superscript H denotes conjugate transpose, the superscript T denotes transpose, a (θ) denotes a transmit array steering vector of the MIMO radar at an angle θ, and a (θ) [1, …, e ]^j(n-1)α,…,e^j(N-1)α]^Tα is 2 pi dsin theta/lambda, lambda represents the wavelength of the chirp signals transmitted by the MIMO radar, d represents the spacing between the transmitting array elements of the MIMO radar, theta represents the space angle of the MIMO radar, superscript is conjugate, N ∈ {1,2, …, N } represents the number of the chirp signals transmitted by the MIMO radar.