CN111352080B - Design Method of Low Intercept Frequency Controlled Array MIMO Radar System Under PAPR and Similarity Constraints - Google Patents

Abstract

The invention discloses a design method of a low-interception frequency controlled array MIMO radar system under PAPR and similarity constraints, including: S0: constructing an optimization problem, initializing the number of iterations of the outer loop, the number of iterations of the inner loop, and randomly initializing a transmit waveform matrix; S1: fixed For the current transmit waveform matrix, use the MVDR method to solve the optimization problem and calculate the receive filter; S2: Fix the receive filter under this iteration, calculate and update the transmit waveform vector based on the alternating direction multiplier method and the effective set method; S3: Repeat Steps S1-S2, until the iteration end condition is reached. The invention considers the clutter, interference and noise environment and the condition that the transmit waveform satisfies the PAPR and similarity, constructs the optimization problem into a multi-proportional fractional programming problem, and uses the loop iteration method, ADMM and ASM to jointly optimize the transmit signal.

Description

Design Method of Low Intercept Frequency Controlled Array MIMO Radar System Under PAPR and Similarity Constraints

technical field

The invention belongs to the technical field of array signal processing, and in particular relates to a design method of a low-interception frequency-controlled array MIMO radar system under PAPR and similarity constraints.

Background technique

In modern electronic countermeasures, the increasingly changing and complex radar electromagnetic environment has put forward new requirements for low interception technology. low interception effect. Low probability of intercept (LPI) radar can detect targets while reducing the probability of being discovered by the enemy, providing security for the radar and its carrier. It is increasingly urgent to study LPI radar and its realization technology. The key point is that the technology makes it impossible for the enemy to obtain the radiation energy emitted by the radar.

The research of low-interception technology on the radar transmitter mainly includes three aspects: 1) Disperse the energy in the frequency domain to design an ultra-wideband waveform; 2) Disperse the energy in the time domain to design a waveform with a high duty cycle; 3) Disperse the energy in the space domain and design a wider main lobe of the antenna radiation pattern.

Since the concept of MIMO (Multiple-Input Multiple-Output, multiple input multiple output) radar was proposed in 2003, a large number of scholars have emerged to conduct in-depth research on its key technologies and related aspects. Compared with phased array, MIMO radar uses waveform diversity technology to form a wide beam with low gain in space, which can reduce the probability of radar being intercepted. Since target detection and parameter estimation depend on the output signal-to-clutter-noise ratio (SCNR), the design of MIMO radars to maximize the output SCNR has received much attention in recent years. The design of joint transmit and receive is mainly divided into two categories: one is to maximize the output SINR by jointly designing the transmit waveform and the receive filter. The other is to maximize the output SCNR by designing joint transmit and receive beamforming.

Frequency diverse array (FDA) technology is the latest radar technology, and its array factor is a function of angle, time and distance. Unlike phased array beams that do not depend on distance parameters, the most important feature of frequency array is The array pattern is range-dependent and can effectively control the range-direction of its transmit beam.

Therefore, the application of frequency-controlled array and MIMO technology to LPI radar can realize that the signal energy of the transmit beam can form a small energy radiation in the area of interest, and at the same time reduce the peak power of the transmit signal by widening the transmit beam width. Reducing radar interception provides a new way of thinking.

SUMMARY OF THE INVENTION

The purpose of the present invention is to consider the constraints of PAPR and similarity under the clutter environment, and provide a design method of a low-interception frequency controlled array MIMO radar system under the constraints of PAPR and similarity, which reduces the probability of radar being intercepted while reducing the probability of radar being intercepted. , which guarantees target detection.

The idea of the present invention is:

Taking the minimization of the transmit energy radiation of the MIMO radar and the maximization of the output SCNR as the dual-objective optimization, the dual-objective optimization is transformed into a multi-fraction programming problem with PAPR and similarity constraints by using the weighted sum method. Then, using the loop iteration method, The optimization problem is transformed into two sub-optimization problems: when the transmit waveform is fixed, the MVDR method (adaptive beamforming method) is used to solve the receiving filter; when the receiving filter is fixed, the ADMM method (alternating direction multiplier method) is used to optimize the problem. The problem is transformed into a multivariate solution, and the emission waveform is solved using ASM (effective ensemble method).

The technical scheme of the present invention is as follows:

The design method of the low-intercept frequency controlled array MIMO radar system under the PAPR and similarity constraints provided by the present invention includes:

初始化外循环迭代次数k＝0，初始化内循环迭代次数n＝0，随机初始化发射波形矩阵S，记为

s_m ⁰表示第m个发射天线对应的发射波形向量初始值，m＝1，2，…M_t；s＝vec(S)；S0: Build an optimization problem

Initialize the outer loop iteration number k=0, initialize the inner loop iteration number n=0, and randomly initialize the transmit waveform matrix S, denoted as

s _m ⁰ represents the initial value of the transmit waveform vector corresponding to the mth transmit antenna, m=1, 2, ... M _t ; s=vec(S);

where: ω _p is the weight of the p-th objective function, ω _p ∈ [0,1], and satisfy

P(S) is the spatial transmit power of the transmitted signal, SCNR(x,S) is the output signal-to-noise ratio of the signal at the receiving end after passing through the receiving filter; PAPR(s) represents the PAPR constraint, s ₀ represents the reference waveform, σ and ξ represents the control parameter;

当前所计算的接收滤波器即第k次迭代下的接收滤波器，记为x^k；S1: Fix the current transmit waveform matrix, use the MVDR method to solve the optimization problem, and calculate the receive filter

The currently calculated receiving filter is the receiving filter under the k-th iteration, denoted as x ^k ;

表示M_t×M_t的单位矩阵；v(r,θ)定义为：虚拟阵列的导向向量，

b(θ)表示接收天线阵列的导向向量，a(r,θ)表示发射天线阵列的导向向量；where: W ₁ is defined as:

represents the identity matrix of M _t ×M _t ; v(r, θ) is defined as: the steering vector of the virtual array,

b(θ) represents the steering vector of the receiving antenna array, a(r, θ) represents the steering vector of the transmitting antenna array;

The definition of R _cje is: R _cje =R _c +R _j +R _e , where R _c , R _j and R _e are the clutter covariance matrix, the interference covariance matrix and the noise covariance matrix, respectively;

Under the kth outer loop iteration, step S2 is executed:

S2: fix the receive filter x ^k under this iteration, calculate and update the transmit waveform vector s based on the alternating direction multiplier method and the effective set method;

带上标n的参数表示在第n次内循环迭代开始时的参数值；本步骤进一步包括：Know the current iteration value

The parameter with the superscript n represents the parameter value at the beginning of the nth inner loop iteration; this step further includes:

S201: Update the auxiliary variable h _r , and this sub-step further includes:

t_1,r,t_2,r,s_0,r,s_r,R_A,r,R_cvx,r,R_vx,r,E_n,r分别表示t₁,t₂,s₀,s,R_A,R_cvx,R_vx,E_n的实数值形式；S201a: Construct objective function in real form

t _1,r ,t _2,r ,s _0,r ,s _r ,RA _,r ,R _cvx,r ,R _vx,r ,E _n,r represent t ₁ ,t ₂ ,s ₀ ,s, R _A , R _cvx , R _vx , the real-valued form of E _n ;

其中，R_A、R_cvx、R_vx分别定义为：Parameters _t1 and _t2 are defined as:

Among them, R _A , R _cvx , and R _vx are respectively defined as:

S201b: Under the ADMM framework, by introducing variables z _1,r ,z _2,r ,ur _r ,v _r , transform the above objective function into the augmented Lagrangian function f _t,r (s _r ,h _r , t _1,r ,t _2,r ,z _1,r ,z _2,r ,ur _r ,v _r ) to obtain the objective function:

Among them, ρ ₁ , ρ ₂ , ρ ₃ , ρ ₄ are all penalty parameters, and all are greater than 0; R _At is defined as: R _At = _RA -t ₁ /M _t E _t ; R _xt is defined as: R _xt = R _cvx -t ₂ R _vx ; R _At,r and R _xt,r represent the real-valued forms of R _At and R _xt , respectively;

利用有效集合法求解h_r，本次求解得到的h_r记为

S201c: Construct the objective function in S201b into standard ASM form:

Using the effective set method to solve _hr , the _hr obtained by this solution is recorded as

Among them, Q, p, α _i , b _i are auxiliary variables, which are defined as follows:

将f_t,r(s_r,h_r,t_1,r,t_2,r,z_1,r,z_2,r,u_r,v_r)转换为如下目标函数：S202: Known iteration value

Transform f _t,r (s _r ,h _r ,t _1,r ,t _{2,r ,} z _1,r ,z _2,r ,ur ,v _r ) into the following objective function:

Construct the objective function into a standard ASM form, and use the effective set method to solve s _r . The s _r obtained by this solution is recorded as

将f_t,r(s_r,h_r,t_1,r,t_2,r,z_1,r,z_2,r,u_r,v_r)转换为如下目标函数：S203: Known iteration value

Transform f _t,r (s _r ,h _r ,t _1,r ,t _{2,r ,} z _1,r ,z _2,r ,ur ,v _r ) into the following objective function:

求解t_1,r和t_2,r，本次求解得到的t_1,r和t_2,r记为

和

make

Solve for t _1,r and t _2,r , the t _1,r and t _2,r obtained by this solution are recorded as

and

利用如下公式求解{z_1,r,z_2,r,u_r,v_r}，本次求解得到的求解{z_1,r,z_2,r,u_r,v_r}记为

S204: Known iteration value

Use the following formula to solve {z _1,r ,z _2,r ,ur _r ,v _r }, and the solution {z _1,r ,z _2,r ,ur _r ,v _r } obtained this time is denoted as

S205: set n=n+1, repeat the iterations S201-S204 until the number of iterations reaches the preset maximum number of iterations of the inner loop, output the last s _r , and then perform step S3;

S3: Let k=k+1, and repeat steps S1-S2 until the number of iterations reaches the preset maximum number of outer loop iterations or |SINR ^(k+1) -SINR ^(k) |/SINR ^(k) <ε, where , ε>0.

Further, the space transmit power P(S) is defined as:

其是发射阵列的导向向量；

表示相位差，in,

is the steering vector of the transmit array;

represents the phase difference,

c表示光速，d_t表示发射阵列的阵元间隔。

c represents the speed of light, and d _t represents the element spacing of the emission array.

Further, the PAPR constraint is defined as:

Among them, L represents the number of interfering signals.

Further, the clutter covariance matrix

Interference covariance matrix

covariance matrix of noise

in:

Q represents the number of clutter scatterers, and q represents the qth clutter scatterer;

表示第q个杂波的协方差；In order to distinguish the distance and angle from the target, rc _,q and θc _,q are used to represent the distance and angle at the qth clutter, respectively,

represents the covariance of the qth clutter;

表示第l个干扰信号的协方差；I_K表示K×K的单位矩阵；b(θ_j,l)表示第l个干扰信号在接收天线阵列上的导向向量；L represents the number of interference signals from different directions, and l represents the l-th interference signal; also in order to distinguish the angle from the target, θ _j,l represents the angle of the l-th interference;

Represents the covariance of the l-th interference signal; I _K represents the K×K identity matrix; b(θ _j,l ) represents the steering vector of the l-th interference signal on the receiving antenna array;

表示噪声的协方差；

表示M_rK×M_rK阶的单位矩阵。

represents the covariance of noise;

represents an identity matrix of order _Mr K × _{Mr K.}

Further, the calculation formula of the signal-to-interference-noise ratio is:

The present invention has the following advantages and beneficial effects:

The invention uses the ADMM method, combined with the frequency-controlled array technology, takes the MIMO radar's transmission energy radiation minimization and target detection maximization as dual optimization objectives, and considers the clutter, interference and noise environment and the transmission waveform meets the conditions of PAPR and similarity. , the optimization problem is constructed as a multi-scale fractional programming problem, and the transmitted signal is jointly optimized by the loop iteration method, ADMM and ASM. The invention realizes the target detection while reducing the probability of radar being intercepted by designing the transmitting signal to form a null on the target area.

Description of drawings

Figure 1 shows the comparison between the objective function and the number of iterations under different PAPRs and different similarity constraints in the simulation test. Figure (a) is the comparison of the objective function and the number of iterations under different PAPRs, and Figure (b) is under different similarity constraints. Comparison of objective function and number of iterations;

Fig. 2 is the emission pattern under different PAPR and different similarity constraints in the simulation test, wherein, Fig. (a) is the emission pattern in the angle dimension, and Fig. (b) is the emission pattern in the distance dimension;

Fig. 3 is the receiving pattern under different PAPR and different similarity constraints in the simulation test, wherein, Fig. (a) is the transmitting pattern in the angle dimension, and Fig. (b) is the transmitting pattern in the distance dimension;

Figure 4 is the receiving pattern of the transmitted waveform at different positions under different PAPR and different similarity constraints in the simulation test, among which, picture (a) is the receiving pattern in the angle dimension at 25m, and picture (b) is the angle dimension at 75m. The receiving pattern, Figure (c) is the receiving pattern of the distance dimension at 40°.

Detailed ways

The relevant theories and specific implementation processes on which the implementation of the present invention is based will be described in detail below, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, and the protection scope of the present invention can be more clearly defined. define.

(1) Construction of signal model

Consider the model of a narrowband frequency-controlled array MIMO radar system. The array is composed of M _t transmitting antennas and M _r receiving antennas. Let the different signals transmitted on each antenna be s _i (l), i = 1, 2, ... ,M _t ,l=1,2,...,L, where L is the number of samples. The transmit waveform matrix of sampling L points on M _t transmit antennas is S=[s(1),s(2),...,s(L)] ^T , where (·) ^T represents the transposition operation, let its vector The form is s=vec(S). Let the carrier frequency on the mth antenna f _m =f ₀ +(m-1)Δf, f ₀ is the carrier frequency of the first array element, Δf is the frequency increment, assuming f ₀ <<Δf, K≤ _Mt.

Considering the far-field condition, the received signal at the angle θ and the distance r relative to the first element of the transmitting array is:

a ^T (r,θ)S (1)

是发射阵列的导向向量，其中，

可表示为：in,

is the steering vector of the transmit array, where,

can be expressed as:

In formula (2), c represents the speed of light, and d _t represents the element spacing of the transmitting array.

The Doppler transfer of the scatterer is not considered for now, but for a stationary target, the transmitted signal is scattered and reflected by the target, and after down-conversion and matched filtering at the receiving end, the received signal Y _s can be expressed as:

Y _s =β(r,θ)b(θ)a ^T (r,θ)S (3)

In formula (3):

( ) ^H represents the conjugate transpose;

β(r, θ) represents the amplitude of the target scatterer at an angle θ and a distance r relative to the first element of the transmitting array;

b(θ) represents the receiving steering vector at the angle θ. In this specific embodiment, the receiving antenna adopts a phased array, so b(θ) is defined as:

In formula (4), d _r is the element spacing of the receiving array.

The received signals are stacked, and the matrix form of equation (3) is converted into the vector form y _s , namely:

In formula (5):

vec( ) represents the operation of converting a matrix into a vector;

表示Kronecker积；

represents the Kronecker product;

表示M_r×M_r阶的单位矩阵；

represents an identity matrix of order M _r ×M _r ;

为发射波形矩阵S与单位矩阵

的Kronecker积，即

is the transmit waveform matrix S and the identity matrix

The Kronecker product of , i.e.

v(r,θ) is defined as the steering vector of the "virtual array", i.e.

Considering that the echo signal received by the frequency-controlled array MIMO radar, in addition to the target signal of interest, also contains clutter signals, interference and noise signals coherent with the target signal. Assuming that there are Q clutter scatterers, the clutter signal y _c received by the radar is:

In formula (6):

q represents the qth clutter scatterer, q=1, 2, ..., Q;

In order to distinguish it from the amplitude, distance and angle of the target, β _c,q , rc _,q , θ _c,q represent the amplitude and distance of the qth clutter scatterer at (rc _,q ,θ _c,q ), respectively and angle;

(rc _,q ,θ _c,q ) represents the position of the qth clutter scatterer, and the position is: the angle relative to the first element of the transmitting array is θ _c,q , and the distance is rc _,q .

At the same time, assuming that there are L interference signals from different directions, the received interference signal y _j is expressed as:

In formula (7):

的循环对称高斯分布，E[·]表示取数学期望；β _j,l and θ _j,l represent the amplitude and angle information of the l-th interfering signal, respectively, and β _j,l obeys the mean value of zero, and the covariance is

The cyclic symmetric Gaussian distribution of , E[ ] represents the mathematical expectation;

d _j,l represents a random vector containing interfering signals and obeys a zero-mean Gaussian distribution.

Therefore, in the presence of clutter signals, interference signals and noise, the total received signal y at the receiving end of the frequency-controlled array MIMO radar is:

y = y _s + y _c + y _j + e (8)

In Equation (8), e is complex Gaussian noise with zero mean.

(2) Problem description

Assuming the receiving filter x, the output SCNR of the signal at the receiving end after the filter is:

In formula (9):

表示期望目标信号的协方差，

represents the covariance of the desired target signal,

R _c , R _j and R _e are the clutter covariance matrix, the interference covariance matrix and the noise covariance matrix, respectively, which are expressed as follows:

表示杂波的协方差，

in,

represents the covariance of the clutter,

At the same time, combined with the formula a ^T (r, θ) S, the space transmission power P(S) of the transmitted signal at the target (r, θ) is defined as:

In formula (10), ||·|| ₂ represents the matrix 2 norm.

The present invention considers that under the constraints of PAPR and similarity, the transmit waveform and the receive filter are jointly designed, so that the radiated power at the target is minimized while the output SCNR is maximized, and the following optimization problem can be obtained:

ω _p is an empirical value, and the optimal value is obtained by adjusting its value through simulation experiments.

Among them, s ₀ represents the reference waveform, σ and ξ represent the control parameters, which are empirical values; the first constraint is the PAPR constraint, which is defined as:

Among them, s(n) represents the nth sampling point of s.

The second constraint in equation (11) represents the similarity constraint, which can be expressed as:

(ss ₀ ) ^H E _n (ss ₀ )≤ξ ² (12b)

_En (ss ₀ ) is a custom function, which is defined as follows:

For Equation (11), the optimization problem is transformed into two sub-optimization problems using the loop iteration method:

When the transmit waveform matrix S is fixed, the MVDR method (adaptive beamforming method) is used to solve the receiving filter x; when x is fixed, the ADMM method (alternating direction multiplier method) is used to convert the optimization problem into multiple variables to solve, and The transmit waveform matrix S is solved using ASM (effective set method).

The solution process of the two sub-optimization problems will be described in detail below.

In the first part, when the emission waveform matrix S is fixed, the objective function is transformed into:

The objective function (13a) is solved by the MVDR method, and its optimal solution is:

R_cje＝R_c+R_j+R_e。Among them, for convenience, we define

R _cje =R _c +R _j +R _e .

In the second part, when the receiving filter x is fixed, the ADMM method is used to solve S.

In order to efficiently solve equation (11), two parameters t ₁ and t ₂ are defined, which are respectively as follows:

For convenience, R _A , R _cvx , and R _vx are defined respectively;

P represents the switching matrix, and X is the matrix formed by the receiving filter, that is, x=vec(X), A(r, θ)=a(r, θ) a ^H (r, θ).

At this point, the objective function formula (11) can be transformed into:

To solve Equation (15), first convert Equation (15) into real-valued form:

Among them, t _1,r ,t _2,r ,s _0,r ,s _r ,RA _,r ,R _cvx,r ,R _vx,r ,E _n,r respectively represent t ₁ ,t ₂ ,s ₀ , Real _- valued form of s, _RA , _Rcvx , _Rvx ,En.

It should be noted that, not only here, but in the present invention, any parameter X _*.r with a subscript *.r means the real value form of the parameter X _* .

In order to obtain an efficient solution of Equation (16 ₎ , an auxiliary variable hr is introduced, and let hr =s _r , Equation (16 ₎ is transformed into:

Equation (17) is solved using the scaled form of the ADMM method. In the framework of ADMM, by introducing variables z _1,r ,z _{2,r ,ur ,v r ,} the equality constraints can be transformed into the augmented Lagrangian function, the augmented Lagrangian of Eq. (17) The Longian function is as follows:

In formula (18), ρ ₁ , ρ ₂ , ρ ₃ , ρ ₄ >0 are all penalty parameters, and the penalty parameters are all empirical values; for convenience, let: R _At,r =RA _,r -t ₁ , R _xt,r =R _cvx,r -t ₂ R _vx,r .

So, Equation (18) is transformed into:

Based on the ADMM method, the formula (19) is solved by the loop iteration method. This loop iteration is recorded as the inner loop. At the (n+1)th iteration, the solution process consists of the following steps:

求解

忽略常数部分，优化问题转换为：1) Know the nth iteration value

solve

Ignoring the constant part, the optimization problem transforms into:

Equation (2) is solved using the efficient set method (ASM), so Equation (17) is written in the standard ASM form:

In formula (21), c is a constant, and the set Φ={1, . . . , 2M _t L}.

For convenience, let Q, p, α _i , and b _i be respectively:

求解

2) Know the iteration value

solve

Transform the optimization problem (18) into:

的求解过程，利用有效集合法求解式(26)。similar to

The solution process of , using the efficient set method to solve Equation (26).

的情况下，求解{t_1,r,t_2,r}。3) Know the iteration value

In the case of , solve {t _1,r ,t _2,r }.

The optimization problem (18) transforms into:

可得：Similarly, so that

Available:

求解{z_1,r,z_2,r,u_r,v_r}。4) Know the iteration value

Solve for {z _1,r ,z _2,r ,u _r ,v _r }.

Based on the above solution ideas, the steps of the design method of low intercept FDA-MIMO radar under PAPR and similarity constraints are given below:

s_m ⁰表示第m个发射天线对应的发射波形波束向量初始值，m＝1，2，…M_t。S0: This step is the initial step, assuming that the outer iteration and inner iteration times of the design method of the present invention are represented by k and n respectively, initialize the outer loop iteration number k=0, initialize the inner loop iteration number n=0, and randomly initialize the emission waveform matrix S, denoted as

s _m ⁰ represents the initial value of the transmit waveform beam vector corresponding to the mth transmit antenna, m=1, 2, ... M _t .

计算第k次迭代下的接收滤波器x，记为接收滤波器x^k；S1: fix the current transmit waveform matrix, use the function of formula (13b)

Calculate the receive filter x under the k-th iteration, denoted as receive filter x ^k ;

Step S2 is executed under the kth outer loop iteration:

S2: Fix the receive filter x ^k in this iteration, update R _cvx , and calculate the transmit beam vector s.

本步骤进一步包括：Known the nth iteration value

This step further includes:

表示经第n次内循环迭代更新后的h_r；S201: Use equation (21) to solve _hr based on the effective set method, and record the updated _hr as

Represents h _r updated by the nth inner loop iteration;

表示经第n次内循环迭代更新后的s_r；S202: Use equation (26) to solve s _r based on the effective set method, and record the updated s _r as

represents the s _r updated by the nth inner loop iteration;

和

表示经第n次内循环迭代更新后的t_1,r和t_2,r；S203: Using equations (28) and (29), update t _1,r and t _2,r , and record the updated t _1,r and t _2,r as

and

Represents t _1,r and t _2,r updated by the nth inner loop iteration;

表示经第n次内循环迭代更新后的{z_1,r,z_2,r,u_r,v_r}；S204: Using equations (30) to (33), update {z _1,r ,z _{2,r ,} ur ,v _r }, and update the updated {z _1,r ,z _2,r ,ur _r ,v _r } is denoted as

represents {z _1,r ,z _2,r ,ur _r ,v _r } after the nth inner loop iteration update;

S205: set n=n+1, repeat the iterations S201-S204 until the number of iterations reaches the preset maximum number of iterations of the inner loop, output the last s _r , and then perform step S3;

S3: Let k=k+1, repeat steps S1-S2 until the number of iterations reaches the preset maximum number of outer loop iterations or |SCNR ^(k+1) -SCNR ^(k) |/SCNR ^(k) <ε, where , ε>0.

(4) Simulation experiment

其中，i＝1,2,…,M_t，l＝1,2,…,L，于是参考信号s₀＝vec(S₀)。In this simulation experiment, the number of transmitting and receiving antennas of the frequency-controlled array MIMO radar system is considered to be M _t =6 and _Mr = 8 respectively. The carrier frequency f ₀ =1 GHz, and the frequency increment Δf = 3 MHz. Transmitted energy E _t =1 on each antenna. The sequence length L=16 of the transmitted signal. The reference signal selects the quadrature LFM signal, which is defined as:

where i=1,2,...,M _t , l=1,2,...,L, so the reference signal s ₀ =vec(S ₀ ).

In addition, it is assumed that the target signal is located at (50m, 10°) and its power is 20dB; the clutter signal is located at (50m, -50°), (25m, 10°) and (75m, 40°), and the clutter power is both 30dB; the interference signal comes from two directions of -30° and 60°, and its power is 35dB; the covariance of Gaussian noise is

Considering the PAPR constraints of the frequency-controlled array MIMO radar system, take σ=1, 1.1, 1.5, ξ′=0.5, 1.0, 1.2, 2.0 respectively, (for the convenience of writing, define ξ′=ξ/M _t L, where ξ= 0.5, 1.0, 1.2, 2.0.) Referring to Figure 1, the comparison between the objective function and the number of iterations under different PAPR and different similarity constraints is given. From Figure 1(a), it can be seen that the objective function decreases with the increase of PAPR, And after 80 iterations, the scalar functions coincide in the two cases of σ=1.1 and σ=1.5. It can be seen from Figure 1(b) that the objective functions all decrease with the increase of the similarity constraint.

Figure 2 shows the transmit pattern comparison of the designed transmit waveforms under different PAPRs and different similarity constraints. It can be seen from Figures 2(a) and 2(b) that no matter in the angle dimension or the distance dimension, under the same PAPR constraint, the nulling of the emission pattern at the target increases with the increase of the similarity constraint; similarly, in Under the same similarity constraint, the nulling of the emission pattern at the target increases as the PAPR constraint increases.

Figure 3 shows the comparison of the receive patterns of the designed transmit waveforms at the target location under different PAPRs and different similarity constraints. It can be seen from Figure 3(a) and 3(b) that no matter in the angle dimension or the distance dimension, a good energy focus is formed at the target position (10° and 50m); at the clutter position (-50° and 25m) ) and the interference positions (-30° and -60°) both form a null over -89.5dB.

Figure 4 shows the comparison of receive patterns of the designed transmit waveforms at positions 25m, 75m and 40° under different PAPRs and different similarity constraints. It can be seen from Fig. 4(a) that in the receiving pattern of the angle dimension at 25m, the receiving pattern forms a zero above -59.5dB at the clutter position (10°) and the interference position (-30° and -60°). trap. Similarly, it can be seen from Figure 4(b) that in the receiving pattern of the angle dimension at 75m, the receiving pattern is more than -85.1dB at the clutter position (40°) and the interference position (-30° and -60°). of zero. As can be seen from Figure 4(c), in the receiving pattern of the distance dimension at 40°, the receiving pattern forms a null over -63.5dB at the clutter position (75m).

In summary, the launch pattern also has significantly deeper nulls at the target location. In addition, good energy focusing is formed at the target positions (10° and 50m), clutter positions (-50°, 10°, 40° and 25m, 75m) and interference positions (-30° and -60°) ) have formed a better null.

The above descriptions are only the embodiments of the present invention, and are not intended to limit the scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the description and drawings of the present invention, or directly or indirectly applied to other related technologies Fields are similarly included in the scope of patent protection of the present invention.

Claims (5)

1. The design method of the low-intercept frequency controlled array MIMO radar system under the constraint of PAPR and similarity, is characterized in that, comprises: S0: Build an optimization problem

Initialize the outer loop iteration number k=0, initialize the inner loop iteration number n=0, and randomly initialize the transmit waveform matrix S, denoted as

s _m ⁰ represents the initial value of the transmit waveform vector corresponding to the mth transmit antenna, m=1, 2, ... M _t , M _t represents the M _t transmit antennas; s=vec(S); where: ω _p is the weight of the p-th objective function, ω _p ∈ [0,1], and satisfy

P(S) is the spatial transmit power of the transmitted signal, SCNR(x,S) is the output signal-to-interference-noise ratio of the signal at the receiving end after the receiving filter; PAPR(s) represents the PAPR constraint of s, s ₀ represents the reference waveform, σ and ξ represent control parameters; S1: Fix the current transmit waveform matrix, use the MVDR method to solve the optimization problem, and calculate the receive filter

The currently calculated receiving filter is the receiving filter under the k-th iteration, denoted as x ^k ; where: W ₁ is defined as:

represents the identity matrix of M _t ×M _t ; v(r, θ) is defined as: the steering vector of the virtual array,

b(θ) represents the steering vector of the receiving antenna array, a(r, θ) represents the steering vector of the transmitting antenna array; The definition of R _cje is: R _cje =R _c +R _j +R _e , where R _c , R _j and R _e are the clutter covariance matrix, the interference covariance matrix and the noise covariance matrix, respectively; Under the kth outer loop iteration, step S2 is executed: S2: Fix the receive filter x ^k under this iteration, calculate and update the transmit waveform vector s based on the alternating direction multiplier method and the effective set method; the current iteration value is known

The parameter with the superscript n represents the parameter value at the beginning of the nth inner loop iteration; this step further includes: S201: Update the auxiliary variable h _r , and this sub-step further includes: S201a: Construct objective function in real form

t _1,r ,t _2,r ,s _0,r ,s _r ,RA _,r ,R _cvx,r ,R _vx,r ,E _n,r represent t ₁ ,t ₂ ,s ₀ ,s, R _A , R _cvx , R _vx , the real-valued form of E _n ; Parameters _t1 and _t2 are defined as:

Among them, R _A , R _cvx , and R _vx are respectively defined as:

A(r, θ)=a(r, θ) a ^H (r, θ);

P represents the switching matrix, X is the matrix formed by the receiving filter, that is, x=vec(X); L represents the number of interference signals; rc _,q and θc _,q represent the distance and angle at the qth clutter, respectively ; S201b: Under the ADMM framework, by introducing variables z _1,r ,z _2,r ,ur _r ,v _r , transform the above objective function into the augmented Lagrangian function f _t,r (s _r ,h _r , t _1,r ,t _2,r ,z _1,r ,z _2,r ,ur _r ,v _r ) to obtain the objective function:

Among them, ρ ₁ , ρ ₂ , ρ ₃ , ρ ₄ are all penalty parameters, and all are greater than 0; R _At is defined as: R _At = _RA -t ₁ /M _t E _t ; R _xt is defined as: R _xt = R _cvx -t ₂ R _vx ; R _At,r and R _xt,r represent the real-valued forms of R _At and R _xt , respectively; S201c: Construct the objective function in S201b into standard ASM form:

Using the effective set method to solve _hr , the _hr obtained by this solution is recorded as

Among them, Q, p, α _i , b _i are auxiliary variables, which are defined as follows:

S202: Known iteration value

Transform f _t,r (s _r ,h _r ,t _1,r ,t _{2,r ,} z _1,r ,z _2,r ,ur ,v _r ) into the following objective function:

Construct the objective function into a standard ASM form, and use the effective set method to solve s _r . The s _r obtained by this solution is recorded as

S203: Known iteration value

Transform f _t,r (s _r ,h _r ,t _1,r ,t _{2,r ,} z _1,r ,z _2,r ,ur ,v _r ) into the following objective function:

make

Solve for t _1,r and t _2,r , the t _1,r and t _2,r obtained by this solution are recorded as

and

S204: Known iteration value

Use the following formula to solve {z _1,r ,z _2,r ,ur _r ,v _r }, and the solution {z _1,r ,z _2,r ,ur _r ,v _r } obtained this time is denoted as

S205: set n=n+1, repeat the iterations S201-S204 until the number of iterations reaches the preset maximum number of iterations of the inner loop, output the last s _r , and then perform step S3; S3: Let k=k+1, repeat steps S1-S2 until the number of iterations reaches the preset maximum number of outer loop iterations or |SCNR ^(k+1) -SCNR ^(k) |/SCNR ^(k) <ε, where , ε>0. 2. the design method of low intercept frequency controlled array MIMO radar system under PAPR as claimed in claim 1 and similarity constraint, it is characterized in that: The space transmit power P(S) is defined as:

in,

is the steering vector of the transmitting array, and θ represents the angle;

represents the phase difference,

c represents the speed of light, d _t represents the element spacing of the transmitting array, and Δf represents the frequency increment. 3. the design method of low intercept frequency controlled array MIMO radar system under PAPR as claimed in claim 1 and similarity constraint, it is characterized in that: PAPR constraints are defined as:

Among them, L represents the number of interference signals, and s(n) represents the nth sampling point of s. 4. the design method of low intercept frequency controlled array MIMO radar system under PAPR as claimed in claim 1 and similarity constraint, it is characterized in that: Clutter covariance matrix

Interference covariance matrix

covariance matrix of noise

in: Q represents the number of clutter scatterers, and q represents the qth clutter scatterer; In order to distinguish the distance and angle from the target, rc _,q and θc _,q are used to represent the distance and angle at the qth clutter, respectively,

represents the covariance of the qth clutter; L represents the number of interference signals from different directions, and l represents the l-th interference signal; also in order to distinguish the angle from the target, θ _j,l represents the angle of the l-th interference;

Represents the covariance of the l-th interference signal; I _K represents the K×K identity matrix; b(θ _j,l ) represents the steering vector of the l-th interference signal on the receiving antenna array;

represents the covariance of noise _; I _MrK represents the identity matrix of order Mr K×M _r K. 5. the design method of low intercept frequency controlled array MIMO radar system under PAPR as claimed in claim 1 and similarity constraint, it is characterized in that: The formula for calculating the signal-to-interference-to-noise ratio is:

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