CN115015860B - Transmitting signal optimization method and system for improving radar detection performance - Google Patents

Transmitting signal optimization method and system for improving radar detection performance Download PDF

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CN115015860B
CN115015860B CN202210622033.4A CN202210622033A CN115015860B CN 115015860 B CN115015860 B CN 115015860B CN 202210622033 A CN202210622033 A CN 202210622033A CN 115015860 B CN115015860 B CN 115015860B
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CN115015860A (en
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唐波
王海
黄中瑞
张峻宁
李达
秦立龙
王旭阳
吴文俊
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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
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    • 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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Abstract

The invention provides a method and a system for optimizing a transmitting signal for improving radar detection performance, which belong to the technical field of radar signal processing and comprise the following steps: setting radar signal emission energy, a reference coding sequence, a coding sequence similarity coefficient and the maximum energy of radar signal leakage to each adjacent communication system; estimating an inverse matrix of a radar interference covariance matrix; estimating an interference covariance matrix of each adjacent communication system; determining a first matrix, a set of signal transmission reference matrices, a second matrix and an initial radar transmission signal coding sequence; according to the signal emission reference matrix set, the second matrix and the scaling scale of the reference coding sequence, carrying out iterative optimization on the initial radar emission signal coding sequence; and performing amplitude modulation and phase modulation processing on the radar signal by adopting the iteratively optimized radar emission signal coding sequence. The frequency spectrum of the transmitting signal can form a notch in the frequency band of the adjacent communication system and increase the output signal-to-interference-and-noise ratio of the radar system.

Description

Transmitting signal optimization method and system for improving radar detection performance
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a method and a system for optimizing a transmitting signal for improving radar detection performance.
Background
Spectral resources are a scarce, limited, precious resource that has a significant strategic significance to countries around the world. Through the efficient utilization of spectrum resources, the method can realize the bearing and transmission of information, and has important application in a plurality of fields such as radar detection, mobile communication, navigation positioning, broadcast television and the like. However, with the rapid development of broadband mobile communication technology and the general popularization of smart devices, the demand for spectrum resources by frequency-using devices is more urgent, resulting in the spectrum resources becoming more scarce. When various frequency-using devices compete with each other for spectrum resources, the frequency-using devices working in the same or similar frequency bands generate various electromagnetic wave signals with complex patterns and dynamic randomness, which are very easy to cause spectrum congestion and have serious interference with each other, so that the performance of the devices is obviously reduced.
In order to improve the detection performance of the radar system in a spectrum congestion environment and reduce the mutual interference between the radar system and the adjacent communication system, one feasible thinking is to optimize the radar emission signal so that a notch is formed in a frequency band where the adjacent communication system is located by the signal spectrum, and the output signal-to-interference-and-noise ratio of the radar system is maximized through a receiving filter design. In order to make the radar signal have the above characteristics, italian student Aubry models the radar signal design problem as a quadratic function optimization problem under a quadratic constraint in the document Forcing Multiple Spectral Compatibility Constraints in Radar Waveforms [ J ] (IEEE Signal Processing Letters,2016,23 (4): 483-487), and proposes to use a transmission signal optimization method based on semi-normal relaxation (Semidefinite Relaxation, SDR), but the method has high computational complexity and is difficult to design a long coding sequence, so that it is difficult to use in a broadband radar system.
Disclosure of Invention
One of the purposes of the present invention is to provide a method for optimizing a transmission signal for improving radar detection performance, where the spectrum of the transmission signal obtained by the optimizing method can form a notch in a frequency band where a proximity communication system is located, and increase the output signal-to-interference-and-noise ratio of the radar system.
Another object of the present invention is to provide a transmission signal optimizing system for improving radar detection performance.
In order to achieve one of the above purposes, the present invention is implemented by the following technical scheme:
a transmit signal optimization method for improving radar detection performance, the transmit signal optimization method comprising:
step S1, setting radar signal emission energy, a reference coding sequence, a coding sequence similarity coefficient and maximum energy allowing radar signals to leak to frequency bands where all adjacent communication systems are located;
the code element number of the reference code sequence is N;
s2, radar echo data without target signals are obtained to estimate an inverse matrix R corresponding to an N-dimension Lei Dagan interference covariance matrix;
step S3, acquiring the working frequency bands of the radar and each adjacent communication system to estimate an N-by-N-dimensional interference covariance matrix corresponding to the working frequency band of each adjacent communication system;
The operating frequency band includes a lower sideband cutoff frequency and an upper sideband cutoff frequency;
s4, determining a first matrix A according to the radar signal emission energy and the reference coding sequence 0 ；
Step S5, according to the first matrix A 0 Determining a signal emission reference matrix set according to the coding sequence similarity coefficient, the interference covariance matrix corresponding to the working frequency band of each adjacent communication system and the maximum energy of allowing radar signals to leak to the frequency band of each adjacent communication system;
the set of signal transmission reference matrices includes radar parametersExamination matrix B 0 And a signal transmission reference matrix for each adjacent communication system;
s6, determining a second matrix according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the signal transmission reference matrix set;
s7, determining an initial radar transmitting signal coding sequence according to the radar signal transmitting energy and the reference coding sequence;
s8, carrying out iterative optimization on the initial radar emission signal coding sequence according to the signal emission reference matrix set and the second matrix;
and S9, performing amplitude modulation and phase modulation processing on the radar signal by adopting the iteratively optimized radar emission signal coding sequence to obtain a radar emission signal.
Further, between the step S1 and the step S2, the method for optimizing a transmission signal further includes:
and when the emission energy corresponding to the reference coding sequence is not equal to the emission energy of the radar signal, carrying out normalization processing on the reference coding sequence.
Further, in the step S3, the specific process of determining the n×n interference covariance matrix corresponding to the operating frequency band of each adjacent communication system includes:
step S31, adopting the working frequency bands of the radar, and carrying out normalization processing on the working frequency bands of all the adjacent communication systems according to the following formula;
Figure BDA0003677145620000031
Figure BDA0003677145620000032
B＝g u -g l ；
wherein ,
Figure BDA0003677145620000033
and />
Figure BDA0003677145620000034
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the k-th adjacent communication system after normalization processing are respectively; />
Figure BDA0003677145620000035
and />
Figure BDA0003677145620000036
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the kth adjacent communication system are respectively; g u and gl The upper sideband cut-off frequency and the lower sideband cut-off frequency of the radar are respectively; b is radar bandwidth; k=1, 2, …, K being the number of proximity communication systems;
step S32, according to the working frequency bands of all the adjacent communication systems after normalization processing, calculating all element values in an interference covariance matrix corresponding to the working frequency bands of all the adjacent communication systems according to the following formula;
Figure BDA0003677145620000041
wherein ,
Figure BDA0003677145620000042
and h=1, 2, …, N, l=1, 2, …, N, which are element values of the h th row and the first column in the interference covariance matrix corresponding to the operating frequency band of the kth adjacent communication system.
Further, in the step S5, each signal transmission reference matrix in the signal transmission reference matrix set is:
Figure BDA0003677145620000043
Figure BDA0003677145620000044
wherein ,Bk 'is the kth signal transmission reference matrix, when k' =0, then B 0 Transmitting a reference matrix for the signals of the radar; when k' =k, then B k Transmitting a reference matrix for signals of a kth adjacent communication system; a is that 0 Is a first matrix; i is an identity matrix of N x N dimensions; e, e t Transmitting energy for the radar signal; s is(s) 0 Is a reference coding sequence; epsilon 0 Is a coding sequence similarity coefficient; e (E) I k To allow radar signals to leak to the maximum energy of the frequency band in which the kth proximity communication system is located; r is R I k Is the interference covariance matrix corresponding to the working frequency band of the kth adjacent communication system.
Further, in the step S7, the initial radar transmission signal coding sequence is:
S＝[S 1 S2…S n …S N ] T
Figure BDA0003677145620000051
s is an initial radar transmitting signal coding sequence; s is S n A value corresponding to an nth code element in the initial radar transmitting signal coding sequence; θ n Is a random variable uniformly distributed in the interval of [0,2 pi ]; n=1, 2, …, N being the number of symbols of the reference coding sequence.
Further, in the step S8, the specific process of iterative optimization includes:
step S801, setting the kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k The initial values of' are all 0;
step S802, calculating a second auxiliary variable z according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the initial radar transmission signal coding sequence S;
step S803, according to the inverse matrix R corresponding to the Lei Dagan interference covariance matrix, the kth' firstAuxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k ' and the second auxiliary variable z and the respective signal-emission reference matrix B of the signal-emission reference matrix set k ' calculating a first auxiliary vector t;
step S804, setting the iteration number m=1;
step S805, calculating a third auxiliary variable v according to the first auxiliary vector T, the second matrix T and the radar signal emission energy;
step S806, calculating a radar transmission signal coding sequence S after the mth iteration according to the second matrix T, the first auxiliary vector T and the third auxiliary variable v (m) ；
Step S807, according to the initial radar transmitting signal coding sequence S after the mth iteration (m) Calculating a second auxiliary vector q after the mth iteration by the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the first Lagrangian multiplier vector d (m) ；
Step S808, according to the second auxiliary vector q after the mth iteration (m) And a preset punishment coefficient, calculating a second auxiliary variable z after the mth iteration (m) ；
Step S809, according to each signal emission reference matrix in the signal emission reference matrix set, the m-th iterated radar emission signal coding sequence S (m) And the kth' second Lagrangian multiplier vector C k ' calculating a fourth auxiliary variable after the mth iteration
Figure BDA0003677145620000061
/>
Step S810, judging the kth' second auxiliary variable z after the m iterations (m) If the square of the 2 norm of (2) is less than or equal to 1, if so, the kth' fourth auxiliary variable after the mth iteration is obtained
Figure BDA0003677145620000062
As the mth iterationk' first auxiliary variables y k ’ (m) Step S811 is entered; if not, the kth' fourth auxiliary variable +.>
Figure BDA0003677145620000063
Dividing by the kth' fourth auxiliary variable after the mth iteration +.>
Figure BDA0003677145620000064
Is taken as the kth' first auxiliary variable y after the mth iteration after the 2 norm of (2) k ’ (m) Step S811 is entered;
step S811, according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the second auxiliary variable z after the mth iteration (m) The code sequence S of the radar transmitting signal after the mth iteration (m) The kth' first auxiliary variable y after the mth iteration k ’ (m) Each signal emission reference matrix in the signal emission reference matrix set is used for calculating a residual vector after the mth iteration;
step S812, judging whether the 2 norm of the residual vector is smaller than a threshold value, if so, outputting the radar transmission signal coding sequence S after the mth iteration (m) Ending; if not, go to step S813;
step S813, according to the kth' second Lagrangian multiplier vector C k 'kth' first auxiliary variable y after mth iteration k ’ (m) The code sequence S of the radar transmitting signal after the mth iteration (m) And each signal-emission reference matrix B in the signal-emission reference matrix set k 'calculating the kth' second Lagrange multiplier vector c after the mth iteration k ’ (m) ；
Step S814, according to the first Lagrangian multiplier vector d and the second auxiliary variable z after the mth iteration (m) The code sequence S of the radar transmitting signal after the mth iteration (m) An inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix is calculated, and the mth iteration is performedLagrangian multiplier vector d (m) ；
Step S815, the kth' first auxiliary variable y after the mth iteration is processed k ’(m) The kth' second Lagrangian multiplier vector C after the mth iteration k ’ (m) A first Lagrangian multiplier vector d after the mth iteration (m) The code sequence S of the initial radar transmitting signal after the mth iteration (m) And a second auxiliary variable z after the mth iteration (m) Respectively assigned to the kth' first auxiliary variable y k 'said kth' second lagrangian multiplier vector C k ' the first Lagrangian multiplier vector d, the initial radar transmit signal coding sequence S and a second auxiliary variable z after an mth iteration (m) And m+1 is assigned to m, returning to step S805.
In order to achieve the second purpose, the invention adopts the following technical scheme:
a transmit signal optimization system for improving radar detection performance, the transmit signal optimization system comprising:
a setting module configured to: setting radar signal emission energy, a reference coding sequence, a coding sequence similarity coefficient and maximum energy allowing radar signals to leak to frequency bands where each adjacent communication system is located;
The code element number of the reference code sequence is N;
a first acquisition module configured to: acquiring radar echo data without target signals to estimate an inverse matrix R corresponding to an N-dimension Lei Dagan interference covariance matrix;
a second acquisition module configured to: acquiring the working frequency bands of a radar and each adjacent communication system to estimate an N-dimension interference covariance matrix corresponding to the working frequency band of each adjacent communication system;
the operating frequency band includes a lower sideband cutoff frequency and an upper sideband cutoff frequency;
a first determination module configured to: determining a first matrix A according to the radar signal emission energy and a reference coding sequence 0 ；
A second determination module configured to: according to the first matrix A 0 Determining a signal emission reference matrix set according to the coding sequence similarity coefficient, the interference covariance matrix corresponding to the working frequency band of each adjacent communication system and the maximum energy of allowing radar signals to leak to the frequency band of each adjacent communication system;
the signal transmission reference matrix set comprises a radar reference matrix B 0 And a signal transmission reference matrix for each adjacent communication system;
a third determination module configured to: determining a second matrix according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the signal transmission reference matrix set;
A fourth determination module configured to: determining an initial radar transmission signal coding sequence according to the radar signal transmission energy and the reference coding sequence;
an iterative optimization module configured to: according to the signal transmission reference matrix set and the second matrix, carrying out iterative optimization on the initial radar transmission signal coding sequence;
an amplitude modulation and phase modulation processing module configured to: and carrying out amplitude modulation and phase modulation processing on the radar signal by adopting the iterative optimized radar emission signal coding sequence to obtain a radar emission signal.
Further, between the setting module and the obtaining module, the emission signal optimizing system further includes:
a normalization processing module configured to: and when the emission energy corresponding to the reference coding sequence is not equal to the emission energy of the radar signal, carrying out normalization processing on the reference coding sequence.
Further, the second obtaining module includes:
a normalization processing sub-module configured to: adopting the working frequency bands of the radars, and carrying out normalization processing on the working frequency bands of all adjacent communication systems according to the following formula;
Figure BDA0003677145620000091
Figure BDA0003677145620000092
B＝g u -g l ；
wherein ,
Figure BDA0003677145620000093
and />
Figure BDA0003677145620000094
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the k-th adjacent communication system after normalization processing are respectively; / >
Figure BDA0003677145620000095
and />
Figure BDA0003677145620000096
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the kth adjacent communication system are respectively; g u and gl The upper sideband cut-off frequency and the lower sideband cut-off frequency of the radar are respectively; b is radar bandwidth; k=1, 2, …, K being the number of proximity communication systems;
a first computing sub-module configured to: according to the working frequency bands of all adjacent communication systems after normalization processing, calculating all element values in an interference covariance matrix corresponding to the working frequency bands of all adjacent communication systems according to the following formula;
Figure BDA0003677145620000097
wherein ,
Figure BDA0003677145620000098
the first column of the h row in the interference covariance matrix corresponding to the working frequency band of the kth adjacent communication systemElemental values, h=1, 2, …, N, l=1, 2, …, N.
Further, the iterative optimization module includes:
a first setting sub-module configured to: setting the kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k The initial values of' are all 0;
a second computing sub-module configured to: calculating a second auxiliary variable z according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the initial radar transmission signal coding sequence S;
A third computing sub-module configured to: according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix, the kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k ' and the second auxiliary variable z and the respective signal-emission reference matrix B of the signal-emission reference matrix set k ' calculating a first auxiliary vector t;
a second setting sub-module configured to: setting the iteration number m=1;
a fourth calculation submodule for calculating a third auxiliary variable v according to the first auxiliary vector T, the second matrix T and the radar signal emission energy;
a fifth calculation sub-module configured to: according to the second matrix T, the first auxiliary vector T and the third auxiliary variable v, calculating a radar transmitting signal coding sequence S after the mth iteration (m) ；
A sixth calculation sub-module configured to: according to the code sequence s of the initial radar transmitting signal after the mth iteration (m) Calculating a second auxiliary vector q after the mth iteration by the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the first Lagrangian multiplier vector d (m) ；
A seventh calculation sub-module configured to: according to the second auxiliary vector q after the mth iteration (m) And a preset punishment coefficient, calculating a second auxiliary after the mth iterationAuxiliary variable z (m) ；
An eighth calculation sub-module configured to: according to each signal emission reference matrix in the signal emission reference matrix set and the m-th iterated radar emission signal coding sequence S (m) And the kth' second Lagrangian multiplier vector C k ' calculating a fourth auxiliary variable after the mth iteration
Figure BDA0003677145620000101
A first determination submodule configured to: judging the kth' second auxiliary variable z after m iterations (m) If the square of the 2 norm of (2) is less than or equal to 1, if so, the kth' fourth auxiliary variable after the mth iteration is obtained
Figure BDA0003677145620000102
As the kth' first auxiliary variable y after the mth iteration k ’ (m) And send to the eighth calculation sub-module; if not, the kth' fourth auxiliary variable +.>
Figure BDA0003677145620000103
Dividing by the kth' fourth auxiliary variable after the mth iteration +.>
Figure BDA0003677145620000104
Is taken as the kth' first auxiliary variable y after the mth iteration after the 2 norm of (2) k ’ (m) And send to the eighth calculation sub-module;
a ninth calculation sub-module configured to: according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the second auxiliary variable z after the mth iteration (m) The code sequence S of the radar transmitting signal after the mth iteration (m) The kth' first auxiliary variable y after the mth iteration k ’ (m) Each signal emission reference matrix in the signal emission reference matrix set is used for calculating a residual vector after the mth iteration;
a second determination submodule configured to: judging whether the 2 norm of the residual vector is smaller than a threshold value, if so, outputting the radar emission signal coding sequence S after the mth iteration (m) Ending; if not, transmitting the code sequence of the radar emission signal after the mth iteration to a tenth computing sub-module;
a tenth calculation sub-module configured to: according to the kth' second Lagrangian multiplier vector C k 'kth' first auxiliary variable y after mth iteration k ’ (m) The code sequence S of the radar transmitting signal after the mth iteration (m) And each signal-emission reference matrix B in the signal-emission reference matrix set k 'calculating the kth' second Lagrange multiplier vector c after the mth iteration k ’ (m) ；
An eleventh computing sub-module configured to: according to the first Lagrangian multiplier vector d and the second auxiliary variable z after the mth iteration (m) The code sequence S of the radar transmitting signal after the mth iteration (m) An inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix is calculated, and a first Lagrange multiplier vector d after the mth iteration is calculated (m) ；
An assign sub-module configured to: the kth' first auxiliary variable y after the mth iteration is processed k ’ (m) The kth' second Lagrangian multiplier vector C after the mth iteration k ’ (m) A first Lagrangian multiplier vector d after the mth iteration (m) The code sequence S of the initial radar transmitting signal after the mth iteration (n) And a second auxiliary variable z after the mth iteration (m) Respectively assigned to the kth' first auxiliary variable y k 'said kth' second lagrangian multiplier vector C k ' the first Lagrangian multiplier vector d, the initial radar transmit signal coding sequence S and a second auxiliary variable z after an mth iteration (m) And m+1 is assigned to m and returned to the fourth calculation sub-module.
In summary, the scheme provided by the invention has the following technical effects:
according to the method, the inverse matrix corresponding to the Lei Dagan interference covariance matrix and the interference covariance matrix corresponding to the working frequency bands of all adjacent communication systems are determined by acquiring radar echo data and the working frequency bands of the radar and all adjacent communication systems; determining a first matrix by setting radar signal emission energy and a reference coding sequence; determining a signal emission reference matrix set according to the first matrix, the coding sequence similarity coefficient, an interference covariance matrix corresponding to the working frequency band of each adjacent communication system and the maximum energy allowing radar signals to leak to the frequency band of each adjacent communication system; determining a second matrix by using an inverse matrix corresponding to the Lei Dagan interference covariance matrix and a signal transmission reference matrix set; determining an initial radar transmitting signal coding sequence according to the radar signal transmitting energy and the reference coding sequence; according to the signal emission reference matrix set and the second matrix, carrying out iterative optimization on the initial radar emission signal coding sequence; finally, an iterative optimized radar emission signal coding sequence is adopted to carry out amplitude modulation and phase modulation on the radar signals to obtain radar emission signals, so that a deeper notch is formed in a frequency band where a radar signal frequency spectrum is located in an adjacent communication system, and mutual interference with the adjacent communication system is avoided; the radar emission signal obtained by the method improves the output signal-to-interference-and-noise ratio of the radar system and improves the target detection performance of the radar system in a spectrum congestion background; the radar emission signal code has better similarity with the existing radar emission signal, thereby enjoying excellent fuzzy function characteristics; the radar emission signal coding optimization design method provided by the invention is simple to realize, has high running speed, and is beneficial to quickly adjusting the radar emission signal in a spectrum congestion environment.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow diagram of a method for optimizing a transmit signal for improving radar detection performance according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a radar transmit signal coding sequence according to an embodiment of the present invention;
fig. 3 is a schematic diagram of the energy spectral density of a radar signal according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment provides a method for optimizing a transmission signal for improving radar detection performance, and referring to fig. 1, the method for optimizing a transmission signal includes:
step S1, radar signal emission energy, a reference coding sequence, a coding sequence similarity coefficient and maximum energy allowing radar signals to leak to frequency bands where the adjacent communication systems are located are set.
The number of symbols of the reference code sequence of this embodiment is N. Setting radar signal emission energy e according to radar action distance, tactical requirement, maximum output power of transmitter and the like t . If the radar signal transmission energy of the agreed shaped pulse is 1, the radar signal transmission energy depends on the transmission energy of the encoded signal.
The reference coding sequence s of this embodiment 0 Is generally extracted from the radar signal which has been coded and has the same length as the coding sequence, and refers to the coding sequence s 0 The method meets the following conditions:
Figure BDA0003677145620000131
in order to obtain good signal characteristics, a certain similarity is required between the coding sequence to be designed and the reference coding sequence, and the similarity coefficient between the coding sequence to be designed and the reference coding sequence is that
Figure BDA0003677145620000132
0≤ε 0 ≤2e t 。
When referring to the coding sequence s 0 Is not equal to the radar signal transmission energy e t Then the reference code sequence s is required 0 Normalization is performed to make the reference code sequence s 0 Is equal to the radar signal transmission energy e t Namely, between the step S1 and the step S2, the method further comprises:
and when the emission energy corresponding to the reference coding sequence is not equal to the emission energy of the radar signal, carrying out normalization processing on the reference coding sequence. Normalization is performed according to the following formula:
Figure BDA0003677145620000141
the maximum energy in this embodiment that allows radar signals to leak into the frequency band of the nearby communication system
Figure BDA0003677145620000142
Is->
Figure BDA0003677145620000143
Far less than the radar signal emission energy e t ，k＝1,…,K。
And S2, acquiring radar echo data without target signals to estimate an inverse matrix R corresponding to the Lei Dagan interference covariance matrix of N-dimension.
The radar echo data in this embodiment refers to radar echo data after down-conversion, amplification, and analog-to-digital conversion. In estimating the interference covariance matrix, snapshot data (radar echo data) of neighboring units, which do not contain the target signal, in the vicinity of the unit to be detected is generally utilized. In estimating the interference covariance matrix, the estimation is generally performed using radar echo data that does not contain the target signal in the vicinity of the unit to be detected. The inverse matrix corresponding to the Lei Dagan interference covariance matrix in n×n dimensions in this embodiment is:
Figure BDA0003677145620000144
R＝M -1 ；
Wherein M is a Lei Dagan interference covariance matrix of N dimension; r is an inverse matrix of N x N dimensions; n is n p Is the p-th radar echo data; p=1, 2, …, P is the number of radar echo data.
And S3, acquiring the radar and the working frequency bands of each adjacent communication system to estimate an N-dimension interference covariance matrix corresponding to the working frequency bands of each adjacent communication system.
The operating band of this embodiment includes a lower sideband cutoff frequency and an upper sideband cutoff frequency.
In the step S3, the specific process of determining the n×n-dimensional interference covariance matrix corresponding to the operating frequency band of each adjacent communication system includes:
step S31, adopting the working frequency bands of the radar, and carrying out normalization processing on the working frequency bands of all the adjacent communication systems according to the following formula;
Figure BDA0003677145620000151
/>
Figure BDA0003677145620000152
B＝g u -g l ；
wherein ,
Figure BDA0003677145620000153
and />
Figure BDA0003677145620000154
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the k-th adjacent communication system after normalization processing are respectively; />
Figure BDA0003677145620000155
and />
Figure BDA0003677145620000156
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the kth adjacent communication system are respectively; g u and gl The upper sideband cut-off frequency and the lower sideband cut-off frequency of the radar are respectively; b is radar bandwidth; k=1, 2, …, K being the number of proximity communication systems;
And step S32, according to the working frequency bands of the adjacent communication systems after normalization processing, calculating each element value in the interference covariance matrix corresponding to the working frequency bands of the adjacent communication systems according to the following formula.
Figure BDA0003677145620000157
wherein ,
Figure BDA0003677145620000158
and h=1, 2, …, N, l=1, 2, …, N, which are element values of the h th row and the first column in the interference covariance matrix corresponding to the operating frequency band of the kth adjacent communication system.
S4, determining a first matrix A according to the radar signal emission energy and the reference coding sequence 0 。
In this embodiment, the following formula is adopted to determine the first matrix:
Figure BDA0003677145620000161
wherein ,A0 Is a first matrix; i is an identity matrix of N x N dimensions; e, e t Transmitting energy for the radar signal; s is(s) 0 Is a reference coding sequence.
Step S5, according to the first matrix A 0 And determining a signal emission reference matrix set according to the coding sequence similarity coefficient, the interference covariance matrix corresponding to the working frequency band of each adjacent communication system and the maximum energy of allowing radar signals to leak to the frequency band where each adjacent communication system is located.
The set of signal transmission reference matrices of the present embodiment includes a radar and signal transmission reference matrices of respective adjacent communication systems. Each signal emission reference matrix in the signal emission reference matrix set is:
Figure BDA0003677145620000162
wherein ,Bk 'is the kth signal transmission reference matrix, when k' =0, then B 0 Is a radar reference matrix; when k' =k, then B k Transmitting a reference matrix for signals of a kth adjacent communication system; a is that 0 Is a first matrix; epsilon 0 Is a coding sequence similarity coefficient; e (E) I k To allow radar signals to leak to the maximum energy of the frequency band in which the kth proximity communication system is located; r is R I k Is the interference covariance matrix corresponding to the working frequency band of the kth adjacent communication system.
And S6, determining a second matrix according to the inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the signal transmission reference matrix set.
And S7, determining an initial radar transmitting signal coding sequence according to the radar signal transmitting energy and the reference coding sequence.
The initial radar transmission signal coding sequence of this embodiment is:
S＝[S 1 S 2 …S n …S N ] T
Figure BDA0003677145620000171
wherein S is an initial radar transmitting signal coding sequenceReference is made to fig. 2; s is S n A value corresponding to an nth code element in the initial radar transmitting signal coding sequence; θ n Is a random variable uniformly distributed in the interval of [0,2 pi ]; n=1, 2, …, N being the number of symbols of the reference coding sequence.
And S8, performing iterative optimization on the initial radar transmission signal coding sequence according to the signal transmission reference matrix set and the second matrix.
In this embodiment, the specific process of iterative optimization includes:
step S801, setting the kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k The initial values of' are all 0.
And step S802, calculating a second auxiliary variable z according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the initial radar transmission signal coding sequence S.
The second auxiliary variable of this embodiment is:
z＝R 1/2 s；
wherein z is a second auxiliary variable; r is an inverse matrix corresponding to the Lei Dagan interference covariance matrix; s is the initial radar transmit signal code sequence.
Step S803, according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix, the kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k ' and the second auxiliary variable z and the respective signal-emission reference matrix B of the signal-emission reference matrix set k ' calculating a first auxiliary vector t;
the first auxiliary vector of this embodiment is:
Figure BDA0003677145620000181
wherein t is a first auxiliary vector; r is an inverse matrix corresponding to the Lei Dagan interference covariance matrix; y is k 'is the kth' first auxiliary variable; d is the first Bragg Langerhans multiplier vector, C k 'is the kth' second Lagrangian multiplier vector, z is the second auxiliary variable and B k The 'k' th signal transmission reference matrix in the set of signal transmission reference matrices.
Step S804, setting the iteration number m=1;
step S805, calculating a third auxiliary variable v according to the first auxiliary vector T, the second matrix T and the radar signal emission energy.
Step S806, calculating a radar transmission signal coding sequence S after the mth iteration according to the second matrix T, the first auxiliary vector T and the third auxiliary variable v (m) 。
In this embodiment, the code sequence of the radar transmission signal after the mth iteration is:
S (m) ＝(T+νI) -1 t
Figure BDA0003677145620000182
(t) H (T+νI) -2 t＝e t
wherein ,S(m) Transmitting a signal coding sequence for the radar after the mth iteration; t is a second matrix; v is a third auxiliary variable.
Step S807, according to the initial radar transmitting signal coding sequence S after the mth iteration (m) Calculating a second auxiliary vector q after the mth iteration by the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the first Lagrangian multiplier vector d (m) 。
In this embodiment, the second auxiliary vector after the mth iteration is:
q (m) ＝R 1/2 s (m) -d；
wherein ,q(m) A second auxiliary vector after the mth iteration;
step S808, according to the second auxiliary vector q after the mth iteration (m) And a preset punishment coefficient, calculating a second auxiliary variable z after the mth iteration (m) 。
In this embodiment, the second auxiliary variable after the mth iteration is:
Figure BDA0003677145620000191
wherein ,z(m) Is the second auxiliary variable after the mth iteration; mu is a preset punishment coefficient, and the punishment coefficient mu is more than 2, preferably 3-5.
Step S809, according to each signal emission reference matrix in the signal emission reference matrix set, the m-th iterated radar emission signal coding sequence S (m) And the kth' second Lagrangian multiplier vector C k ' calculating a fourth auxiliary variable after the mth iteration
Figure BDA0003677145620000192
In this embodiment, the fourth auxiliary variable after the mth iteration is:
Figure BDA0003677145620000193
wherein ,
Figure BDA0003677145620000194
a kth' second auxiliary variable after an mth iteration;
step S810, judging the kth' second auxiliary variable z after the m iterations (m) If the square of the 2 norm of (2) is less than or equal to 1, if so, the kth' fourth auxiliary variable after the mth iteration is obtained
Figure BDA0003677145620000195
As the kth' first auxiliary variable y after the mth iteration k ’ (m) Step S811 is entered; if not, the kth' fourth auxiliary variable +.>
Figure BDA0003677145620000201
Dividing by the kth' fourth auxiliary variable after the mth iteration +. >
Figure BDA0003677145620000202
Is taken as the kth' first auxiliary variable y after the mth iteration after the 2 norm of (2) k ’ (m) Step S811 is entered;
in this embodiment, the kth' fourth auxiliary variable after the mth iteration
Figure BDA0003677145620000203
The 2 norms of (2) are: />
Figure BDA0003677145620000204
Step S811, according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the second auxiliary variable z after the mth iteration (m) The code sequence S of the radar transmitting signal after the mth iteration (m) The kth' first auxiliary variable y after the mth iteration k ’ (m) And each signal emission reference matrix in the signal emission reference matrix set is used for calculating the residual vector after the mth iteration.
In this embodiment, the residual vector after the mth iteration is:
Figure BDA0003677145620000205
wherein ,r(m) Is the residual vector after the mth iteration.
Step S812, judging whether the 2 norm of the residual vector is smaller than a threshold value, if so, outputting the radar transmission signal coding sequence S after the mth iteration (m) Ending; if not, go to step S813;
step S813, according to the kth' second Lagrangian multiplier vector C k 'kth' first auxiliary variable y after mth iteration k ’ (m) After the mth iterationRadar transmit signal coding sequence S (m) And each signal-emission reference matrix B in the signal-emission reference matrix set k 'calculating the kth' second Lagrange multiplier vector c after the mth iteration k ’ (m) 。
In this embodiment, the kth' second lagrangian multiplier vector after the mth iteration is:
Figure BDA0003677145620000211
wherein ,C’k (m) The k' th second Lagrangian multiplier vector after the m-th iteration;
step S814, according to the first Lagrangian multiplier vector d and the second auxiliary variable z after the mth iteration (m) The code sequence S of the radar transmitting signal after the mth iteration (m) An inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix is calculated, and a first Lagrange multiplier vector d after the mth iteration is calculated (m) ；
In this embodiment, the first lagrangian multiplier vector after the (m+1) th iteration is:
d (m) ＝d+z (m) -R 1/2 s (m) ；
wherein ,d(m) Is the first lagrangian multiplier vector after the mth iteration.
Step S815, the kth' first auxiliary variable y after the mth iteration is processed k ’ (m) The kth' second Lagrangian multiplier vector C after the mth iteration k ’ (m) A first Lagrangian multiplier vector d after the mth iteration (m) The code sequence S of the initial radar transmitting signal after the mth iteration (m) And a second auxiliary variable z after the mth iteration (m) Respectively assigned to the kth' first auxiliary variable y k 'said kth' second lagrangian multiplier vector C k ' the first Lagrangian multiplier vector d, the initial radar transmit signal coding sequence S and the mth iterationSecond auxiliary variable z (m) And m+1 is assigned to m, returning to step S805.
And S9, performing amplitude modulation and phase modulation processing on the radar signal by adopting the iteratively optimized radar emission signal coding sequence to obtain a radar emission signal.
Coding sequence { S } obtained by using optimization method 1 ，S 2 ，......，S N And modulating the amplitude and the phase of the formed pulse in sequence, and taking the modulated signal as a radar transmitting signal.
The beneficial effects of this embodiment are further illustrated by the following simulations:
simulation conditions: the radar signal pulse width is 20 mus, the sub pulse width is 0.1 mus, and the energy of the transmitted signal is set to 1. The adjacent communication stations have 7 parts in total, and normalized frequency bands are respectively:
Figure BDA0003677145620000221
the signal to noise ratio of all stations is 10dB. The external narrowband has 2 parts of active interference, the normalized frequencies are 0.7 and 0.75 respectively, and the dry-noise ratio is 50dB and 40dB. When the signal coding sequence is designed, a linear frequency modulation signal is used as a reference coding sequence, the similarity coefficient is set to be 0.35, the maximum energy of radar signals which are allowed to leak to frequency bands where a 3 rd radio station and a 6 th radio station are located is-30 dB, and the maximum energy of radar signals which are allowed to leak to frequency bands where other radio stations are located is-20 dB. When using the alternate direction multiplier method, the penalty coefficient is set to 4, and the decision threshold is set to 5×10 -10 . Fig. 3 shows the energy spectrum density of the designed radar signal, and it can be seen that the spectrum of the radar signal can form a deeper notch in the frequency band of the radio station, so that the mutual interference between the radar system and the communication radio station can be effectively avoided. In addition, through calculation, the output signal-to-interference-and-noise ratio of the radar signal of the embodiment is 0.74, the improvement of 2.26dB is achieved, and the required running time can be reduced by 82.5%.
The above embodiment may be implemented by using a transmit signal optimization system for improving radar detection performance as described in the following embodiments:
another embodiment provides a transmit signal optimization system for improving radar detection performance, the transmit signal optimization system comprising:
a setting module configured to: setting radar signal emission energy, a reference coding sequence, a coding sequence similarity coefficient and maximum energy allowing radar signals to leak to frequency bands where each adjacent communication system is located;
the code element number of the reference code sequence is N;
a first acquisition module configured to: acquiring radar echo data without target signals to estimate an inverse matrix R corresponding to an N-dimension Lei Dagan interference covariance matrix;
a second acquisition module configured to: acquiring the working frequency bands of a radar and each adjacent communication system to estimate an N-dimension interference covariance matrix corresponding to the working frequency band of each adjacent communication system; the operating band includes a lower sideband cutoff frequency and an upper sideband cutoff frequency. The second acquisition module includes:
A normalization processing sub-module configured to: adopting the working frequency bands of the radars, and carrying out normalization processing on the working frequency bands of all adjacent communication systems according to the following formula;
Figure BDA0003677145620000231
Figure BDA0003677145620000232
B＝g u -g l ；
wherein ,
Figure BDA0003677145620000233
and />
Figure BDA0003677145620000234
Lower sideband cut-off frequencies of k-th adjacent communication systems after normalization processingAnd an upper sideband cutoff frequency; />
Figure BDA0003677145620000235
and />
Figure BDA0003677145620000236
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the kth adjacent communication system are respectively; g u and gl The upper sideband cut-off frequency and the lower sideband cut-off frequency of the radar are respectively; b is radar bandwidth; k=1, 2, …, K being the number of proximity communication systems;
a first computing sub-module configured to: according to the working frequency bands of all adjacent communication systems after normalization processing, calculating all element values in an interference covariance matrix corresponding to the working frequency bands of all adjacent communication systems according to the following formula;
Figure BDA0003677145620000237
wherein ,
Figure BDA0003677145620000238
and h=1, 2, …, N, l=1, 2, …, N, which are element values of the h th row and the first column in the interference covariance matrix corresponding to the operating frequency band of the kth adjacent communication system.
A first determination module configured to: determining a first matrix A according to the radar signal emission energy and a reference coding sequence 0 ；
A second determination module configured to: according to the first matrix A 0 Determining a signal emission reference matrix set according to the coding sequence similarity coefficient, the interference covariance matrix corresponding to the working frequency band of each adjacent communication system and the maximum energy of allowing radar signals to leak to the frequency band of each adjacent communication system;
the signal transmission reference matrix set comprises a radar reference matrix B 0 And a signal transmission reference matrix for each adjacent communication system;
a third determination module configured to: determining a second matrix according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the signal transmission reference matrix set;
a fourth determination module configured to: determining an initial radar transmission signal coding sequence according to the radar signal transmission energy and the reference coding sequence;
an iterative optimization module configured to: and carrying out iterative optimization on the initial radar transmission signal coding sequence according to the signal transmission reference matrix set and the second matrix. The iterative optimization module comprises:
a first setting sub-module configured to: setting the kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k The initial values of' are all 0;
a second computing sub-module configured to: calculating a second auxiliary variable z according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the initial radar transmission signal coding sequence S;
a third computing sub-module configured to: according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix, the kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k ' and the second auxiliary variable z and the respective signal-emission reference matrix B of the signal-emission reference matrix set k ' calculating a first auxiliary vector t;
a second setting sub-module configured to: setting the iteration number m=1;
a fourth calculation submodule for calculating a third auxiliary variable v according to the first auxiliary vector T, the second matrix T and the radar signal emission energy;
a fifth calculation sub-module configured to: according to the second matrix T, the first auxiliary vector T and the third auxiliary variable v, calculating a radar emission signal coding sequence S after the mth iteration (m) ；
A sixth calculation sub-module configured to: according toThe m-th iteration is followed by an initial radar transmission signal coding sequence s (m) Calculating a second auxiliary vector q after the mth iteration by the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the first Lagrangian multiplier vector d (m) ；
A seventh calculation sub-module configured to: according to the second auxiliary vector q after the mth iteration (m) And a preset punishment coefficient, calculating a second auxiliary variable z after the mth iteration (m) ；
An eighth calculation sub-module configured to: according to each signal emission reference matrix in the signal emission reference matrix set and the m-th iterated radar emission signal coding sequence S (m) And the kth' second Lagrangian multiplier vector C k ' calculating a fourth auxiliary variable after the mth iteration
Figure BDA0003677145620000251
A first determination submodule configured to: judging the kth' second auxiliary variable z after m iterations (m) A kind of electronic device 2 Whether the square of the norm is less than or equal to 1 If so, the kth' fourth auxiliary variable after the mth iteration is obtained
Figure BDA0003677145620000252
As the kth' first auxiliary variable y after the mth iteration k ’ (m) And send to the eighth calculation sub-module; if not, the kth' fourth auxiliary variable +.>
Figure BDA0003677145620000253
Dividing by the kth' fourth auxiliary variable after the mth iteration +.>
Figure BDA0003677145620000254
Is taken as the kth' first auxiliary variable y after the mth iteration after the 2 norm of (2) k ’ (m) And send to the eighth calculation sub-module;
ninth meterAn operator module configured to: according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the second auxiliary variable z after the mth iteration (m) The code sequence S of the radar transmitting signal after the mth iteration (m) The kth' first auxiliary variable y after the mth iteration k ’ (m) Each signal emission reference matrix in the signal emission reference matrix set is used for calculating a residual vector after the mth iteration;
a second determination submodule configured to: judging whether the 2 norm of the residual vector is smaller than a threshold value, if so, outputting the radar emission signal coding sequence S after the mth iteration (m) Ending; if not, transmitting the code sequence of the radar emission signal after the mth iteration to a tenth computing sub-module;
a tenth calculation sub-module configured to: according to the kth' second Lagrangian multiplier vector C k 'kth' first auxiliary variable y after mth iteration k ’ (m) The code sequence S of the radar transmitting signal after the mth iteration (m) And each signal-emission reference matrix B in the signal-emission reference matrix set k 'calculating the kth' second Lagrange multiplier vector c after the mth iteration k ’ (m) ；
An eleventh computing sub-module configured to: according to the first Lagrangian multiplier vector d and the second auxiliary variable z after the mth iteration (m) The code sequence S of the radar transmitting signal after the mth iteration (m) An inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix is calculated, and a first Lagrange multiplier vector d after the mth iteration is calculated (m) ；
An assign sub-module configured to: the kth' first auxiliary variable y after the mth iteration is processed k ’ (m) The kth' second Lagrangian multiplier vector C after the mth iteration k ’ (m) A first Lagrangian multiplier vector d after the mth iteration (m) The code sequence S of the initial radar transmitting signal after the mth iteration (m) And the mthSecond auxiliary variable z after multiple iterations (m) Respectively assigned to the kth' first auxiliary variable y k 'said kth' second lagrangian multiplier vector C k ' the first Lagrangian multiplier vector d, the initial radar transmit signal coding sequence S and a second auxiliary variable z after an mth iteration (m) And m+1 is assigned to m and returned to the fourth calculation sub-module.
An amplitude modulation and phase modulation processing module configured to: and carrying out amplitude modulation and phase modulation processing on the radar signal by adopting the iterative optimized radar emission signal coding sequence to obtain a radar emission signal.
The embodiment further includes, between the setting module and the obtaining module:
a normalization processing module configured to: and when the emission energy corresponding to the reference coding sequence is not equal to the emission energy of the radar signal, carrying out normalization processing on the reference coding sequence.
The technical terms, formulas and parameter definitions in the formulas according to the above embodiments are applicable, and are not described in detail herein.
Note that the technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be regarded as the scope of the description. The foregoing examples represent only a few embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that it would be apparent to those skilled in the art that various modifications and improvements could be made without departing from the spirit of the present application, which would be within the scope of the present application. Accordingly, the scope of protection of the present application is to be determined by the claims appended hereto.

Claims (10)

1. A transmit signal optimization method for improving radar detection performance, the transmit signal optimization method comprising:
step S1, setting radar signal emission energy, a reference coding sequence, a coding sequence similarity coefficient and maximum energy allowing radar signals to leak to frequency bands where all adjacent communication systems are located;
the code element number of the reference code sequence is N;
s2, radar echo data without target signals are obtained to estimate an inverse matrix R corresponding to an N-dimension Lei Dagan interference covariance matrix;
step S3, acquiring the working frequency bands of the radar and each adjacent communication system to estimate an N-by-N-dimensional interference covariance matrix corresponding to the working frequency band of each adjacent communication system;
the operating frequency band includes a lower sideband cutoff frequency and an upper sideband cutoff frequency;
s4, determining a first matrix A according to the radar signal emission energy and the reference coding sequence 0 ；
The first matrix is:
Figure FDA0004164909020000011
wherein ,A0 Is a first matrix; i is an identity matrix of N x N dimensions; e, e t Transmitting energy for the radar signal; s is(s) 0 Is a reference coding sequence;
step S5, according to the first matrix A 0 Determining a signal emission reference matrix set according to the coding sequence similarity coefficient, the interference covariance matrix corresponding to the working frequency band of each adjacent communication system and the maximum energy of allowing radar signals to leak to the frequency band of each adjacent communication system;
The signal transmission reference matrix set comprises a radar reference matrix B 0 And a signal transmission reference matrix for each adjacent communication system;
s6, determining a second matrix according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the signal transmission reference matrix set;
the second matrix is:
Figure FDA0004164909020000021
wherein T is a second matrix; r is an inverse matrix corresponding to the Lei Dagan interference covariance matrix; b (B) k 'is the kth' signal transmission reference matrix in the signal transmission reference matrix set;
s7, determining an initial radar transmitting signal coding sequence according to the radar signal transmitting energy and the reference coding sequence;
s8, carrying out iterative optimization on the initial radar emission signal coding sequence according to the signal emission reference matrix set and the second matrix;
and S9, performing amplitude modulation and phase modulation processing on the radar signal by adopting the iteratively optimized radar emission signal coding sequence to obtain a radar emission signal.
2. The transmission signal optimizing method according to claim 1, characterized in that between the step S1 and the step S2, the transmission signal optimizing method further comprises:
and when the emission energy corresponding to the reference coding sequence is not equal to the emission energy of the radar signal, carrying out normalization processing on the reference coding sequence.
3. The method according to claim 2, wherein in the step S3, the specific process of determining the N x N dimensional interference covariance matrix corresponding to the operating frequency band of each neighboring communication system includes:
step S31, adopting the working frequency bands of the radar, and carrying out normalization processing on the working frequency bands of all the adjacent communication systems according to the following formula;
Figure FDA0004164909020000022
Figure FDA0004164909020000031
B＝g u -g l ；
wherein ,
Figure FDA0004164909020000032
and />
Figure FDA0004164909020000033
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the k-th adjacent communication system after normalization processing are respectively; />
Figure FDA0004164909020000034
and />
Figure FDA0004164909020000035
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the kth adjacent communication system are respectively; g u and gl The upper sideband cut-off frequency and the lower sideband cut-off frequency of the radar are respectively; b is radar bandwidth; k=1, 2, …, K being the number of proximity communication systems;
step S32, according to the working frequency bands of all the adjacent communication systems after normalization processing, calculating all element values in an interference covariance matrix corresponding to the working frequency bands of all the adjacent communication systems according to the following formula;
Figure FDA0004164909020000036
wherein ,
Figure FDA0004164909020000037
and h=1, 2, …, N, l=1, 2, …, N, which are element values of the h th row and the first column in the interference covariance matrix corresponding to the operating frequency band of the kth adjacent communication system.
4. A transmitted signal optimization method according to claim 3, characterized in that in said step S5, each signal transmission reference matrix in said set of signal transmission reference matrices is:
Figure FDA0004164909020000038
wherein ,Bk 'is the kth signal transmission reference matrix, when k' =0, then B 0 Transmitting a reference matrix for the signals of the radar; when k' =k, then B k Transmitting a reference matrix for signals of a kth adjacent communication system; a is that 0 Is a first matrix; epsilon 0 Is a coding sequence similarity coefficient; e (E) I k To allow radar signals to leak to the maximum energy of the frequency band in which the kth proximity communication system is located; r is R I k Is the interference covariance matrix corresponding to the working frequency band of the kth adjacent communication system.
5. The method according to claim 4, wherein in the step S7, the initial radar transmission signal coding sequence is:
S＝[s 1 s 2 …s n …s N ] T ；
Figure FDA0004164909020000041
s is an initial radar transmitting signal coding sequence; s is(s) n A value corresponding to an nth code element in the initial radar transmitting signal coding sequence; θ n Is a random variable uniformly distributed in the interval of [0,2 pi ]; n=1, 2, …, N being the number of symbols of the reference coding sequence.
6. The method according to claim 5, wherein in the step S8, the iterative optimization comprises:
Step S801, set upThe kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k’ The initial values of (2) are all 0;
step S802, calculating a second auxiliary variable z according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the initial radar transmission signal coding sequence S;
step S803, according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix, the kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k’ Each signal emission reference matrix B of the second auxiliary variable z and the signal emission reference matrix set k ' calculating a first auxiliary vector t;
step S804, setting the iteration number m=1;
step S805, calculating a third auxiliary variable v according to the first auxiliary vector T, the second matrix T and the radar signal emission energy;
step S806, calculating a radar transmission signal coding sequence S after the mth iteration according to the second matrix T, the first auxiliary vector T and the third auxiliary variable v (m) ；
Step S807, according to the initial radar transmitting signal coding sequence S after the mth iteration (m) Calculating a second auxiliary vector q after the mth iteration by the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the first Lagrangian multiplier vector d (m) ；
Step S808, according to the second auxiliary vector q after the mth iteration (m) And a preset punishment coefficient, calculating a second auxiliary variable z after the mth iteration (m) ；
Step S809, according to each signal emission reference matrix in the signal emission reference matrix set, the m-th iterated radar emission signal coding sequence S (m) And the kth' second Lagrangian multiplier vector C k’ Calculating a fourth auxiliary variable after the mth iteration
Figure FDA0004164909020000051
Step S810, judging the kth' second auxiliary variable z after the m iterations (m) If the square of the 2 norm of (2) is less than or equal to 1, if so, the kth' fourth auxiliary variable after the mth iteration is obtained
Figure FDA0004164909020000052
As the kth' first auxiliary variable y after the mth iteration k’ (m) Step S811 is entered; if not, the kth' fourth auxiliary variable after the mth iteration is processed
Figure FDA0004164909020000053
Dividing by the kth' fourth auxiliary variable after the mth iteration +.>
Figure FDA0004164909020000054
Is taken as the kth' first auxiliary variable y after the mth iteration after the 2 norm of (2) k’ (m) Step S811 is entered;
step S811, according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the second auxiliary variable z after the mth iteration (m) The code sequence s of the radar emission signal after the mth iteration (m) The kth' first auxiliary variable y after the mth iteration k’ (m) Each signal emission reference matrix in the signal emission reference matrix set is used for calculating a residual vector after the mth iteration;
step S812, judging whether the 2 norm of the residual vector is smaller than a threshold value, if so, outputting the radar transmission signal coding sequence S after the mth iteration (m) Ending; if not, go to step S813;
step S813, according to the kth' second Lagrangian multiplier vector C k’ The kth' first auxiliary variable y after the mth iteration k ’ (m) The code sequence s of the radar emission signal after the mth iteration (m) And each signal-emission reference matrix B in the signal-emission reference matrix set k’ Calculating a kth' second Lagrange multiplier vector c after the mth iteration k’ (m) ；
Step S814, according to the first Lagrangian multiplier vector d and the second auxiliary variable z after the mth iteration (m) The code sequence s of the radar emission signal after the mth iteration (m) An inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix is calculated, and a first Lagrange multiplier vector d after the mth iteration is calculated (m) ；
Step S815, the kth' first auxiliary variable y after the mth iteration is processed k ’ (m) The kth' second Lagrangian multiplier vector C after the mth iteration k’ (m) A first Lagrangian multiplier vector d after the mth iteration (m) The m-th iteration is followed by an initial radar transmission signal coding sequence s (m) And a second auxiliary variable z after the mth iteration (m) Respectively assigned to the kth' first auxiliary variable y k 'said kth' second lagrangian multiplier vector C k’ The first Lagrangian multiplier vector d, the initial radar transmission signal coding sequence S and a second auxiliary variable z after the mth iteration (m) And m+1 is assigned to m, returning to step S805.
7. A transmit signal optimization system for improving radar detection performance, the transmit signal optimization system comprising:
a setting module configured to: setting radar signal emission energy, a reference coding sequence, a coding sequence similarity coefficient and maximum energy allowing radar signals to leak to frequency bands of each adjacent communication system;
the code element number of the reference code sequence is N;
a first acquisition module configured to: acquiring radar echo data without target signals to estimate an inverse matrix R corresponding to an N-dimension Lei Dagan interference covariance matrix;
A second acquisition module configured to: acquiring the working frequency bands of a radar and each adjacent communication system to estimate an N-dimension interference covariance matrix corresponding to the working frequency band of each adjacent communication system;
the operating frequency band includes a lower sideband cutoff frequency and an upper sideband cutoff frequency;
a first determination module configured to: determining a first matrix A according to the radar signal emission energy and a reference coding sequence 0 ；
The first matrix:
Figure FDA0004164909020000071
wherein ,A0 Is a first matrix; i is an identity matrix of N x N dimensions; e, e t Transmitting energy for the radar signal; s is(s) 0 Is a reference coding sequence;
a second determination module configured to: according to the first matrix A 0 Determining a signal emission reference matrix set according to the coding sequence similarity coefficient, the interference covariance matrix corresponding to the working frequency band of each adjacent communication system and the maximum energy of allowing radar signals to leak to the frequency band of each adjacent communication system;
the signal transmission reference matrix set comprises a radar reference matrix B 0 And a signal transmission reference matrix for each adjacent communication system;
a third determination module configured to: determining a second matrix according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the signal transmission reference matrix set;
The second matrix is:
Figure FDA0004164909020000072
wherein T is a second matrix; r is an inverse matrix corresponding to the Lei Dagan interference covariance matrix; b (B) k 'is the kth' signal transmission reference matrix in the signal transmission reference matrix set;
a fourth determination module configured to: determining an initial radar transmission signal coding sequence according to the radar signal transmission energy and the reference coding sequence;
an iterative optimization module configured to: according to the signal transmission reference matrix set and the second matrix, carrying out iterative optimization on the initial radar transmission signal coding sequence;
an amplitude modulation and phase modulation processing module configured to: and carrying out amplitude modulation and phase modulation processing on the radar signal by adopting the iterative optimized radar emission signal coding sequence to obtain a radar emission signal.
8. The transmit signal optimization system of claim 7, wherein the transmit signal optimization system further comprises:
a normalization processing module configured to: and when the emission energy corresponding to the reference coding sequence is not equal to the emission energy of the radar signal, carrying out normalization processing on the reference coding sequence.
9. The transmit signal optimization system of claim 8 wherein the second acquisition module comprises:
A normalization processing sub-module configured to: adopting the working frequency bands of the radars, and carrying out normalization processing on the working frequency bands of all adjacent communication systems according to the following formula;
Figure FDA0004164909020000081
Figure FDA0004164909020000082
B＝g u -g l ；
wherein ,
Figure FDA0004164909020000083
and />
Figure FDA0004164909020000084
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the k-th adjacent communication system after normalization processing are respectively; />
Figure FDA0004164909020000085
and />
Figure FDA0004164909020000086
The lower sideband cutoff frequency and the upper sideband cutoff frequency of the kth adjacent communication system are respectively; g u and gl The upper sideband cut-off frequency and the lower sideband cut-off frequency of the radar are respectively; b is radar bandwidth; k=1, 2, …, K being the number of proximity communication systems;
a first computing sub-module configured to: according to the working frequency bands of all adjacent communication systems after normalization processing, calculating all element values in an interference covariance matrix corresponding to the working frequency bands of all adjacent communication systems according to the following formula;
Figure FDA0004164909020000091
wherein ,
Figure FDA0004164909020000092
and h=1, 2, …, N, l=1, 2, …, N, which are element values of the h th row and the first column in the interference covariance matrix corresponding to the operating frequency band of the kth adjacent communication system.
10. The transmit signal optimization system of claim 9, wherein the iterative optimization module comprises:
A first setting sub-module configured to: setting the kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k’ The initial values of (2) are all 0;
a second computing sub-module configured to: calculating a second auxiliary variable z according to an inverse matrix R corresponding to the Lei Dagan interference covariance matrix and the initial radar transmission signal coding sequence S;
a third computing sub-module configured to: according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix, the kth' first auxiliary variable y k 'first Lagrangian multiplier vector d and kth' second Lagrangian multiplier vector C k’ Each signal emission reference matrix B of the second auxiliary variable z and the signal emission reference matrix set k ' calculating a first auxiliary vector t;
a second setting sub-module configured to: setting the iteration number m=1;
a fourth calculation sub-module for calculating a third auxiliary variable v according to the first auxiliary vector T, the second matrix T and the radar signal emission energy;
a fifth calculation sub-module configured to: according to the second matrix T, the first auxiliary vector T and the third auxiliary variable v, calculating a radar emission signal coding sequence s after the mth iteration (m) ；
A sixth calculation sub-module configured to: according to the code sequence s of the initial radar transmitting signal after the mth iteration (m) Calculating a second auxiliary vector q after the mth iteration by the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the first Lagrangian multiplier vector d (m) ；
A seventh calculation sub-module configured to: according to the second auxiliary vector q after the mth iteration (m) And a preset punishment coefficient, calculating a second auxiliary variable z after the mth iteration (m) ；
An eighth calculation sub-module configured to: according to each signal emission reference matrix in the signal emission reference matrix set and the radar emission signal coding sequence s after the mth iteration (m) And the kth' second Lagrangian multiplier vector C k’ Calculating a fourth auxiliary variable after the mth iteration
Figure FDA0004164909020000101
A first determination submodule configured to: judging the kth' second auxiliary variable z after m iterations (m) If the square of the 2 norm of (2) is less than or equal to 1, if so, the kth' fourth auxiliary variable after the mth iteration is obtained
Figure FDA0004164909020000102
As the kth' first auxiliary variable y after the mth iteration k’ (m) And send to the eighth calculation sub-module; if not, the kth' fourth auxiliary variable +. >
Figure FDA0004164909020000103
Dividing by the kth' fourth auxiliary variable after the mth iteration +.>
Figure FDA0004164909020000104
Is taken as the kth' first auxiliary variable y after the mth iteration after the 2 norm of (2) k’ (m) And send to the eighth calculation sub-module;
a ninth calculation sub-module configured to: according to the inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix and the second auxiliary variable z after the mth iteration (m) The code sequence s of the radar emission signal after the mth iteration (m) The kth' first auxiliary variable y after the mth iteration k’ (m) Each signal emission reference matrix in the signal emission reference matrix set is used for calculating a residual vector after the mth iteration;
a second determination submodule configured to: judging whether the 2 norm of the residual vector is smaller than a threshold value, if so, outputting the radar emission signal coding sequence s after the mth iteration (m) Ending; if not, transmitting the code sequence of the radar emission signal after the mth iteration to a tenth computing sub-module;
tenth calculation sub-dieA block configured to: according to the kth' second Lagrangian multiplier vector C k’ The kth' first auxiliary variable y after the mth iteration k ’ (m) The code sequence s of the radar emission signal after the mth iteration (m) And each signal-emission reference matrix B in the signal-emission reference matrix set k 'calculating the kth' second Lagrange multiplier vector c after the mth iteration k’ (m) ；
An eleventh computing sub-module configured to: according to the first Lagrangian multiplier vector d and the second auxiliary variable z after the mth iteration (m) The code sequence s of the radar emission signal after the mth iteration (m) An inverse matrix R corresponding to the Lei Dagan disturbance covariance matrix is calculated, and a first Lagrange multiplier vector d after the mth iteration is calculated (m) ；
An assign sub-module configured to: the kth' first auxiliary variable y after the mth iteration is processed k ’ (m) The kth' second Lagrangian multiplier vector C after the mth iteration k’ (m) A first Lagrangian multiplier vector d after the mth iteration (m) The m-th iteration is followed by an initial radar transmission signal coding sequence s (m) And a second auxiliary variable z after the mth iteration (m) Respectively assigned to the kth' first auxiliary variable y k 'said kth' second lagrangian multiplier vector C k’ The first Lagrangian multiplier vector d, the initial radar transmission signal coding sequence S and a second auxiliary variable z after the mth iteration (m) And m+1 is assigned to m and returned to the fourth calculation sub-module.
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