CN116027280B - Low peak sidelobe frequency coding radar waveform design method - Google Patents

Low peak sidelobe frequency coding radar waveform design method Download PDF

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CN116027280B
CN116027280B CN202310327419.7A CN202310327419A CN116027280B CN 116027280 B CN116027280 B CN 116027280B CN 202310327419 A CN202310327419 A CN 202310327419A CN 116027280 B CN116027280 B CN 116027280B
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optimal adaptation
echo signal
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CN116027280A (en
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吴耀君
徐俊彤
杜思予
全英汇
刘智星
邢孟道
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Xidian University
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Abstract

The invention discloses a low peak sidelobe frequency coding radar waveform design method, which comprises the following steps: the intra-pulse agile radar transmits signals and receives echo signals, and carries out frequency mixing processing and sectional pulse compression processing on the echo signals and corresponding transmitting carrier frequencies in sequence to obtain echo signals after pulse compression; establishing a frequency coding optimization model based on echo signals after pulse pressure; according to the echo signals after pulse pressure, a group of frequency codes are randomly generated, and initial values are used as the current individual optimal adaptation values and the global optimal adaptation values; and solving the frequency coding optimization model based on a particle swarm algorithm to obtain the minimum peak side lobe ratio of the echo signal after pulse pressure and the corresponding frequency coding. The method has better ranging precision and ranging resolution, and the optimized frequency coding waveform has lower peak sidelobe ratio relative to the frequency coding waveform which is not optimized, so that the radar has excellent anti-interference performance and simultaneously improves the detection capability of a small target in a complex scene.

Description

Low peak sidelobe frequency coding radar waveform design method
Technical Field
The invention belongs to the technical field of wideband radar signal waveform design and processing, and particularly relates to a low-peak sidelobe frequency coding radar waveform design method.
Background
The broadband radar has the characteristic of instantaneous large bandwidth, and the instantaneous large bandwidth radar waveform is divided into a plurality of small bandwidths and is coded to obtain the intra-pulse frequency coding waveform. Compared to non-frequency coded wideband radar waveforms, intra-pulse frequency coded radar systems have significant advantages in: (1) strong anti-interference capability: the signal frequency of the intra-pulse frequency coding radar jumps randomly in one pulse, so that the difficulty of interference caused by the fact that an interference machine transmits the same-frequency signal is greatly improved; (2) improving the detection imaging performance of the radar; (3) distance resolution and doppler resolution are improved: the frequency encoded radar signal has a functional characteristic of a narrow main lobe through pulse compression, which means that the frequency encoded radar has the ability to provide high resolution for both range and speed.
In the current intra-pulse frequency coding radar processing technology, the main problems are that a target has higher side lobes after pulse compression, the higher side lobes are easy to be processed as main lobes, so that false targets are easy to be misjudged, and small targets are easy to be missed due to the high side lobes, so that the anti-interference performance of the radar is seriously affected.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a low-peak sidelobe frequency coding radar waveform design method. The technical problems to be solved by the invention are realized by the following technical scheme:
a low peak sidelobe frequency coding radar waveform design method comprises the following steps:
step 1: the intra-pulse agile radar transmits a signal and receives an echo signal, and sequentially carries out frequency mixing processing and sectional pulse compression processing on the echo signal and a corresponding transmitting carrier frequency to obtain an echo signal after pulse compression;
step 2: establishing a frequency coding optimization model based on echo signals after pulse pressure;
step 3: according to the echo signals after pulse pressure, a group of frequency codes are randomly generated, and initial values are used as the current individual optimal adaptation values and the global optimal adaptation values;
step 4: and solving the frequency coding optimization model based on a particle swarm PSO algorithm to obtain the minimum peak side lobe ratio of the echo signal after pulse pressure and the corresponding frequency coding.
In one embodiment of the present invention, step 1 comprises:
11 Equally dividing each pulse intoQSub-pulses, frequency agility between sub-pulses, and randomly selected from themMThe sub-pulse is transmitted, then
Figure SMS_1
First pulse->
Figure SMS_2
The transmit signals of the sub-pulses are:
Figure SMS_3
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_4
indicate->
Figure SMS_7
First pulse->
Figure SMS_8
Sub-pulse transmit signal,/->
Figure SMS_6
Time of presentation->
Figure SMS_9
Representing a rectangular window function, +.>
Figure SMS_11
Representing the slope of the chirp signal,/->
Figure SMS_14
Representing pulse repetition period, +.>
Figure SMS_5
Representing the pulse width of each sub-pulse, +.>
Figure SMS_10
Representing imaginary units, ++>
Figure SMS_12
Is natural index (i.e.)>
Figure SMS_13
Is the circumference ratio;
Figure SMS_15
is->
Figure SMS_16
First pulse->
Figure SMS_17
The carrier frequency of the sub-pulse is expressed as:
Figure SMS_18
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_19
，/>
Figure SMS_22
representing intra-pulse frequency hopping coding, < >>
Figure SMS_25
Indicate->
Figure SMS_21
Carrier frequency of individual pulses>
Figure SMS_23
For the initial carrier frequency +.>
Figure SMS_24
Coding for inter-pulse frequency hopping, < >>
Figure SMS_26
For frequency hopping bandwidth, < >>
Figure SMS_20
The bandwidth for each sub-pulse;
12 Receiving the first
Figure SMS_27
First pulse->
Figure SMS_28
Echo signals corresponding to the transmitting signals of the sub-pulses are expressed as follows:
Figure SMS_29
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_31
indicate->
Figure SMS_34
First pulse->
Figure SMS_35
Echo signals corresponding to the transmit signals of the individual sub-pulses, ">
Figure SMS_32
Indicating the total number of pulses +.>
Figure SMS_37
Representing the total number of targets->
Figure SMS_40
Is->
Figure SMS_43
No. 5 of the individual object>
Figure SMS_30
Time delay between the pulse echo signal and the transmission signal, < >>
Figure SMS_36
For the speed of light->
Figure SMS_38
Is->
Figure SMS_41
Distance of individual target->
Figure SMS_33
Is->
Figure SMS_39
Speed of individual target->
Figure SMS_42
Is the first
Figure SMS_44
Scattering coefficients of the individual targets;
13 For the first pair
Figure SMS_45
First pulse->
Figure SMS_46
The sub-pulses are subjected to sectional pulse pressure processing, and the formula is expressed as follows:
Figure SMS_47
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_49
indicate->
Figure SMS_51
First pulse->
Figure SMS_52
The sub-pulses are used for segmenting pulse pressure signals,
Figure SMS_50
the +.f. indicating intra-pulse frequency encoded radar reception>
Figure SMS_53
Echo signals of the individual pulses; />
Figure SMS_54
In order for the convolution operation to be performed,
Figure SMS_55
representation->
Figure SMS_48
A corresponding matched filter function per sub-pulse, which is +.>
Figure SMS_56
Is a conjugate function of (2);
Figure SMS_57
；
14 To be within one pulseMThe segmented pulse pressure results of the sub-pulses are added to obtain echo signals after pulse pressure, and the expression is as follows:
Figure SMS_58
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_59
echo signal after the representation of pulse pressure, +.>
Figure SMS_60
Indicate->
Figure SMS_61
The amplitude after the individual target pulse pressures,
Figure SMS_62
，/>
Figure SMS_63
for the total number of targets->
Figure SMS_64
Representing the envelope formed by the accumulation of each sub-pulse after pulse pressure processing,
Figure SMS_65
representing noise.
In one embodiment of the present invention, step 2 comprises:
taking the modulus of the echo signal after pulse pressure, and constructing an optimization model taking frequency codes as independent variables based on the dB value of the peak value corresponding to each point in the function, wherein the objective function of the optimization model is as follows:
Figure SMS_66
。
in one embodiment of the present invention, step 4 comprises:
41 Initializing PSO algorithm parameters of a particle swarm;
42 Calculating an optimal fitness value for the current position and velocity of each particle;
43 Comparing and judging the optimal adaptation value of the current position and the speed of each particle with the individual historical optimal adaptation value of each particle, and updating the historical optimal adaptation value and the position of each particle;
44 Comparing and judging the current iteration group optimal adaptation value with the group history optimal adaptation value, and updating the group history optimal adaptation value and the position;
45 Updating the speed and position of the particles;
46 According to the operations of steps 42) to 45), carrying out iterative updating until the maximum iterative times are reached, and outputting the group history optimal adaptation value and the position to obtain the minimum peak side lobe ratio of the echo signal after pulse compression and the corresponding frequency code.
In one embodiment of the invention, in step 45), the speed and position of the particles are updated according to the following formula:
Figure SMS_67
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_70
is a weight coefficient>
Figure SMS_75
And->
Figure SMS_78
For learning factors->
Figure SMS_69
And->
Figure SMS_74
Is [0,1]Random value between->
Figure SMS_76
And
Figure SMS_77
an individual optimum adaptation value and a global optimum adaptation value, respectively->
Figure SMS_68
And->
Figure SMS_72
Respectively +.>
Figure SMS_79
The latest position and velocity of the particle at the time of the iteration, < >>
Figure SMS_80
And->
Figure SMS_71
Respectively +.>
Figure SMS_73
The most recent position and velocity of the particle at the time of the iteration.
The invention has the beneficial effects that:
1. compared with the traditional method, the method has better ranging precision and ranging resolution, and the optimized frequency coding waveform has lower peak side lobe ratio relative to the frequency coding waveform which is not optimized, so that the radar has excellent anti-interference performance and simultaneously improves the detection capability of small targets in complex scenes;
2. the invention uses the inter-pulse frequency agile waveform while using the intra-pulse frequency coded waveform, thereby further improving the anti-interference performance;
3. when the invention designs the frequency coding waveform in the pulse, the sub-pulse with all small bandwidths is not used in one pulse, but a subset of the sub-pulses with all small bandwidths is selected, the waveform diversity is increased, and better orthogonality exists among different sub-pulses;
4. the particle swarm PSO algorithm adopted by the invention has high convergence rate, and can efficiently finish the task of optimizing the waveform.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
FIG. 1 is a schematic flow chart of a method for designing a low peak sidelobe frequency coded radar waveform according to an embodiment of the present invention;
FIG. 2 is a flowchart of a particle swarm algorithm according to an embodiment of the present invention;
FIG. 3 is a schematic illustration of simulation of intra-pulse frequency coded radar echoes in a simulation experiment;
FIG. 4 is a graph showing pulse pressure results before frequency coding optimization in a simulation experiment;
FIG. 5 is a schematic diagram of the pulse pressure results after frequency coding optimization in simulation experiments;
FIG. 6 is a schematic diagram of the pulse compression sidelobe ratio before optimization in a simulation experiment;
FIG. 7 is a schematic diagram of the pulse compression sidelobe ratio after optimization in a simulation experiment;
FIG. 8 is a schematic diagram of simulation iterations based on PSO algorithm in a simulation experiment;
FIG. 9 is a top view of the correlation accumulation prior to optimization in a simulation experiment;
fig. 10 is a top view of the correlation accumulation after optimization in the simulation experiment.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but embodiments of the present invention are not limited thereto.
Example 1
Referring to fig. 1, fig. 1 is a flow chart of a low peak sidelobe frequency coding radar waveform design method according to an embodiment of the invention, which includes:
step 1: and receiving echo signals by the pulse agile radar transmitting signals, and sequentially carrying out frequency mixing processing and sectional pulse compression processing on the echo signals and corresponding transmitting carrier frequencies to obtain echo signals after pulse compression.
Specifically, step 1 includes:
11 Equally dividing each pulse intoQSub-pulses, frequency agility between sub-pulses, and randomly selected from themMThe sub-pulses are transmitted.
Specifically, the pulse width and the bandwidth of each signal pulse are respectively set as
Figure SMS_83
And->
Figure SMS_84
The pulse width of each sub-pulse is
Figure SMS_85
Bandwidth is +.>
Figure SMS_81
Randomly select fromMSub-pulse emission, the pulse width of the emitted pulse
Figure SMS_86
Bandwidth->
Figure SMS_87
. For this purposeMSub-pulse reordering, then +.>
Figure SMS_88
First pulse->
Figure SMS_82
The carrier frequencies of the sub-pulses are:
Figure SMS_89
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_90
，/>
Figure SMS_91
representing intra-pulse frequency hopping coding, < >>
Figure SMS_92
Is->
Figure SMS_93
Carrier frequency of individual pulses>
Figure SMS_94
For the initial carrier frequency +.>
Figure SMS_95
Coding for inter-pulse frequency hopping, < >>
Figure SMS_96
Is the frequency hopping bandwidth.
Then the first
Figure SMS_97
First pulse->
Figure SMS_98
The transmit signals of the sub-pulses are:
Figure SMS_99
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_102
indicate->
Figure SMS_103
First pulse->
Figure SMS_105
Sub-pulse transmit signal,/->
Figure SMS_101
The time is represented by the time period of the day,
Figure SMS_107
representing a rectangular window function, +.>
Figure SMS_108
For the slope of the chirp signal>
Figure SMS_109
Representing pulse repetition cyclesStage (1)>
Figure SMS_100
Representing imaginary units, ++>
Figure SMS_104
Is natural index (i.e.)>
Figure SMS_106
Is the circumference ratio.
12 Receiving the first
Figure SMS_110
First pulse->
Figure SMS_111
Echo signals corresponding to the transmission signals of the sub-pulses.
Specifically, assume that the total number of moving objects in the measurement scene is
Figure SMS_112
First->
Figure SMS_113
The distance and speed of the individual targets are set to +.>
Figure SMS_114
And->
Figure SMS_115
And the target fluctuation models are all of the Swerling I type, the echo signals of the intra-pulse frequency coding radar can be written as:
Figure SMS_116
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_117
indicate->
Figure SMS_121
First pulse->
Figure SMS_122
Echo signals corresponding to the transmit signals of the individual sub-pulses, ">
Figure SMS_119
Indicating the total number of pulses +.>
Figure SMS_124
Representing the total number of targets->
Figure SMS_128
Is->
Figure SMS_131
No. 5 of the individual object>
Figure SMS_118
Time delay between the pulse echo signal and the transmission signal, < >>
Figure SMS_123
For the speed of light->
Figure SMS_126
Is->
Figure SMS_129
Distance of individual target->
Figure SMS_120
Is->
Figure SMS_125
Speed of individual target->
Figure SMS_127
Is->
Figure SMS_130
Scattering coefficient of the individual targets. />
13 For the first pair
Figure SMS_132
First pulse->
Figure SMS_133
The sub-pulses are subjected to a segmented pulse pressure process.
Specifically, since the pulse compression cannot be directly completed by using a matched filter, the pulse compression method of the present embodiment is constructed by a segmented pulse compression techniqueMSub-matched filter pairMThe pulse compression processing is respectively carried out on different sub-pulse echoes.
Suppose the first received by the radar receiver
Figure SMS_134
Echo signal of each pulse is +.>
Figure SMS_135
The matched filter function of each sub-pulse corresponding thereto is +.>
Figure SMS_136
Then->
Figure SMS_137
First pulse->
Figure SMS_138
The specific expression of the sectional pulse pressure treatment of each sub-pulse is as follows:
Figure SMS_139
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_141
indicate->
Figure SMS_143
First pulse->
Figure SMS_144
The sub-pulses are used for segmenting pulse pressure signals,
Figure SMS_142
the +.f. indicating intra-pulse frequency encoded radar reception>
Figure SMS_145
Echo signals of the individual pulses; />
Figure SMS_147
In order for the convolution operation to be performed,
Figure SMS_148
representation->
Figure SMS_140
A corresponding matched filter function per sub-pulse, which is +.>
Figure SMS_146
Is a conjugate function of (2);
Figure SMS_149
。
14 To be within one pulseMThe segmented pulse pressure results of the sub-pulses are added to obtain echo signals after pulse pressure, and the expression is as follows:
Figure SMS_150
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_151
echo signal after the representation of pulse pressure, +.>
Figure SMS_152
Indicate->
Figure SMS_153
The amplitude after the individual target pulse pressures,
Figure SMS_154
，/>
Figure SMS_155
for the total number of targets->
Figure SMS_156
Representing each sub-pulsePulse pressure treatment is carried out on pulse signals to form an envelope which is accumulated, and the pulse signals are +.>
Figure SMS_157
Representing noise.
In the embodiment, when the frequency coding waveform design in the pulse is performed, all the sub-pulses with small bandwidth are not used in one pulse, but a subset of all the sub-pulses with small bandwidth is selected, so that the waveform diversity is increased, and better orthogonality exists among different sub-pulses. In addition, the present embodiment further improves the anti-interference performance by using the inter-pulse frequency agile waveform while using the intra-pulse frequency encoded waveform.
Step 2: and establishing a frequency coding optimization model based on the echo signals after pulse pressure.
Specifically, the echo signal after pulse pressure is taken as a model value, and an optimized model using frequency coding as an independent variable is constructed based on the dB value of the peak value corresponding to each point in the function.
More specifically, the maximum value of the subpulse compression accumulation function of the echo signal after pulse pressure obtained in the step 2 is
Figure SMS_158
The pulse compression accumulation function is:
Figure SMS_159
。
an objective function with frequency coding as a variable can be established as follows:
Figure SMS_160
；
the function is in dB and its optimization aims at finding the minimum of the objective function, provided it is outside the main lobe region.
Step 3: and according to the echo signals after pulse pressure, a group of frequency codes are randomly generated, and the initial values are used as the current individual optimal adaptation value and the global optimal adaptation value.
In this embodiment, a set of intra-pulse frequency codes is randomly selectedCode, calculating correspondent peak side lobe ratio as global initial value, using initial value as first individual optimum adaptive value
Figure SMS_161
And is regarded as global optimum adaptation value +.>
Figure SMS_162
。
Step 4: and solving the frequency coding optimization model based on a particle swarm PSO (Particle swarm optimization) algorithm to obtain the minimum peak side lobe ratio of the echo signal after pulse pressure and the corresponding frequency coding.
Referring to fig. 2, fig. 2 is a flowchart of a particle swarm algorithm according to an embodiment of the invention, which specifically includes the following steps:
41 Initializing particle swarm PSO algorithm parameters.
Specifically, initial parameters of a particle swarm PSO algorithm are set: weight coefficient
Figure SMS_165
Maximum number of iterations->
Figure SMS_166
Particle swarm individual number->
Figure SMS_168
Particle dimension->
Figure SMS_164
Randomly initializing the position of the particle>
Figure SMS_167
And speed->
Figure SMS_169
Learning factor->
Figure SMS_170
And->
Figure SMS_163
And set a limiting speedDegree boundaries and limit position boundaries.
42 Calculating an optimal fitness value for the current position and velocity of each particle.
43 Comparing and judging the optimal adaptation value of the current position and the speed of each particle with the individual historical optimal adaptation value of each particle, and updating the historical optimal adaptation value and the position of each particle.
Specifically, each iteration, the optimal adaptation value of the current position and speed of each particle is calculated and compared with the individual historical optimal adaptation value of each particle, when the difference between the adaptation values before and after the iteration meets the optimization requirement, the particle updates the position of the particle, otherwise, the position is unchanged.
44 Comparing and judging the current iteration group optimal adaptation value with the group history optimal adaptation value, and updating the group history optimal adaptation value and the position.
45 Updating the velocity and position of the particles.
In this embodiment, the speed and position of the particles are updated according to the following formula:
Figure SMS_171
；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_175
is a weight coefficient>
Figure SMS_176
And->
Figure SMS_177
For learning factors->
Figure SMS_174
And->
Figure SMS_180
Is [0,1]Random value between->
Figure SMS_181
And
Figure SMS_183
an individual optimum adaptation value and a global optimum adaptation value, respectively->
Figure SMS_172
And->
Figure SMS_179
Respectively +.>
Figure SMS_182
The latest position and velocity of the particle at the time of the iteration, < >>
Figure SMS_184
And->
Figure SMS_173
Respectively +.>
Figure SMS_178
The most recent position and velocity of the particle at the time of the iteration.
46 According to the operations of steps 42) to 45), carrying out iterative updating until the maximum iterative times are reached, and outputting the group history optimal adaptation value and the position to obtain the minimum peak side lobe ratio of the echo signal after pulse compression and the corresponding frequency code.
Compared with the traditional method, the method has better ranging precision and ranging resolution, and the optimized frequency coding waveform has lower peak side lobe ratio compared with the frequency coding waveform which is not optimized, so that the radar has excellent anti-interference performance and simultaneously improves the detection capability of small targets in complex scenes. In addition, the particle swarm PSO algorithm has high convergence rate, and can efficiently complete the task of optimizing waveforms.
Example two
The beneficial effects of the invention are verified and illustrated by simulation tests.
1. Simulation conditions:
the input pulse width is 10 mu s, the pulse bandwidth is 40MHz, the sampling frequency is 80MHz, the number of frequency codes is 10, 1-10 random frequency codes are selected, M=9 sub-pulse segments are selected for transmission, the pulse width of each sub-pulse is 1 mu s, the sub-pulse bandwidth is 4MHz, the total pulse width of a transmitted signal is 9 mu s, the total bandwidth is 36 MHz, and an intra-pulse frequency code radar signal is generated in a rapid time sampling sequence. Pulse pressure processing is respectively carried out on each sub-pulse, and then the sub-pulses are accumulated, and a weight coefficient is set
Figure SMS_185
Learning factor->
Figure SMS_186
And->
Figure SMS_187
All equal to 1, the particle dimension is 10, and the maximum number of iterations is set to 200. The particle velocity is up and down bounded by [ -1,1]Particle position limitation within the frequency encoding range [1,10 ]]And ensures that the ten numbers of the random code sequences are different.
2. Simulation content and result analysis:
the simulation result of the whole process can be obtained by using the low-peak sidelobe frequency coding radar waveform design method. The simulation of the intra-pulse frequency coded radar echo adopted in the test is shown in fig. 3.
Referring to fig. 4-5, fig. 4 is a schematic diagram of pulse pressure results before frequency coding optimization in a simulation experiment, and fig. 5 is a schematic diagram of pulse pressure results after frequency coding optimization in a simulation experiment. As is evident from comparing fig. 4 and 5, the optimized maximum sidelobe value is reduced a lot.
The simulation test also performs a dB conversion on the pulse compression results before and after the optimization, please refer to fig. 6-7, fig. 6 is a schematic diagram of the pulse compression sidelobe ratio before the optimization in the simulation test, and fig. 7 is a schematic diagram of the pulse compression sidelobe ratio after the optimization in the simulation test. And after multiple experiments and averaging, the conclusion that the optimized peak side lobe ratio is reduced by about 5dB can be obtained, and the peak side lobe ratio is from about-12 dB to about-17 dB.
Fig. 8 is a schematic diagram of simulation iteration based on the PSO algorithm in a simulation experiment, it can be seen that after about 100 iterations, a final convergence value can be achieved, and the start and end positions of the simulation graph also correspond to peak sidelobe ratios in fig. 7 of fig. 6, respectively, so that the correctness of the simulation can be demonstrated.
The result of each iteration can optimize the waveform through multiple simulation tests, the convergence speed is high (convergence is finished in 100 iterations in most cases), waveform optimization can be realized with high efficiency, and the algorithm successfully realizes optimization of the signal waveform within an acceptable optimization range, so that the final purpose of reducing side lobes is achieved.
In addition, in order to verify whether the detection capability of the invention on the small target is improved, two targets are respectively set to be a strong target which is out of a distance of 1000m and a weak target which is out of a distance of 1100m, and under the condition that the speeds are equal, two coherent accumulation simulations are carried out, and the results are shown in fig. 9 and 10, wherein fig. 9 is a coherent accumulation top view before optimization, and fig. 10 is a coherent accumulation top view after optimization. From the simulation result graph, it is easy to draw the conclusion: the weak target before optimization is easily influenced by the side lobe of the strong target, so that missed judgment is caused, and the position of the weak target can be clearly determined through the coherent accumulation simulation after optimization of the invention. The invention thus also has the advantage of improving the detection capability of small objects.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.

Claims (4)

1. The method for designing the low-peak sidelobe frequency coding radar waveform is characterized by comprising the following steps of:
step 1: the intra-pulse agile radar transmits a signal and receives an echo signal, and sequentially carries out frequency mixing processing and sectional pulse compression processing on the echo signal and a corresponding transmitting carrier frequency to obtain an echo signal after pulse compression; comprising the following steps:
11 Equally dividing each pulse into Q sub-pulses, enabling the frequency among the sub-pulses to be agile, randomly selecting M sub-pulses from the sub-pulses to transmit, and enabling the M sub-pulses of the nth pulse to transmit as follows:
Figure FDA0004221763430000011
wherein T represents time, rect (·) represents a rectangular window function, κ represents the slope of the chirp signal, T r Representing pulse repetition period, T sub Representing the pulse width of each sub-pulse, j representing the imaginary unit;
f m the carrier frequency of the mth sub-pulse which is the nth pulse is expressed as follows:
Figure FDA0004221763430000012
wherein c m ∈[1,2,…,Q]，m＝[1,2,…,M]Representing intra-pulse frequency hopping coding, f n ＝f 0 +a n Δf represents the carrier frequency of the nth pulse, f 0 For the initial carrier frequency, a n For inter-pulse frequency hopping coding, Δf is the frequency hopping bandwidth, B sub The bandwidth for each sub-pulse;
12 Receiving an echo signal corresponding to the transmission signal of the m sub-pulse of the n-th pulse, wherein the expression is as follows:
Figure FDA0004221763430000013
where N represents the total number of pulses, K represents the total number of targets,
Figure FDA0004221763430000014
the time delay between the nth pulse echo signal and the transmitting signal of the kth target is that c is the speed of light, r k Distance to the kth target, v k For the speed of the kth target, σ k A scattering coefficient for the kth target;
13 The mth sub-pulse of the nth pulse is subjected to the segmented pulse pressure processing, and the formula is as follows:
Figure FDA0004221763430000021
wherein s is r (n, t) represents an echo signal of an nth pulse received by the intra-pulse frequency-coded radar;
Figure FDA0004221763430000022
representation s r (n, t) a matched filter function of each sub-pulse corresponding to s ref A conjugate function of (n, m, -t);
Figure FDA0004221763430000023
14 Adding the segmented pulse pressure results of M sub-pulses in one pulse to obtain an echo signal after pulse pressure of the pulse, wherein the expression is as follows:
Figure FDA0004221763430000024
wherein y (n, t) represents echo signal after pulse pressure, A k Represents the amplitude after the kth target pulse pressure, k= [1,2, …, K]K is the total number of targets, sinc () represents the envelope formed by accumulating each sub-pulse after pulse pressure processing, and beta (t) represents noise;
step 2: establishing a frequency coding optimization model based on echo signals after pulse pressure;
step 3: according to the echo signals after pulse pressure, a group of frequency codes are randomly generated, and initial values are used as the current individual optimal adaptation values and the global optimal adaptation values;
step 4: and solving the frequency coding optimization model based on a particle swarm PSO algorithm to obtain the minimum peak side lobe ratio of the echo signal after pulse pressure and the corresponding frequency coding.
2. The method of designing a low peak sidelobe frequency coded radar waveform of claim 1, wherein step 2 comprises:
taking a modulus value of the echo signal after pulse pressure, and constructing an optimization model taking frequency codes as independent variables based on dB values of peak values corresponding to each point in the function, wherein the objective function of the optimization model is as follows:
Figure FDA0004221763430000031
3. the method of designing a low peak sidelobe frequency coded radar waveform of claim 2, wherein step 4 comprises:
41 Initializing PSO algorithm parameters of a particle swarm;
42 Calculating an optimal fitness value for the current position and velocity of each particle;
43 Comparing and judging the optimal adaptation value of the current position and the speed of each particle with the individual historical optimal adaptation value of each particle, and updating the historical optimal adaptation value and the position of each particle;
44 Comparing and judging the current iteration group optimal adaptation value with the group history optimal adaptation value, and updating the group history optimal adaptation value and the position;
45 Updating the speed and position of the particles;
46 According to the operations of steps 42) to 45), carrying out iterative updating until the maximum iterative times are reached, and outputting the group history optimal adaptation value and the position to obtain the minimum peak side lobe ratio of the echo signal after pulse compression and the corresponding frequency code.
4. The method of claim 3, wherein in step 45), the formula for updating the velocity and position of the particles is:
Figure FDA0004221763430000041
wherein ω is a weight coefficient, c 1 And c 2 R is the learning factor 1 And r 2 Is [0,1]Random value between, P best And G best Respectively an individual optimal adaptation value and a global optimal adaptation value, P iter And V iter The latest position and velocity of the particle at the ith iteration, P iter+1 And V iter+1 The latest position and velocity of the particle at item+1 iteration, respectively.
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