CN111142080A - A Fast Constant Modulus MIMO Radar Tracking Waveform Synthesis Method for Interference Suppression - Google Patents

Abstract

The invention belongs to the technical field of radar, and in particular relates to a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression. Enter the interference steering vector formula to obtain the interference spatial steering vector; construct the interference subspace matrix according to the interference spatial steering vector; bring the target azimuth and the interference subspace matrix into the first cost function to obtain several subimpulse functions; obtain several subimpulse functions according to several subimpulse functions Sub-pulse; construct several sub-pulse proportional equations according to several target direction energy distribution ratios, convert several sub-pulse proportional equations into matrix form to obtain matrix-form sub-pulse proportional equations; construct transmit waveform matrix according to matrix-form sub-pulse proportional equations. Ensure that each array element transmit power amplifier works at the maximum working efficiency, reducing the interception probability of the interference source and the beneficial effect of reflected power.

Description

A Fast Constant Modulus MIMO Radar Tracking Waveform Synthesis Method for Interference Suppression

technical field

The invention belongs to the technical field of radar, and in particular relates to a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression.

Background technique

The widespread application of digital components in radar systems has produced MIMO radars. Different from traditional phased array radars, each element of MIMO radars can transmit different signals. It is this waveform diversity capability that makes MIMO radars different from traditional phased array radars. Compared with , has more advantages. MIMO radars can be divided into distributed MIMO radars and centralized MIMO radars according to the distance between the transmitting and receiving antennas. For distributed MIMO radar, because the observation angles of each antenna to the target are different and the echoes are independent. The centralized MIMO radar has the ability to freely design the emission waveform of each array element. Compared with the phased array radar, its degree of freedom is significantly improved, so it has the ability to design adaptive emission pattern. In the actual working environment of the radar, there are usually interferences that affect the ability of the radar to detect the target. Therefore, it is necessary for the radar to reduce the interference power in the echo signal by designing the transmitting waveform at the transmitting end. MIMO radar can obtain a specific pattern by designing the transmit waveform matrix, so as to achieve the purpose of anti-jamming.

In their paper "Transmit Signal Design in Colocated MIMORadar Without Covariance Matrix Optimization" ([J]. "IEEE Transactions on Aerospace & Electronic Systems", 2017, PP(99): 1-1), S Imani et al. Semidefinite Relaxation (SDR: Semidefinite Relaxation) MIMO radar transmit waveform synthesis method. The basic steps of the method are: firstly obtain the desired transmit pattern according to the prior information, then construct the SDR model according to the desired transmit pattern, and solve the model to obtain the MIMO radar transmit waveform matrix. The disadvantage of this method is that the SDR model only approximates the desired emission pattern with the least squares criterion, ignoring the anti-jamming condition, so the emission waveform synthesized by the SDR model cannot realize the anti-jamming function.

The patented technology "a MIMO radar emission pattern and waveform design method" (application number: 201510299652.4 authorization announcement number: CN 105158736B), a patented technology owned by the 28th Research Institute of China Electronics Technology Group Corporation, discloses a MIMO radar emission direction Diagram and Waveform Design Methods. The specific steps of the patented technology are: first, model the desired transmission pattern according to the prior information, then construct the transmission signal as a weighted summation of a set of orthogonal sequences, and design the orthogonal sequence by drawing on and improving the DPS sequence generation principle. The optimization problem of the number and weights of , and the optimized waveform and the optimized emission pattern are simultaneously obtained by solving the optimization problem. The disadvantage of this method is that in the actual operation of the radar, in order to ensure the maximum working efficiency of the transmitting power amplifier of each array element, the transmitting waveform must have a constant mode characteristic, and this method cannot generate a constant mode transmitting waveform.

SUMMARY OF THE INVENTION

In order to solve the above problems existing in the prior art, the present invention provides a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression. The technical problem to be solved by the present invention is realized by the following technical solutions:

A fast constant-modulus MIMO radar tracking waveform synthesis method for interference suppression, comprising:

Obtaining several target azimuths, several interference azimuths, and several target direction energy distribution ratios corresponding to the target azimuths;

Bring the interference azimuth into the interference steering vector formula to obtain the interference airspace steering vector;

constructing an interference subspace matrix according to the interference spatial steering vector;

Bringing the target azimuth and the interference subspace matrix into the first cost function to obtain several subimpulse functions;

solving the several sub-pulse functions to obtain several sub-pulses;

Construct several sub-pulse proportional equations according to the several target direction energy distribution ratios, and convert the several sub-pulse proportional equations into a matrix form to obtain a matrix-form sub-pulse proportional equation;

A transmit waveform matrix is constructed according to the matrix-form sub-pulse proportional equation.

In an embodiment of the present invention, the interference steering vector formula is:

Among them, a(θ _i ) is the interference airspace steering vector at the ith interference azimuth θ _i , the value range of i is [1, J], J is the number of interference azimuths, and exp is the base of the natural constant The exponential operation of , j is an imaginary number, d is the distance between radar antenna elements, n is the serial number of radar antenna elements, the value range of n is [0, N-1], N is the total number of radar antenna elements, sin is a sine, and λ is the wavelength of the radar transmit signal.

In an embodiment of the present invention, the interference subspace matrix expression is:

J=[a(θ _j )],

Among them, J is the interference subspace matrix, [] is the matrix operation, a(θ _i ) is the interference spatial steering vector at the ith interference azimuth θ _i , and the value range of i is [1, J], J is the number of interference azimuths.

In an embodiment of the present invention, the first cost function is:

为第k个目标方位角θ_k处的目标空域导向矢量，θ_k为第k个目标方位角，k的取值范围为[1，K]，目标方位角有K个，x_nk为所述第k个子脉冲x_k的第n个元素，n为雷达天线阵元序号，n的取值范围为[0,N-1]，N为雷达天线阵元总数，j为虚数。Among them, w is the weighting parameter, x _k is the k-th sub-pulse, (·) ^H is the conjugate transpose operation of the matrix, J is the interference subspace matrix,

is the target airspace steering vector at the k-th target azimuth angle θ _k , θ _k is the k-th target azimuth angle, the value range of k is [1, K], there are K target azimuth angles, and x _nk is the The nth element of the kth sub-pulse x _k , n is the serial number of the radar antenna array element, the value range of n is [0, N-1], N is the total number of radar antenna array elements, and j is an imaginary number.

In an embodiment of the present invention, the sub-pulse proportional equation is:

为第j个子脉冲所占比例，P_k(θ_k)为第k个子脉冲的方向图函数，β_k为第k个目标方位角θ_k的发射能量，k的取值范围为[1,K]，目标方位角有K个。in,

is the proportion of the j-th sub-pulse, P _k (θ _k ) is the pattern function of the k-th sub-pulse, β _k is the emission energy of the k-th target azimuth θ _k , and the value range of k is [1,K ], there are K target azimuths.

In an embodiment of the present invention, the matrix-form sub-pulse proportional equation is:

目标方位发射能量矩阵β＝[β₁ β₂ … β_K]^T。Among them, the sub-pulse pattern function matrix p _k =[P _k (θ ₁ ) P _k (θ ₂ ) … P _k (θ _K )] ^T , the sub-pulse ratio matrix

Target azimuth emission energy matrix β=[β ₁ β ₂ … β _K ] ^T .

In an embodiment of the present invention, constructing a transmit waveform matrix according to the matrix-form sub-pulse proportional equation, including:

Convert the matrix-type sub-pulse proportional equation into the sub-pulse number form:

为第k个子脉冲所占比例，k的取值范围为[1,K]，[·]为四舍五入取整操作；Among them, α _k is the number of the kth sub-pulse, L is the total number of pulses,

is the proportion of the kth sub-pulse, the value range of k is [1, K], and [ ] is the rounding operation;

Construct the transmit waveform matrix according to the number of sub-pulses:

Among them, X is the transmit waveform matrix, and x _k is the kth sub-pulse x.

Beneficial effects of the present invention:

First, the present invention simplifies the waveform optimization into the design of a limited number of sub-pulses, and uses the proposed fast MM algorithm to solve the cost function, so that each sub-pulse beam has a main lobe and forms a notch in the interference azimuth. Since each sub-pulse is uncorrelated, it can be generated in parallel. Furthermore, a sub-pulse combination assignment method is proposed, which can quickly synthesize the generated sub-pulses into the required transmit waveform matrix.

Second, for multi-target scenarios, the present invention can synthesize multi-beam waveforms, and while irradiating all targets, deep notches can be generated in the direction of the interference source, effectively reducing the interception probability and reflected power of the interference source.

Third, in order to maintain the constant mode characteristic, a constant mode constraint is carried out on each sub-pulse, and the final synthesized radar transmit waveform also has the constant mode characteristic, so that the synthesized transmit waveform has the constant mode characteristic. In the actual operation of the radar, in order to ensure the maximum working efficiency of the transmitting power amplifier of each array element, the transmitting waveform must have constant mode characteristics, so the radar transmitting waveform generated by the present invention can ensure the maximum working efficiency of the transmitting power amplifier of each array element. .

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

Description of drawings

1 is a schematic flowchart of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression provided by an embodiment of the present invention;

2 is a transmission pattern of a radar transmission waveform synthesized by a simulation experiment of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression provided by an embodiment of the present invention;

3 is a sub-pulse emission pattern obtained by a simulation experiment of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression provided by an embodiment of the present invention;

FIG. 4 is an amplitude diagram of each radar array element transmit waveform obtained by a simulation experiment of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression provided by an embodiment of the present invention.

Detailed ways

The present invention will be described in further detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

Please refer to FIG. 1. FIG. 1 is a schematic flowchart of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression provided by an embodiment of the present invention, including:

Obtaining several target azimuths, several interference azimuths, and several target direction energy distribution ratios corresponding to the target azimuths;

Bring the interference azimuth into the interference steering vector formula to obtain the interference airspace steering vector;

constructing an interference subspace matrix according to the interference spatial steering vector;

Bringing the target azimuth and the interference subspace matrix into the first cost function to obtain several subimpulse functions;

solving the several sub-pulse functions to obtain several sub-pulses;

Construct several sub-pulse proportional equations according to the several target direction energy distribution ratios, and convert the several sub-pulse proportional equations into a matrix form to obtain a matrix-form sub-pulse proportional equation;

A transmit waveform matrix is constructed according to the matrix-form sub-pulse proportional equation.

First, the present invention simplifies the waveform optimization into the design of a limited number of sub-pulses, and uses the proposed fast MM algorithm to solve the cost function, so that each sub-pulse beam has a main lobe and forms a notch in the interference azimuth. Since each sub-pulse is uncorrelated, it can be generated in parallel. Furthermore, a sub-pulse combination assignment method is proposed, which can quickly synthesize the generated sub-pulses into the required transmit waveform matrix.

Second, for multi-target scenarios, the present invention can synthesize multi-beam waveforms, and while irradiating all targets, deep notches can be generated in the direction of the interference source, effectively reducing the interception probability and reflected power of the interference source.

Third, in order to maintain the constant mode characteristic, a constant mode constraint is carried out on each sub-pulse, and the final synthesized radar transmit waveform also has the constant mode characteristic, so that the synthesized transmit waveform has the constant mode characteristic. In the actual operation of the radar, in order to ensure the maximum working efficiency of the transmitting power amplifier of each array element, the transmitting waveform must have constant mode characteristics, so the radar transmitting waveform generated by the present invention can ensure the maximum working efficiency of the transmitting power amplifier of each array element. .

In an embodiment of the present invention, the interference steering vector formula is:

Among them, a(θ _i ) is the interference airspace steering vector at the ith interference azimuth θ _i , the value range of i is [1, J], J is the number of interference azimuths, and exp is the base of the natural constant The exponential operation of , j is an imaginary number, d is the distance between radar antenna elements, n is the serial number of radar antenna elements, the value range of n is [0, N-1], N is the total number of radar antenna elements, sin is a sine, and λ is the wavelength of the radar transmit signal.

In an embodiment of the present invention, the interference subspace matrix expression is:

J=[a(θ _j )],

Among them, J is the interference subspace matrix, [] is the matrix operation, a(θ _i ) is the interference spatial steering vector at the ith interference azimuth θ _i , and the value range of i is [1, J], J is the number of interference azimuths.

In an embodiment of the present invention, the first cost function is:

为第k个目标方位角θ_k处的目标空域导向矢量，θ_k为第k个目标方位角，k的取值范围为[1，K]，目标方位角有K个，x_nk为所述第k个子脉冲x_k的第n个元素，n为雷达天线阵元序号，n的取值范围为[0,N-1]，N为雷达天线阵元总数，j为虚数。Among them, w is the weighting parameter, x _k is the k-th sub-pulse, (·) ^H is the conjugate transpose operation of the matrix, J is the interference subspace matrix,

is the target airspace steering vector at the k-th target azimuth angle θ _k , θ _k is the k-th target azimuth angle, the value range of k is [1, K], there are K target azimuth angles, and x _nk is the The nth element of the kth sub-pulse x _k , n is the serial number of the radar antenna array element, the value range of n is [0, N-1], N is the total number of radar antenna array elements, and j is an imaginary number.

In an embodiment of the present invention, the sub-pulse proportional equation is:

为第j个子脉冲所占比例，P_k(θ_k)为第k个子脉冲的方向图函数，β_k为第k个目标方位角θ_k的发射能量，k的取值范围为[1,K]，目标方位角有K个。in,

is the proportion of the j-th sub-pulse, P _k (θ _k ) is the pattern function of the k-th sub-pulse, β _k is the emission energy of the k-th target azimuth θ _k , and the value range of k is [1,K ], there are K target azimuths.

In an embodiment of the present invention, the matrix-form sub-pulse proportional equation is:

目标方位发射能量矩阵β＝[β₁ β₂… β_K]^T。Among them, the sub-pulse pattern function matrix pk=[P _k (θ ₁ ) P _k (θ ₂ ) … P _k (θ _K )] ^T , the sub-pulse ratio matrix

Target azimuth emission energy matrix β=[β ₁ β ₂ … β _K ] ^T .

In an embodiment of the present invention, constructing a transmit waveform matrix according to the matrix-form sub-pulse proportional equation, including:

Convert the matrix-type sub-pulse proportional equation into the sub-pulse number form:

为第k个子脉冲所占比例，k的取值范围为[1,K]，[·]为四舍五入取整操作；Among them, α _k is the number of the kth sub-pulse, L is the total number of pulses,

is the proportion of the kth sub-pulse, the value range of k is [1, K], and [ ] is the rounding operation;

Construct the transmit waveform matrix according to the number of sub-pulses:

Among them, X is the transmit waveform matrix, and x _k is the kth sub-pulse x.

Further, the steps to obtain several sub-pulses are as follows:

(1) Initialize the sub-pulse iteration value x ⁽⁰⁾ , construct the second cost function L=wJJ ^H -a(θ _k )a ^H (θ _k ),

(2) Estimate the upper bound λ _u (L) of the second cost function according to the second cost function, and construct an intermediate variable M according to the upper bound of the second cost function, M=λ _u (L)I,

n为第二代价函数的阶数；Among them, λ _min (L) is the minimum value of the second cost function, λ _max (L) is the maximum value of the second cost function, I is the eigenvector, t is the number of iterations, t=0, where y and s are the middle variable,

n is the order of the second cost function;

(3) Calculation

q,v,α为中间变量，angle(·)为取相位运算，||·||₂为取2范数操作，(·)^H为对矩阵进行共轭转置操作；in,

q, v, α are intermediate variables, angle(·) is the phase operation, ||·|| ₂ is the 2-norm operation, (·) ^H is the conjugate transpose operation of the matrix;

(4) When (x ^(t+1) ) ^H Lx ^(t+1) > (x ^(t) ) ^H Lx ^(t) , let α=(α-1)/2, and jump to step (3) ); otherwise, proceed to the next step;

(5) When |x ^(t+1) -x ^(t) |≤ε, output x; otherwise, set t=t+1, and jump to step (3)

The effect of the present invention will be further described below in conjunction with the simulation data.

1. Simulation conditions:

The simulation running system of the present invention is Intel(R) Core(TM) i7-2600 CPU 650@3.40GHz, 32-bit Windows operating system, and the simulation software adopts MATLAB (R 2012b).

2. Simulation data and result analysis:

The parameters of the simulation experiment of the present invention are set as the total number of radar array elements is 32, the distance between the radar antenna array elements is 0.5 mm, the wavelength of the radar transmit signal is 1 mm, the total number of interference sources is 2, and the azimuth angle of the interference sources is -59.5 ° and 20.5°, the total number of targets is 3, the target azimuth angles are -35°, 0°, 45°, respectively, and the power distribution is 1:1:1.

Please refer to FIG. 2. FIG. 2 is a transmit pattern of a radar transmit waveform synthesized by a simulation experiment of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression provided by an embodiment of the present invention. The abscissa in Figure 2 represents the airspace azimuth, and its value range is [-90°, 90°], and the ordinate represents the power gain of the radar transmit waveform synthesized by the simulation experiment at each airspace azimuth, in dB. By drawing the power gain of the radar transmit waveform synthesized by the simulation experiment at each airspace azimuth angle, the emission pattern of the radar transmit waveform synthesized by the simulation experiment can be obtained.

The power gain of the radar transmit waveform synthesized by the simulation experiment at each airspace azimuth is obtained by the following formula:

P(θ)=a(θ) ^H XX ^H a(θ),

Among them, P(θ) represents the power gain of the radar transmit waveform synthesized by simulation experiments at the airspace azimuth angle θ, a(θ) represents the airspace steering vector at the airspace azimuth angle θ, H represents the conjugate transpose operation, and X is the The multi-input multi-output constant-modulus transmit waveform matrix synthesized by the simulation experiment.

As can be seen from Figure 2, the radar has a strong power gain of 25dB at the target azimuth angles of -35°, 0°, and 45°, and only a very weak power gain at the interference source azimuth angles of -59.5° and 20.5°. are -34dB and -38dB, so it can be seen that the radar transmit waveform synthesized by the present invention has anti-interference function.

Please refer to FIG. 3 and FIG. 4. FIG. 3 is a sub-pulse emission pattern obtained by a simulation experiment of a fast constant-modulus MIMO radar tracking waveform synthesis method for interference suppression provided by an embodiment of the present invention, and FIG. 4 is provided by an embodiment of the present invention. The amplitude diagram of the emission waveform of each radar array element obtained from the simulation experiment of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression. The amplitude value of each row element in the multi-input multi-output constant-modulus emission waveform matrix synthesized by the simulation experiment is taken as the amplitude value of the emission waveform of each radar array element, and the corresponding amplitude of each radar array element can be obtained. Amplitude graph.

In Figure 3, the abscissa represents the number of radar array elements, and its value range is [1, 32], and the ordinate represents the amplitude value of the waveform emitted by the corresponding array element. It can be seen from Figure 3 that the amplitudes of the transmitted waveforms of the radar array elements are equal and all are 1. Therefore, it is considered that the transmit waveform synthesized by the present invention has a constant mode characteristic, which can ensure the maximum working efficiency of the transmit power amplifier of each array element.

The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be considered that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field of the present invention, without departing from the concept of the present invention, some simple deductions or substitutions can be made, which should be regarded as belonging to the protection scope of the present invention.

Claims (7)

1. a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression is characterized in that, comprising: Obtaining several target azimuths, several interference azimuths, and several target direction energy distribution ratios corresponding to the target azimuths; Bring the interference azimuth into the interference steering vector formula to obtain the interference airspace steering vector; constructing an interference subspace matrix according to the interference spatial steering vector; Bringing the target azimuth and the interference subspace matrix into the first cost function to obtain several subimpulse functions; solving the several sub-pulse functions to obtain several sub-pulses; Construct several sub-pulse proportional equations according to the several target direction energy distribution ratios, and convert the several sub-pulse proportional equations into a matrix form to obtain a matrix-form sub-pulse proportional equation; A transmit waveform matrix is constructed according to the matrix-form sub-pulse proportional equation. 2. The fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to claim 1, wherein the interference steering vector formula is:

Among them, a(θ _i ) is the interference airspace steering vector at the ith interference azimuth θ _i , the value range of i is [1, J], J is the number of interference azimuths, and exp is the base of the natural constant The exponential operation of , j is an imaginary number, d is the distance between radar antenna elements, n is the serial number of radar antenna elements, the value range of n is [0, N-1], N is the total number of radar antenna elements, sin is a sine, and λ is the wavelength of the radar transmit signal. 3. the fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to claim 1, is characterized in that, described interference subspace matrix expression is: J=[a(θ _j )], Among them, J is the interference subspace matrix, [] is the matrix operation, a(θ _i ) is the interference spatial steering vector at the ith interference azimuth θ _i , and the value range of i is [1, J], J is the number of interference azimuths. 4. The fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to claim 1, wherein the first cost function is:

Among them, w is the weighting parameter, x _k is the k-th sub-pulse, (·) ^H is the conjugate transpose operation of the matrix, J is the interference subspace matrix,

is the target airspace steering vector at the k-th target azimuth angle θ _k , θ _k is the k-th target azimuth angle, the value range of k is [1, K], there are K target azimuth angles, and x _nk is the The nth element of the kth sub-pulse x _k , n is the serial number of the radar antenna array element, the value range of n is [0, N-1], N is the total number of radar antenna array elements, and j is an imaginary number. 5. The fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to claim 1, wherein the sub-pulse proportional equation is:

in,

is the proportion of the j-th sub-pulse, P _k (θ _k ) is the pattern function of the k-th sub-pulse, β _k is the emission energy of the k-th target azimuth θ _k , and the value range of k is [1, K ], there are K target azimuths. 6. the fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to claim 5, is characterized in that, described matrix form sub-pulse proportional equation is:

Among them, the sub-pulse pattern function matrix p _k =[P _k (θ ₁ ) P _k (θ ₂ )…P _k (θ _K )] ^T , the sub-pulse ratio matrix

Target azimuth emission energy matrix β=[β ₁ β ₂ ···β _K ] ^T . 7. The fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to claim 1, characterized in that, constructing a transmit waveform matrix according to the matrix form sub-pulse proportional equation, comprising: Convert the matrix-type sub-pulse proportional equation into the sub-pulse number form:

Among them, α _k is the number of the kth sub-pulse, L is the total number of pulses,

is the proportion of the kth sub-pulse, the value range of k is [1, K], and [ ] is the rounding operation; Construct the transmit waveform matrix according to the number of sub-pulses:

Among them, X is the transmit waveform matrix, and x _k is the kth sub-pulse x.

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