CN111142080A - Rapid constant modulus MIMO radar tracking waveform synthesis method aiming at interference suppression - Google Patents

Rapid constant modulus MIMO radar tracking waveform synthesis method aiming at interference suppression Download PDF

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CN111142080A
CN111142080A CN201911384798.3A CN201911384798A CN111142080A CN 111142080 A CN111142080 A CN 111142080A CN 201911384798 A CN201911384798 A CN 201911384798A CN 111142080 A CN111142080 A CN 111142080A
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CN111142080B (en
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纠博
谢少鹏
郑浩
刘宏伟
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/42—Diversity systems specially adapted for radar

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Abstract

The invention belongs to the technical field of radars, and particularly relates to a method for synthesizing a tracking waveform of a rapid constant modulus MIMO radar aiming at interference suppression, which comprises the following steps: acquiring a plurality of target azimuth angles, a plurality of interference azimuth angles and a plurality of target direction energy distribution proportions; substituting the interference azimuth angle into an interference steering vector formula to obtain an interference airspace steering vector; constructing an interference subspace matrix according to the interference airspace guide vector; substituting the target azimuth angle and the interference subspace matrix into a first cost function to obtain a plurality of sub-pulse functions; obtaining a plurality of sub-pulses according to a plurality of sub-pulse functions; constructing a plurality of sub-pulse proportion equations according to the energy distribution proportion of a plurality of target directions, and converting the plurality of sub-pulse proportion equations into a matrix form to obtain a matrix form sub-pulse proportion equation; and constructing a transmitting waveform matrix according to a matrix form sub-pulse proportion equation. The method has the beneficial effects of reducing the interception probability and the reflected power of the interference source under the condition of ensuring that each array element transmitting power amplifier works at the maximum working efficiency.

Description

Rapid constant modulus MIMO radar tracking waveform synthesis method aiming at interference suppression
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a method for synthesizing a tracking waveform of a rapid constant modulus MIMO radar aiming at interference suppression.
Background
The general application of digital components in a radar system generates an MIMO radar, which is different from the traditional phased array radar, and each array element of the MIMO radar can transmit different signals. The MIMO radar may be classified into a distributed MIMO radar and a centralized MIMO radar according to the size of the spacing between the transmitting and receiving antennas. For the distributed MIMO radar, the observation angles of the antennas to the target are different, and the echoes are independent. Compared with a phased array radar, the degree of freedom of the centralized MIMO radar is remarkably improved, and therefore the centralized MIMO radar has the capability of designing a self-adaptive emission directional diagram. In the actual operating environment of a radar, there are often disturbances that affect the ability of the radar to detect targets. Therefore, it is necessary for the radar to reduce interference power in the echo signal by designing the transmission waveform at the transmitting end. The MIMO radar can obtain a specific directional diagram through the design of a transmitting waveform matrix, so that the aim of resisting interference is fulfilled.
S Imani et al, in its published paper, "Transmit Signal Design in colored MIMO random Without Covariance Matrix Optimization" ([ J ]. IEEE Transactions on Aerospace & Electronic Systems, 2017, PP (99):1-1), propose a method for synthesizing MIMO radar Transmit waveforms based on semi-positive Relaxation (SDR). The method comprises the following basic steps: firstly, obtaining an expected emission directional diagram according to prior information, then constructing an SDR model according to the expected emission directional diagram, and solving the model to obtain an MIMO radar emission waveform matrix. The method has the following defects: the SDR model only approaches an expected transmitting directional diagram by a least square criterion, and an anti-interference condition is ignored, so that an anti-interference function cannot be realized by using a transmitting waveform synthesized by the SDR model.
A MIMO radar emission pattern and waveform design method is disclosed in a patent technology 'an MIMO radar emission pattern and waveform design method' (application number: 201510299652.4 grant publication number: CN 105158736B) owned by the twenty-eighth research institute of China electronics science and technology group company. The patent technology comprises the following specific steps: firstly, modeling an expected emission directional diagram according to prior information, then constructing an emission signal into weighted summation of a group of orthogonal sequences, designing an optimization problem about the number and weight of the orthogonal sequences by using and improving a DPS sequence generation principle, and simultaneously obtaining an optimized waveform and an optimized emission directional diagram by solving the optimization problem. The method has the following defects: in actual radar operation, in order to ensure the maximum working efficiency of each array element transmitting power amplifier, a transmitting waveform is required to have constant modulus characteristics, and the method cannot generate the constant modulus transmitting waveform.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method for synthesizing a tracking waveform of a fast constant modulus MIMO radar aiming at interference suppression. The technical problem to be solved by the invention is realized by the following technical scheme:
a method for synthesizing a tracking waveform of a fast constant modulus MIMO radar aiming at interference suppression comprises the following steps:
acquiring a plurality of target azimuth angles, a plurality of interference azimuth angles and a plurality of target direction energy distribution proportions corresponding to the target azimuth angles;
substituting the interference azimuth angle into an interference steering vector formula to obtain an interference airspace steering vector;
constructing an interference subspace matrix according to the interference airspace guide vector;
substituting the target azimuth angle and the interference subspace matrix into a first cost function to obtain a plurality of sub-pulse functions;
solving the plurality of sub-pulse functions to obtain a plurality of sub-pulses;
constructing a plurality of sub-pulse proportion equations according to the energy distribution proportions of the target directions, and converting the sub-pulse proportion equations into a matrix form to obtain a matrix form sub-pulse proportion equation;
and constructing a transmitting waveform matrix according to the matrix form sub-pulse proportion equation.
In one embodiment of the present invention, the interference steering vector formula is:
Figure BDA0002343270470000031
wherein ,a(θi) For the ith interference azimuth angle thetaiThe value range of i is [1, J]J is the number of interference azimuth angles, exp is exponential operation with natural constant as base, J is an imaginary number, d is the distance between radar antenna array elements, N is the serial number of the radar antenna array elements, and the value range of N is [0, N-1 ]]N is the total number of the radar antenna elements, sin is sine, and lambda is the wavelength of the radar emission signal.
In an embodiment of the present invention, the interference subspace matrix expression is:
J＝[a(θj)]，
wherein J is an interference subspace matrix, [ alpha ], [ alpha]For matrixing operation, a (θ)i) For the ith interference azimuth angle thetaiThe value range of i is [1, J]And J is the number of interference azimuths.
In one embodiment of the invention, the first cost function is:
Figure BDA0002343270470000032
wherein w is a weighting parameter, xkFor the kth sub-pulse, (.)HTo perform a conjugate transpose operation on the matrix, J is the interference subspace matrix,
Figure BDA0002343270470000033
for the k-th target azimuth angle thetakTarget space vector of (a) ([ theta ])kIs the kth target azimuth angle, and the value range of K is [1, K]The target azimuth angle has K, xnkFor the k sub-pulse xkN is the serial number of the radar antenna array element, and the value range of N is [0, N-1 ]]N is the total number of radar antenna elementsAnd j is an imaginary number.
In one embodiment of the present invention, the sub-pulse ratio equation is:
Figure BDA0002343270470000041
wherein ,
Figure BDA0002343270470000042
is the proportion of the jth sub-pulse, Pk(θk) As a function of the pattern of the kth sub-pulse, βkFor the k-th target azimuth angle thetakK has a value in the range of [1, K ]]And the number of the target azimuth angles is K.
In one embodiment of the present invention, the matrix form sub-pulse ratio equation is:
Figure BDA0002343270470000043
wherein the function matrix p of the sub-pulse directional diagramk＝[Pk(θ1) Pk(θ2) … Pk(θK)]TProportional matrix of subpulse
Figure BDA0002343270470000044
Target orientation emission energy matrix β ═ β1β2… βK]T。
In one embodiment of the present invention, constructing a transmit waveform matrix according to the matrix form sub-pulse proportion equation comprises:
converting the matrix type sub-pulse proportion equation into a sub-pulse number form:
Figure BDA0002343270470000045
wherein ,αkIs the kth sub-pulse number, L is the total pulse number,
Figure BDA0002343270470000046
is the ratio of the kth sub-pulse, and the value range of K is [1, K]，[·]Rounding operation is performed for rounding;
constructing a transmitting waveform matrix according to the number form of the sub-pulses:
Figure BDA0002343270470000047
wherein X is a transmit waveform matrix, XkIs the k-th sub-pulse x.
The invention has the beneficial effects that:
first, the invention simplifies waveform optimization into a design of limited sub-pulses, and solves a cost function by using the proposed fast MM algorithm, so that each sub-pulse beam has a main lobe and forms a notch in an interference orientation. Since each sub-pulse is uncorrelated, it can be generated in parallel. And further provides a sub-pulse combination distribution method, and the generated sub-pulses can be quickly synthesized into a required transmitting waveform matrix.
Secondly, aiming at a multi-target scene, the multi-beam interference source system can synthesize multi-beam waveforms, can generate a deeper notch in the direction of an interference source while irradiating all targets, and effectively reduces the interception probability and the reflection power of the interference source.
Thirdly, in order to maintain the constant modulus characteristic, each sub pulse is subjected to constant modulus constraint, and the finally synthesized radar transmitting waveform also has the constant modulus characteristic, so that the synthesized transmitting waveform has the constant modulus characteristic. In the actual operation of the radar, in order to ensure the maximum working efficiency of each array element transmitting power amplifier, the transmitting waveform is required to have constant modulus characteristics, so that the radar transmitting waveform generated by the invention can ensure the maximum working efficiency of each array element transmitting power amplifier.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a schematic flowchart of a method for synthesizing a tracking waveform of a fast constant modulus MIMO radar for interference suppression according to an embodiment of the present invention;
fig. 2 is a transmission directional diagram of a radar transmission waveform synthesized by a simulation experiment of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to an embodiment of the present invention;
fig. 3 is a sub-pulse emission directional diagram obtained by a simulation experiment of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to an embodiment of the present invention;
fig. 4 is an amplitude diagram of a radar array element emission waveform obtained by a simulation experiment of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Referring to fig. 1, fig. 1 is a schematic flow chart of a method for synthesizing a tracking waveform of a fast constant modulus MIMO radar for interference suppression according to an embodiment of the present invention, including:
acquiring a plurality of target azimuth angles, a plurality of interference azimuth angles and a plurality of target direction energy distribution proportions corresponding to the target azimuth angles;
substituting the interference azimuth angle into an interference steering vector formula to obtain an interference airspace steering vector;
constructing an interference subspace matrix according to the interference airspace guide vector;
substituting the target azimuth angle and the interference subspace matrix into a first cost function to obtain a plurality of sub-pulse functions;
solving the plurality of sub-pulse functions to obtain a plurality of sub-pulses;
constructing a plurality of sub-pulse proportion equations according to the energy distribution proportions of the target directions, and converting the sub-pulse proportion equations into a matrix form to obtain a matrix form sub-pulse proportion equation;
and constructing a transmitting waveform matrix according to the matrix form sub-pulse proportion equation.
First, the invention simplifies waveform optimization into a design of limited sub-pulses, and solves a cost function by using the proposed fast MM algorithm, so that each sub-pulse beam has a main lobe and forms a notch in an interference orientation. Since each sub-pulse is uncorrelated, it can be generated in parallel. And further provides a sub-pulse combination distribution method, and the generated sub-pulses can be quickly synthesized into a required transmitting waveform matrix.
Secondly, aiming at a multi-target scene, the multi-beam interference source system can synthesize multi-beam waveforms, can generate a deeper notch in the direction of an interference source while irradiating all targets, and effectively reduces the interception probability and the reflection power of the interference source.
Thirdly, in order to maintain the constant modulus characteristic, each sub pulse is subjected to constant modulus constraint, and the finally synthesized radar transmitting waveform also has the constant modulus characteristic, so that the synthesized transmitting waveform has the constant modulus characteristic. In the actual operation of the radar, in order to ensure the maximum working efficiency of each array element transmitting power amplifier, the transmitting waveform is required to have constant modulus characteristics, so that the radar transmitting waveform generated by the invention can ensure the maximum working efficiency of each array element transmitting power amplifier.
In one embodiment of the present invention, the interference steering vector formula is:
Figure BDA0002343270470000071
wherein ,a(θi) For the ith interference azimuth angle thetaiThe value range of i is [1, J]J is the number of interference azimuth angles, exp is exponential operation with natural constant as base, J is an imaginary number, d is the distance between radar antenna array elements, N is the serial number of the radar antenna array elements, and the value range of N is [0, N-1 ]]N is the total number of the radar antenna elements, sin is sine, and lambda is the wavelength of the radar emission signal.
In an embodiment of the present invention, the interference subspace matrix expression is:
J＝[a(θj)]，
wherein J is an interference subspace matrix, [ alpha ], [ alpha]For matrixing operation, a (θ)i) Is as followsi interference azimuth angles thetaiThe value range of i is [1, J]And J is the number of interference azimuths.
In one embodiment of the invention, the first cost function is:
Figure BDA0002343270470000072
wherein w is a weighting parameter, xkFor the kth sub-pulse, (.)HTo perform a conjugate transpose operation on the matrix, J is the interference subspace matrix,
Figure BDA0002343270470000073
for the k-th target azimuth angle thetakTarget space vector of (a) ([ theta ])kIs the kth target azimuth angle, and the value range of K is [1, K]The target azimuth angle has K, xnkFor the k sub-pulse xkN is the serial number of the radar antenna array element, and the value range of N is [0, N-1 ]]N is the total number of the array elements of the radar antenna, and j is an imaginary number.
In one embodiment of the present invention, the sub-pulse ratio equation is:
Figure BDA0002343270470000081
wherein ,
Figure BDA0002343270470000082
is the proportion of the jth sub-pulse, Pk(θk) As a function of the pattern of the kth sub-pulse, βkFor the k-th target azimuth angle thetakK has a value in the range of [1, K ]]And the number of the target azimuth angles is K.
In one embodiment of the present invention, the matrix form sub-pulse ratio equation is:
Figure BDA0002343270470000083
wherein, the function matrix pk of the sub-pulse directional diagram is [ P ═ Pk(θ1) Pk(θ2) … Pk(θK)]TProportional matrix of subpulse
Figure BDA0002343270470000084
Target orientation emission energy matrix β ═ β1β2… βK]T。
In one embodiment of the present invention, constructing a transmit waveform matrix according to the matrix form sub-pulse proportion equation comprises:
converting the matrix type sub-pulse proportion equation into a sub-pulse number form:
Figure BDA0002343270470000085
wherein ,αkIs the kth sub-pulse number, L is the total pulse number,
Figure BDA0002343270470000086
is the ratio of the kth sub-pulse, and the value range of K is [1, K]，[·]Rounding operation is performed for rounding;
constructing a transmitting waveform matrix according to the number form of the sub-pulses:
Figure BDA0002343270470000087
wherein X is a transmit waveform matrix, XkIs the k-th sub-pulse x.
Further, the steps of solving to obtain a plurality of sub-pulses are as follows:
(1) initializing a sub-pulse iteration value x(0)Construct the second cost function L wJJH-a(θk)aH(θk)，
(2) Estimating an upper bound λ of a second cost function from said second cost functionu(L) and constructing an intermediate variable M, M ═ λ, from the upper bound of said second cost functionu(L)I，
Figure BDA0002343270470000091
wherein ,λmin(L) is the minimum of the second cost function, λmax(L) is the maximum of the second cost function, I is the feature vector, t is the number of iterations, t is 0, where y and s are intermediate variables,
Figure BDA0002343270470000092
n is the order of the second cost function;
(3) computing
Figure BDA0002343270470000093
wherein ,
Figure BDA0002343270470000094
Figure BDA0002343270470000095
q, v, α is an intermediate variable, and angle () is a phase operation, | | | u2To operate in 2 norms, (.)HPerforming conjugate transpose operation on the matrix;
(4) when (x)(t+1))HLx(t+1)＞(x(t))HLx(t)If α is equal to (α -1)/2, jumping to the step (3), otherwise, proceeding to the next step;
(5) when | x(t+1)-x(t)If | < epsilon, outputting x; otherwise, let t be t +1 and jump to step (3)
The effect of the present invention will be further described with reference to the simulation data.
1. Simulation conditions are as follows:
the simulation running system is an Intel (R) core (TM) i7-2600 CPU 650@3.40GHz 32-bit Windows operating system, and simulation software adopts MATLAB (R2012 b).
2. Simulation data and result analysis:
the parameters of the simulation experiment of the invention are set as that the total number of radar array elements is 32, the spacing between the radar antenna array elements is 0.5 mm, the wavelength of radar emission signals is 1 mm, the total number of interference sources is 2, the azimuth angles of the interference sources are respectively-59.5 degrees and 20.5 degrees, the total number of targets is 3, the azimuth angles of the targets are respectively-35 degrees, 0 degrees and 45 degrees, and the power distribution is 1:1: 1.
Referring to fig. 2, fig. 2 is a transmitting direction diagram of a radar transmitting waveform synthesized by a simulation experiment according to a method for synthesizing a fast constant modulus MIMO radar tracking waveform for interference suppression provided by an embodiment of the present invention. The abscissa in fig. 2 represents the airspace azimuth angle, the range of the azimuth angle is [ -90 degrees, 90 degrees ], and the ordinate represents the power gain of the radar transmission waveform synthesized by the simulation experiment at each airspace azimuth angle, and the unit is dB. And drawing the power gain of the radar transmitting waveform synthesized by the simulation experiment at each airspace azimuth to obtain the transmitting directional diagram of the radar transmitting waveform synthesized by the simulation experiment.
The power gain of the radar transmitting waveform synthesized by the simulation experiment at each airspace azimuth is obtained by the following formula:
P(θ)＝a(θ)HXXHa(θ)，
p (theta) represents the power gain of a radar transmitting waveform synthesized in a simulation experiment at an airspace azimuth angle theta, a (theta) represents an airspace guide vector at the airspace azimuth angle theta, H represents a conjugate transpose operation, and X is a multi-input multi-output constant-modulus transmitting waveform matrix synthesized in the simulation experiment.
As can be seen from FIG. 2, the radar has stronger power gain of 25dB at the target azimuth angles of-35 degrees, 0 degrees and 45 degrees and only weak power gains of-34 dB and-38 dB at the interference source azimuth angles of-59.5 degrees and 20.5 degrees, so that the radar transmission waveform synthesized by the method has an anti-interference function.
Referring to fig. 3 and 4, fig. 3 is a sub-pulse emission directional diagram obtained by a simulation experiment of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to an embodiment of the present invention, and fig. 4 is an amplitude diagram of an emission waveform of each array element of a radar obtained by a simulation experiment of a fast constant modulus MIMO radar tracking waveform synthesis method for interference suppression according to an embodiment of the present invention. And taking the amplitude values of each row of elements in the multi-input multi-output constant modulus transmission waveform matrix synthesized by the simulation experiment as the amplitude values of the transmission waveforms of each array element of the radar, and drawing the corresponding amplitude of each array element of the radar to obtain an amplitude chart of the transmission waveforms of each array element of the radar.
In fig. 3, the abscissa represents the number of radar array elements, the value range is [1,32], and the ordinate represents the amplitude value of the waveform transmitted by the corresponding array element. As can be seen from fig. 3, the transmitting waveforms of the array elements of the radar are equal in amplitude and are all 1. Therefore, the synthesized transmitting waveform has constant modulus characteristic, and the maximum working efficiency of each array element transmitting power amplifier can be ensured.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (7)

1. A method for synthesizing a tracking waveform of a fast constant modulus MIMO radar aiming at interference suppression is characterized by comprising the following steps:
acquiring a plurality of target azimuth angles, a plurality of interference azimuth angles and a plurality of target direction energy distribution proportions corresponding to the target azimuth angles;
substituting the interference azimuth angle into an interference steering vector formula to obtain an interference airspace steering vector;
constructing an interference subspace matrix according to the interference airspace guide vector;
substituting the target azimuth angle and the interference subspace matrix into a first cost function to obtain a plurality of sub-pulse functions;
solving the plurality of sub-pulse functions to obtain a plurality of sub-pulses;
constructing a plurality of sub-pulse proportion equations according to the energy distribution proportions of the target directions, and converting the sub-pulse proportion equations into a matrix form to obtain a matrix form sub-pulse proportion equation;
and constructing a transmitting waveform matrix according to the matrix form sub-pulse proportion equation.
2. The method of claim 1, wherein the interference steering vector formula is:
Figure FDA0002343270460000011
wherein ,a(θi) For the ith interference azimuth angle thetaiThe value range of i is [1, J]J is the number of interference azimuth angles, exp is exponential operation with natural constant as base, J is an imaginary number, d is the distance between radar antenna array elements, N is the serial number of the radar antenna array elements, and the value range of N is [0, N-1 ]]N is the total number of the radar antenna elements, sin is sine, and lambda is the wavelength of the radar emission signal.
3. The method of claim 1, wherein the interference subspace matrix expression is:
J＝[a(θj)]，
wherein J is an interference subspace matrix, [ alpha ], [ alpha]For matrixing operation, a (θ)i) For the ith interference azimuth angle thetaiThe value range of i is [1, J]And J is the number of interference azimuths.
4. The method of claim 1, wherein the first cost function is:
Figure FDA0002343270460000021
wherein w is a weighting parameter, xkFor the kth sub-pulse, (.)HTo perform a conjugate transpose operation on the matrix, J is the interference subspace matrix,
Figure FDA0002343270460000022
for the k-th target azimuth angle thetakTarget space vector of (a) ([ theta ])kIs the kth target azimuth angle, and the value range of K is [1, K]The target azimuth angle has K, xnkFor the k sub-pulse xkN is the serial number of the radar antenna array element, and the value range of N is [0, N-1 ]]N is the total number of the array elements of the radar antenna, and j is an imaginary number.
5. The method of claim 1, wherein the sub-pulse ratio equation is:
Figure FDA0002343270460000023
wherein ,
Figure FDA0002343270460000024
is the proportion of the jth sub-pulse, Pk(θk) As a function of the pattern of the kth sub-pulse, βkFor the k-th target azimuth angle thetakK has a value in the range of [1, K ]]And the number of the target azimuth angles is K.
6. The method of claim 5, wherein the matrix form subpulse proportion equation is as follows:
Figure FDA0002343270460000025
wherein the function matrix p of the sub-pulse directional diagramk＝[Pk(θ1) Pk(θ2)…Pk(θK)]TProportional matrix of subpulse
Figure FDA0002343270460000026
Target orientation emission energy matrix β ═ β1β2…βK]T。
7. The method of claim 1, wherein constructing a transmit waveform matrix according to the matrix form sub-pulse proportion equation comprises:
converting the matrix type sub-pulse proportion equation into a sub-pulse number form:
Figure FDA0002343270460000031
wherein ,αkIs the kth sub-pulse number, L is the total pulse number,
Figure FDA0002343270460000032
is the ratio of the kth sub-pulse, and the value range of K is [1, K]，[·]Rounding operation is performed for rounding;
constructing a transmitting waveform matrix according to the number form of the sub-pulses:
Figure FDA0002343270460000033
wherein X is a transmit waveform matrix, XkIs the k-th sub-pulse x.
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