CN116047453A - Radar waveform design method, device, computer equipment and storage medium - Google Patents

Radar waveform design method, device, computer equipment and storage medium Download PDF

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CN116047453A
CN116047453A CN202310026948.3A CN202310026948A CN116047453A CN 116047453 A CN116047453 A CN 116047453A CN 202310026948 A CN202310026948 A CN 202310026948A CN 116047453 A CN116047453 A CN 116047453A
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radar
waveform
model
echo
echo signal
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杨威
张文鹏
沈亲沐
刘永祥
黎湘
杨晨
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National University of Defense Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/418—Theoretical aspects
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/282—Transmitters
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/35—Details of non-pulse systems
    • 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
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
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  • Computer Networks & Wireless Communication (AREA)
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  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
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Abstract

The application relates to a radar waveform design method, a radar waveform design device, a computer device and a storage medium. The method comprises the following steps: and determining the echo signal-to-noise ratio according to the target echo signal of the radar receiver. And constructing a radar echo optimization model by taking waveform energy and waveform equivalent bandwidth of a target echo signal as design variables and maximizing echo signal-to-noise ratio as an optimization target. And discretizing and decomposing the radar echo optimizing model to obtain a discrete optimizing model, approximating the discrete optimizing model through a Ding Keer Bach rule to obtain a second-order cone planning model, and carrying out iterative solution on the second-order cone planning model by utilizing a second-order cone planning algorithm to obtain a transmitting waveform power spectrum of the radar echo optimizing model. And synthesizing a transmitting waveform power spectrum through a phase recovery algorithm to obtain a radar optimized time domain waveform. The method can solve the problem of heuristic signal-to-interference-and-noise ratio performance loss, and simultaneously ensures the high-precision requirements of target tracking and measurement.

Description

Radar waveform design method, device, computer equipment and storage medium
Technical Field
The present disclosure relates to the field of radar detection technologies, and in particular, to a method and apparatus for designing radar waveforms, a computer device, and a storage medium.
Background
Along with the development of radar detection field technology, in order to facilitate the remote detection, tracking and recognition of targets by the radar in a complex environment, a task modularized serial processing mode is generally adopted. The waveform is used as a carrier for acquiring information by the radar, and the signal-to-noise ratio of a weak target echo can be improved to a greater extent by the current radar water injection waveform design method for the radar weak target detection task, but the designed waveform equivalent bandwidth is too narrow, so that the follow-up tracking processing task is not facilitated; the waveform design method for the radar target precise tracking task can better improve the tracking precision under the complex background, but the premise is that the waveform design method has a larger target echo signal-to-noise ratio so as to ensure the detection performance.
At present, the conventional radar waveform design only considers a single task, such as a radar weak target detection task or a radar target precise tracking task, or a radar target recognition task, but in fact, three tasks of radar target detection, tracking and recognition are tightly coupled, constraint relations exist between the three tasks, and the conventional waveform design method has the problem that the two tasks are difficult to combine.
Disclosure of Invention
In view of the foregoing, it is desirable to provide a radar waveform design method, apparatus, computer device, and storage medium that can simultaneously consider the requirements of radar weak target detection and radar target precise tracking.
A method of radar waveform design, the method comprising:
and determining the echo signal-to-noise ratio according to the target echo signal of the radar receiver.
And constructing a radar echo optimization model by taking waveform energy and waveform equivalent bandwidth of a target echo signal as design variables and maximizing echo signal-to-noise ratio as an optimization target.
And discretizing and decomposing the radar echo optimizing model to obtain a discrete optimizing model, approximating the discrete optimizing model through a Ding Keer Bach rule to obtain a second-order cone planning model, and carrying out iterative solution on the second-order cone planning model by utilizing a second-order cone planning algorithm to obtain a transmitting waveform power spectrum of the radar echo optimizing model.
And synthesizing a transmitting waveform power spectrum through a phase recovery algorithm to obtain a radar optimized time domain waveform.
In one embodiment, the method further comprises: under the condition that the working bandwidth of the radar receiver is W, according to a frequency response function H (f) of the radar, calculating an echo signal-to-noise ratio of the target echo signal in a frequency domain according to the Pasteur theorem, wherein the echo signal-to-noise ratio is as follows:
Figure BDA0004045470850000021
wherein X (f) is the frequency spectrum of the echo waveform, S c (f) Power spectrum distribution for radar working background clutter, S n (f) For noise power spectral distribution, E x Is the waveform energy of echo signal, W e Is the waveform equivalent bandwidth of the echo signal.
In one embodiment, the invention takes waveform energy and waveform equivalent bandwidth of a target echo signal as design variables, takes maximized echo signal-to-noise ratio as an optimization target, and constructs a radar echo optimization model as follows:
Figure BDA0004045470850000022
subject to ∫ W |X(f)| 2 df＝E x
Figure BDA0004045470850000023
wherein, |X (f) | 2 Is the transmitted waveform energy spectrum of the radar transmitter.
In one embodiment, the method further comprises: optimizing radar returns |X (f) |in model 2 、|H(f)| 2 、S c (f) S and S n (f) Performing discretization decomposition to respectively obtain discrete complex vectors x, h, c and N with N multiplied by 1 dimensions, and constructing a discrete optimization model according to the discrete complex vectors as follows:
Figure BDA0004045470850000024
Figure BDA0004045470850000025
Figure BDA0004045470850000026
x≥0
in one embodiment, the method further comprises: using Ding Keer Bach rules, a Ding Keer Bach efficacy factor μ was introduced k Taking a discrete optimization model as an optimization target, and expressing an approximate model of the discrete optimization model as:
Figure BDA0004045470850000031
Figure BDA0004045470850000032
Figure BDA0004045470850000033
Figure BDA0004045470850000034
-x≤0
let A 0 ＝A 1 ＝A 2 ＝0，b 0 ＝0.5(h T -μ k c T ) T ，b 1 ＝-b 2 ＝-0.5，
Figure BDA0004045470850000035
A 3 ＝E，b 3 ＝0，
Figure BDA0004045470850000036
A 4 ＝0，b 4 ＝0.5，c 4 =0, resulting in a second order cone planning model expressed as:
Figure BDA0004045470850000037
Figure BDA0004045470850000038
Figure BDA0004045470850000039
Figure BDA00040454708500000310
Figure BDA00040454708500000311
/>
in one embodiment, the method further comprises: solving a second-order cone planning model by using a second-order cone planning algorithm to obtain a transmitting waveform power spectrum (x) of the radar transmitter opt Substituting the power spectrum of the transmitted waveform into the objective function
Figure BDA00040454708500000312
And (5) performing error judgment to obtain the optimal transmitting waveform power spectrum of the radar echo optimizing model.
In one embodiment, the method further comprises: let the error threshold be ζ, when |f ((x) opt )|<When xi, the next Buckel Bach efficiency factor is introduced into the second order cone planning model
Figure BDA00040454708500000313
Performing optimization iteration to obtain the power spectrum of the next transmitting waveform until the power spectrum is equal to |f ((x) opt )|<Xi, the optimal transmitting waveform power spectrum (x) is obtained opt 。
A radar waveform design apparatus, the apparatus comprising:
and the signal receiving module is used for determining the echo signal-to-noise ratio according to the target echo signal of the radar receiver.
The echo waveform optimization module is used for constructing a radar echo optimization model by taking waveform energy and waveform equivalent bandwidth of a target echo signal as design variables and maximizing echo signal-to-noise ratio as an optimization target.
The echo waveform processing module is used for carrying out discretization decomposition on the radar echo optimization model to obtain a discrete optimization model, approximating the discrete optimization model through a Ding Keer Bach rule to obtain a second-order cone planning model, and carrying out iterative solution on the second-order cone planning model by utilizing a second-order cone planning algorithm to obtain a transmitting waveform power spectrum of the radar echo optimization model.
And the transmitting waveform synthesis module synthesizes the transmitting waveform power spectrum through a phase recovery algorithm to obtain the radar optimized time domain waveform.
A computer device comprising a memory storing a computer program and a processor which when executing the computer program performs the steps of:
and determining the echo signal-to-noise ratio according to the target echo signal of the radar receiver.
And constructing a radar echo optimization model by taking waveform energy and waveform equivalent bandwidth of a target echo signal as design variables and maximizing echo signal-to-noise ratio as an optimization target.
And discretizing and decomposing the radar echo optimizing model to obtain a discrete optimizing model, approximating the discrete optimizing model through a Ding Keer Bach rule to obtain a second-order cone planning model, and carrying out iterative solution on the second-order cone planning model by utilizing a second-order cone planning algorithm to obtain a transmitting waveform power spectrum of the radar echo optimizing model.
And synthesizing a transmitting waveform power spectrum through a phase recovery algorithm to obtain a radar optimized time domain waveform.
A computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of:
and determining the echo signal-to-noise ratio according to the target echo signal of the radar receiver.
And constructing a radar echo optimization model by taking waveform energy and waveform equivalent bandwidth of a target echo signal as design variables and maximizing echo signal-to-noise ratio as an optimization target.
And discretizing and decomposing the radar echo optimizing model to obtain a discrete optimizing model, approximating the discrete optimizing model through a Ding Keer Bach rule to obtain a second-order cone planning model, and carrying out iterative solution on the second-order cone planning model by utilizing a second-order cone planning algorithm to obtain a transmitting waveform power spectrum of the radar echo optimizing model.
And synthesizing a transmitting waveform power spectrum through a phase recovery algorithm to obtain a radar optimized time domain waveform.
Compared with the existing waveform design method, the method has the advantages of wide application range and high accuracy of radar detection, identification and tracking performance. Through the technical scheme, the invention has the following beneficial technical effects that: the signal-to-noise ratio in the echo signal of the radar receiver is maximized, the waveform energy and waveform equivalent bandwidth constraint condition of the echo signal are increased, a radar echo optimization model is built, the requirements of weak target detection and precise tracking of the radar can be better considered, the potential of a radar detection and identification system is exerted and released to the greatest extent, the radar echo optimization model is converted into a series of convex second order cone planning models through discretization decomposition and a Buckel Bach rule, the model has polynomial time complexity, finally, a transmitting waveform power spectrum is synthesized through a phase recovery algorithm, a radar optimization time domain waveform is obtained, the application range is further expanded, and the cognitive energy efficiency of the radar is improved.
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FIG. 1 is a flow chart of a method of designing radar waveforms in one embodiment;
FIG. 2 is a block diagram of a radar waveform design apparatus according to one embodiment;
FIG. 3 is an internal block diagram of a computer device in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the present application.
The method for designing radar waveforms provided by the application, as shown in fig. 1, specifically includes the following steps:
step 102, determining echo signal-noise ratio according to target echo signal of radar receiver.
The echo signal received by the radar receiver may be a target echo signal transmitted from a satellite, or may be an echo signal directly reflected by a target in a radar execution task, or may be in the form of a pulse radar signal, a continuous wave radar signal, a pulse compression radar signal, a frequency agile radar signal, or the like.
Specifically, the echo signal-to-noise ratio is defined by the combined action of the self working bandwidth of the radar, the frequency spectrum of an echo waveform, the power spectrum distribution of radar working background clutter, the noise power spectrum distribution and a radar frequency response function, and the more rigorous signal-to-noise ratio definition in the frequency domain is constructed through the Pasteur theorem, wherein the frequency response function of the radar is constructed by the frequency of a target to be detected by the radar and the frequency of a radar tracking target.
And 104, constructing a radar echo optimization model by taking waveform energy and waveform equivalent bandwidth of a target echo signal as design variables and maximizing echo signal-to-noise ratio as an optimization target.
It is worth to say that, the energy spectrum of the echo waveform is increased by the waveform energy of the target echo signal, so that the signal-to-noise ratio of the echo waveform is maximized, and at the same time, the equivalent bandwidth of the waveform is increased on the maximized signal-to-noise ratio of the echo waveform, so that the equivalent bandwidth of the echo waveform is widened, the follow-up target tracking and recognition task is conveniently executed, and the signal-to-noise ratio is optimized through the two design variables, so that the radar echo optimization model is obtained.
And 106, discretizing and decomposing the radar echo optimizing model to obtain a discrete optimizing model, approximating the discrete optimizing model through a Ding Keer Bach rule to obtain a second-order cone planning model, and carrying out iterative solution on the second-order cone planning model by utilizing a second-order cone planning algorithm to obtain a transmitting waveform power spectrum of the radar echo optimizing model.
It is worth to say that, discretizing the radar echo optimizing model, mainly constructing a discrete model by using the energy spectrum, the frequency response function, the power spectrum distribution of clutter and the discrete complex vector corresponding to the noise power spectrum distribution of the echo waveform, wherein the discrete complex vector is n×1 dimension, and further obtaining an equivalent discrete optimizing model. On the basis, the Buckel Bach rule is utilized, buckel Bach efficiency factors are added into the discrete optimization model, so that the discrete optimization model is approximated to be a second-order cone planning model, and further, the Buckel Bach efficiency factors are iterated through a second-order cone planning algorithm, so that the optimal discrete value corresponding to the energy spectrum of the radar emission waveform, namely the emission waveform power spectrum of the radar, is finally obtained.
And step 108, synthesizing a transmitting waveform power spectrum through a phase recovery algorithm to obtain a radar optimized time domain waveform.
The phase recovery algorithm can be a GS algorithm, a Young's algorithm, an ST improvement algorithm and the like, or can be a lamination algorithm PIE, an ePIE, a Newton method and the like, and can be matched with a phase recovery algorithm with higher accuracy, higher performance and higher operation efficiency according to an actual radar cognitive system. In addition, the obtained radar optimized time domain waveform is used as a transmitting waveform for executing tasks such as target tracking, target recognition and the like by the subsequent radar, and the precision of the radar tracking and target recognition can be ensured on the premise of effective target detection.
Compared with the existing waveform design method, the radar waveform design method has the advantages of wide application range and high accuracy of radar detection, identification and tracking performance. Through the technical scheme, the invention has the following beneficial technical effects that: the signal-to-noise ratio in the echo signal of the radar receiver is maximized, the waveform energy and waveform equivalent bandwidth constraint condition of the echo signal are increased, a radar echo optimization model is built, the requirements of weak target detection and precise tracking of the radar can be better considered, the potential of a radar detection and identification system is exerted and released to the greatest extent, the radar echo optimization model is converted into a series of convex second order cone planning models through discretization decomposition and a Buckel Bach rule, the model has polynomial time complexity, finally, a transmitting waveform power spectrum is synthesized through a phase recovery algorithm, a radar optimization time domain waveform is obtained, the application range is further expanded, and the cognitive energy efficiency of the radar is improved.
In one embodiment, in the case that the working bandwidth of the radar receiver is W, according to the frequency response function H (f) of the radar, the echo signal-noise ratio of the target echo signal is calculated in the frequency domain according to the paswa theorem as follows:
Figure BDA0004045470850000071
wherein X (f) is the frequency spectrum of the echo waveform, S c (f) Power spectrum distribution for radar working background clutter, S n (f) For noise power spectral distribution, E x Is the waveform energy of echo signal, W e Is the waveform equivalent bandwidth of the echo signal.
Therefore, the echo signal-noise-ratio model adopts strict signal-to-interference-and-noise-ratio definition, and solves the problem of performance loss caused by adopting heuristic signal-to-interference-and-noise-ratio definition in the traditional radar water injection waveform design method.
In one embodiment, the invention takes waveform energy and waveform equivalent bandwidth of a target echo signal as design variables, takes maximized echo signal-to-noise ratio as an optimization target, and constructs a radar echo optimization model as follows:
Figure BDA0004045470850000072
subject to ∫ W |X(f)| 2 df＝E x
Figure BDA0004045470850000073
wherein, |X (f) | 2 Is the transmitted waveform energy spectrum of the radar transmitter.
Therefore, on the basis of the traditional radar water injection waveform design method, an equivalent bandwidth constraint is added, the measurement accuracy requirement for the radar target precise tracking task can be considered, and the radar echo optimization model has better robustness.
In one embodiment, |X (f) | in the radar echo optimization model 2 、|H(f)| 2 、S c (f) S and S n (f) Performing discretization decomposition to respectively obtain discrete complex vectors x, h, c and N with N multiplied by 1 dimensions, and constructing a discrete optimization model according to the discrete complex vectors as follows:
Figure BDA0004045470850000074
/>
Figure BDA0004045470850000075
Figure BDA0004045470850000076
x≥0
in one embodiment, the Ding Keer Bach rule is utilized to introduceDing Keer Bach efficacy factor mu k Taking a discrete optimization model as an optimization target, and expressing an approximate model of the discrete optimization model as:
Figure BDA0004045470850000081
Figure BDA0004045470850000082
Figure BDA0004045470850000083
Figure BDA0004045470850000084
-x≤0
let A 0 ＝A 1 ＝A 2 ＝0，b 0 ＝0.5(h T -μ k c T ) T ，b 1 ＝-b 2 ＝-0.5，
Figure BDA0004045470850000085
A 3 ＝E，b 3 ＝0，
Figure BDA0004045470850000086
A 4 ＝0，b 4 ＝0.5，c 4 =0, resulting in a second order cone planning model expressed as:
Figure BDA0004045470850000087
Figure BDA0004045470850000088
Figure BDA0004045470850000089
Figure BDA00040454708500000810
Figure BDA00040454708500000811
in one embodiment, a second order cone programming algorithm is utilized to solve a second order cone programming model to obtain a transmit waveform power spectrum (x) of the radar transmitter opt Substituting the power spectrum of the transmitted waveform into the objective function
Figure BDA00040454708500000812
And (5) performing error judgment to obtain the optimal transmitting waveform power spectrum of the radar echo optimizing model.
Figure BDA00040454708500000813
The waveform power spectrum is transmitted until |f ((x) opt )|<Xi, the optimal transmitting waveform power spectrum (x) is obtained opt 。
Therefore, the Buckel Bach rule is adopted to convert the cognitive radar echo optimization model into a series of convex second order cone planning models, the polynomial time complexity is achieved, the solving mode is simplified, and meanwhile, the waveform design energy efficiency is improved.
It should be understood that, although the steps in the flowchart of fig. 1 are shown in sequence as indicated by the arrows, the steps are not necessarily performed in sequence as indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least some of the steps in fig. 1 may include multiple sub-steps or stages that are not necessarily performed at the same time, but may be performed at different times, nor do the order in which the sub-steps or stages are performed necessarily performed in sequence, but may be performed alternately or alternately with at least a portion of other steps or sub-steps of other steps.
In one embodiment, as shown in fig. 2, there is provided a radar waveform design apparatus including: a signal receiving module 202, an echo waveform optimizing module 204, an echo waveform processing module 206, and a transmit waveform synthesizing module 208, wherein:
the signal receiving module 202 is configured to determine an echo signal-to-noise ratio according to a target echo signal of the radar receiver.
The echo waveform optimizing module 204 is configured to construct a radar echo optimizing model by taking waveform energy and waveform equivalent bandwidth of a target echo signal as design variables and maximizing echo signal-to-noise ratio as an optimizing target.
The echo waveform processing module 206 is configured to discretize the radar echo optimization model to obtain a discrete optimization model, approximate the discrete optimization model through Ding Keer balch rule to obtain a second-order cone planning model, and iteratively solve the second-order cone planning model by using a second-order cone planning algorithm to obtain a transmit waveform power spectrum of the radar echo optimization model.
The transmit waveform synthesis module 208 synthesizes the transmit waveform power spectrum by a phase recovery algorithm to obtain a radar optimized time domain waveform.
For a specific limitation of a radar waveform design apparatus, reference may be made to the limitation of a radar waveform design method hereinabove, and the description thereof will not be repeated here. Each of the modules in the above-described one radar waveform design apparatus may be implemented in whole or in part by software, hardware, and a combination thereof. The above modules may be embedded in hardware or may be independent of a processor in the computer device, or may be stored in software in a memory in the computer device, so that the processor may call and execute operations corresponding to the above modules.
In one embodiment, a computer device is provided, which may be a terminal, and the internal structure of which may be as shown in fig. 3. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a method of radar waveform design. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, can also be keys, a track ball or a touch pad arranged on the shell of the computer equipment, and can also be an external keyboard, a touch pad or a mouse and the like.
It will be appreciated by those skilled in the art that the structure shown in fig. 3 is merely a block diagram of some of the structures associated with the present application and is not limiting of the computer device to which the present application may be applied, and that a particular computer device may include more or fewer components than shown, or may combine certain components, or have a different arrangement of components.
In one embodiment, a computer device is provided comprising a memory storing a computer program and a processor that when executing the computer program performs the steps of:
and determining the echo signal-to-noise ratio according to the target echo signal of the radar receiver.
And constructing a radar echo optimization model by taking waveform energy and waveform equivalent bandwidth of a target echo signal as design variables and maximizing echo signal-to-noise ratio as an optimization target.
And discretizing and decomposing the radar echo optimizing model to obtain a discrete optimizing model, approximating the discrete optimizing model through a Ding Keer Bach rule to obtain a second-order cone planning model, and carrying out iterative solution on the second-order cone planning model by utilizing a second-order cone planning algorithm to obtain a transmitting waveform power spectrum of the radar echo optimizing model.
And synthesizing a transmitting waveform power spectrum through a phase recovery algorithm to obtain a radar optimized time domain waveform.
In one embodiment, the processor when executing the computer program further performs the steps of:
the target echo signal includes: under the condition that the working bandwidth of the radar receiver is W, according to a frequency response function H (f) of the radar, calculating an echo signal-to-noise ratio of the target echo signal in a frequency domain according to the Pasteur theorem, wherein the echo signal-to-noise ratio is as follows:
Figure BDA0004045470850000101
wherein X (f) is the frequency spectrum of the echo waveform, S c (f) Power spectrum distribution for radar working background clutter, S n (f) For noise power spectral distribution, E x Is the waveform energy of echo signal, W e Is the waveform equivalent bandwidth of the echo signal.
In one embodiment, the processor when executing the computer program further performs the steps of:
the invention takes waveform energy and waveform equivalent bandwidth of a target echo signal as design variables, takes maximized echo signal-noise ratio as an optimization target, and constructs a radar echo optimization model as follows:
Figure BDA0004045470850000111
subject to ∫ W |X(f)| 2 df＝E x
Figure BDA0004045470850000112
wherein, |X (f) | 2 Is the transmitted waveform energy spectrum of the radar transmitter.
In one embodiment, the processor when executing the computer program further performs the steps of:
optimizing radar echo in modelIs |X (f) | 2 、|H(f)| 2 、S c (f) S and S n (f) Performing discretization decomposition to respectively obtain discrete complex vectors x, h, c and N with N multiplied by 1 dimensions, and constructing a discrete optimization model according to the discrete complex vectors as follows:
Figure BDA0004045470850000113
Figure BDA0004045470850000114
Figure BDA0004045470850000115
x≥0
in one embodiment, the processor when executing the computer program further performs the steps of:
using Ding Keer Bach rules, a Ding Keer Bach efficacy factor μ was introduced k Taking a discrete optimization model as an optimization target, and expressing an approximate model of the discrete optimization model as:
Figure BDA0004045470850000116
Figure BDA0004045470850000117
Figure BDA0004045470850000118
Figure BDA0004045470850000119
/>
-x≤0
let A 0 ＝A 1 ＝A 2 ＝0，b 0 ＝0.5(h T -μ k c T ) T ，b 1 ＝-b 2 ＝-0.5，
Figure BDA00040454708500001110
A 3 ＝E，b 3 ＝0，
Figure BDA0004045470850000121
A 4 ＝0，b 4 ＝0.5，c 4 =0, resulting in a second order cone planning model expressed as:
Figure BDA0004045470850000122
Figure BDA0004045470850000123
Figure BDA0004045470850000124
Figure BDA0004045470850000125
Figure BDA0004045470850000126
in one embodiment, the processor when executing the computer program further performs the steps of:
solving a second-order cone planning model by using a second-order cone planning algorithm to obtain a transmitting waveform power spectrum (x) of the radar transmitter opt Substituting the power spectrum of the transmitted waveform into the objective function
Figure BDA0004045470850000127
And (5) performing error judgment to obtain the optimal transmitting waveform power spectrum of the radar echo optimizing model.
In one embodiment, the processor when executing the computer program further performs the steps of:
Figure BDA0004045470850000128
when |f ((x) opt )|<When x, the optimal transmitting waveform power spectrum (x) is obtained opt 。
In one embodiment, a computer readable storage medium is provided having a computer program stored thereon, which when executed by a processor, performs the steps of:
and determining the echo signal-to-noise ratio according to the target echo signal of the radar receiver.
And constructing a radar echo optimization model by taking waveform energy and waveform equivalent bandwidth of a target echo signal as design variables and maximizing echo signal-to-noise ratio as an optimization target.
And discretizing and decomposing the radar echo optimizing model to obtain a discrete optimizing model, approximating the discrete optimizing model through a Ding Keer Bach rule to obtain a second-order cone planning model, and carrying out iterative solution on the second-order cone planning model by utilizing a second-order cone planning algorithm to obtain a transmitting waveform power spectrum of the radar echo optimizing model.
And synthesizing a transmitting waveform power spectrum through a phase recovery algorithm to obtain a radar optimized time domain waveform.
In one embodiment, the computer program when executed by the processor further performs the steps of:
under the condition that the working bandwidth of the radar receiver is W, according to a frequency response function H (f) of the radar, calculating an echo signal-to-noise ratio of the target echo signal in a frequency domain according to the Pasteur theorem, wherein the echo signal-to-noise ratio is as follows:
Figure BDA0004045470850000129
wherein X (f) is the frequency spectrum of the echo waveform, S c (f) Power spectrum distribution for radar working background clutter, S n (f) For noise power spectral distribution, E x As waves of echo signalsShape energy, W e Is the waveform equivalent bandwidth of the echo signal.
In one embodiment, the computer program when executed by the processor further performs the steps of:
the invention takes waveform energy and waveform equivalent bandwidth of a target echo signal as design variables, takes maximized echo signal-noise ratio as an optimization target, and constructs a radar echo optimization model as follows:
Figure BDA0004045470850000131
subject to ∫ W |X(f)| 2 df＝E x
Figure BDA0004045470850000132
wherein, |X (f) | 2 Is the transmitted waveform energy spectrum of the radar transmitter.
In one embodiment, the computer program when executed by the processor further performs the steps of:
optimizing radar returns |X (f) |in model 2 、|H(f)| 2 、S c (f) S and S n (f) Performing discretization decomposition to respectively obtain discrete complex vectors x, h, c and N with N multiplied by 1 dimensions, and constructing a discrete optimization model according to the discrete complex vectors as follows:
Figure BDA0004045470850000133
Figure BDA0004045470850000134
Figure BDA0004045470850000135
x≥0
in one embodiment, the computer program when executed by the processor further performs the steps of:
using Ding Keer Bach rules, a Ding Keer Bach efficacy factor μ was introduced k Taking a discrete optimization model as an optimization target, and expressing an approximate model of the discrete optimization model as:
Figure BDA0004045470850000141
Figure BDA0004045470850000142
Figure BDA0004045470850000143
Figure BDA0004045470850000144
-x≤0
let A 0 ＝A 1 ＝A 2 ＝0，b 0 ＝0.5(h T -μ k c T ) T ，b 1 ＝-b 2 ＝-0.5，
Figure BDA0004045470850000145
A 3 ＝E，b 3 ＝0，
Figure BDA0004045470850000146
A 4 ＝0，b 4 ＝0.5，c 4 =0, resulting in a second order cone planning model expressed as:
Figure BDA0004045470850000147
Figure BDA0004045470850000148
Figure BDA0004045470850000149
/>
Figure BDA00040454708500001410
Figure BDA00040454708500001411
in one embodiment, the computer program when executed by the processor further performs the steps of:
solving a second-order cone planning model by using a second-order cone planning algorithm to obtain a transmitting waveform power spectrum (x) of the radar transmitter opt Substituting the power spectrum of the transmitted waveform into the objective function
Figure BDA00040454708500001412
And (5) performing error judgment to obtain the optimal transmitting waveform power spectrum of the radar echo optimizing model.
In one embodiment, the computer program when executed by the processor further performs the steps of:
Figure BDA00040454708500001413
when |f ((x) opt )|<Xi, the optimal transmitting waveform power spectrum (x) is obtained opt 。
Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the various embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), memory bus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
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 considered as the scope of the description.
The above examples merely represent 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 method of radar waveform design, the method comprising:
determining an echo signal-to-noise ratio according to a target echo signal of the radar receiver;
taking the waveform energy and the waveform equivalent bandwidth of the target echo signal as design variables and maximizing the echo signal-to-noise ratio as an optimization target to construct a radar echo optimization model;
performing discretization decomposition on the radar echo optimization model to obtain a discrete optimization model, approximating the discrete optimization model through Ding Keer Bach rules to obtain a second-order cone planning model, and performing iterative solution on the second-order cone planning model by using a second-order cone planning algorithm to obtain a transmitting waveform power spectrum of the radar echo optimization model;
and synthesizing the power spectrum of the transmitting waveform by a phase recovery algorithm to obtain a radar optimized time domain waveform.
2. The method of claim 1, wherein determining an echo signal-to-noise ratio from a target echo signal of the radar receiver comprises:
under the condition that the working bandwidth of the radar receiver is W, according to a frequency response function H (f) of the radar, calculating an echo signal-to-noise ratio of the target echo signal in a frequency domain according to the Pasteur theorem, wherein the echo signal-to-noise ratio is as follows:
Figure FDA0004045470840000011
wherein X (f) is the frequency spectrum of the echo waveform, S c (f) Power spectrum distribution for radar working background clutter, S n (f) For noise power spectral distribution, E x Is the waveform energy of echo signal, W e Is the waveform equivalent bandwidth of the echo signal.
3. The method of claim 2, wherein constructing a radar echo optimization model with the waveform energy and waveform equivalent bandwidth of the target echo signal as design variables and with maximizing the echo signal-to-noise ratio as optimization targets is:
Figure FDA0004045470840000012
subject to∫ W |X(f)| 2 df＝E x
Figure FDA0004045470840000013
wherein, |X (f) | 2 Is the transmitted waveform energy spectrum of the radar transmitter.
4. A method according to claim 3, wherein discretizing the radar echo optimization model to obtain a discrete optimization model comprises:
-adapting |x (f) | in the radar echo optimization model 2 、|H(f)| 2 、S c (f) S and S n (f) Performing discretization decomposition to respectively obtain discrete complex vectors x, h, c and N with N multiplied by 1 dimensions, and constructing a discrete optimization model according to the discrete complex vectors as follows:
Figure FDA0004045470840000021
Figure FDA0004045470840000022
Figure FDA0004045470840000023
5. the method of claim 4, wherein approximating the discrete optimization model by Ding Keer bach rules results in a second order cone planning model, comprising:
using Ding Keer Bach rules, a Ding Keer Bach efficacy factor μ was introduced k Taking the discrete optimization model as an optimization target, wherein an approximation model of the discrete optimization model is expressed as:
Figure FDA0004045470840000024
Figure FDA0004045470840000025
Figure FDA0004045470840000026
Figure FDA0004045470840000027
-x≤0
let A 0 ＝A 1 ＝A 2 ＝0，b 0 ＝0.5(h T -μ k c T ) T ，b 1 ＝-b 2 ＝-0.5，
Figure FDA0004045470840000028
A 3 ＝E，b 3 ＝0，
Figure FDA0004045470840000029
A 4 ＝0，b 4 ＝0.5，c 4 =0, resulting in a second order cone planning model expressed as:
Figure FDA00040454708400000210
Figure FDA00040454708400000211
Figure FDA00040454708400000212
Figure FDA00040454708400000213
Figure FDA00040454708400000214
6. the method of claim 5, wherein iteratively solving the second order cone planning model using a second order cone planning algorithm results in a transmit waveform power spectrum of the radar echo optimization model, comprising:
solving the second-order cone planning model by utilizing a second-order cone planning algorithm to obtain a transmitting waveform power spectrum (x) of the radar transmitter opt Substituting the power spectrum of the transmitting waveform into an objective function
Figure FDA0004045470840000031
And performing error judgment to obtain the optimal transmitting waveform power spectrum of the radar echo optimizing model.
7. The method of claim 6, wherein the transmit waveform power spectrum is substituted into an objective function
Figure FDA0004045470840000032
Performing error judgment to obtain an optimal transmitting waveform power spectrum of the radar echo optimization model, wherein the method comprises the following steps:
let the error threshold be ζ, when |f ((x) opt )|<When xi, the next Buckel Bach efficiency factor is introduced into the second order cone planning model
Figure FDA0004045470840000033
Performing optimization iteration to obtain the next emitted waveform power spectrum until |f ((x) opt )|<Xi, the optimal power spectrum (x) of the emission waveform is obtained opt 。
8. A radar waveform design apparatus, the apparatus comprising:
the signal receiving module is used for determining echo signal-to-noise ratio according to a target echo signal of the radar receiver;
the echo waveform optimization module is used for constructing a radar echo optimization model by taking waveform energy and waveform equivalent bandwidth of the target echo signal as design variables and maximizing the echo signal-to-noise ratio as an optimization target;
the echo waveform processing module is used for carrying out discretization decomposition on the radar echo optimization model to obtain a discrete optimization model, approximating the discrete optimization model through Ding Keer Bach rules to obtain a second-order cone planning model, and carrying out iterative solution on the second-order cone planning model by utilizing a second-order cone planning algorithm to obtain a transmitting waveform power spectrum of the radar echo optimization model;
and the transmitting waveform synthesis module synthesizes the transmitting waveform power spectrum through a phase recovery algorithm to obtain a radar optimized time domain waveform.
9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the method of any of claims 1 to 7 when the computer program is executed.
10. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method of any of claims 1 to 7.
CN202310026948.3A 2023-01-09 2023-01-09 Radar waveform design method, device, computer equipment and storage medium Pending CN116047453A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116381612A (en) * 2023-06-05 2023-07-04 中国人民解放军国防科技大学 Cognitive radar waveform design method and device based on split quadratic programming

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116381612A (en) * 2023-06-05 2023-07-04 中国人民解放军国防科技大学 Cognitive radar waveform design method and device based on split quadratic programming
CN116381612B (en) * 2023-06-05 2023-08-11 中国人民解放军国防科技大学 Cognitive radar waveform design method and device based on split quadratic programming

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