CN115015860A

CN115015860A - Transmitting signal optimization method and system for improving radar detection performance

Info

Publication number: CN115015860A
Application number: CN202210622033.4A
Authority: CN
Inventors: 唐波; 王海; 黄中瑞; 张峻宁; 李达; 秦立龙; 王旭阳; 吴文俊
Original assignee: National University of Defense Technology
Current assignee: National University of Defense Technology
Priority date: 2022-06-02
Filing date: 2022-06-02
Publication date: 2022-09-06
Anticipated expiration: 2042-06-02
Also published as: CN115015860B

Abstract

The invention provides a method and a system for optimizing a transmitting signal for improving the detection performance of a radar, 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 leaked to each adjacent communication system by the radar signal; estimating an inverse matrix of a radar interference covariance matrix; estimating an interference covariance matrix of each neighboring communication system; determining a first matrix, a signal transmission reference matrix set, a second matrix and an initial radar transmission signal coding sequence; performing iterative optimization on the initial radar transmission signal coding sequence according to the signal transmission reference matrix set, the second matrix and the scaling of the reference coding sequence; and amplitude modulation and phase modulation processing are carried out on the radar signals by adopting the radar transmitting signal coding sequence after iterative optimization. The frequency spectrum of the transmitted signal of the invention can form a notch in the frequency band where the adjacent communication system is positioned, and the output signal-to-interference-and-noise ratio of the radar system is increased.

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 transmitted signal optimization method and a transmitted signal optimization system for improving radar detection performance.

Background

The frequency spectrum resource is a rare and limited precious resource which has important strategic significance to countries in the world. The method can realize bearing and transmission of information by efficiently utilizing frequency spectrum resources, and has important application in multiple fields of radar detection, mobile communication, navigation positioning, broadcast television and the like. However, with the rapid development of broadband mobile communication technology and the overall popularization of intelligent devices, the demand of frequency-using devices for spectrum resources is more urgent, so that the spectrum resources become more scarce. When various frequency utilization devices compete for frequency spectrum resources mutually, the frequency utilization devices working in the same or similar frequency bands generate electromagnetic wave signals with various quantities, complex patterns and dynamic randomness, so that frequency spectrum congestion is easily caused, the mutual interference is serious, and the performance of the devices is obviously reduced.

In order to improve the detection performance of a radar system in a spectrum congestion environment and reduce mutual interference between the radar system and a neighboring communication system, a feasible idea is to optimize a radar transmission signal, so that a signal spectrum forms a notch in a frequency band where the neighboring communication system is located, and an 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 austry models the Radar Signal design problem as a quadratic function optimization problem under a quadratic constraint in the literature, "shaping Multiple Spectral Compatibility in Radar waves [ J ] (IEEE Signal Processing Letters,2016,23(4): 483-.

Disclosure of Invention

One of the objectives of the present invention is to provide a method for optimizing a transmission signal for improving radar detection performance, wherein the spectrum of the transmission signal obtained by the optimization method can form a notch in a frequency band where a neighboring communication system is located, and increase the output signal-to-interference-and-noise ratio of the radar system.

It is a further object of the present invention to provide a transmitted signal optimization system for improving radar detection performance.

In order to achieve one of the purposes, the invention adopts the following technical scheme:

a transmission signal optimization method for improving radar detection performance, the transmission signal optimization method comprising:

step S1, setting radar signal emission energy, a reference coding sequence, a coding sequence similarity coefficient and the maximum energy of the frequency band where the radar signal is allowed to leak to each adjacent communication system;

the code element number of the reference coding sequence is N;

step S2, radar echo data without target signals are obtained to estimate an inverse matrix R corresponding to the radar interference covariance matrix with dimension N x N;

step S3, obtaining the working frequency bands of the radar and each adjacent communication system to estimate an N-by-N interference covariance matrix corresponding to the working frequency bands of each adjacent communication system;

the operating frequency band comprises a lower sideband cut-off frequency and an upper sideband cut-off frequency;

step 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 by 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 the frequency band where the radar signal is allowed to leak to each adjacent communication system;

the signal emission reference matrix set comprises a radar reference matrix B ₀ And signal transmission reference matrixes of the adjacent communication systems;

step S6, determining a second matrix according to the inverse matrix R corresponding to the radar interference covariance matrix and the signal transmission reference matrix set;

step S7, determining an initial radar emission signal coding sequence according to the radar signal emission energy and the reference coding sequence;

step S8, performing iterative optimization on the initial radar emission signal coding sequence according to the signal emission reference matrix set and the second matrix;

and step S9, performing amplitude modulation and phase modulation processing on the radar signal by adopting the radar transmitting signal coding sequence after iterative optimization to obtain a radar transmitting signal.

Further, between the step S1 and the step S2, the method for optimizing the 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, performing normalization processing on the reference coding sequence.

Further, in step S3, the specific process of determining the N × N interference covariance matrix corresponding to the operating frequency band of each neighboring communication system includes:

step S31, adopting the working frequency band of the radar, and carrying out normalization processing on the working frequency band of each adjacent communication system according to the following formula;

B＝g ^u -g ^l ；

wherein ,

and

respectively the lower sideband cut-off frequency and the upper sideband cut-off frequency of the kth adjacent communication system after normalization processing;

and

a lower sideband cutoff frequency and an upper sideband cutoff frequency of a kth adjacent communication system, respectively; g ^u and g^l The upper sideband cut-off frequency and the lower sideband cut-off frequency of the radar are respectively; b is the radar bandwidth; k is 1,2, …, K is the number of adjacent communication systems;

step S32, according to the working frequency band of each adjacent communication system after normalization processing, calculating each element value in the interference covariance matrix corresponding to the working frequency band of each adjacent communication system according to the following formula;

wherein ,

for the values of the elements in the h-th row and l-th column of the interference covariance matrix corresponding to the operating frequency band of the kth adjacent communication system, h is 1,2, …, and N, l is 1,2, …, N.

Further, in step S5, each signal transmission reference matrix in the signal transmission reference matrix set is:

wherein ,B_k ' is k ' th signal transmission reference matrix, when k ' is 0, then B ₀ Transmitting a reference matrix for a signal of the radar; when k ═ k, then B _k Transmitting a reference matrix for a signal of a kth neighboring communication system; a. the ₀ Is a first matrix; i is an N-by-N dimensional identity matrix; e.g. of the type _t Transmitting energy for the radar signal; s ₀ Is a reference coding sequence; epsilon ₀ Is the coding sequence similarity coefficient; e _I ^k The maximum energy for allowing the radar signal to leak to the frequency band of the kth adjacent communication system; r _I ^k An interference covariance matrix corresponding to an operating frequency band of the kth neighboring communication system.

Further, in step S7, the initial radar-emitting signal encoding sequence is:

S＝[S ₁ S2…S _n …S _N ] ^T

wherein, S is an initial radar emission signal coding sequence; s _n The value corresponding to the nth code element in the initial radar transmitting signal coding sequence is obtained; theta _n Random variables uniformly distributed in the interval of [0,2 pi); n is 1,2, …, and N is the number of code elements of the reference code sequence.

Further, in the step S8, the specific process of the iterative optimization includes:

step S801, setting the kth first auxiliary variable y _k ', a first Lagrange multiplier vector d and a kth' second Lagrange multiplier vector C _k ' the initial values are all 0;

step S802, calculating a second auxiliary variable z according to an inverse matrix R corresponding to the radar interference covariance matrix and the initial radar transmitting signal coding sequence S;

step S803, according to the radar interference covariance momentThe inverse matrix R corresponding to the matrix and the k' th first auxiliary variable y _k ', a first Lagrange multiplier vector d and a kth' second Lagrange multiplier vector C _k ' and said second auxiliary variable z and each signal transmission reference matrix B in said set of signal transmission reference matrices _k ', calculating a first auxiliary vector t;

step S804, setting the iteration number m to 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 emission 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 emission signal coded sequence S after the mth iteration ^(m) Calculating an inverse matrix R corresponding to the radar interference covariance matrix and the first Lagrange multiplier vector d, and calculating a second auxiliary vector q after the mth iteration ^(m) ；

Step S808, according to the second auxiliary vector q after the mth iteration ^(m) And a preset penalty 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 and the radar emission signal coding sequence S after the mth iteration ^(m) And said kth second Lagrangian multiplier vector C _k ', calculating the fourth auxiliary variable after the mth iteration

Step S810, judging the kth second auxiliary variable z after the m iterations ^(m) If the square of the 2 norm of (a) is less than or equal to 1, if so, the kth' fourth auxiliary variable after the mth iteration is added

As the kth' first auxiliary variable y after the mth iteration _k ’ ^(m) The process advances to step S811; if not, the kth' fourth auxiliary variable after the mth iteration is used

Divided by the kth' fourth auxiliary variable after the mth iteration

After 2 norms as the kth' first auxiliary variable y after the m iteration _k ’ ^(m) The process advances to step S811;

step S811, according to the inverse matrix R corresponding to the radar interference covariance matrix and the second auxiliary variable z after the mth iteration ^(m) And the radar emission signal coding sequence S after the mth iteration ^(m) The kth' first auxiliary variable y after the mth iteration _k ’ ^(m) Calculating a residual vector after the mth iteration by using each signal transmission reference matrix in the signal transmission reference matrix set;

step S812, judging whether the 2 norm of the residual error vector is smaller than a threshold value, if so, outputting the radar transmitting signal coding sequence S after the mth iteration ^(m) And ending; if not, go to step S813;

step S813 according to the k' th second Lagrange multiplier vector C _k ', the kth' first auxiliary variable y after the m-th iteration _k ’ ^(m) And the radar emission signal coding sequence S 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 Lagrange multiplier vector d and the second auxiliary variable z after the mth iteration ^(m) And the radar emission signal coding sequence S after the mth iteration ^(m) An inverse corresponding to the radar interference covariance matrixMatrix R, calculating first Lagrange multiplier vector d after mth iteration ^(m) ；

Step S815, the kth' first auxiliary variable y after the mth iteration _k ^’(m) The kth' second Lagrangian multiplier vector C after the mth iteration _k ’ ^(m) The first Lagrangian multiplier vector d after the mth iteration ^(m) And the initial radar emission signal coding sequence S after the mth iteration ^(m) And a second auxiliary variable z after said m-th iteration ^(m) Respectively assigned to the k' th first auxiliary variable y _k ', the k-th second Lagrange multiplier vector C _k ', the first Lagrange multiplier vector d, the initial radar emission signal coding sequence S and the second auxiliary variable z after the m-th iteration ^(m) And m +1 is given 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 setup 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 the adjacent communication systems are located;

the code element number of the reference coding sequence is N;

a first acquisition module configured to: acquiring radar echo data without target signals to estimate an inverse matrix R corresponding to the radar interference covariance matrix of dimension N x N;

a second acquisition module configured to: acquiring the working frequency bands of the radar and each adjacent communication system to estimate an N-by-N interference covariance matrix corresponding to the working frequency bands of each adjacent communication system;

a first determination module configured to: transmitting energy and reference code according to the radar signalSequence, determining a first matrix A ₀ ；

A second determination module configured to: according to the first matrix A ₀ Determining a signal emission reference matrix set by 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 the frequency band where the radar signal is allowed to leak to each adjacent communication system;

a third determination module configured to: determining a second matrix according to the inverse matrix R corresponding to the radar interference covariance matrix and the signal transmission reference matrix set;

a fourth determination module configured to: determining an initial radar emission signal coding sequence according to the radar signal emission energy and the reference coding sequence;

an iterative optimization module configured to: performing iterative optimization on the initial radar transmission signal coding sequence according to the signal transmission reference matrix set and the second matrix;

an amplitude modulation and phase modulation processing module configured to: and carrying out amplitude modulation and phase modulation processing on the radar signals by adopting the radar transmitting signal coding sequence after iterative optimization to obtain the radar transmitting signals.

Further, between the setting module and the obtaining module, the transmission 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, performing normalization processing on the reference coding sequence.

Further, the second obtaining module includes:

a normalization processing sub-module configured to: adopting the working frequency band of the radar, and carrying out normalization processing on the working frequency band of each adjacent communication system according to the following formula;

B＝g ^u -g ^l ；

wherein ,

and

and

a first computation submodule configured to: according to the working frequency bands of the adjacent communication systems after normalization processing, calculating each element value in an interference covariance matrix corresponding to the working frequency bands of the adjacent communication systems according to the following formula;

wherein ,

interference covariance matrix corresponding to operating frequency band of kth adjacent communication systemThe values of the elements in the h-th row and the l-th column are

h

1,2, …, N,

l

1,2, …, N.

Further, the iterative optimization module comprises:

a first setup submodule configured to: setting the k' th first auxiliary variable y _k ', a first Lagrange multiplier vector d and a kth' second Lagrange multiplier vector C _k ' the initial values are all 0;

a second computation submodule configured to: calculating a second auxiliary variable z according to an inverse matrix R corresponding to the radar interference covariance matrix and the initial radar transmission signal coding sequence S;

a third computing submodule configured to: according to the inverse matrix R corresponding to the radar interference covariance matrix and the kth first auxiliary variable y _k ', a first Lagrangian multiplier vector d, and a kth second Lagrangian multiplier vector C _k ' and said second auxiliary variable z and each signal transmission reference matrix B in said set of signal transmission reference matrices _k ', calculating a first auxiliary vector t;

a second setup submodule configured to: setting the iteration number m to be 1;

the fourth calculation submodule calculates a third auxiliary variable v according to the first auxiliary vector T, the second matrix T and the radar signal emission energy;

a fifth computation submodule configured to: calculating a radar emission 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) ；

A sixth computation submodule configured to: according to the initial radar emission signal coding sequence s after the mth iteration ^(m) Calculating an inverse matrix R corresponding to the radar interference covariance matrix and the first Lagrange multiplier vector d, and calculating a second auxiliary vector q after the mth iteration ^(m) ；

A seventh computing submodule configured to: according to the second auxiliary vector q after the mth iteration ^(m) And a predetermined penalty coefficient, calculating the mth timeSecond auxiliary variable z after iteration ^(m) ；

An eighth computation submodule 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 said kth second Lagrangian multiplier vector C _k ', calculating the fourth auxiliary variable after the m-th iteration

A first judgment sub-module configured to: judging the kth second auxiliary variable z after the m iterations ^(m) If the square of the 2 norm of (a) is less than or equal to 1, if so, the kth' fourth auxiliary variable after the mth iteration is added

As the kth' first auxiliary variable y after the mth iteration _k ’ ^(m) And sending the data to an eighth calculation submodule; if not, the kth' fourth auxiliary variable after the mth iteration is used

Divided by the kth' fourth auxiliary variable after the mth iteration

After 2 norms as the kth' first auxiliary variable y after the m iteration _k ’ ^(m) And sending the data to an eighth calculation submodule;

a ninth computation submodule configured to: according to the inverse matrix R corresponding to the radar interference covariance matrix and the second auxiliary variable z after the mth iteration ^(m) And the radar emission signal coding sequence S after the mth iteration ^(m) The kth' first auxiliary variable y after the mth iteration _k ’ ^(m) Calculating a residual vector after the mth iteration by using each signal transmission reference matrix in the signal transmission reference matrix set;

a second determination submodule configured to: judging whether the 2 norm of the residual error vector is smaller than a threshold value, if so, outputting the radar transmitting signal coded sequence S after the mth iteration ^(m) And ending; if not, transmitting the radar transmitting signal coded sequence after the mth iteration to a tenth calculation submodule;

a tenth computation submodule configured to: according to the k' th second Lagrange multiplier vector C _k ', the kth' first auxiliary variable y after the m-th iteration _k ’ ^(m) And the radar emission signal coding sequence S 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 computation submodule configured to: according to the first Lagrange multiplier vector d and the second auxiliary variable z after the mth iteration ^(m) And the radar transmitting signal coding sequence S after the mth iteration ^(m) Calculating an inverse matrix R corresponding to the radar interference covariance matrix, and calculating a first Lagrange multiplier vector d after the mth iteration ^(m) ；

An assignment 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) The first Lagrangian multiplier vector d after the mth iteration ^(m) And the initial radar emission signal coding sequence S after the mth iteration ⁽ⁿ⁾ And a second auxiliary variable z after said m-th iteration ^(m) Respectively assigned to the k' th first auxiliary variable y _k ', the k-th second Lagrange multiplier vector C _k ', the first Lagrange multiplier vector d, the initial radar emission signal coding sequence S and the second auxiliary variable z after the m-th iteration ^(m) And m +1 is assigned to m and returned to the fourth computation submodule.

In summary, the scheme provided by the invention has the following technical effects:

according to the method, the inverse matrix corresponding to the radar interference covariance matrix and the interference covariance matrix corresponding to the working frequency band of each adjacent communication system are determined by acquiring radar echo data and the working frequency bands of the radar and each adjacent communication system; 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 which allows 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 radar interference covariance matrix and a signal transmission reference matrix set; determining an initial radar emission signal coding sequence according to the radar signal emission energy and the reference coding sequence; performing iterative optimization on the initial radar transmitting signal coding sequence according to a signal transmitting reference matrix set and a second matrix; finally, amplitude modulation and phase modulation are carried out on the radar signals by adopting a radar transmitting signal coding sequence after iterative optimization to obtain the radar transmitting signals, so that a deeper notch is formed in the frequency band of the radar signal frequency spectrum in which the adjacent communication system is located, and mutual interference between the radar transmitting signal frequency spectrum and the adjacent communication system is avoided; the radar emission signal obtained by the invention improves the output signal-to-interference-and-noise ratio of the radar system and improves the target detection performance of the radar system in the spectrum congestion background; the radar transmitting signal code has better similarity with the existing radar transmitting signal, thereby enjoying excellent fuzzy function characteristic; the radar transmitting signal coding optimization design method provided by the invention is simple to realize and high in operation speed, and is beneficial to a radar system to quickly adjust the radar transmitting signal in a frequency spectrum congestion environment.

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 description of the embodiments or the prior art will be 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 by those skilled in the art without creative efforts.

FIG. 1 is a schematic flow chart of a transmitted signal optimization method for improving radar detection performance according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a radar transmission signal encoding sequence according to an embodiment of the present invention;

fig. 3 is a schematic diagram of energy spectral density of a radar signal 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 clearly and completely described below 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 embodiment provides a transmission signal optimization method for improving radar detection performance, and referring to fig. 1, the transmission signal optimization method includes:

and step S1, setting the radar signal transmitting energy, the reference coding sequence, the coding sequence similarity coefficient and the maximum energy allowing the radar signal to leak to the frequency band of each adjacent communication system.

The number of symbols of the reference code sequence of this embodiment is N. Setting the transmitting energy e of the radar signal according to the radar action distance, tactical requirements, the maximum output power of a transmitter and the like _t . If the radar signal transmission energy of the shaping pulse is agreed to be 1, the transmission energy of the radar signal depends on the transmission energy of the code signal.

Reference code sequence s of this example ₀ Generally extracted from radar signals which are coded and have the same length as the coded sequence, and the reference coded sequence s ₀ Satisfies the following conditions:

in order to obtain good signal characteristics, it is required that the coding sequence to be designed has a certain similarity with the reference coding sequence, and the similarity coefficient between the two is

0≤ε ₀ ≤2e _t 。

When referring to the coding sequence s ₀ Is not equal to the radar signal emission energy e _t Then the reference coding sequence s needs to be aligned ₀ Normalization treatment is carried out to make the reference coding sequence s ₀ Is equal to the radar signal emission energy e _t Namely, between the step S1 and the step S2, the method further includes:

and when the emission energy corresponding to the reference coding sequence is not equal to the emission energy of the radar signal, performing normalization processing on the reference coding sequence. Normalization is performed according to the following formula:

in the embodiment, the maximum energy allowing the radar signal to leak to the frequency band adjacent to the communication system

Is composed of

Far less than the radar signal emission energy e _t ，k＝1,…,K。

And step S2, radar echo data without target signals are obtained to estimate an inverse matrix R corresponding to the radar interference covariance matrix with dimension of N x N.

The radar echo data in this embodiment refers to radar echo data after down-conversion, amplification, and analog-to-digital conversion. When estimating the interference covariance matrix, snapshot data (radar echo data) of neighboring cells near the cell to be detected, which do not contain the target signal, is generally used. When estimating the interference covariance matrix, generally, radar echo data that does not include a target signal near a unit to be detected is used for estimation. In this embodiment, the inverse matrix corresponding to the N × N dimensional radar interference covariance matrix is:

R＝M ^-1 ；

wherein M is a radar interference covariance matrix of dimension N x N; r is an inverse matrix of dimension N x N; n is _p The p-th radar echo data; p is 1,2, …, and P is the number of radar echo data.

Step S3, obtaining the operating frequency bands of the radar and each neighboring communication system, so as to estimate an N × N interference covariance matrix corresponding to the operating frequency band of each neighboring communication system.

The operating band of this embodiment includes a lower sideband cutoff frequency and an upper sideband cutoff frequency.

In step S3, the specific process of determining the N × N interference covariance matrix corresponding to the operating frequency band of each neighboring communication system includes:

B＝g ^u -g ^l ；

wherein ,

and

and

a lower sideband cutoff frequency and an upper sideband cutoff frequency of a kth adjacent communication system, respectively; g is a radical of formula ^u and g^l The upper sideband cut-off frequency and the lower sideband cut-off frequency of the radar are respectively; b is the radar bandwidth; k is 1,2, …, K is the number of adjacent communication systems;

step S32, calculating each element value in the interference covariance matrix corresponding to the operating frequency band of each neighboring communication system according to the following formula based on the operating frequency band of each neighboring communication system after the normalization processing.

wherein ,

Step 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:

wherein ,A₀ Is a first matrix; i is an N-by-N dimensional identity matrix; e.g. of a cylinder _t Transmitting energy for the radar signal; 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 the frequency band where the radar signal is allowed to leak to each adjacent communication system.

The signal emission reference matrix set of the present embodiment includes signal emission reference matrices of radar and respective proximity communication systems. Each signal transmission reference matrix in the signal transmission reference matrix set is:

wherein ,B_k ' is k ' th signal transmission reference matrix, when k ' is 0, then B ₀ Is a radar reference matrix; when k ═ k, then B _k Transmitting a reference matrix for a signal of a kth neighboring communication system; a. the ₀ Is a first matrix; epsilon ₀ Is the coding sequence similarity coefficient; e _I ^k The maximum energy for allowing the radar signal to leak to the frequency band of the kth adjacent communication system; r _I ^k An interference covariance matrix corresponding to an operating frequency band of the kth neighboring communication system.

And step S6, determining a second matrix according to the inverse matrix R corresponding to the radar interference covariance matrix and the signal transmission reference matrix set.

And step S7, determining an initial radar emission signal coding sequence according to the radar signal emission 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

wherein S is an initial radar emission signal encodingCode sequence, refer to fig. 2; s _n The value corresponding to the nth code element in the initial radar transmitting signal coding sequence is obtained; theta _n Random variables uniformly distributed in the interval of [0,2 pi); n is 1,2, …, and N is the number of code elements of the reference code sequence.

And step 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 ', a first Lagrange multiplier vector d and a kth' second Lagrange multiplier vector C _k The initial values of' are all 0.

And S802, calculating a second auxiliary variable z according to the inverse matrix R corresponding to the radar 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 radar interference covariance matrix; and s is an initial radar transmitting signal coding sequence.

Step S803, according to the inverse matrix R corresponding to the radar interference covariance matrix and the kth first auxiliary variable y _k ', a first Lagrange multiplier vector d and a kth' second Lagrange multiplier vector C _k ' and said second auxiliary variable z and each signal transmission reference matrix B in said set of signal transmission reference matrices _k ', calculating a first auxiliary vector t;

the first auxiliary vector of this embodiment is:

wherein t is a first auxiliary vector; r is an inverse matrix corresponding to the radar interference covariance matrix; y is _k 'is the k' th first auxiliary variable; d is the firstA Lagrange multiplier vector, C _k 'is the k' th second Lagrange multiplier vector, z is the second auxiliary variable and B _k 'is the k' signal transmission reference matrix in the signal transmission reference matrix set.

Step S804, setting iteration number m equal to 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 emission 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 radar transmission signal coding sequence after the mth iteration is:

S ^(m) ＝(T+νI) ^-1 t

(t) ^H (T+νI) ^-2 t＝e _t

wherein ,S^(m) Coding sequences of the radar emission signals 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 an inverse matrix R corresponding to the radar interference covariance matrix and the first Lagrange multiplier vector d, and calculating a second auxiliary vector q after the mth iteration ^(m) 。

In this embodiment, the second auxiliary vector after the mth iteration is:

q ^(m) ＝R ^1/2 s ^(m) -d；

wherein ,q^(m) The second auxiliary vector after the mth iteration;

step S808, according to the second auxiliary vector q after the mth iteration ^(m) And a preset penalty coefficient, and calculating a second auxiliary variable z after the mth iteration ^(m) 。

In this embodiment, the second auxiliary variable after the mth iteration is:

wherein ,z^(m) Is the second auxiliary variable after the mth iteration; mu is a preset penalty coefficient, and the value of the penalty coefficient mu is more than 2, preferably between 3 and 5.

In this embodiment, the fourth auxiliary variable after the mth iteration is:

wherein ,

is the kth second auxiliary variable after the mth iteration;

Divided by the kth' fourth auxiliary variable after the mth iteration

in this embodiment, the kth' fourth auxiliary variable after the mth iteration

The 2 norm of (d) is:

step S811, according to the inverse matrix R corresponding to the radar interference covariance matrix and the second auxiliary variable z after the mth iteration ^(m) And the radar emission signal coding sequence S after the mth iteration ^(m) The kth' first auxiliary variable y after the mth iteration _k ’ ^(m) And calculating the residual vector after the mth iteration by using each signal transmission reference matrix in the signal transmission reference matrix set.

In this embodiment, the residual vector after the mth iteration is:

wherein ,r^(m) Is the residual vector after the mth iteration.

step S813 according to the k' th second Lagrange multiplier vector C _k ', the kth' first auxiliary variable y after the m-th iteration _k ’ ^(m) After the m-th iterationRadar emission 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:

wherein ,C’_k ^(m) Is the kth second Lagrangian multiplier vector after the mth iteration;

step S814, according to the first Lagrange multiplier vector d and the second auxiliary variable z after the mth iteration ^(m) And the radar transmitting signal coding sequence S after the mth iteration ^(m) Calculating an inverse matrix R corresponding to the radar interference covariance matrix, and calculating a first Lagrange multiplier vector d after the mth iteration ^(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 _k ’ ^(m) The kth' second Lagrangian multiplier vector C after the mth iteration _k ’ ^(m) The first Lagrangian multiplier vector d after the mth iteration ^(m) And the initial radar emission signal coding sequence S after the mth iteration ^(m) And a second auxiliary variable z after said m-th iteration ^(m) Respectively assigned to the k' th first auxiliary variable y _k ', the k-th second Lagrange multiplier vector C _k ', said first Lagrange multiplier vector d, said initial radar emission signal encoding sequence S and after the m-th iterationSecond auxiliary variable z ^(m) And m +1 is given to m, returning to step S805.

Code sequence { S obtained by optimization method ₁ ，S ₂ ，......，S _N And (6) carrying out amplitude modulation and phase modulation on the forming pulse in sequence, and taking the modulated signal as a radar transmitting signal.

The following simulation further illustrates the beneficial effects of the present embodiment:

simulation conditions are as follows: the pulse width of the radar signal is 20 mus, the sub-pulse width is 0.1 mus, and the energy of the transmitted signal is set to be 1. The adjacent communication stations share 7 parts, and normalized frequency bands are respectively as follows:

the signal to noise ratio for all stations is 10 dB. The external narrow-band active interference is 2 parts in total, the normalized frequency is 0.7 and 0.75 respectively, and the interference-to-noise ratio is 50dB and 40 dB. And when a 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 the radar signal leaked to the frequency bands of the 3 rd radio station and the 6 th radio station is allowed to be-30 dB, and the maximum energy of the radar signal leaked to the frequency bands of other radio stations is allowed to be-20 dB. When the alternative direction multiplier method is used, the penalty coefficient is set to 4, and the decision threshold is set to 5 multiplied by 10 ^-10 . Fig. 3 shows the energy spectral density of the designed radar signal, and it can be seen that the frequency spectrum of the radar signal can form a deeper notch in the frequency band where the radio station is located, so that mutual interference between the radar system and the communication radio station can be effectively avoided. In addition, the output signal to interference plus noise ratio of the radar signal of the embodiment is calculated to be 0.74, which is improved by 2.26dB, and the required operation time can be reduced by 82.5%.

The foregoing embodiments may be implemented by using a transmitted signal optimization system for improving radar detection performance, which is provided in the following embodiments:

another embodiment provides a transmission signal optimization system for improving radar detection performance, the transmission signal optimization system including:

the code element number of the reference coding sequence is N;

a second acquisition module configured to: acquiring the working frequency bands of the radar and each adjacent communication system to estimate an N-by-N interference covariance matrix corresponding to the working frequency bands 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:

B＝g ^u -g ^l ；

wherein ,

and

respectively the lower sideband cut-off frequency sum of the k adjacent communication system after the normalization processingAn upper sideband cutoff frequency;

and

wherein ,

for the element values of the ith row and the ith column in the interference covariance matrix corresponding to the operating frequency band of the kth adjacent communication system, h is 1,2, …, N, l is 1,2, …, N.

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 third determination module configured to: determining a second matrix according to an inverse matrix R corresponding to the radar interference covariance matrix and the signal transmission reference matrix set;

an iterative optimization module configured to: and performing iterative optimization on the initial radar transmitting signal coding sequence according to the signal transmitting reference matrix set and the second matrix. The iterative optimization module comprises:

a first setup submodule configured to: setting the k' th first auxiliary variable y _k ', a first Lagrangian multiplier vector d, and a kth second Lagrangian multiplier vector C _k ' the initial values are all 0;

a third computing submodule configured to: according to the inverse matrix R corresponding to the radar interference covariance matrix and the kth first auxiliary variable y _k ', a first Lagrange multiplier vector d and a kth' second Lagrange multiplier vector C _k ' and said second auxiliary variable z and each signal transmission reference matrix B in said set of signal transmission reference matrices _k ', calculating a first auxiliary vector t;

a second setup submodule configured to: setting the iteration number m to be 1;

a fifth computation submodule configured to: calculating a radar transmitting 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) ；

A sixth computation submodule configured to: according to the m timesIterative initial radar emission signal coding sequence s ^(m) Calculating an inverse matrix R corresponding to the radar interference covariance matrix and the first Lagrange multiplier vector d, and calculating a second auxiliary vector q after the mth iteration ^(m) ；

A seventh computing submodule configured to: according to the second auxiliary vector q after the mth iteration ^(m) And a preset penalty coefficient, calculating a second auxiliary variable z after the mth iteration ^(m) ；

An eighth computation submodule 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 said kth second Lagrangian multiplier vector C _k ', calculating the fourth auxiliary variable after the mth iteration

A first judgment sub-module configured to: judging the kth second auxiliary variable z after the m iterations ^(m) Is/are as follows ² Whether the square of norm is less than or equal to ¹ If so, the kth' fourth auxiliary variable after the mth iteration is added

Dividing by a kth' fourth auxiliary variable after the mth iteration

a ninth calculation submodule configured toThe method comprises the following steps: according to the inverse matrix R corresponding to the radar interference covariance matrix and the second auxiliary variable z after the mth iteration ^(m) And the radar emission signal coding sequence S after the mth iteration ^(m) The kth' first auxiliary variable y after the mth iteration _k ’ ^(m) Calculating a residual vector after the mth iteration by using each signal transmission reference matrix in the signal transmission reference matrix set;

An eleventh computation submodule configured to: according to the first Lagrange multiplier vector d and the second auxiliary variable z after the mth iteration ^(m) And the radar emission signal coding sequence S after the mth iteration ^(m) Calculating an inverse matrix R corresponding to the radar interference covariance matrix, and calculating a first Lagrange multiplier vector d after the mth iteration ^(m) ；

An assignment 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) The first Lagrangian multiplier vector d after the mth iteration ^(m) And the initial radar emission signal coding sequence S after the mth iteration ^(m) And a second after the m-th iterationAuxiliary variable z ^(m) Respectively assigned to the k' th first auxiliary variable y _k ', the k-th second Lagrange multiplier vector C _k ', the first Lagrange multiplier vector d, the initial radar emission signal coding sequence S and the second auxiliary variable z after the m-th iteration ^(m) And m +1 is assigned to m and returned to the fourth computation submodule.

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 radar transmitting signal coding sequence after iterative optimization to obtain a radar transmitting signal.

This embodiment is in between setting up module and the acquisition module, still include:

The terms, formulas and parameter definitions in the formulas in the above embodiments are all applicable, and are not described in detail here.

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 examples 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

1. A transmission signal optimization method for improving radar detection performance, the transmission signal optimization method comprising:

the code element number of the reference coding sequence is N;

2. The transmission signal optimization method according to claim 1, wherein between the step S1 and the step S2, the transmission signal optimization method further comprises:

3. The method of claim 2, wherein in step S3, the specific process of determining the N × N interference covariance matrix corresponding to the operating frequency band of each neighboring communication system includes:

B＝g ^u -g ^l ；

wherein ,

and

and

a lower sideband cut-off frequency and an upper sideband cut-off frequency of the kth adjacent communication system respectively; g ^u and g^l The upper sideband cut-off frequency and the lower sideband cut-off frequency of the radar are respectively; b is the radar bandwidth; k is 1,2, …, K is the number of adjacent communication systems;

wherein ,

4. The method of claim 3, wherein in step S5, each signal transmission reference matrix in the set of signal transmission reference matrices is:

wherein ,B_k ' is k ' th signal transmission reference matrix, when k ' is 0, then B ₀ Transmitting a reference matrix for a signal of the radar; when k' is k, then B _k Transmitting a reference matrix for a signal of a kth neighboring communication system; a. the ₀ Is a first matrix; i is N x N dimensionalAn identity matrix; e.g. of the type _t Transmitting energy for the radar signal; s ₀ Is a reference coding sequence; epsilon ₀ Is the coding sequence similarity coefficient; e _I ^k The maximum energy for allowing the radar signal to leak to the frequency band of the kth adjacent communication system; r _I ^k An interference covariance matrix corresponding to an operating frequency band of the kth neighboring communication system.

5. The transmission signal optimization method according to claim 4, wherein in step S7, the initial radar transmission signal encoding sequence is:

S＝[S ₁ S ₂ …S _n …S _N ] ^T ；

wherein, S is an initial radar transmitting signal coding sequence; s _n The value corresponding to the nth code element in the initial radar transmitting signal coding sequence is obtained; theta _n Random variables uniformly distributed in the interval of [0,2 pi); n is 1,2, …, and N is the number of code elements of the reference code sequence.

6. The method of claim 5, wherein in the step S8, the specific process of iterative optimization includes:

step S803, according to the inverse matrix R corresponding to the radar interference covariance matrix and the kth first auxiliary variable y _k ', a first Lagrangian multiplier vector d, and a kth' second LagrangianMultiplier vector C _k ' and said second auxiliary variable z and each signal transmission reference matrix B in said set of signal transmission reference matrices _k ', calculating a first auxiliary vector t;

step S804, setting the iteration number m to 1;

step S806, calculating a radar transmitting 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) ；

As the kth' first auxiliary variable y after the mth iteration _k ’ ^(m) The process advances to step S811; if the answer is no, the user can select the new type of the product,the kth' fourth auxiliary variable after the mth iteration is added

Divided by the kth' fourth auxiliary variable after the mth iteration

Step S814, according to the first Lagrange multiplier vector d and the second auxiliary variable z after the mth iteration ^(m) And the radar emission signal coding sequence S after the mth iteration ^(m) Calculating an inverse matrix R corresponding to the radar interference covariance matrix, and calculating a first Lagrange multiplier vector d after the mth iteration ^(m) ；

Step S815, the kth' first auxiliary variable y after the mth iteration _k ’ ^(m) The kth' second Lagrangian multiplier vector C after the mth iteration _k ’ ^(m) The first Lagrangian multiplier vector d after the mth iteration ^(m) And the initial radar emission signal coding sequence S after the mth iteration ^(m) And a second auxiliary variable z after said m-th iteration ^(m) Respectively assigned to the k' th first auxiliary variable y _k ', the k-th second Lagrange multiplier vector C _k ', the first Lagrange multiplier vector d, the initial radar emission signal coding sequence S and the second auxiliary variable z after the m-th iteration ^(m) And m +1 is given to m, returning to step S805.

7. A transmission signal optimization system for improving radar detection performance, the transmission signal optimization system comprising:

the code element number of the reference coding sequence is N;

a first determination module configured to: determining a first matrix A according to the radar signal emission energy and a reference code sequence ₀ ；

A second determination module configured to: according to the first matrix A ₀ The above-mentioned braidDetermining a signal emission reference matrix set by using the code sequence similarity coefficient, the interference covariance matrix corresponding to the working frequency band of each adjacent communication system and the maximum energy of the frequency band where the radar signal is allowed to leak to each adjacent communication system;

8. The transmit signal optimization system of claim 7, further comprising:

9. The transmit signal optimization system of claim 8, wherein the second acquisition module comprises:

B＝g ^u -g ^l ；

wherein ,

and

and

wherein ,

10. The transmit signal optimization system of claim 9, wherein the iterative optimization module comprises:

a second setup submodule configured to: setting the iteration number m to be 1;

the fourth calculation submodule is used 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 sixth computation submodule configured to: according to the initial radar emission signal coding sequence s after the mth iteration ^(m) Calculating a second auxiliary matrix after the mth iteration according to an inverse matrix R corresponding to the radar interference covariance matrix and the first Lagrange multiplier vector dHelper vector q ^(m) ；

Divided by the kth' fourth auxiliary variable after the mth iteration

a ninth computation submodule configured to: according to the inverse matrix R corresponding to the radar interference covariance matrix and the second auxiliary variable z after the mth iteration ^(m) The radar emission signal after the mth iterationCoding sequence S ^(m) The kth' first auxiliary variable y after the mth iteration _k ’ ^(m) Calculating a residual vector after the mth iteration by using each signal transmission reference matrix in the signal transmission reference matrix set;

An assignment 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) And a first Lagrangian multiplier vector d after the mth iteration ^(m) And the initial radar emission signal coding sequence S after the mth iteration ^(m) And a second auxiliary variable z after said m-th iteration ^(m) Respectively assigned to the k' th first auxiliary variable y _k ', the k-th second Lagrange multiplier vector C _k ', said first Lagrangian multiplicationA sub-vector d, the initial radar emission 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 computation submodule.