CN114839604A - Orthogonal waveform design method and system for MIMO radar - Google Patents

Orthogonal waveform design method and system for MIMO radar Download PDF

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CN114839604A
CN114839604A CN202210236598.9A CN202210236598A CN114839604A CN 114839604 A CN114839604 A CN 114839604A CN 202210236598 A CN202210236598 A CN 202210236598A CN 114839604 A CN114839604 A CN 114839604A
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waveform
model
transmitting
mimo radar
spectrum
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黄中瑞
唐波
王海
王贵生
张峻宁
王旭阳
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National University of Defense 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
    • G01S7/28—Details of pulse systems
    • G01S7/282—Transmitters
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

The invention provides a method and a system for designing orthogonal waveforms of an MIMO radar. The method designs orthogonal waveforms of the MIMO radar by constraining the shape of a frequency spectrum, wherein the MIMO radar is a multi-input multi-output radar, and the method comprises the following steps: acquiring a transmitting waveform of a signal transmitted by an MIMO radar transmitting platform, and constructing a non-periodic related signal model of the transmitting signal based on the transmitting waveform, wherein the non-periodic related signal model is represented by a non-periodic autocorrelation function and a non-periodic cross-correlation function; establishing a spectrum model of the transmitting waveform to construct a spectrum matching model of the transmitting waveform, and further determining an optimization model of the transmitting waveform based on spectrum shape constraint based on the spectrum matching model and an optimization model of the transmitting waveform based on expected correlation performance matching; and (3) calculating the optimal transmitting waveform by using an optimization model of the transmitting waveform based on the frequency spectrum shape constraint through cyclic iterative computation, wherein the cutoff condition of the iterative computation is that the change of the adjacent iteration step objective function is less than a threshold value.

Description

Orthogonal waveform design method and system for MIMO radar
Technical Field
The invention belongs to the field of radar systems and radar signal processing, and particularly relates to a method and a system for designing an orthogonal waveform of an MIMO radar.
Background
The MIMO radar has been widely noticed by many scholars since it is proposed as a radar of a new system. Compared with the traditional phased array radar, the MIMO radar can emit any waveform, has higher degree of freedom, and has very superior performance in the aspects of target detection, parameter estimation and the like. According to different antenna configuration modes, the antenna configuration modes can be divided into a statistical MIMO radar and a coherent MIMO radar. The configuration interval of the statistic MIMO radar receiving and transmitting array elements is large, and the target can be observed from different directions, so that the space gain, the structure gain and the polarization gain are good, and the RCS flicker effect of the target can be effectively overcome. The target echo of the coherent MIMO radar can be subjected to coherent processing after matching and filtering, so that good waveform diversity gain is obtained, and the detection of a weak target under a strong interference background is facilitated.
The waveform design is an important basis for exerting the excellent performance of the MIMO radar. Under different working conditions, the performance of waveforms required by the MIMO radar is different, and the corresponding waveform design criteria are also different. In general, MIMO radar waveform design can be classified into the following cases: the design of a transmitting waveform under the matching of an expected directional diagram aims to realize the focusing of transmitting power in a specified airspace by controlling the correlation of the waveform and increase the signal-to-noise ratio of data at a receiving array; secondly, the waveform design of the signal-to-interference-and-noise ratio is output to the maximum extent, and the purpose is to improve the detection capability of a receiving array on a space target signal; the design of orthogonal waveforms aims to realize matched filtering of space signals by optimizing the correlation among the waveforms, extract phase information of different transceiving path pairs and lay a foundation for subsequent efficient parameter estimation; in addition, the method also comprises waveform design based on information theory, and waveform design based on similarity constraint or low peak-to-average ratio constraint or constant modulus constraint and the like, which is more in line with practical engineering application. The invention mainly takes orthogonal waveform design as a research object.
In the existing method, when orthogonal waveforms are designed, cost functions are mostly established by taking the self/cross correlation performance of the waveforms as an optimization target, and although the orthogonality among the waveforms can be improved, the mutual interference among different systems can be still caused in a complex electromagnetic environment. The presence of interfering signals in actual operation tends to degrade the performance of the radar system.
Disclosure of Invention
Aiming at the defects in the prior art, the MIMO radar orthogonal waveform design scheme is provided by further considering the mutual interference problem among different electronic devices on the basis of the traditional orthogonal waveform design, the orthogonal waveform meeting the system performance requirement is designed by utilizing the idle frequency spectrum gap in space, the preset radar function can be completed, and the orthogonal waveform can coexist with other radars and communication devices of the own party.
The invention discloses a MIMO radar orthogonal waveform design method in a first aspect. The method designs orthogonal waveforms of the MIMO radar by constraining the spectral shape, the MIMO radar being a multiple-input multiple-output radar, the method comprising:
step S1, acquiring a transmitting waveform of a signal transmitted by the MIMO radar transmitting platform, and constructing a non-periodic related signal model of the transmitting signal based on the transmitting waveform, wherein the non-periodic related signal model is characterized by a non-periodic autocorrelation function and a non-periodic cross-correlation function;
step S2, establishing a spectrum model of the emission waveform to construct a spectrum matching model of the emission waveform, and further determining an optimization model of the emission waveform based on spectrum shape constraint based on the spectrum matching model and an optimization model of the emission waveform based on expected correlation performance matching;
and step S3, calculating the optimal transmitting waveform through loop iteration calculation by using the transmitting waveform optimization model based on the frequency spectrum shape constraint, wherein the cutoff condition of the iteration calculation is that the change of the adjacent iteration step objective function is less than a threshold value.
According to the method of the first aspect of the present invention, in the step S1, the aperiodic autocorrelation function a of the aperiodic correlation signal model l,k And said aperiodic cross-correlation function C p,q,k Respectively as follows:
Figure BDA0003540166430000031
Figure BDA0003540166430000032
wherein A is l,k Representing the autocorrelation, C, of the l-th transmitted waveform at the k-th time delay p,q,k Represents the cross-correlation of the p-th and q-th transmit waveforms at the k-th time delay, L represents the number of transmit waveforms, N represents the code length of the transmit waveforms, L, p, q ≠ q, k ≠ 0,1 l (n) represents the value of the l-th emission waveform at the n-th moment, and leads
Figure BDA0003540166430000033
For the k delay shift matrix:
Figure BDA0003540166430000034
wherein the content of the first and second substances,
Figure BDA0003540166430000035
the (l, m) -th element of the k time delay shift matrix is represented, delta is an impact function, and a matrix J is defined p,q,k The following were used:
Figure BDA0003540166430000036
wherein Z is p,q An L x L-dimensional matrix representing that the (p, q) -th element is 1 and the remaining elements are 0,
Figure BDA0003540166430000037
representing the Kronecker product, based on the matrix J p,q,k The compact expression of the aperiodic autocorrelation function and the compact expression of the aperiodic cross-correlation function of the transmit waveform are respectively:
A l,k ＝s H J l,l,k s
C p,q,k ＝s H J p,q,k s
wherein s ═ s 1 ,s 2 ,...,s L ] H Is a vector representation of the transmit waveform.
According to the method of the first aspect of the present invention, in said step S2:
(1) the spectrum model of the transmitted waveform is:
y z ＝s H F z
wherein the content of the first and second substances,
Figure BDA0003540166430000041
I L an L-dimensional unit matrix is shown.
(2) The optimization model of the transmitting waveform based on the expected correlation performance matching is as follows:
Figure BDA0003540166430000042
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, w k ≧ 0 denotes a weighting coefficient over different delays,
Figure BDA0003540166430000043
representing expected correlation levels of the p-th transmit waveform and the q-th transmit waveform at the k-th time delay;
(3) the constructed frequency spectrum matching model of the transmitting waveform is as follows:
Figure BDA0003540166430000044
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure BDA0003540166430000045
representing the weighting factor at the z-th frequency point, d z ＝[d z1 ,d z2 ,...,d zL ]For the desired power spectral density vector to be,
Figure BDA0003540166430000046
representing a Hadamard product, wherein alpha is more than 0 and is a scale factor used for reducing the mismatch between a desired frequency spectrum and an actual frequency spectrum;
(4) the optimization model of the emission waveform based on the spectral shape constraint is as follows:
Figure BDA0003540166430000047
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, beta is more than or equal to 0 and less than or equal to 1, which is a weighting coefficient used for compromising the correlation performance and the spectrum matching performance of the emission waveform.
According to the method of the first aspect of the present invention, in the step S3, an equivalent optimization model of the transmit waveform based on the spectral shape constraint is obtained:
Figure BDA0003540166430000051
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure BDA0003540166430000052
θ z ＝[θ z1 ,θ z2 ,...,θ zL ]， Φ＝[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ]is a predefined auxiliary variable.
According to the method of the first aspect of the present invention, in step S3, the performing the loop iteration calculation process by using the equivalent optimization model specifically includes:
(1) input variable w ═ w 1-N ,...,w N-1 ]、
Figure BDA0003540166430000053
Figure BDA0003540166430000054
And an initial value of β.
(2) Let t denote the number of current external iterations and initialize t to 0 and s (t) 。
(3) Let t be t +1 and calculate the following:
Figure BDA0003540166430000055
Figure BDA0003540166430000056
Figure BDA0003540166430000057
(4) let b denote the number of internal iterations and initialize b to 0 and s (t,b) ＝s (t-1) S is updated by the following equation:
Figure BDA0003540166430000058
s.t.|s(m)|＝1,m＝1,2,...,LN
the above equation is reduced to an equality constrained linear programming problem:
Figure BDA0003540166430000059
s.t.|s(m)|＝1,m＝1,2,...,LN
where Re (-) represents the operation of the real part, solving the closed-form solution of s as: s ═ e (jarg(βu+(1-β)v)) The specific updating process is as follows:
(4.1) update u (t,b) ：
Figure BDA0003540166430000061
Figure BDA0003540166430000062
Figure BDA0003540166430000063
Wherein the content of the first and second substances,
Figure BDA0003540166430000064
further solving the following steps:
Figure BDA0003540166430000065
wherein the content of the first and second substances,
Figure BDA0003540166430000066
diag (-) denotes matrixing vector elements with the diagonal elements, E LN Representing a vector with elements all 1.
(4.2) update v (t,b) ：
Figure BDA0003540166430000067
Figure BDA0003540166430000068
Further solving the following steps:
v (t,b) ＝λ max (P)s (t,b) +α (t) q (t,b) -Ps (t,b)
wherein the content of the first and second substances,
Figure BDA0003540166430000069
(4.3) let b be b +1, update s (t,b) ：
Figure BDA00035401664300000610
Judging whether an internal convergence condition is met, wherein the internal convergence condition is that whether the change of target function values of two adjacent iteration steps is smaller than a first preset threshold, if so, turning to the step (5), otherwise, turning to the step (4.1);
(5) let s (t) ＝s (t,b) Judging whether an external convergence condition is met, wherein the external convergence condition is whether the change of target function values of two adjacent iteration steps is smaller than a second preset threshold, if so, turning to the step (6), and otherwise, turning to the step (3);
(6) obtaining the optimal transmit waveform as s * ＝s (t) 。
The invention discloses a MIMO radar orthogonal waveform design system in a second aspect. The system designs orthogonal waveforms of the MIMO radar, which is a multiple-input multiple-output radar, by constraining the spectral shape, the system comprising:
the MIMO radar transmitting platform comprises a first processing unit, a second processing unit and a third processing unit, wherein the first processing unit is configured to acquire a transmitting waveform of a signal transmitted by the MIMO radar transmitting platform, and construct an aperiodic correlation signal model of the transmitting signal based on the transmitting waveform, and the aperiodic correlation signal model is characterized by an aperiodic autocorrelation function and an aperiodic cross-correlation function;
a second processing unit configured to build a spectrum model of the transmit waveform to construct a spectrum matching model of the transmit waveform, and determine an optimization model of the transmit waveform based on a spectrum shape constraint based further on the spectrum matching model and an optimization model of the transmit waveform based on an expected correlation performance match;
and the third processing unit is configured to use the optimization model of the emission waveform based on the frequency spectrum shape constraint to obtain the optimal emission waveform through loop iteration calculation, wherein the cutoff condition of the iteration calculation is that the change of the target function of adjacent iteration steps is smaller than a threshold value.
According to the system of the second aspect of the present invention, the first processing unit 401 is specifically configured to: the aperiodic autocorrelation function A of the aperiodic correlation signal model l,k And said non-periodic correlation function C p,q,k Respectively as follows:
Figure BDA0003540166430000071
Figure BDA0003540166430000072
wherein A is l,k Representing the autocorrelation, C, of the l-th transmitted waveform at the k-th time delay p,q,k Represents the cross-correlation of the p-th and q-th transmit waveforms at the k-th time delay, L represents the number of transmit waveforms, N represents the code length of the transmit waveforms, L, p, q ≠ q, k ≠ 0,1 l (n) represents the value of the l-th emission waveform at the n-th moment, and leads
Figure BDA0003540166430000081
For the k delay shift matrix:
Figure BDA0003540166430000082
wherein the content of the first and second substances,
Figure BDA0003540166430000083
the (l, m) -th element of the k time delay shift matrix is represented, delta is an impact function, and a matrix J is defined p,q,k The following were used:
Figure BDA0003540166430000084
wherein Z is p,q An L x L dimensional matrix representing that the (p, q) -th element is 1 and the remaining elements are 0,
Figure BDA0003540166430000086
represents the Kronecker product, basisIn the matrix J p,q,k The compact expression of the aperiodic autocorrelation function and the compact expression of the aperiodic cross-correlation function of the transmit waveform are respectively:
A l,k ＝s H J l,l,k s
C p,q,k ＝s H J p,q,k s
wherein s ═ s 1 ,s 2 ,...,s L ] H Is a vector representation of the transmit waveform.
According to the system of the second aspect of the present invention, the second processing unit 402 is specifically configured to:
(1) the spectrum model of the transmitted waveform is:
y z ＝s H F z
wherein the content of the first and second substances,
Figure BDA0003540166430000085
I L an L-dimensional unit matrix is shown.
(2) The optimization model of the emission waveform based on the expected correlation performance matching is as follows:
Figure BDA0003540166430000091
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, w k ≧ 0 denotes a weighting coefficient over different delays,
Figure BDA0003540166430000092
representing expected correlation levels of the p-th transmit waveform and the q-th transmit waveform at the k-th time delay;
(3) the constructed frequency spectrum matching model of the transmitting waveform is as follows:
Figure BDA0003540166430000093
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure BDA0003540166430000094
representing the weighting factor at the z-th frequency point, d z ＝[d z1 ,d z2 ,...,d zL ]For the desired power spectral density vector to be,
Figure BDA0003540166430000095
representing a Hadamard product, wherein alpha is more than 0 and is a scale factor used for reducing the mismatch between a desired frequency spectrum and an actual frequency spectrum;
(4) the optimization model of the emission waveform based on the spectral shape constraint is as follows:
Figure BDA0003540166430000096
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, beta is more than or equal to 0 and less than or equal to 1, which is a weighting coefficient used for compromising the correlation performance and the spectrum matching performance of the emission waveform.
In the system according to the second aspect of the present invention, the third processing unit 403 is specifically configured to obtain an equivalent optimization model of the transmit waveform based on the spectral shape constraint:
Figure BDA0003540166430000097
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure BDA0003540166430000098
θ z ＝[θ z1 ,θ z2 ,...,θ zL ]， Φ＝[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ]is a predefined auxiliary variable.
According to the system of the second aspect of the present invention, the third processing unit 403 is specifically configured to execute the loop iteration calculation process by using the equivalent optimization model, and specifically includes:
(1) input variable w ═ w 1-N ,...,w N-1 ]、
Figure BDA0003540166430000101
Figure BDA0003540166430000102
And an initial value of β.
(2) Let t denote the number of current external iterations and initialize t to 0 and s (t) 。
(3) Let t be t +1 and calculate the following:
Figure BDA0003540166430000103
Figure BDA0003540166430000104
Figure BDA0003540166430000105
(4) let b denote the number of internal iterations and initialize b to 0 and s (t,b) ＝s (t-1) S is updated by the following equation:
Figure BDA0003540166430000106
s.t.|s(m)|＝1,m＝1,2,...,LN
the above equation is reduced to an equality constrained linear programming problem:
Figure BDA0003540166430000107
s.t.|s(m)|＝1,m＝1,2,...,LN
where Re (-) represents the operation of the real part, and the closed-form solution for s is found as: s ═ e (jarg(βu+(1-β)v)) The specific updating process is as follows:
(4.1) update u (t,b) ：
Figure BDA0003540166430000108
Figure BDA0003540166430000111
Figure BDA0003540166430000112
Wherein the content of the first and second substances,
Figure BDA0003540166430000113
further solving the following steps:
Figure BDA0003540166430000114
wherein the content of the first and second substances,
Figure BDA0003540166430000115
diag (-) denotes matrixing vector elements with the diagonal elements, E LN Representing a vector with elements all 1.
(4.2) update v (t,b) ：
Figure BDA0003540166430000116
Figure BDA0003540166430000117
Further solving the following steps:
v (t,b) ＝λ max (P)s (t,b) +α (t) q (t,b) -Ps (t,b)
wherein，
Figure BDA0003540166430000118
(4.3) updating s by setting b to 1 (t,b) ：
Figure BDA0003540166430000119
Judging whether an internal convergence condition is met, wherein the internal convergence condition is that whether the change of target function values of two adjacent iteration steps is smaller than a first preset threshold, if so, turning to the step (5), and otherwise, turning to the step (4.1);
(5) let s (t) ＝s (t,b) Judging whether an external convergence condition is met, wherein the external convergence condition is whether the change of target function values of two adjacent iteration steps is smaller than a second preset threshold, if so, turning to the step (6), and otherwise, turning to the step (3);
(6) obtaining the optimal transmit waveform as s * ＝s (t) 。
A third aspect of the invention discloses an electronic device. The electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method for designing orthogonal waveforms of the MIMO radar according to any one of the first aspect of the disclosure when executing the computer program.
A fourth aspect of the invention discloses a computer-readable storage medium. The computer readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps of a MIMO radar orthogonal waveform design method according to any one of the first aspect of the present disclosure.
In conclusion, the beneficial effects of the invention are as follows: (1) the invention constructs a generalized MIMO radar waveform design criterion, and can well compromise the integral sidelobe electrical frequency and peak sidelobe level of a waveform correlation function by adjusting the expected correlation performance, and the existing MIMO radar orthogonal waveform design can be regarded as a special case of the invention; (2) according to the invention, the orthogonal waveform design of the MIMO radar under the spectrum constraint is considered, and the correlation performance of the transmitted waveform is optimized, and meanwhile, the spectrum shape of the transmitted waveform can be effectively controlled, so that the orthogonal waveform can be electromagnetically compatible with other radars and communication equipment in a complex electromagnetic environment; (3) the invention provides a combined optimization method of twice Minorization-maximization (MM) technology and an acceleration strategy, so that the original non-convex problem is converted into a series of linear programming problems, and compared with the existing SDR or gradient algorithm and the like, the method has lower calculation complexity and better optimization effect, and lays a favorable foundation for online design of the MIMO radar transmitting waveform.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the description in the prior art are briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained according to the drawings without creative efforts for those skilled in the art.
Fig. 1 is a flowchart of a MIMO radar orthogonal waveform design method according to an embodiment of the present invention;
FIG. 2 shows a correlation function for optimizing a waveform obtained by simulation of a second embodiment according to the first embodiment of the present invention;
FIG. 3 shows a frequency spectrum of a waveform obtained by a simulation of the second embodiment according to the first embodiment of the present invention;
fig. 4 is a structural diagram of a MIMO radar orthogonal waveform design system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention discloses a MIMO radar orthogonal waveform design method in a first aspect. The method designs orthogonal waveforms of the MIMO radar by constraining the spectral shape, the MIMO radar being a multiple-input multiple-output radar. Fig. 1 is a flowchart of a MIMO radar orthogonal waveform design method according to an embodiment of the present invention; as shown in fig. 1, the method includes:
step S1, acquiring a transmitting waveform of a signal transmitted by the MIMO radar transmitting platform, and constructing a non-periodic related signal model of the transmitting signal based on the transmitting waveform, wherein the non-periodic related signal model is characterized by a non-periodic autocorrelation function and a non-periodic cross-correlation function;
step S2, establishing a spectrum model of the emission waveform to construct a spectrum matching model of the emission waveform, and further determining an optimization model of the emission waveform based on spectrum shape constraint based on the spectrum matching model and an optimization model of the emission waveform based on expected correlation performance matching;
and step S3, calculating the optimal transmitting waveform through loop iteration calculation by using the transmitting waveform optimization model based on the frequency spectrum shape constraint, wherein the cutoff condition of the iteration calculation is that the change of the adjacent iteration step objective function is less than a threshold value.
In some embodiments, in said step S1, said non-periodic autocorrelation function a of a non-periodic correlation signal model l,k And said aperiodic cross-correlation function C p,q,k Respectively as follows:
Figure BDA0003540166430000141
Figure BDA0003540166430000142
wherein A is l,k Indicating the l-th transmitted waveform at the k-th time delayAutocorrelation of, C p,q,k Represents the cross-correlation of the p-th and q-th transmit waveforms at the k-th time delay, L represents the number of transmit waveforms, N represents the code length of the transmit waveforms, L, p, q ≠ q, k ≠ 0,1 l (n) represents the value of the l-th emission waveform at the n-th moment, and leads
Figure BDA0003540166430000143
For the k delay shift matrix:
Figure BDA0003540166430000144
wherein the content of the first and second substances,
Figure BDA0003540166430000145
the (l, m) -th element of the k time delay shift matrix is represented, delta is an impact function, and a matrix J is defined p,q,k The following were used:
Figure BDA0003540166430000146
wherein Z is p,q An L x L dimensional matrix representing that the (p, q) -th element is 1 and the remaining elements are 0,
Figure BDA0003540166430000147
representing the Kronecker product, based on the matrix J p,q,k The compact expression of the aperiodic autocorrelation function and the compact expression of the aperiodic cross-correlation function of the transmit waveform are respectively:
A l,k ＝s H J l,l,k s
C p,q,k ＝s H J p,q,k s
wherein s ═ s 1 ,s 2 ,...,s L ] H Is a vector representation of the transmit waveform.
In some embodiments, in said step S2:
(1) the spectrum model of the transmitted waveform is:
y z ＝s H F z
wherein the content of the first and second substances,
Figure BDA0003540166430000151
I L an L-dimensional unit matrix is shown.
(2) The optimization model of the transmitting waveform based on the expected correlation performance matching is as follows:
Figure BDA0003540166430000152
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, w k ≧ 0 denotes a weighting coefficient over different delays,
Figure BDA0003540166430000153
representing expected correlation levels of the p-th transmit waveform and the q-th transmit waveform at the k-th time delay;
(3) the constructed frequency spectrum matching model of the transmitting waveform is as follows:
Figure BDA0003540166430000154
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure BDA0003540166430000155
representing the weighting factor at the z-th frequency point, d z ＝[d z1 ,d z2 ,...,d zL ]For the desired power spectral density vector to be,
Figure BDA0003540166430000156
representing a Hadamard product, wherein alpha is more than 0 and is a scale factor used for reducing the mismatch between a desired frequency spectrum and an actual frequency spectrum;
(4) the optimization model of the emission waveform based on the spectral shape constraint is as follows:
Figure BDA0003540166430000157
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, beta is more than or equal to 0 and less than or equal to 1, which is a weighting coefficient used for compromising the correlation performance and the spectrum matching performance of the emission waveform.
In some embodiments, in the step S3, an equivalent optimization model of the transmit waveform based on the spectral shape constraint is obtained:
Figure BDA0003540166430000161
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure BDA0003540166430000162
θ z ＝[θ z1 ,θ z2 ,...,θ zL ]， Φ＝[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ]is a predefined auxiliary variable.
In some embodiments, in the step S3, the performing the loop iteration calculation process by using the equivalent optimization model specifically includes:
(1) input variable w ═ w 1-N ,...,w N-1 ]、
Figure BDA0003540166430000163
Figure BDA0003540166430000164
And an initial value of β.
(2) Let t denote the number of current external iterations and initialize t to 0 and s (t) 。
(3) Let t be t +1 and calculate the following:
Figure BDA0003540166430000165
Figure BDA0003540166430000166
Figure BDA0003540166430000167
(4) let b denote the number of internal iterations and initialize b to 0 and s (t,b) ＝s (t-1) S is updated by the following equation:
Figure BDA0003540166430000168
s.t.|s(m)|＝1,m＝1,2,...,LN
the above equation is reduced to an equality constrained linear programming problem:
Figure BDA0003540166430000171
s.t.|s(m)|＝1,m＝1,2,...,LN
where Re (-) represents the operation of the real part, solving the closed-form solution of s as: s ═ e (jarg(βu+(1-β)v)) The specific updating process is as follows:
(4.1) update u (t,b) ：
Figure BDA0003540166430000172
Figure BDA0003540166430000173
Figure BDA0003540166430000174
Wherein the content of the first and second substances,
Figure BDA0003540166430000175
further solving the following steps:
Figure BDA0003540166430000176
wherein the content of the first and second substances,
Figure BDA0003540166430000177
diag (-) denotes matrixing vector elements with the diagonal elements, E LN Representing a vector with elements all being 1.
(4.2) update v (t,b) ：
Figure BDA0003540166430000178
Figure BDA0003540166430000179
Further solving the following steps:
v (t,b) ＝λ max (P)s (t,b) +α (t) q (t,b) -Ps (t,b)
wherein the content of the first and second substances,
Figure BDA00035401664300001710
(4.3) let b be b +1, update s (t,b) ：
Figure BDA0003540166430000181
Judging whether an internal convergence condition is met, wherein the internal convergence condition is that whether the change of target function values of two adjacent iteration steps is smaller than a first preset threshold, if so, turning to the step (5), and otherwise, turning to the step (4.1);
(5) let s (t) ＝s (t,b) Determine whether the outside is satisfiedThe external convergence condition is that whether the change of the target function values of two adjacent iteration steps is smaller than a second preset threshold, if so, the step (6) is carried out, and if not, the step (3) is carried out;
(6) obtaining the optimal transmit waveform as s * ＝s (t) 。
First embodiment
1. Constructing an aperiodic correlation signal model of MIMO radar transmitting waveform, and specifically constructing an aperiodic autocorrelation function A l,k And cross correlation function C p,q,k The expression of (a) is as follows:
Figure BDA0003540166430000182
Figure BDA0003540166430000183
wherein L, p, q ≠ q, k ═ 0, 1., N-1.
Order to
Figure BDA0003540166430000184
In order to shift the matrix, the matrix is shifted,
Figure BDA0003540166430000185
where δ is the shock function, defining a matrix J p,q,k The following were used:
Figure BDA0003540166430000186
wherein Z is p,q An L x L dimensional matrix representing that the (p, q) -th element is 1 and the remaining elements are 0,
Figure BDA0003540166430000187
representing the Kronecker product.
Based on the above definition, a compact expression of the aperiodic correlation function of the transmit waveform of the MIMO radar can be given as follows:
A l,k ＝s H J l,l,k s
C p,q,k ＝s H J p,q,k s
wherein s ═ s 1 ,s 2 ,...,s L ] H 。
2. Constructing a frequency spectrum model of an MIMO radar transmitting waveform:
definition matrix
Figure BDA0003540166430000191
Figure BDA0003540166430000192
Wherein, z is 0,1 L An L-dimensional unit matrix is represented.
The spectrum of the transmit waveform s can be expressed as:
y z ＝s H F z
3. constructing an MIMO radar transmitting waveform optimization model based on spectrum shape constraint:
(1) establishing an MIMO radar transmitting waveform optimization model based on expected correlation performance matching:
Figure BDA0003540166430000193
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, w k ≧ 0 denotes a weighting coefficient over different delays,
Figure BDA0003540166430000194
indicating the desired correlation level.
(2) Establishing a spectrum matching model of a transmitting waveform:
Figure BDA0003540166430000195
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure BDA0003540166430000196
representing the weighting factor at the z-th frequency point, d z ＝[d z1 ,d z2 ,...,d zL ]For the desired power spectral density vector,
Figure BDA0003540166430000197
representing a Hadamard product, with alpha > 0 being a scaling factor to trade off mismatch between the desired spectrum and the actual spectrum.
(3) Based on the two expressions, an MIMO radar transmitting waveform optimization model based on spectrum shape constraint can be given:
Figure BDA0003540166430000201
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, beta is more than or equal to 0 and less than or equal to 1, which is a weighting coefficient used for compromising the correlation performance and the spectrum matching performance of the emission waveform.
4. Iterative solution optimization problem based on MM method:
the MIMO radar transmitting waveform optimization model based on the frequency spectrum shape constraint is a quartic optimization problem under the constant modulus constraint, the problem has high non-convexity, the existing algorithm is difficult to solve, and therefore an equivalent optimization model provided by the invention is as follows:
Figure BDA0003540166430000202
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure BDA0003540166430000203
θ z ＝[θ z1 ,θ z2 ,...,θ zL ]and phi is ═ phi 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ]Is a defined auxiliary variable. For the above problem, a loop iteration algorithm may be used to solve the problem, which is specifically as follows:
(1) input variable w ═ w 1-N ,...,w N-1 ]，
Figure BDA0003540166430000204
Figure BDA0003540166430000205
Figure BDA0003540166430000206
And an initial value of β.
(2) Let t denote the number of current external iterations and initialize t to 0 and s (t) 。
(3) Let t be t +1 and calculate the following:
Figure BDA0003540166430000207
Figure BDA0003540166430000208
Figure BDA0003540166430000209
(4) let b denote the number of internal iterations and initialize b to 0 and s (t,b) ＝s (t-1) S needs to be updated as follows, and the corresponding optimization model is:
Figure BDA0003540166430000211
s.t.|s(m)|＝1,m＝1,2,...,LN
for the above formula, the algorithm of two Minorientation-attenuation (MM) operations can be simplified into an equality-constrained linear programming problem, which is as follows:
Figure BDA0003540166430000212
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein Re (. cndot.) represents the operation of the real part. The closed-form solution of s is easily found from the above equation: s ═ e (jarg (βu+(1-β)v)) The specific updating process is as follows:
(4.1) update u (t,b) The method comprises the following steps:
Figure BDA0003540166430000213
Figure BDA0003540166430000214
Figure BDA0003540166430000215
wherein the content of the first and second substances,
Figure BDA0003540166430000216
can be obtained from the above formula
Figure BDA0003540166430000217
Wherein the content of the first and second substances,
Figure BDA0003540166430000218
diag (-) denotes matrixing vector elements with the diagonal elements, E LN Representing a vector with elements all 1.
(4.2) update v (t,b) The method comprises the following steps:
Figure BDA0003540166430000219
Figure BDA00035401664300002110
from the above equation:
v (t,b) ＝λ max (P)s (t,b) +α (t) q (t,b) -Ps (t,b)
wherein the content of the first and second substances,
Figure BDA0003540166430000221
(4.3) let b be b +1, update s (t,b) ：
Figure BDA0003540166430000222
And judging whether an internal convergence condition is met, wherein the convergence condition is whether the change of the target function values of two adjacent iteration steps is smaller than a preset threshold. And (5) if the condition is met, otherwise, the step (4.1) is carried out. For the solution of s, the Minorientation-attenuation (MM) algorithm can be used in combination with an acceleration algorithm, so that the convergence rate of the inner loop can be further improved.
(5) Let s (t) ＝s (t,b) And judging whether an external convergence condition is met, wherein the convergence condition is whether the change of the target function values of two adjacent iteration steps is smaller than a preset threshold. And (4) if the condition is met, switching to the step (6), and if not, switching to the step (3).
(6) Obtaining an optimal transmit waveform s for the MIMO radar * ＝s (t) 。
Second embodiment (simulation of the first embodiment)
Simulation conditions are as follows: the number of the array elements of the MIMO radar is L-3, and the coding length of each array element transmitting waveform is N-256. And when the change of the target function value of the adjacent iteration steps is less than 0.1, stopping iteration.
FIG. 2 shows a correlation function for optimizing a waveform obtained by simulation of a second embodiment according to the first embodiment of the present invention; as shown in fig. 2, the correlation side lobe level of the optimized MIMO radar waveform is very low, which provides a good basis for matched filtering between different waveforms.
FIG. 3 shows a frequency spectrum of a waveform obtained by a simulation of the second embodiment according to the first embodiment of the present invention; as shown in fig. 3, the frequency spectrum of the optimized MIMO radar waveform is approximated to the expected frequency spectrum with high precision, which provides technical support for the MIMO radar to synthesize the required signal by using the available frequency spectrum gap in the space, and lays a favorable condition for the MIMO radar to realize electromagnetic compatibility with other electronic devices.
The invention discloses a MIMO radar orthogonal waveform design system in a second aspect. The system designs orthogonal waveforms for the MIMO radar, which is a multiple-input multiple-output radar, by constraining the spectral shape. FIG. 4 is a block diagram of a MIMO radar orthogonal waveform design system according to an embodiment of the present invention; as shown in fig. 4, the system 400 includes:
a first processing unit 401, configured to obtain a transmission waveform of a signal transmitted by a MIMO radar transmission platform, and construct an aperiodic correlation signal model of the transmission signal based on the transmission waveform, where the aperiodic correlation signal model is characterized by an aperiodic autocorrelation function and an aperiodic cross-correlation function;
a second processing unit 402 configured to build a spectrum model of the transmit waveform to construct a spectrum matching model of the transmit waveform, and determine an optimization model of the transmit waveform based on a spectrum shape constraint further based on the spectrum matching model and an optimization model of the transmit waveform based on an expected correlation performance match;
a third processing unit 403, configured to use an optimization model of the transmit waveform based on the spectral shape constraint to obtain an optimal transmit waveform through a loop iteration calculation, where a cutoff condition of the iteration calculation is that a change of an adjacent iteration step objective function is smaller than a threshold.
According to the system of the second aspect of the present invention, the first processing unit 401 is specifically configured to: the non-periodically related signal modeForm of said aperiodic autocorrelation function A l,k And said non-periodic correlation function C p,q,k Respectively as follows:
Figure BDA0003540166430000231
Figure BDA0003540166430000232
wherein A is l,k Representing the autocorrelation, C, of the l-th transmitted waveform at the k-th time delay p,q,k Indicating the cross-correlation between the p-th and the q-th transmit waveforms in the k-th time delay, L indicating the number of transmit waveforms, N indicating the code length of the transmit waveforms, L, p, q ≠ q, k ≠ 0,1 l (n) represents the value of the l-th emission waveform at the n-th moment, and leads
Figure BDA0003540166430000233
For the k delay shift matrix:
Figure BDA0003540166430000241
wherein the content of the first and second substances,
Figure BDA0003540166430000242
the (l, m) -th element of the k time delay shift matrix is represented, delta is an impact function, and a matrix J is defined p,q,k The following were used:
Figure BDA0003540166430000243
wherein Z is p,q An L x L dimensional matrix representing that the (p, q) -th element is 1 and the remaining elements are 0,
Figure BDA0003540166430000247
representing the Kronecker product, based on the matrix J p,q,k The compact expression of the aperiodic autocorrelation function and the compact expression of the aperiodic cross-correlation function of the transmit waveform are respectively:
A l,k ＝s H J l,l,k s
C p,q,k ＝s H J p,q,k s
wherein s ═ s 1 ,s 2 ,...,s L ] H Is a vector representation of the transmit waveform.
According to the system of the second aspect of the present invention, the second processing unit 402 is specifically configured to:
(1) the spectrum model of the transmitted waveform is:
y z ＝s H F z
wherein the content of the first and second substances,
Figure BDA0003540166430000244
I L an L-dimensional unit matrix is shown.
(2) The optimization model of the transmitting waveform based on the expected correlation performance matching is as follows:
Figure BDA0003540166430000245
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, w k ≧ 0 denotes a weighting coefficient over different delays,
Figure BDA0003540166430000246
representing expected correlation levels of the p-th transmit waveform and the q-th transmit waveform at the k-th time delay;
(3) the constructed frequency spectrum matching model of the transmitting waveform is as follows:
Figure BDA0003540166430000251
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein，
Figure BDA0003540166430000252
Representing the weighting factor at the z-th frequency point, d z ＝[d z1 ,d z2 ,...,d zL ]For the desired power spectral density vector to be,
Figure BDA0003540166430000253
representing a Hadamard product, wherein alpha is more than 0 and is a scale factor used for reducing the mismatch between a desired frequency spectrum and an actual frequency spectrum;
(4) the optimization model of the emission waveform based on the spectral shape constraint is as follows:
Figure BDA0003540166430000254
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, beta is more than or equal to 0 and less than or equal to 1, which is a weighting coefficient used for compromising the correlation performance and the spectrum matching performance of the emission waveform.
In the system according to the second aspect of the present invention, the third processing unit 403 is specifically configured to obtain an equivalent optimization model of the transmit waveform based on the spectral shape constraint:
Figure BDA0003540166430000255
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure BDA0003540166430000256
θ z ＝[θ z1 ,θ z2 ,...,θ zL ]， Φ＝[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ]is a predefined auxiliary variable.
According to the system of the second aspect of the present invention, the third processing unit 403 is specifically configured to execute the loop iteration calculation process by using the equivalent optimization model, and specifically includes:
(1) input variable w ═ w 1-N ,...,w N-1 ]、
Figure BDA0003540166430000257
Figure BDA0003540166430000258
And an initial value of β.
(2) Let t denote the number of current external iterations and initialize t to 0 and s (t) 。
(3) Let t be t +1 and calculate the following:
Figure BDA0003540166430000261
Figure BDA0003540166430000262
Figure BDA0003540166430000263
(4) let b denote the number of internal iterations and initialize b to 0 and s (t,b) ＝s (t-1) S is updated by the following equation:
Figure BDA0003540166430000264
s.t.|s(m)|＝1,m＝1,2,...,LN
the above equation is reduced to an equality constrained linear programming problem:
Figure BDA0003540166430000265
s.t.|s(m)|＝1,m＝1,2,...,LN
where Re (-) represents the operation of the real part, solving the closed-form solution of s as: s ═ e (jarg(βu+(1-β)v)) In which it is specifically updatedThe process is as follows:
(4.1) update u (t,b) ：
Figure BDA0003540166430000266
Figure BDA0003540166430000267
Figure BDA0003540166430000268
Wherein the content of the first and second substances,
Figure BDA0003540166430000269
further solving the following steps:
Figure BDA00035401664300002610
wherein the content of the first and second substances,
Figure BDA0003540166430000271
diag (-) denotes matrixing vector elements with the diagonal elements, E LN Representing a vector with elements all 1.
(4.2) update v (t,b) ：
Figure BDA0003540166430000272
Figure BDA0003540166430000273
Further solving the following steps:
v (t,b) ＝λ max (P)s (t,b) +α (t) q (t,b) -Ps (t,b)
wherein the content of the first and second substances,
Figure BDA0003540166430000274
(4.3) let b be b +1, update s (t,b) ：
Figure BDA0003540166430000275
Judging whether an internal convergence condition is met, wherein the internal convergence condition is that whether the change of target function values of two adjacent iteration steps is smaller than a first preset threshold, if so, turning to the step (5), and otherwise, turning to the step (4.1);
(5) let s (t) ＝s (t,b) Judging whether an external convergence condition is met, wherein the external convergence condition is whether the change of target function values of two adjacent iteration steps is smaller than a second preset threshold, if so, turning to the step (6), and otherwise, turning to the step (3);
(6) obtaining the optimal transmit waveform as s * ＝s (t) 。
A third aspect of the invention discloses an electronic device. The electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method for designing orthogonal waveforms of the MIMO radar according to any one of the first aspect of the disclosure when executing the computer program.
A fourth aspect of the invention discloses a computer-readable storage medium. The computer readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps of a MIMO radar orthogonal waveform design method according to any one of the first aspect of the present disclosure.
In conclusion, the beneficial effects of the invention are as follows: (1) the invention constructs a generalized MIMO radar waveform design criterion, and can well compromise the integral sidelobe electrical frequency and peak sidelobe level of a waveform correlation function by adjusting the expected correlation performance, and the existing MIMO radar orthogonal waveform design can be regarded as a special case of the invention; (2) the orthogonal waveform design of the MIMO radar under the spectrum constraint is considered, the correlation performance of the transmitted waveform is optimized, and simultaneously, the spectrum shape of the transmitted waveform can be effectively controlled, so that the orthogonal waveform design can be electromagnetically compatible with other radars and communication equipment in a complex electromagnetic environment; the invention (3) provides a combined optimization method of twice Minorization-maximization (MM) technology and an acceleration strategy, so that the original non-convex problem is converted into a series of linear programming problems, and compared with the existing SDR or gradient algorithm and the like, the method has lower calculation complexity and better optimization effect, and lays a favorable foundation for designing the MIMO radar transmitting waveform on line.
It should be noted that the technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, however, as long as there is no contradiction between the combinations of the technical features, the scope of the present description should be considered. The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (8)

1. A MIMO radar orthogonal waveform design method, wherein the method designs an orthogonal waveform of the MIMO radar by constraining a spectrum shape, wherein the MIMO radar is a multiple-input multiple-output radar, and wherein the method comprises:
step S1, acquiring a transmitting waveform of a signal transmitted by the MIMO radar transmitting platform, and constructing a non-periodic related signal model of the transmitting signal based on the transmitting waveform, wherein the non-periodic related signal model is characterized by a non-periodic autocorrelation function and a non-periodic cross-correlation function;
step S2, establishing a spectrum model of the emission waveform to construct a spectrum matching model of the emission waveform, and further determining an optimization model of the emission waveform based on spectrum shape constraint based on the spectrum matching model and an optimization model of the emission waveform based on expected correlation performance matching;
and step S3, calculating the optimal transmitting waveform through circular iterative calculation by using the optimizing model of the transmitting waveform based on the frequency spectrum shape constraint, wherein the cutoff condition of the iterative calculation is that the change of the adjacent iteration step objective function is less than a threshold value.
2. The method as claimed in claim 1, wherein in step S1, the aperiodic autocorrelation function a of the aperiodic correlation signal model is used as the autocorrelation function of the MIMO radar with constrained spectrum shape l,k And said aperiodic cross-correlation function C p,q,k Respectively as follows:
Figure FDA0003540166420000011
Figure FDA0003540166420000012
wherein A is l,k Representing the autocorrelation, C, of the l-th transmitted waveform at the k-th time delay p,q,k Represents the cross-correlation of the p-th and q-th transmit waveforms at the k-th time delay, L represents the number of transmit waveforms, N represents the code length of the transmit waveforms, L, p, q ≠ q, k ≠ 0,1 l (n) represents the value of the l-th emission waveform at the n-th moment, and leads
Figure FDA0003540166420000013
For the k delay shift matrix:
Figure FDA0003540166420000021
wherein the content of the first and second substances,
Figure FDA0003540166420000022
the (l, m) -th element of the k time delay shift matrix is represented, delta is an impact function, and the matrix J is defined p,q,k The following were used:
Figure FDA0003540166420000023
wherein Z is p,q An L x L dimensional matrix representing that the (p, q) -th element is 1 and the remaining elements are 0,
Figure FDA0003540166420000024
representing the Kronecker product, based on the matrix J p,q,k The compact expression of the aperiodic autocorrelation function and the compact expression of the aperiodic cross-correlation function of the transmit waveform are respectively:
A l,k ＝s H J l,l,k s
C p,q,k ＝s H J p,q,k s
wherein s ═ s 1 ,s 2 ,...,s L ] H Is a vector representation of the transmit waveform.
3. The method of claim 2, wherein in step S2:
(1) the spectrum model of the transmitted waveform is:
y z ＝s H F z
wherein the content of the first and second substances,
Figure FDA0003540166420000025
I L an L-dimensional unit matrix is represented.
(2) The optimization model of the transmitting waveform based on the expected correlation performance matching is as follows:
Figure FDA0003540166420000026
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, w k ≧ 0 denotes a weighting coefficient over different delays,
Figure FDA0003540166420000031
representing expected correlation levels of the p-th transmit waveform and the q-th transmit waveform at the k-th time delay;
(3) the constructed frequency spectrum matching model of the transmitting waveform is as follows:
Figure FDA0003540166420000032
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure FDA0003540166420000033
representing the weighting factor at the z-th frequency point, d z ＝[d z1 ,d z2 ,...,d zL ]In order for the desired power spectral density vector to be,
Figure FDA0003540166420000037
representing a Hadamard product, wherein alpha > 0 is a scale factor and is used for compromising the mismatch between the expected frequency spectrum and the actual frequency spectrum;
(4) the optimization model of the emission waveform based on the spectral shape constraint is as follows:
Figure FDA0003540166420000034
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein, beta is more than or equal to 0 and less than or equal to 1, which is a weighting coefficient used for compromising the correlation performance and the spectrum matching performance of the emission waveform.
4. The method according to claim 3, wherein in step S3, an equivalent optimization model of the transmit waveform based on the spectrum shape constraint is obtained:
Figure FDA0003540166420000035
s.t.|s(m)|＝1,m＝1,2,...,LN
wherein the content of the first and second substances,
Figure FDA0003540166420000036
θ z ＝[θ z1 ,θ z2 ,...,θ zL ]，Φ＝[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ]is a predefined auxiliary variable.
5. The method of claim 4, wherein in step S3, the iterative computation process is performed using the equivalent optimization model, and specifically includes:
(1) input variable w ═ w 1-N ,...,w N-1 ]、
Figure FDA0003540166420000041
Figure FDA0003540166420000042
And an initial value of β.
(2) Let t denote the number of current external iterations and initialize t to 0 and s (t) ；
(3) Let t be t +1 and calculate the following:
Figure FDA0003540166420000043
Figure FDA0003540166420000044
Figure FDA0003540166420000045
(4) let b denote the number of internal iterations and initialize b to 0 and s (t,b) ＝s (t-1) S is updated by the following equation:
Figure FDA0003540166420000046
s.t.|s(m)|＝1,m＝1,2,...,LN
the above equation is reduced to an equality constrained linear programming problem:
Figure FDA0003540166420000047
s.t.|s(m)|＝1,m＝1,2,...,LN
where Re (-) represents the operation of the real part, solving the closed-form solution of s as: s ═ e (jarg(βu+(1-β)v)) The specific updating process is as follows:
(4.1) update u (t,b) ：
Figure FDA0003540166420000048
Figure FDA0003540166420000049
Figure FDA00035401664200000410
Wherein the content of the first and second substances,
Figure FDA0003540166420000051
further solving the following steps:
Figure FDA0003540166420000052
wherein the content of the first and second substances,
Figure FDA0003540166420000053
diag (-) denotes matrixing vector elements with the diagonal elements, E LN Representing a vector with elements all 1.
(4.2) update v (t,b) ：
Figure FDA0003540166420000054
Figure FDA0003540166420000055
Further solving the following steps:
v (t,b) ＝λ max (P)s (t,b) +α (t) q (t,b) -Ps (t,b)
wherein the content of the first and second substances,
Figure FDA0003540166420000056
(4.3) let b be b +1, update s (t,b) ：
Figure FDA0003540166420000057
Judging whether an internal convergence condition is met, wherein the internal convergence condition is that whether the change of target function values of two adjacent iteration steps is smaller than a first preset threshold, if so, turning to the step (5), otherwise, turning to the step (4.1);
(5) let s (t) ＝s (t,b) Determine whether or not the external condition is satisfiedDetermining an external convergence condition, wherein the external convergence condition is whether the change of target function values of two adjacent iteration steps is smaller than a second preset threshold, if so, turning to the step (6), and otherwise, turning to the step (3);
(6) obtaining the optimal transmit waveform as s * ＝s (t) 。
6. A MIMO radar orthogonal waveform design system that designs orthogonal waveforms of the MIMO radar by constraining the spectral shape, the MIMO radar being a multiple-input multiple-output radar, the system comprising:
the MIMO radar transmitting platform comprises a first processing unit, a second processing unit and a third processing unit, wherein the first processing unit is configured to acquire a transmitting waveform of a signal transmitted by the MIMO radar transmitting platform, and construct an aperiodic correlation signal model of the transmitting signal based on the transmitting waveform, and the aperiodic correlation signal model is characterized by an aperiodic autocorrelation function and an aperiodic cross-correlation function;
a second processing unit configured to build a spectrum model of the transmit waveform to construct a spectrum matching model of the transmit waveform, and determine an optimization model of the transmit waveform based on a spectrum shape constraint based further on the spectrum matching model and an optimization model of the transmit waveform based on an expected correlation performance match;
and the third processing unit is configured to use the optimization model of the emission waveform based on the frequency spectrum shape constraint to obtain the optimal emission waveform through loop iteration calculation, wherein the cutoff condition of iteration calculation is that the change of the adjacent iteration step objective function is smaller than a threshold value.
7. An electronic device, comprising a memory storing a computer program and a processor, wherein the processor, when executing the computer program, implements the steps of a constrained spectral shape MIMO radar orthogonal waveform design method of any of claims 1-5.
8. A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of a method of constrained spectral shape MIMO radar orthogonal waveform design according to any one of claims 1 to 5.
CN202210236598.9A 2022-03-10 2022-03-10 Orthogonal waveform design method and system for MIMO radar Pending CN114839604A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117473687A (en) * 2023-12-28 2024-01-30 深圳大学 Construction method and equipment of redundancy-removing mutual radar array based on single-bit quantization

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117473687A (en) * 2023-12-28 2024-01-30 深圳大学 Construction method and equipment of redundancy-removing mutual radar array based on single-bit quantization
CN117473687B (en) * 2023-12-28 2024-05-10 深圳大学 Construction method and equipment of redundancy-removing mutual radar array based on single-bit quantization

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