CN111352080A - Design method of low-interception frequency-controlled array MIMO radar system under constraint of PAPR and similarity - Google Patents

Design method of low-interception frequency-controlled array MIMO radar system under constraint of PAPR and similarity Download PDF

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CN111352080A
CN111352080A CN202010404534.6A CN202010404534A CN111352080A CN 111352080 A CN111352080 A CN 111352080A CN 202010404534 A CN202010404534 A CN 202010404534A CN 111352080 A CN111352080 A CN 111352080A
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papr
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CN111352080B (en
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巩朋成
谭海明
王兆彬
邓薇
朱鑫潮
周顺
李婕
张正文
丰励
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Hubei University of Technology
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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
    • G01S7/023—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
    • G01S7/28—Details of pulse systems
    • G01S7/282—Transmitters
    • 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
    • G01S7/35—Details of non-pulse systems

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Abstract

The invention discloses a design method of a low-interception frequency-controlled array MIMO radar system under the constraint of PAPR and similarity, which comprises the following steps: s0: constructing an optimization problem, initializing the external loop iteration times and the internal loop iteration times, and randomly initializing a transmitting waveform matrix; s1: fixing a current emission waveform matrix, solving an optimization problem by using an MVDR method, and calculating a receiving filter; s2: fixing a receiving filter under the iteration, calculating and updating a transmitting waveform vector based on an alternative direction multiplier method and an active set method; s3: and repeating the steps S1-S2 until an iteration end condition is reached. The invention considers clutter, interference and noise environment and the condition that the emission waveform meets PAPR and similarity, constructs the optimization problem into a multi-proportion fractional programming problem, and jointly optimizes the emission signal by using a cyclic iteration method, ADMM and ASM.

Description

Design method of low-interception frequency-controlled array MIMO radar system under constraint of PAPR and similarity
Technical Field
The invention belongs to the technical field of array signal processing, and particularly relates to a design method of a low-interception frequency-controlled array MIMO radar system under the constraint of PAPR and similarity.
Background
In modern electronic countermeasure, the increasingly variable and complex radar electromagnetic environment puts new requirements on low interception technology, and a radar system is expected to adjust various parameter indexes of a transmitting end in real time according to changes of targets and the environment so as to achieve better low interception effect. The Low Probability of Interception (LPI) radar can detect a target and reduce the probability of being found by an enemy, thereby providing guarantee for the safety of the radar and a carrier thereof, and the research on the LPI radar and the realization technology thereof is increasingly urgent, and the key point is that the enemy cannot obtain the radiation energy emitted by the radar through an effective technology.
The research of the low-interception technology on the radar transmitting end mainly comprises three aspects: 1) dispersing energy in a frequency domain, and designing an ultra-wideband waveform; 2) dispersing energy in a time domain, and designing a waveform with a high duty ratio; 3) energy is dispersed in a spatial domain, and a wider main lobe of an antenna radiation pattern is designed.
The concept of MIMO (Multiple-Input Multiple-Output) radar was introduced in 2003, and a large number of scholars have intensively studied about their key technologies and related aspects. Compared with a phased array, the MIMO radar forms a low-gain wide beam in space through a waveform diversity technology, so that the probability of radar interception can be reduced. Since target detection and parameter estimation rely on an output signal-to-noise ratio (SCNR), in recent years, MIMO radar designs have been focused on maximizing the output SCNR. The design of joint transmission and reception is mainly divided into two categories: one is by jointly designing the transmit waveform and receive filter such that the output SINR is maximized. The other is by designing joint transmit and receive beamforming such that the output SCNR is maximized.
Frequency-controlled array (FDA) technology, the array factor of which is a function of angle, time, and distance, is one of the latest radar technologies; different from the characteristic that the phased array wave beam does not depend on distance parameters, the frequency control array is mainly characterized in that an array directional diagram has distance dependency and can effectively control the distance direction of the transmitted wave beam.
Therefore, the frequency control array and the MIMO technology are applied to the LPI radar, the signal energy of the transmitting beam can form smaller energy radiation in the interested area, and meanwhile, the peak power of the transmitting signal is reduced by widening the width of the transmitting beam, so that a new thought is provided for reducing the interception of the radar.
Disclosure of Invention
The invention aims to consider the constraints of PAPR and similarity under a clutter environment, and provides a design method of a low-interception frequency-controlled array MIMO radar system under the constraints of PAPR and similarity.
The idea of the invention is as follows:
the method comprises the steps of optimizing double targets by minimizing the emission energy radiation of the MIMO radar and maximizing the output SCNR, and converting the double-target optimization into a multi-component planning problem with PAPR and similarity constraint by using a weighted summation method; and then converting the optimization problem into two sub-optimization problems by using a loop iteration method: when the transmitted wave form is fixed, the MVDR method (adaptive wave beam forming method) is utilized to solve the receiving filter; when the receiving filter is fixed, the optimization problem is converted into a plurality of variables to be solved by using an ADMM method (alternating direction multiplier method), and the transmitting waveform is solved by using an ASM (effective ensemble method).
The technical scheme of the invention is as follows:
the design method of the low interception frequency control array MIMO radar system under the constraint of PAPR and similarity provided by the invention comprises the following steps:
s0: building optimization problems
Figure BDA0002490785590000021
Initializing the external loop iteration number k to 0, initializing the internal loop iteration number n to 0, and randomly initializing the transmission waveform matrix S and recording the transmission waveform matrix S as
Figure BDA0002490785590000022
sm 0Represents the initial value of the transmitting waveform vector corresponding to the mth transmitting antenna, wherein M is 1,2, … Mt；s＝vec(S)；
Wherein: omegapIs the weighting of the p-th objective function, ωp∈[0,1]And satisfy
Figure BDA0002490785590000023
P (S) is the space transmitting power of the transmitting signal, and SCNR (x, S) is the output signal-to-noise ratio of the receiving end signal after passing through a receiving filter; PAPR(s) denotes the PAPR constraint, s0Represents the reference waveform, σ and ξ represent the control parameters;
s1: fixing the current emission waveform matrix, solving the optimization problem by using an MVDR method, and calculating a receiving filter
Figure BDA0002490785590000024
The currently calculated receive filter, i.e. the receive filter at the k iteration, is denoted xk；
Wherein: w1Is defined as:
Figure BDA0002490785590000025
Figure BDA0002490785590000026
represents Mt×MtThe identity matrix of (1); v (r, θ) is defined as: the steering vector of the virtual array is,
Figure BDA0002490785590000027
b (theta) represents the steering vector of the receiving antenna array, and a (r, theta) represents the steering vector of the transmitting antenna array;
Rcjeis defined as: rcje＝Rc+Rj+ReWherein R isc，RjAnd ReRespectively a clutter covariance matrix, an interference covariance matrix and a noise covariance matrix;
at the kth outer loop iteration, step S2 is performed:
s2: fixing the receiving filter x under this iterationkCalculating and updating a transmitting waveform vector s based on an alternating direction multiplier method and an active set method;
knowing the current iteration value
Figure BDA0002490785590000031
The parameter with the superscript n represents the parameter value at the beginning of the nth inner loop iteration; the method further comprises the following steps:
s201: updating the auxiliary variable hrThe method further comprises the following steps:
s201 a: constructing an objective function in real form
Figure BDA0002490785590000032
t1,r,t2,r,s0,r,sr,RA,r,Rcvx,r,Rvx,r,En,rRespectively represent t1,t2,s0,s,RA,Rcvx,Rvx,EnA real numerical form of;
parameter t1And t2Is defined as:
Figure BDA0002490785590000033
wherein R isA、Rcvx、RvxAre respectively defined as:
Figure BDA0002490785590000034
Figure BDA0002490785590000035
Figure BDA0002490785590000036
s201 b: under the ADMM framework, by introducing the variable z1,r,z2,r,ur,vrConverting the target function to an augmented Lagrange function ft,r(sr,hr,t1,r,t2,r,z1,r,z2,r,ur,vr) So as to obtain the objective function:
Figure BDA0002490785590000037
where ρ is1,ρ2,ρ3,ρ4Are punishment parameters which are all larger than 0; rAtIs defined as: rAt＝RA-t1/MtEt；RxtIs defined as: rxt＝Rcvx-t2Rvx；RAt,r、Rxt,rEach represents RAt、RxtA real numerical form of;
s201 c: the objective function in S201b is constructed into a standard ASM form:
Figure BDA0002490785590000041
legal solution of h using active setrH obtained by this solutionrIs marked as
Figure BDA0002490785590000042
Wherein, Q, p, αi,biAre auxiliary variables, defined as follows:
Figure BDA0002490785590000043
Figure BDA0002490785590000044
Figure BDA0002490785590000045
Figure BDA0002490785590000046
s202: knowing the value of the iteration
Figure BDA0002490785590000047
Will f ist,r(sr,hr,t1,r,t2,r,z1,r,z2,r,ur,vr) The following objective function is converted:
Figure BDA0002490785590000048
constructing the objective function into a standard ASM form, and solving for s by using an effective set methodrS obtained by this solutionrIs marked as
Figure BDA0002490785590000049
S203: knowing the value of the iteration
Figure BDA00024907855900000410
Will f ist,r(sr,hr,t1,r,t2,r,z1,r,z2,r,ur,vr) The following objective function is converted:
Figure BDA00024907855900000411
order to
Figure BDA00024907855900000412
Solving for t1,rAnd t2,rT obtained by this solution1,rAnd t2,rIs marked as
Figure BDA00024907855900000413
And
Figure BDA00024907855900000414
s204: knowing the value of the iteration
Figure BDA0002490785590000051
Solving for { z using the following equation1,r,z2,r,ur,vrSolving { z } obtained by the solving at this time1,r,z2,r,ur,vrIs recorded as
Figure BDA0002490785590000052
Figure BDA0002490785590000053
S205: repeating the iteration S201 to S204 until the iteration number reaches the preset maximum internal loop iteration number, and outputting the last SrThen, step S3 is executed; (ii) a
S3: and (5) repeating the steps S1-S2 until the iteration number reaches the preset maximum external loop iteration number or | SINR (signal to interference plus noise ratio)(k+1)-SINR(k)|/SINR(k)< ε, wherein ε >)0。
Further, the spatial transmit power p(s) is defined as:
Figure BDA0002490785590000054
wherein the content of the first and second substances,
Figure BDA0002490785590000055
which is the steering vector of the transmit array;
Figure BDA00024907855900000512
the phase difference is represented by a phase difference,
Figure BDA0002490785590000056
c denotes the speed of light, dtIndicating the array element spacing of the transmit array.
Further, the PAPR constraint is defined as:
Figure BDA0002490785590000057
where L represents the number of interfering signals.
Further, a clutter covariance matrix
Figure BDA0002490785590000058
Interference covariance matrix
Figure BDA0002490785590000059
Covariance matrix of noise
Figure BDA00024907855900000510
Wherein:
q represents the number of clutter scatterers, Q represents the qth clutter scatterer;
for distance and angle discrimination from the target, r is usedc,qAnd thetac,qRepresents the sum of distances at the q-th clutterThe angle of the angle is set to be,
Figure BDA00024907855900000511
represents the covariance of the qth clutter;
l represents the number of interference signals from different directions, L represents the ith interference signal; also for angular discrimination from the target, θj,lRepresents the angle at the ith interference;
Figure BDA0002490785590000061
represents the covariance of the ith interfering signal; i isKAn identity matrix representing K × K, b (theta)j,l) A steering vector representing the l interference signal on the receiving antenna array;
Figure BDA0002490785590000062
represents the covariance of the noise;
Figure BDA0002490785590000064
represents MrK×MrAn identity matrix of order K.
Further, the formula for calculating the signal to interference plus noise ratio is as follows:
Figure BDA0002490785590000063
the invention has the following advantages and beneficial effects:
the invention utilizes an ADMM method and combines a frequency control array technology, takes the minimization of the emission energy radiation and the maximization of the target detection of the MIMO radar as double optimization targets, constructs the optimization problem into a multi-proportion fractional programming problem under the condition that clutter, interference and noise environments and emission waveforms meet PAPR and similarity, and utilizes a cyclic iteration method, an ADMM and an ASM to jointly optimize emission signals. The invention realizes target detection while reducing the probability of interception of the radar by designing the transmitted signal to form null on the target area.
Drawings
FIG. 1 is a comparison of objective functions and iteration times under different PAPR and different similarity constraints in a simulation test, wherein (a) is a comparison of objective functions and iteration times under different PAPR, and (b) is a comparison of objective functions and iteration times under different similarity constraints;
fig. 2 is a transmission directional diagram under different PAPR and different similarity constraints in a simulation test, in which (a) is a transmission directional diagram in an angle dimension, and (b) is a transmission directional diagram in a distance dimension;
fig. 3 is a receiving directional diagram under different PAPR and different similarity constraints in a simulation test, in which (a) is a transmitting directional diagram in an angle dimension, and (b) is a transmitting directional diagram in a distance dimension;
fig. 4 is a receiving directional diagram of a transmitting waveform at different positions under different PAPR and different similarity constraints in a simulation experiment, in which (a) is a receiving directional diagram in an angular dimension of 25m, (b) is a receiving directional diagram in an angular dimension of 75m, and (c) is a receiving directional diagram in a distance dimension of 40 °.
Detailed Description
The following detailed description is given of relevant theories upon which the invention is based and specific implementations such that advantages and features of the invention may be more readily understood by those skilled in the art, and the scope of the invention is more clearly and clearly defined.
(I) Signal model construction
Consider a model of a narrow band frequency controlled array MIMO radar system, the array of which consists of MtA transmitting antenna and MrA receiving antenna, each antenna transmitting different signals si(l),i＝1,2,…,MtL is 1,2, …, L, where L is the number of samples. MtThe matrix of the transmitting waveform of sampling L points on each transmitting antenna is S ═ S (1), S (2), …, S (L)]TWherein (·)TIndicating a transpose operation, let its vector form be s ═ vec(s). Let carrier frequency f on mth antennam＝f0+(m-1)Δf，f0Is the carrier frequency of the 1 st array element, Δ f is the frequency increment, let f be0＜＜Δf，K≤Mt。
Considering the received signal at angle θ, at a distance r from the 1 st array element of the transmit array, under far field conditions, as:
aT(r,θ)S (1)
wherein the content of the first and second substances,
Figure BDA0002490785590000071
is the steering vector of the transmit array, where,
Figure BDA00024907855900000710
can be expressed as:
Figure BDA0002490785590000072
in the formula (2), c represents the speed of light, dtIndicating the array element spacing of the transmit array.
Doppler shift of scatterers is not considered temporarily, and only for a static target, a transmitted signal is scattered and reflected by the target, and a received signal Y is subjected to down-conversion and matched filtering at a receiving endsCan be expressed as:
Ys＝β(r,θ)b(θ)aT(r,θ)S (3)
in formula (3):
(·)Hrepresents a conjugate transpose;
β (r, theta) represents the target scatterer amplitude at angle theta, at a distance r from the 1 st element of the transmit array;
b (θ) represents a reception steering vector at an angle θ, and in this embodiment, the reception antenna employs a phased array, so b (θ) is defined as:
Figure BDA0002490785590000073
in the formula (4), drIs the array element spacing of the receive array.
Stacking the received signals, converting the matrix form of equation (3) into vector form ysNamely:
Figure BDA0002490785590000074
in formula (5):
vec (-) denotes the operation of transforming a matrix into a vector;
Figure BDA0002490785590000075
represents the Kronecker product;
Figure BDA0002490785590000076
represents Mr×MrAn identity matrix of order;
Figure BDA0002490785590000077
is a transmit waveform matrix S and an identity matrix
Figure BDA0002490785590000078
The Kronecker product of
Figure BDA0002490785590000079
v (r, θ) is defined as the steering vector of the "virtual array", i.e. the
Figure BDA0002490785590000081
The echo signals received by the frequency control array MIMO radar are considered to contain clutter signals coherent with target signals, interference signals and noise signals besides the target signals of interest. Assuming that Q clutter scatterers exist, the clutter signal y received by the radarcComprises the following steps:
Figure BDA0002490785590000082
in formula (6):
q represents the qth clutter scatterer, Q is 1,2, …, Q;
β for discrimination from the magnitude, distance and angle of the targetc,q、rc,q、θc,qRespectively represent (r)c,q,θc,q) The amplitude, distance and angle of the qth clutter scatterer;
(rc,q,θc,q) Represents the position of the qth clutter scatterer: the angle of the 1 st array element relative to the transmitting array is thetac,qA distance of rc,q。
Meanwhile, if there are L interference signals from different directions, the received interference signal yjExpressed as:
Figure BDA0002490785590000083
in formula (7):
βj,land thetaj,lRespectively represent the amplitude and angle information of the first interference signal, and βj,lObedience mean is zero and covariance is
Figure BDA0002490785590000084
Of circularly symmetric Gaussian distribution of]Expressing a mathematical expectation;
dj,lrepresenting a random vector containing the interfering signal and obeying a zero-mean gaussian distribution.
Therefore, under the condition that clutter signals, interference signals and noise exist, the total received signal y of the frequency control array MIMO radar receiving end is:
y＝ys+yc+yj+e (8)
in equation (8), e is complex gaussian noise with a mean value of zero.
(II) description of the problems
If the receiving filter x is set, the output SCNR of the receiving end signal after passing through the filter is:
Figure BDA0002490785590000085
in formula (9):
Figure BDA0002490785590000086
represents the covariance of the desired target signal,
Figure BDA0002490785590000087
Rc，Rjand ReClutter covariance matrix, interference covariance matrix, and noise covariance matrix, respectively, are expressed as follows:
Figure BDA0002490785590000091
Figure BDA0002490785590000092
Figure BDA0002490785590000093
wherein the content of the first and second substances,
Figure BDA0002490785590000094
the covariance of the clutter is represented as,
Figure BDA0002490785590000095
at the same time, in combination with formula aT(r, θ) S, defining the spatial transmit power p (S) of the transmit signal at the target (r, θ) as:
Figure BDA0002490785590000096
in the formula (10), | · non-woven phosphor2Representing the matrix 2 norm.
In the invention, under the constraint of PAPR and similarity, a transmitting waveform and a receiving filter are designed in a combined manner, so that the SCNR is maximally output while the radiation power at a target is minimized, and the following optimization problems can be obtained:
Figure BDA0002490785590000097
ωpthe optimal value is obtained by adjusting the value of the empirical value through a simulation experiment.
Wherein s is0Representing the reference waveform, σ and ξ represent the control parameters, which are empirical values, and the 1 st constraint is the PAPR constraint, which is defined as:
Figure BDA0002490785590000098
where s (n) denotes the nth sample point of s.
The 2 nd constraint in equation (11) represents a similarity constraint, which can be expressed as:
(s-s0)HEn(s-s0)≤ξ2(12b)
En(s-s0) Is a custom function, which is defined as follows:
Figure BDA0002490785590000099
for equation (11), the optimization problem is transformed into two sub-optimization problems using a loop iteration method:
when the transmission waveform matrix S is fixed, solving a receiving filter x by using an MVDR method (adaptive beamforming method); when x is fixed, the optimization problem is converted into a plurality of variables to be solved by using an ADMM method (alternating direction multiplier method), and the emission waveform matrix S is solved by using an ASM (effective aggregation method).
The solving process of the two sub-optimization problems will be described in detail below.
First, when the transmit waveform matrix S is fixed, the objective function at this time is converted into:
Figure BDA0002490785590000101
the objective function (13a) is solved by using an MVDR method, and the optimization solution is as follows:
Figure BDA0002490785590000102
wherein, for convenience of representation, are defined separately
Figure BDA0002490785590000103
Rcje＝Rc+Rj+Re。
And a second part, solving S by using an ADMM method when the receiving filter x is fixed.
To solve equation (11) efficiently, two parameters t are defined1And t2Which are respectively as follows:
Figure BDA0002490785590000104
for convenience of presentation, R is defined separatelyA、Rcvx、Rvx；
Figure BDA0002490785590000105
Figure BDA0002490785590000106
Figure BDA0002490785590000107
P denotes a switching matrix, X is a matrix formed by reception filters, i.e., X ═ vec (X), a (r, θ) ═ a (r, θ) aH(r,θ)。
At this time, the objective function equation (11) can be converted into:
Figure BDA0002490785590000108
to solve equation (15), equation (15) is first converted to real-valued form:
Figure BDA0002490785590000111
wherein, t1,r,t2,r,s0,r,sr,RA,r,Rcvx,r,Rvx,r,En,rRespectively represent t1,t2,s0,s,RA,Rcvx,Rvx,EnIn real-valued form.
It should be noted that, not only here, but in the present invention, the parameter X has the subscript r*.rThe meaning of which are all indicated for the parameter X*In real-valued form.
To obtain an efficient solution of equation (16), an auxiliary variable h is introducedrAnd let hr＝srFormula (16) to:
Figure BDA0002490785590000112
equation (17) is solved using a scaled version of the ADMM method. In the framework of ADMM, by introducing the variable z1,r,z2,r,ur,vrThe equality constraint can be translated into an augmented lagrange function, which is the following for equation (17):
Figure BDA0002490785590000113
in the formula (18), p1,ρ2,ρ3,ρ4More than 0 are punishment parameters which are experience values; for convenience of representation, let: rAt,r＝RA,r-t1，Rxt,r＝Rcvx,r-t2Rvx,r。
Then, equation (18) is converted into:
Figure BDA0002490785590000121
solving the formula (19) by using a loop iteration method based on an ADMM method, wherein the loop iteration is recorded as an inner loop, and the solving process comprises the following steps in the (n +1) th iteration:
1) knowing the value of the nth iteration
Figure BDA0002490785590000122
Solving for
Figure BDA0002490785590000123
Ignoring the constant part, the optimization problem transforms to:
Figure BDA0002490785590000124
equation (2) is solved using the Active Set Method (ASM), and then equation (17) is written in the form of a standard ASM:
Figure BDA0002490785590000125
in the formula (21), c is a constant, and the set Φ is {1, …,2M ═tL}。
For convenience, let Q, p, αi,biRespectively as follows:
Figure BDA0002490785590000126
Figure BDA0002490785590000127
Figure BDA0002490785590000128
Figure BDA0002490785590000129
2) knowing the value of the iteration
Figure BDA00024907855900001210
Solving for
Figure BDA00024907855900001211
The optimization problem (18) is converted into:
Figure BDA0002490785590000131
similar to
Figure BDA0002490785590000132
The solving process (26) is carried out by using the effective set legal solution.
3) Knowing the value of the iteration
Figure BDA0002490785590000133
In the case of (2), solve for { t }1,r,t2,r}。
The optimization problem (18) translates into:
Figure BDA0002490785590000134
in the same way, make
Figure BDA0002490785590000135
The following can be obtained:
Figure BDA0002490785590000136
Figure BDA0002490785590000137
4) knowing the value of the iteration
Figure BDA0002490785590000138
Solving for { z1,r,z2,r,ur,vr}。
Figure BDA0002490785590000139
Figure BDA00024907855900001310
Figure BDA00024907855900001311
Figure BDA00024907855900001312
Based on the solution thought, the following steps are given to the design method of the low-interception FDA-MIMO radar under the constraint of PAPR and similarity:
s0: the step is an initial step, and supposing that the external iteration times and the internal iteration times of the design method are respectively represented by k and n, the initialized external loop iteration times k is 0, the initialized internal loop iteration times n is 0, and a random initialization transmitting waveform matrix S is recorded as
Figure BDA00024907855900001313
sm 0Denotes the initial value of the beam vector of the transmission waveform corresponding to the mth transmission antenna, where M is 1,2, … Mt。
S1: fixing the current transmit waveform matrix using the function of equation (13b)
Figure BDA0002490785590000141
Calculating a receiving filter x under the k iteration and recording the receiving filter x as the receiving filter xk；
Step S2 is performed at the kth outer loop iteration:
s2: fixing the receiving filter x under this iterationkUpdate RcvxAnd calculates a transmit beam vector s.
Knowing the value of the nth iteration
Figure BDA0002490785590000142
The method further comprises the following steps:
s201: solving for h based on the active set method using equation (21)rH after updaterIs marked as
Figure BDA0002490785590000143
Represents h after the nth iteration update of the inner loopr；
S202: solving for s based on the active set method using equation (26)rWill updated srIs marked as
Figure BDA0002490785590000144
Representing s after the nth iteration update of the inner loopr；
S203: t is updated by equations (28) and (29)1,rAnd t2,rWill updated t1,rAnd t2,rAre respectively marked as
Figure BDA0002490785590000145
And
Figure BDA0002490785590000146
represents t after the nth iteration update of the inner loop1,rAnd t2,r；
S204: using equations (30) to (33), { z is updated1,r,z2,r,ur,vrWill updated { z }1,r,z2,r,ur,vrIs recorded as
Figure BDA0002490785590000147
Represents z after the nth iteration update of the inner loop1,r,z2,r,ur,vr}；
S205: repeating the iteration S201 to S204 until the iteration number reaches the preset maximum internal loop iteration number, and outputting the last SrThen, step S3 is executed; (ii) a
S3: and (5) repeating the steps S1-S2 until the iteration number reaches a preset maximum external loop iteration number or | SCNR |, wherein k is k +1(k+1)-SCNR(k)|/SCNR(k)< ε, wherein ε > 0.
(IV) simulation experiment
In the simulation experiment, the numbers of transmitting antennas and receiving antennas of the frequency control array MIMO radar system are respectively Mt＝6，MrAnd 8, the antenna arrays are arranged according to a uniform linear array, and the interval between the transmitting antennas and the receiving antennas is half wavelength. Carrier frequency f01GHz, frequency increment Δ f 3 MHz. Transmitted energy E on each antenna t1. The sequence length L of the transmitted signal is 16. The reference signal selects the orthogonal LFM signal, which is defined as:
Figure BDA0002490785590000148
wherein, i is 1,2, …, MtL1, 2, …, L, then the reference signal s0＝vec(S0)。
Further, assume that the target signal is located at (50m,10 °), its power is 20 dB; the clutter signals are located at (50m, -50 degrees), (25m,10 degrees) and (75m,40 degrees), and the clutter power is 30 dB; interference signals come from two directions of-30 degrees and 60 degrees respectively, and the power of the interference signals is 35 dB; covariance of Gaussian noise of
Figure BDA0002490785590000149
Considering PAPR constraints of the frequency-controlled array MIMO radar system, σ ═ 1,1.1,1.5, ξ ═ 0.5,1.0,1.2,2.0, respectively, (for convenience of writing, ξ ═ ξ/M is definedtL, where ξ ═ 0.5,1.0,1.2, 2.0.) referring to fig. 1, a comparison of the objective function with the number of iterations under different PAPR and different similarity constraints is given, from fig. 1(a), the objective functions all decrease as the PAPR increases, and after 80 iterations, in both cases σ ═ 1.1 and σ ═ 1.5, the scalar numbers coincide, from fig. 1(b), the objective functions all decrease as the similarity constraint increases.
Fig. 2 shows a comparison of the transmission patterns of the designed transmission waveforms under different PAPR and different similarity constraints. As can be seen from fig. 2(a) and 2(b), the null of the emission pattern at the target increases with increasing similarity constraint under the same PAPR constraint, regardless of the angle dimension or the distance dimension; also, under the same similarity constraint, the null of the transmit pattern at the target increases as the PAPR constraint increases.
Fig. 3 shows a reception pattern comparison of a designed transmit waveform at a target location under different PAPR and different similarity constraints. As can be seen from fig. 3(a) and 3(b), good energy focusing is formed at the target positions (10 ° and 50m), whether in the angular dimension or the distance dimension; nulls of at least-89.5 dB or more are formed at both the clutter positions (-50 deg. and 25m) and the interference positions (-30 deg. and-60 deg.).
Fig. 4 shows a reception pattern comparison of the designed transmission waveform at positions 25m, 75m, and 40 ° under different PAPR and different similarity constraints. As can be seen from fig. 4(a), in the reception pattern in the angular dimension of 25m, the reception pattern forms nulls of-59.5 dB or more at the clutter position (10 °) and the interference positions (-30 ° and-60 °). Similarly, as can be seen from fig. 4(b), in the reception pattern in the angular dimension of 75m, the reception pattern forms nulls of-85.1 dB or more at the clutter position (40 °) and the interference position (-30 ° and-60 °). As can be seen from fig. 4(c), in the reception pattern in the distance dimension of 40 °, the reception pattern forms a null of-63.5 dB or more at the clutter position (75 m).
In summary, the emission pattern also has significantly deeper nulls at the target location. In addition, better energy focusing was formed at both the target positions (10 ° and 50m), and better nulls were formed at both the clutter positions (-50 °,10 °,40 ° and 25m, 75m) and the interference positions (-30 ° and-60 °).
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (5)

  1. A design method of a low interception frequency control array MIMO radar system under the constraint of PAPR and similarity is characterized by comprising the following steps:
    s0: building optimization problems
    Figure FDA0002490785580000011
    Initializing the external loop iteration number k to 0, initializing the internal loop iteration number n to 0, and randomly initializing the transmission waveform matrix S and recording the transmission waveform matrix S as
    Figure FDA0002490785580000012
    sm 0Represents the initial value of the transmitting waveform vector corresponding to the mth transmitting antenna, wherein M is 1,2, … Mt；s＝vec(S)；
    Wherein: omegapIs the weighting of the p-th objective function, ωp∈[0,1]And satisfy
    Figure FDA0002490785580000013
    P (S) is the space transmitting power of the transmitting signal, and SCNR (x, S) is the output signal-to-interference-and-noise ratio of the receiving end signal after passing through a receiving filter; PAPR(s) denotes the PAPR constraint of s, s0Represents the reference waveform, σ and ξ represent the control parameters;
    s1: fixing the current emission waveform matrix, solving the optimization problem by using an MVDR method, and calculating a receiving filter
    Figure FDA0002490785580000014
    The currently calculated receive filter, i.e. the receive filter at the k iteration, is denoted xk；
    Wherein: w1Is defined as:
    Figure FDA0002490785580000015
    Figure FDA0002490785580000016
    represents Mt×MtThe identity matrix of (1); v (r, θ) is defined as: the steering vector of the virtual array is,
    Figure FDA0002490785580000017
    b (theta) represents the steering vector of the receiving antenna array, and a (r, theta) represents the steering vector of the transmitting antenna array;
    Rcjeis defined as: rcje＝Rc+Rj+ReWherein R isc，RjAnd ReRespectively a clutter covariance matrix, an interference covariance matrix and a noise covariance matrix;
    at the kth outer loop iteration, step S2 is performed:
    s2: fixing the receiving filter x under this iterationkCalculating and updating a transmitting waveform vector s based on an alternating direction multiplier method and an active set method; knowing the current iteration value
    Figure FDA0002490785580000018
    The parameter with the superscript n represents the parameter value at the beginning of the nth inner loop iteration; the method further comprises the following steps:
    s201: updating the auxiliary variable hrThe method further comprises the following steps:
    s201 a: constructing an objective function in real form
    Figure FDA0002490785580000021
    t1,r,t2,r,s0,r,sr,RA,r,Rcvx,r,Rvx,r,En,rRespectively represent t1,t2,s0,s,RA,Rcvx,Rvx,EnA real numerical form of;
    parameter t1And t2Is defined as:
    Figure FDA0002490785580000022
    wherein R isA、Rcvx、RvxAre respectively defined as:
    Figure FDA0002490785580000023
    Figure FDA0002490785580000024
    Figure FDA0002490785580000025
    s201 b: under the ADMM framework, by introducing the variable z1,r,z2,r,ur,vrConverting the target function to an augmented Lagrange function ft,r(sr,hr,t1,r,t2,r,z1,r,z2,r,ur,vr) So as to obtain the objective function:
    Figure FDA0002490785580000026
    where ρ is1,ρ2,ρ3,ρ4Are punishment parameters which are all larger than 0; rAtIs defined as: rAt＝RA-t1/MtEt；RxtIs defined as: rxt＝Rcvx-t2Rvx；RAt,r、Rxt,rEach represents RAt、RxtA real numerical form of;
    s201 c: the objective function in S201b is constructed into a standard ASM form:
    Figure FDA0002490785580000027
    legal solution of h using active setrH obtained by this solutionrIs marked as
    Figure FDA0002490785580000028
    Wherein, Q, p, αi,biAre auxiliary variables, defined as follows:
    Figure FDA0002490785580000031
    Figure FDA0002490785580000032
    Figure FDA0002490785580000033
    Figure FDA0002490785580000034
    s202: knowing the value of the iteration
    Figure FDA0002490785580000035
    Will f ist,r(sr,hr,t1,r,t2,r,z1,r,z2,r,ur,vr) The following objective function is converted:
    Figure FDA0002490785580000036
    constructing the objective function into a standard ASM form, and solving for s by using an effective set methodrS obtained by this solutionrIs marked as
    Figure FDA0002490785580000037
    S203: knowing the value of the iteration
    Figure FDA0002490785580000038
    Will f ist,r(sr,hr,t1,r,t2,r,z1,r,z2,r,ur,vr) The following objective function is converted:
    Figure FDA0002490785580000039
    order to
    Figure FDA00024907855800000310
    Solving for t1,rAnd t2,rT obtained by this solution1,rAnd t2,rIs marked as
    Figure FDA00024907855800000311
    And
    Figure FDA00024907855800000312
    s204: knowing the value of the iteration
    Figure FDA00024907855800000313
    Solving for { z using the following equation1,r,z2,r,ur,vrSolving { z } obtained by the solving at this time1,r,z2,r,ur,vrIs recorded as
    Figure FDA00024907855800000314
    Figure FDA00024907855800000315
    S205: repeating the iteration S201 to S204 until the iteration number reaches the preset maximum internal loop iteration number, and outputting the last SrThen, step S3 is executed; (ii) a
    S3: and (5) repeating the steps S1-S2 until the iteration number reaches a preset maximum external loop iteration number or | SCNR |, wherein k is k +1(k+1)-SCNR(k)|/SCNR(k)< ε, wherein ε > 0.
  2. 2. The method for designing a low-intercept frequency-controlled array MIMO radar system under PAPR and similarity constraints of claim 1, wherein:
    the spatial transmit power p(s) is defined as:
    Figure FDA0002490785580000041
    wherein the content of the first and second substances,
    Figure FDA0002490785580000042
    which is the steering vector of the transmit array;
    Figure FDA0002490785580000043
    the phase difference is represented by a phase difference,
    Figure FDA0002490785580000044
    c denotes the speed of light, dtIndicating the array element spacing of the transmit array.
  3. 3. The method for designing a low-intercept frequency-controlled array MIMO radar system under PAPR and similarity constraints of claim 1, wherein:
    the PAPR constraint is defined as:
    Figure FDA0002490785580000045
    where L represents the number of interfering signals and s (n) represents the nth sample point of s.
  4. 4. The method for designing a low-intercept frequency-controlled array MIMO radar system under PAPR and similarity constraints of claim 1, wherein:
    clutter covariance matrix
    Figure FDA0002490785580000046
    Interference covariance matrix
    Figure FDA0002490785580000047
    Covariance matrix of noise
    Figure FDA0002490785580000048
    Wherein:
    q represents the number of clutter scatterers, Q represents the qth clutter scatterer;
    for distance and angle discrimination from the target, r is usedc,qAnd thetac,qRepresents the distance and angle at the qth clutter,
    Figure FDA0002490785580000049
    represents the covariance of the qth clutter;
    l represents the number of interference signals from different directions, L represents the ith interference signal; also for angular discrimination from the target, θj,lRepresents the angle at the ith interference;
    Figure FDA0002490785580000051
    represents the covariance of the ith interfering signal; i isKAn identity matrix representing K × K, b (theta)j,l) A steering vector representing the l interference signal on the receiving antenna array;
    Figure FDA0002490785580000052
    represents the covariance of the noise; i isMrKRepresents MrK×MrAn identity matrix of order K.
  5. 5. The method for designing a low-intercept frequency-controlled array MIMO radar system under PAPR and similarity constraints of claim 1, wherein:
    the formula for calculating the signal to interference plus noise ratio is as follows:
    Figure FDA0002490785580000053
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