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

Low peak sidelobe frequency coding radar waveform design method Download PDF

Info

Publication number
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
Authority
CN
China
Prior art keywords
pulse
frequency
sub
fitness value
echo signal
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202310327419.7A
Other languages
Chinese (zh)
Other versions
CN116027280A (en
Inventor
吴耀君
徐俊彤
杜思予
全英汇
刘智星
邢孟道
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xidian University
Original Assignee
Xidian University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xidian University filed Critical Xidian University
Priority to CN202310327419.7A priority Critical patent/CN116027280B/en
Publication of CN116027280A publication Critical patent/CN116027280A/en
Application granted granted Critical
Publication of CN116027280B publication Critical patent/CN116027280B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Landscapes

  • Radar Systems Or Details Thereof (AREA)

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

一种低峰值旁瓣频率编码雷达波形设计方法A design method for low peak sidelobe frequency coded radar waveform

技术领域Technical Field

本发明属于宽带雷达信号波形设计与处理技术领域，具体涉及一种低峰值旁瓣频率编码雷达波形设计方法。The invention belongs to the technical field of broadband radar signal waveform design and processing, and in particular relates to a low peak sidelobe frequency coded radar waveform design method.

背景技术Background Art

宽带雷达具备瞬时大带宽的特性，通过将瞬时大带宽雷达波形分割为多个小带宽并进行编码即为脉内频率编码波形。与非频率编码宽带雷达波形相比，脉内频率编码雷达系统在以下几方面有明显优势：(1)抗干扰能力强：脉内频率编码雷达的信号频率在一个脉冲内随机跳变，极大提高了干扰机发射同频信号进行干扰的难度；(2)提高了雷达的探测成像性能；(3)提高了距离分辨率和多普勒分辨率：频率编码雷达信号经过脉冲压缩具有窄主瓣的函数特性，这就意味着频率编码雷达具有可以同时为距离和速度提供高分辨率的能力。Wideband radar has the characteristic of instantaneous large bandwidth. By dividing the instantaneous large bandwidth radar waveform into multiple small bandwidths and encoding them, it becomes an intra-pulse frequency coded waveform. Compared with non-frequency coded wideband radar waveforms, intra-pulse frequency coded radar systems have obvious advantages in the following aspects: (1) Strong anti-interference ability: The signal frequency of the intra-pulse frequency coded radar randomly jumps within a pulse, which greatly increases the difficulty of the jammer transmitting the same frequency signal for interference; (2) Improved radar detection and imaging performance; (3) Improved distance resolution and Doppler resolution: The frequency coded radar signal has the function characteristic of a narrow main lobe after pulse compression, which means that the frequency coded radar has the ability to provide high resolution for both distance and speed.

在目前的脉内频率编码雷达处理技术中，主要存在的问题是脉压压缩后目标存在较高的旁瓣，而较高的旁瓣易被当成主瓣处理，从而容易误判成虚假目标，且高旁瓣容易导致小目标被漏判，这严重影响了雷达的抗干扰性能。In the current intra-pulse frequency coded radar processing technology, the main problem is that the target has high side lobes after pulse compression, and the high side lobes are easily treated as main lobes, which are easily misjudged as false targets. High side lobes can easily lead to small targets being missed, which seriously affects the radar's anti-interference performance.

发明内容Summary of the invention

为了解决现有技术中存在的上述问题，本发明提供了一种低峰值旁瓣频率编码雷达波形设计方法。本发明要解决的技术问题通过以下技术方案实现：In order to solve the above problems existing in the prior art, the present invention provides a method for designing a low peak sidelobe frequency coded radar waveform. The technical problem to be solved by the present invention is achieved by the following technical solutions:

一种低峰值旁瓣频率编码雷达波形设计方法，包括：A low peak sidelobe frequency coded radar waveform design method, comprising:

步骤1：脉内捷变雷达发射信号并接收回波信号，并将所述回波信号与对应的发射载频依次进行混频处理和分段脉冲压缩处理，得到脉压后的回波信号；Step 1: The intra-pulse agile radar transmits a signal and receives an echo signal, and performs frequency mixing and segmented pulse compression on the echo signal and the corresponding transmission carrier frequency in sequence to obtain an echo signal after pulse compression;

步骤2：基于脉压后的回波信号建立频率编码优化模型；Step 2: Establish a frequency coding optimization model based on the echo signal after pulse compression;

步骤3：根据脉压后的回波信号，随机出一组频率编码，并把初始值作为当前个体最优适应值和全局最优适应值；Step 3: According to the echo signal after pulse compression, a set of frequency codes is randomly generated, and the initial value is used as the current individual optimal fitness value and the global optimal fitness value;

步骤4：基于粒子群PSO算法对所述频率编码优化模型进行求解，得到脉压后的回波信号的最小峰值旁瓣比及其对应的频率编码。Step 4: Solve the frequency coding optimization model based on the particle swarm PSO algorithm to obtain the minimum peak sidelobe ratio of the echo signal after pulse compression and its corresponding frequency coding.

在本发明的一个实施例中，步骤1包括：In one embodiment of the present invention, step 1 comprises:

11)将每个脉冲等分成Q个子脉冲，子脉冲之间频率捷变，并从中随机选取M个子脉冲进行发射，则第

Figure SMS_1
个脉冲的第
Figure SMS_2
个子脉冲的发射信号为：11) Each pulse is equally divided into Q sub-pulses, the sub-pulses are frequency-agile, and M sub-pulses are randomly selected for transmission.
Figure SMS_1
The pulse
Figure SMS_2
The transmitted signal of a sub-pulse is:

Figure SMS_3
；
Figure SMS_3
;

其中，

Figure SMS_4
表示第
Figure SMS_7
个脉冲的第
Figure SMS_8
个子脉冲的发射信号，
Figure SMS_6
表示时间，
Figure SMS_9
表示矩形窗函数，
Figure SMS_11
表示线性调频信号的斜率，
Figure SMS_14
表示脉冲重复周期，
Figure SMS_5
表示每个子脉冲的脉宽，
Figure SMS_10
表示虚数单位，
Figure SMS_12
为自然指数，
Figure SMS_13
为圆周率；in,
Figure SMS_4
Indicates
Figure SMS_7
The pulse
Figure SMS_8
The transmitted signal of sub-pulses is
Figure SMS_6
Indicates time,
Figure SMS_9
represents the rectangular window function,
Figure SMS_11
represents the slope of the linear frequency modulation signal,
Figure SMS_14
represents the pulse repetition period,
Figure SMS_5
represents the pulse width of each sub-pulse,
Figure SMS_10
represents the imaginary unit,
Figure SMS_12
is the natural index,
Figure SMS_13
is the circumference of a circle;

Figure SMS_15
为第
Figure SMS_16
个脉冲的第
Figure SMS_17
个子脉冲的载频，其表达式为：
Figure SMS_15
For the
Figure SMS_16
The pulse
Figure SMS_17
The carrier frequency of the sub-pulse is expressed as:

Figure SMS_18
；
Figure SMS_18
;

其中，

Figure SMS_19
，
Figure SMS_22
表示脉内跳频编码，
Figure SMS_25
表示第
Figure SMS_21
个脉冲的载频，
Figure SMS_23
为初始载频，
Figure SMS_24
为脉间跳频编码，
Figure SMS_26
为跳频带宽，
Figure SMS_20
为每个子脉冲的带宽；in,
Figure SMS_19
,
Figure SMS_22
Indicates intra-pulse frequency hopping coding,
Figure SMS_25
Indicates
Figure SMS_21
The carrier frequency of a pulse,
Figure SMS_23
is the initial carrier frequency,
Figure SMS_24
is the pulse-to-pulse frequency hopping coding,
Figure SMS_26
is the frequency hopping bandwidth,
Figure SMS_20
is the bandwidth of each sub-pulse;

12)接收第

Figure SMS_27
个脉冲的第
Figure SMS_28
个子脉冲的发射信号对应的回波信号，其表达式为：12) Receive the
Figure SMS_27
The pulse
Figure SMS_28
The echo signal corresponding to the transmitted signal of a sub-pulse is expressed as:

Figure SMS_29
；
Figure SMS_29
;

其中，

Figure SMS_31
表示第
Figure SMS_34
个脉冲的第
Figure SMS_35
个子脉冲的发射信号对应的回波信号，
Figure SMS_32
表示脉冲总数，
Figure SMS_37
表示目标总数，
Figure SMS_40
为第
Figure SMS_43
个目标的第
Figure SMS_30
个脉冲回波信号与发射信号之间的时延，
Figure SMS_36
为光速，
Figure SMS_38
为第
Figure SMS_41
个目标的距离，
Figure SMS_33
为第
Figure SMS_39
个目标的速度，
Figure SMS_42
为第
Figure SMS_44
个目标的散射系数；in,
Figure SMS_31
Indicates
Figure SMS_34
The pulse
Figure SMS_35
The echo signal corresponding to the transmitted signal of the sub-pulse is
Figure SMS_32
Indicates the total number of pulses,
Figure SMS_37
represents the total number of targets,
Figure SMS_40
For the
Figure SMS_43
The first target
Figure SMS_30
The time delay between the pulse echo signal and the transmitted signal,
Figure SMS_36
is the speed of light,
Figure SMS_38
For the
Figure SMS_41
The distance to the target,
Figure SMS_33
For the
Figure SMS_39
The speed of the target,
Figure SMS_42
For the
Figure SMS_44
The scattering coefficient of a target;

13)对第

Figure SMS_45
个脉冲的第
Figure SMS_46
个子脉冲进行分段脉压处理，公式表示为：13)
Figure SMS_45
The pulse
Figure SMS_46
The sub-pulses are processed by segmented pulse compression, and the formula is expressed as:

Figure SMS_47
；
Figure SMS_47
;

其中，

Figure SMS_49
表示第
Figure SMS_51
个脉冲的第
Figure SMS_52
个子脉冲进行分段脉压后的信号，
Figure SMS_50
表示脉内频率编码雷达接收的第
Figure SMS_53
个脉冲的回波信号；
Figure SMS_54
为卷积操作，
Figure SMS_55
表示
Figure SMS_48
对应的每个子脉冲的匹配滤波函数，其为
Figure SMS_56
的共轭函数；in,
Figure SMS_49
Indicates
Figure SMS_51
The pulse
Figure SMS_52
The signal after segmented pulse compression of sub-pulses is
Figure SMS_50
Indicates the first
Figure SMS_53
The echo signal of a pulse;
Figure SMS_54
is the convolution operation,
Figure SMS_55
express
Figure SMS_48
The matched filter function corresponding to each sub-pulse is
Figure SMS_56
The conjugate function of

Figure SMS_57
；
Figure SMS_57
;

14)将一个脉冲内M个子脉冲的分段脉压结果相加，得到该脉冲脉压后的回波信号，其表达式为：14) Add the segmented pulse compression results of M sub-pulses in a pulse to obtain the echo signal after the pulse compression, which is expressed as:

Figure SMS_58
；
Figure SMS_58
;

其中，

Figure SMS_59
表示脉压后的回波信号，
Figure SMS_60
表示第
Figure SMS_61
个目标脉压后的幅值，
Figure SMS_62
，
Figure SMS_63
为目标总数，
Figure SMS_64
表示每个子脉冲经过脉压处理后累加形成的包络，
Figure SMS_65
表示噪声。in,
Figure SMS_59
Represents the echo signal after pulse compression,
Figure SMS_60
Indicates
Figure SMS_61
The amplitude after the target pulse pressure,
Figure SMS_62
,
Figure SMS_63
is the total number of targets,
Figure SMS_64
It represents the envelope formed by the accumulation of each sub-pulse after pulse compression processing.
Figure SMS_65
Indicates noise.

在本发明的一个实施例中，步骤2包括：In one embodiment of the present invention, step 2 comprises:

将脉压后的回波信号取模值，并基于函数中每个点对应峰值的dB值，构建一个以频率编码为自变量的优化模型，该优化模型的目标函数为：The echo signal after pulse compression is modulo-valued, and based on the dB value of the peak value corresponding to each point in the function, an optimization model with frequency encoding as the independent variable is constructed. The objective function of the optimization model is:

Figure SMS_66
。
Figure SMS_66
.

在本发明的一个实施例中，步骤4包括：In one embodiment of the present invention, step 4 comprises:

41)初始化粒子群PSO算法参数；41) Initialize the particle swarm PSO algorithm parameters;

42)计算每个粒子的当前位置和速度的最优适应值；42) Calculate the optimal fitness value of the current position and velocity of each particle;

43)将每个粒子的当前位置和速度的最优适应值分别与每个粒子的个体历史最优适应值进行比较判断，并更新每个粒子的历史最优适应值和位置；43) Compare and judge the optimal fitness value of the current position and speed of each particle with the individual historical optimal fitness value of each particle, and update the historical optimal fitness value and position of each particle;

44)将当前次迭代的群体最优适应值与群体历史最优适应值进行比较判断，并更新群体历史最优适应值和位置；44) Compare and judge the optimal fitness value of the group in the current iteration with the historical optimal fitness value of the group, and update the historical optimal fitness value and position of the group;

45)更新粒子的速度与位置；45) Update the velocity and position of the particle;

46)按照步骤42)-45)的操作进行迭代更新，直至达到最大迭代次数，并输出群体历史最优适应值和位置，以得到脉压后的回波信号的最小峰值旁瓣比及其对应的频率编码。46) Perform iterative updates according to the operations of steps 42)-45) until the maximum number of iterations is reached, and output the group's historical optimal fitness value and position to obtain the minimum peak-to-sidelobe ratio of the echo signal after pulse compression and its corresponding frequency coding.

在本发明的一个实施例中，在步骤45)中，按照如下公式更新粒子的速度与位置：In one embodiment of the present invention, in step 45), the velocity and position of the particle are updated according to the following formula:

Figure SMS_67
；
Figure SMS_67
;

其中，

Figure SMS_70
为权重系数，
Figure SMS_75
和
Figure SMS_78
为学习因子，
Figure SMS_69
和
Figure SMS_74
为[0,1]之间的随机值，
Figure SMS_76
和
Figure SMS_77
分别为个体最优适应值和全局最优适应值，
Figure SMS_68
和
Figure SMS_72
分别为第
Figure SMS_79
次迭代时粒子的最新位置和速度，
Figure SMS_80
和
Figure SMS_71
分别为第
Figure SMS_73
次迭代时粒子的最新位置和速度。in,
Figure SMS_70
is the weight coefficient,
Figure SMS_75
and
Figure SMS_78
is the learning factor,
Figure SMS_69
and
Figure SMS_74
is a random value between [0,1],
Figure SMS_76
and
Figure SMS_77
are the individual optimal fitness value and the global optimal fitness value respectively,
Figure SMS_68
and
Figure SMS_72
Respectively
Figure SMS_79
The latest position and velocity of the particle at the iteration,
Figure SMS_80
and
Figure SMS_71
Respectively
Figure SMS_73
The latest position and velocity of the particle at iteration .

本发明的有益效果：Beneficial effects of the present invention:

1、本发明提供的低峰值旁瓣频率编码雷达波形设计方法选用了脉内频率编码雷达波形并采用了粒子群优化算法进行波形优化，与传统方法相比，该方法具有更好的测距精度与测距分辨率，优化后的频率编码波形相对于未经优化的频率编码波形具有更低的峰值旁瓣比，使得雷达在具备优良抗干扰性能的同时，还提升了复杂场景中对小目标的检测能力；1. The low peak sidelobe frequency coded radar waveform design method provided by the present invention selects an intra-pulse frequency coded radar waveform and adopts a particle swarm optimization algorithm for waveform optimization. Compared with the traditional method, the method has better ranging accuracy and ranging resolution. The optimized frequency coded waveform has a lower peak sidelobe ratio than the unoptimized frequency coded waveform, so that the radar has excellent anti-interference performance and also improves the detection capability of small targets in complex scenes;

2、本发明在使用脉内频率编码波形的同时，使用脉间频率捷变波形，进一步提升了抗干扰性能；2. The present invention uses an intra-pulse frequency coding waveform and an inter-pulse frequency agile waveform at the same time, which further improves the anti-interference performance;

3、本发明在进行脉冲内频率编码波形设计时，一个脉冲内并没有使用全部小带宽的子脉冲，而是选择了全部小带宽子脉冲的子集，增加了波形的多样性，并且不同子脉冲间会有更好的正交性；3. When designing the intra-pulse frequency coding waveform, the present invention does not use all the small-bandwidth sub-pulses in one pulse, but selects a subset of all the small-bandwidth sub-pulses, thereby increasing the diversity of the waveform and achieving better orthogonality between different sub-pulses.

4、本发明采用的粒子群PSO算法收敛速度快，可以高效率完成优化波形的任务。4. The particle swarm PSO algorithm adopted in the present invention has a fast convergence speed and can efficiently complete the task of optimizing the waveform.

以下将结合附图及实施例对本发明做进一步详细说明。The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1是本发明实施例提供的一种低峰值旁瓣频率编码雷达波形设计方法的流程示意图；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;

图2是本发明实施例提供的粒子群算法流程图；FIG2 is a flow chart of a particle swarm algorithm provided by an embodiment of the present invention;

图3是仿真实验中脉内频率编码雷达回波的仿真示意图；FIG3 is a schematic diagram of a simulation of an intra-pulse frequency coded radar echo in a simulation experiment;

图4是仿真实验中频率编码优化前的脉压结果示意图；FIG4 is a schematic diagram of pulse pressure results before frequency coding optimization in a simulation experiment;

图5是仿真实验中频率编码优化后的脉压结果示意图；FIG5 is a schematic diagram of pulse pressure results after frequency coding optimization in a simulation experiment;

图6是仿真实验中优化前脉冲压缩旁瓣比示意图；FIG6 is a schematic diagram of the sidelobe ratio of pulse compression before optimization in a simulation experiment;

图7是仿真实验中优化后脉冲压缩旁瓣比示意图；FIG7 is a schematic diagram of the sidelobe ratio of pulse compression after optimization in a simulation experiment;

图8是仿真实验中基于PSO算法的仿真迭代示意图；FIG8 is a schematic diagram of simulation iteration based on the PSO algorithm in the simulation experiment;

图9是仿真实验中优化前相参积累俯视图；FIG9 is a top view of coherent accumulation before optimization in a simulation experiment;

图10是仿真实验中优化后相参积累俯视图。FIG. 10 is a top view of the coherent accumulation after optimization in the simulation experiment.

具体实施方式DETAILED DESCRIPTION

下面结合具体实施例对本发明做进一步详细的描述，但本发明的实施方式不限于此。The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

实施例一Embodiment 1

请参见图1，图1是本发明实施例提供的一种低峰值旁瓣频率编码雷达波形设计方法的流程示意图，其包括：Please refer to FIG. 1 , which is a flow chart of a method for designing a low peak sidelobe frequency coded radar waveform provided by an embodiment of the present invention, which includes:

步骤1：脉内捷变雷达发射信号并接收回波信号，并将所述回波信号与对应的发射载频依次进行混频处理和分段脉冲压缩处理，得到脉压后的回波信号。Step 1: The intra-pulse agile radar transmits a signal and receives an echo signal, and performs frequency mixing and segmented pulse compression on the echo signal and the corresponding transmission carrier frequency in sequence to obtain a pulse compressed echo signal.

具体的，步骤1包括：Specifically, step 1 includes:

11)将每个脉冲等分成Q个子脉冲，子脉冲之间频率捷变，并从中随机选取M个子脉冲进行发射。11) Each pulse is equally divided into Q sub-pulses, with frequency agility between the sub-pulses, and M sub-pulses are randomly selected for transmission.

具体的，设每个信号脉冲的脉宽和带宽分别为

Figure SMS_83
和
Figure SMS_84
，则每个子脉冲的脉宽为
Figure SMS_85
，带宽为
Figure SMS_81
，从中随机选取M个子脉冲发射，则发射脉冲的脉宽
Figure SMS_86
，带宽
Figure SMS_87
。对这M个子脉冲重新排序，则第
Figure SMS_88
个脉冲的第
Figure SMS_82
个子脉冲的载频为：Specifically, let the pulse width and bandwidth of each signal pulse be
Figure SMS_83
and
Figure SMS_84
, then the pulse width of each sub-pulse is
Figure SMS_85
, the bandwidth is
Figure SMS_81
, randomly select M sub-pulses to transmit, then the pulse width of the transmitted pulse is
Figure SMS_86
,bandwidth
Figure SMS_87
. Reorder these M sub-pulses, then
Figure SMS_88
The pulse
Figure SMS_82
The carrier frequency of each sub-pulse is:

Figure SMS_89
；
Figure SMS_89
;

其中，

Figure SMS_90
，
Figure SMS_91
表示脉内跳频编码，
Figure SMS_92
为第
Figure SMS_93
个脉冲的载频，
Figure SMS_94
为初始载频，
Figure SMS_95
为脉间跳频编码，
Figure SMS_96
是跳频带宽。in,
Figure SMS_90
,
Figure SMS_91
Indicates intra-pulse frequency hopping coding,
Figure SMS_92
For the
Figure SMS_93
The carrier frequency of the pulse,
Figure SMS_94
is the initial carrier frequency,
Figure SMS_95
is the pulse-to-pulse frequency hopping coding,
Figure SMS_96
is the frequency hopping bandwidth.

则第

Figure SMS_97
个脉冲的第
Figure SMS_98
个子脉冲的发射信号为：The first
Figure SMS_97
The pulse
Figure SMS_98
The transmitted signal of a sub-pulse is:

Figure SMS_99
；
Figure SMS_99
;

其中，

Figure SMS_102
表示第
Figure SMS_103
个脉冲的第
Figure SMS_105
个子脉冲的发射信号，
Figure SMS_101
表示时间，
Figure SMS_107
表示矩形窗函数，
Figure SMS_108
为线性调频信号的斜率，
Figure SMS_109
表示脉冲重复周期，
Figure SMS_100
表示虚数单位，
Figure SMS_104
为自然指数，
Figure SMS_106
为圆周率。in,
Figure SMS_102
Indicates
Figure SMS_103
The pulse
Figure SMS_105
The transmitted signal of sub-pulses is
Figure SMS_101
Indicates time,
Figure SMS_107
represents the rectangular window function,
Figure SMS_108
is the slope of the linear frequency modulation signal,
Figure SMS_109
represents the pulse repetition period,
Figure SMS_100
represents the imaginary unit,
Figure SMS_104
is the natural index,
Figure SMS_106
is the ratio of pi.

12)接收第

Figure SMS_110
个脉冲的第
Figure SMS_111
个子脉冲的发射信号对应的回波信号。12) Receive the
Figure SMS_110
The pulse
Figure SMS_111
The echo signal corresponding to the transmitted signal of the sub-pulse.

具体的，假定测量场景中运动目标的总个数为

Figure SMS_112
，第
Figure SMS_113
个目标的距离和速度分别设为
Figure SMS_114
和
Figure SMS_115
，且目标起伏模型均为Swerling I型，则脉内频率编码雷达的回波信号可以写作：Specifically, assume that the total number of moving targets in the measurement scene is
Figure SMS_112
,
Figure SMS_113
The distance and speed of each target are set as
Figure SMS_114
and
Figure SMS_115
, and the target fluctuation model is Swerling I type, then the echo signal of the intra-pulse frequency coded radar can be written as:

Figure SMS_116
；
Figure SMS_116
;

其中，

Figure SMS_117
表示第
Figure SMS_121
个脉冲的第
Figure SMS_122
个子脉冲的发射信号对应的回波信号，
Figure SMS_119
表示脉冲总数，
Figure SMS_124
表示目标总数，
Figure SMS_128
为第
Figure SMS_131
个目标的第
Figure SMS_118
个脉冲回波信号与发射信号之间的时延，
Figure SMS_123
为光速，
Figure SMS_126
为第
Figure SMS_129
个目标的距离，
Figure SMS_120
为第
Figure SMS_125
个目标的速度，
Figure SMS_127
为第
Figure SMS_130
个目标的散射系数。in,
Figure SMS_117
Indicates
Figure SMS_121
The pulse
Figure SMS_122
The echo signal corresponding to the transmitted signal of the sub-pulse is
Figure SMS_119
Indicates the total number of pulses,
Figure SMS_124
represents the total number of targets,
Figure SMS_128
For the
Figure SMS_131
The first target
Figure SMS_118
The time delay between the pulse echo signal and the transmitted signal,
Figure SMS_123
is the speed of light,
Figure SMS_126
For the
Figure SMS_129
The distance to the target,
Figure SMS_120
For the
Figure SMS_125
The speed of the target,
Figure SMS_127
For the
Figure SMS_130
The scattering coefficient of a target.

13)对第

Figure SMS_132
个脉冲的第
Figure SMS_133
个子脉冲进行分段脉压处理。13)
Figure SMS_132
The pulse
Figure SMS_133
The sub-pulses are processed by segmented pulse compression.

具体的，由于脉内频率编码雷达无法直接用一个匹配滤波器完成脉冲压缩，因此本实施例通过分段脉压技术，构造M个子匹配滤波器，对M个不同的子脉冲回波分别进行脉冲压缩处理。Specifically, since the intra-pulse frequency coded radar cannot directly use a matched filter to complete pulse compression, this embodiment uses the segmented pulse compression technology to construct M sub-matched filters and perform pulse compression processing on M different sub-pulse echoes respectively.

假设雷达接收机接收到的第

Figure SMS_134
个脉冲的回波信号为
Figure SMS_135
，则其对应的每个子脉冲的匹配滤波函数是
Figure SMS_136
，则第
Figure SMS_137
个脉冲的第
Figure SMS_138
个子脉冲进行分段脉压处理的具体表达式为：Assume that the radar receiver receives the
Figure SMS_134
The echo signal of a pulse is
Figure SMS_135
, then the matched filter function of each sub-pulse is
Figure SMS_136
, then
Figure SMS_137
The pulse
Figure SMS_138
The specific expression for segmented pulse compression processing of sub-pulses is:

Figure SMS_139
；
Figure SMS_139
;

其中，

Figure SMS_141
表示第
Figure SMS_143
个脉冲的第
Figure SMS_144
个子脉冲进行分段脉压后的信号，
Figure SMS_142
表示脉内频率编码雷达接收的第
Figure SMS_145
个脉冲的回波信号；
Figure SMS_147
为卷积操作，
Figure SMS_148
表示
Figure SMS_140
对应的每个子脉冲的匹配滤波函数，其为
Figure SMS_146
的共轭函数；in,
Figure SMS_141
Indicates
Figure SMS_143
The pulse
Figure SMS_144
The signal after segmented pulse compression of sub-pulses is
Figure SMS_142
Indicates the first
Figure SMS_145
The echo signal of a pulse;
Figure SMS_147
is the convolution operation,
Figure SMS_148
express
Figure SMS_140
The matched filter function corresponding to each sub-pulse is
Figure SMS_146
The conjugate function of

Figure SMS_149
。
Figure SMS_149
.

14)将一个脉冲内M个子脉冲的分段脉压结果相加，得到该脉冲脉压后的回波信号，其表达式为：14) Add the segmented pulse compression results of M sub-pulses in a pulse to obtain the echo signal after the pulse compression, which is expressed as:

Figure SMS_150
；
Figure SMS_150
;

其中，

Figure SMS_151
表示脉压后的回波信号，
Figure SMS_152
表示第
Figure SMS_153
个目标脉压后的幅值，
Figure SMS_154
，
Figure SMS_155
为目标总数，
Figure SMS_156
表示每个子脉冲经过脉压处理后累加形成的包络，
Figure SMS_157
表示噪声。in,
Figure SMS_151
Represents the echo signal after pulse compression,
Figure SMS_152
Indicates
Figure SMS_153
The amplitude after the target pulse pressure,
Figure SMS_154
,
Figure SMS_155
is the total number of targets,
Figure SMS_156
It represents the envelope formed by the accumulation of each sub-pulse after pulse compression processing.
Figure SMS_157
Indicates noise.

本实施例在进行脉冲内频率编码波形设计时，一个脉冲内并没有使用全部小带宽的子脉冲，而是选择了全部小带宽子脉冲的子集，增加了波形的多样性，并且不同子脉冲间会有更好的正交性。此外，本实施例在使用脉内频率编码波形的同时，使用脉间频率捷变波形，进一步提升了抗干扰性能。In the design of the intra-pulse frequency coded waveform, the present embodiment does not use all the small bandwidth sub-pulses in one pulse, but selects a subset of all the small bandwidth sub-pulses, thereby increasing the diversity of the waveform and achieving better orthogonality between different sub-pulses. In addition, the present embodiment uses an inter-pulse frequency agile waveform while using the intra-pulse frequency coded waveform, further improving the anti-interference performance.

步骤2：基于脉压后的回波信号建立频率编码优化模型。Step 2: Establish a frequency coding optimization model based on the echo signal after pulse compression.

具体的，将脉压后的回波信号取模值，并基于函数中每个点对应峰值的dB值，构建一个以频率编码为自变量的优化模型。Specifically, the modulus value of the echo signal after pulse compression is taken, and based on the dB value of the peak value corresponding to each point in the function, an optimization model with frequency coding as the independent variable is constructed.

更具体的，根据步骤2得到的脉压后的回波信号，其子脉冲压缩积累函数最大值为

Figure SMS_158
，脉冲压缩积累函数为：More specifically, according to the echo signal after pulse compression obtained in step 2, the maximum value of its sub-pulse compression accumulation function is
Figure SMS_158
, the pulse compression accumulation function is:

Figure SMS_159
。
Figure SMS_159
.

则可以建立一个以频率编码为变量的目标函数如下：Then we can establish an objective function with frequency encoding as a variable as follows:

Figure SMS_160
；
Figure SMS_160
;

该函数的单位为dB，其优化目的是找到目标函数的最小值，条件是在主瓣区域外。The unit of this function is dB, and its optimization purpose is to find the minimum value of the objective function, provided that it is outside the main lobe area.

步骤3：根据脉压后的回波信号，随机出一组频率编码，并把初始值作为当前个体最优适应值和全局最优适应值。Step 3: According to the echo signal after pulse compression, a set of frequency codes is randomly generated, and the initial value is used as the current individual optimal fitness value and the global optimal fitness value.

在本实施例中，随机取一组脉内频率编码，计算对应的峰值旁瓣比，作为全局的初始值，把初始值当作第一个个体最优适应值

Figure SMS_161
，并且当作全局最优适应值
Figure SMS_162
。In this embodiment, a group of intra-pulse frequency codes are randomly selected, and the corresponding peak sidelobe ratio is calculated as the global initial value, and the initial value is taken as the first individual optimal adaptation value.
Figure SMS_161
, and is taken as the global optimal fitness value
Figure SMS_162
.

步骤4：基于粒子群PSO(Particle swarm optimization)算法对所述频率编码优化模型进行求解，得到脉压后的回波信号的最小峰值旁瓣比及其对应的频率编码。Step 4: Solve the frequency coding optimization model based on the particle swarm optimization (PSO) algorithm to obtain the minimum peak-to-sidelobe ratio of the echo signal after pulse compression and its corresponding frequency coding.

请参见图2，图2是本发明实施例提供的粒子群算法流程图，其具体包括如下步骤：Please refer to FIG. 2 , which is a flow chart of a particle swarm algorithm provided by an embodiment of the present invention, which specifically includes the following steps:

41)初始化粒子群PSO算法参数。41) Initialize the particle swarm PSO algorithm parameters.

具体的，设置粒子群PSO算法的初始参数：权重系数

Figure SMS_165
，最大迭代次数
Figure SMS_166
，粒子群个体数目
Figure SMS_168
，粒子维度
Figure SMS_164
，随机初始化粒子的位置
Figure SMS_167
和速度
Figure SMS_169
，学习因子
Figure SMS_170
和
Figure SMS_163
，并且设置限制速度边界和限制位置边界。Specifically, set the initial parameters of the particle swarm PSO algorithm: weight coefficient
Figure SMS_165
, maximum number of iterations
Figure SMS_166
, the number of individual particles in the swarm
Figure SMS_168
, particle dimension
Figure SMS_164
, randomly initialize the particle position
Figure SMS_167
and speed
Figure SMS_169
, learning factor
Figure SMS_170
and
Figure SMS_163
, and set the speed limit boundary and position limit boundary.

42)计算每个粒子的当前位置和速度的最优适应值。42) Calculate the optimal fitness value of the current position and velocity of each particle.

43)将每个粒子的当前位置和速度的最优适应值分别与每个粒子的个体历史最优适应值进行比较判断，并更新每个粒子的历史最优适应值和位置。43) The optimal fitness value of the current position and speed of each particle is compared with the individual historical optimal fitness value of each particle, and the historical optimal fitness value and position of each particle are updated.

具体的，每一次迭代，计算出每个粒子的当前位置和速度的最优适应值，分别与每个粒子各自的个体历史最优适应值进行比较，当迭代前后的适应值之差满足优化要求时，粒子更新它的位置，否则位置不变。Specifically, in each iteration, the optimal fitness value of the current position and speed of each particle is calculated and compared with the individual historical optimal fitness value of each particle. When the difference between the fitness values before and after the iteration meets the optimization requirements, the particle updates its position, otherwise the position remains unchanged.

44)将当前次迭代的群体最优适应值与群体历史最优适应值进行比较判断，并更新群体历史最优适应值和位置。44) Compare and judge the optimal fitness value of the group in the current iteration with the historical optimal fitness value of the group, and update the historical optimal fitness value and position of the group.

45)更新粒子的速度与位置。45) Update the particle's velocity and position.

在本实施例中，按照如下公式更新粒子的速度与位置：In this embodiment, the speed and position of the particle are updated according to the following formula:

Figure SMS_171
；
Figure SMS_171
;

其中，

Figure SMS_175
为权重系数，
Figure SMS_176
和
Figure SMS_177
为学习因子，
Figure SMS_174
和
Figure SMS_180
为[0,1]之间的随机值，
Figure SMS_181
和
Figure SMS_183
分别为个体最优适应值和全局最优适应值，
Figure SMS_172
和
Figure SMS_179
分别为第
Figure SMS_182
次迭代时粒子的最新位置和速度，
Figure SMS_184
和
Figure SMS_173
分别为第
Figure SMS_178
次迭代时粒子的最新位置和速度。in,
Figure SMS_175
is the weight coefficient,
Figure SMS_176
and
Figure SMS_177
is the learning factor,
Figure SMS_174
and
Figure SMS_180
is a random value between [0,1],
Figure SMS_181
and
Figure SMS_183
are the individual optimal fitness value and the global optimal fitness value respectively,
Figure SMS_172
and
Figure SMS_179
Respectively
Figure SMS_182
The latest position and velocity of the particle at the iteration,
Figure SMS_184
and
Figure SMS_173
Respectively
Figure SMS_178
The latest position and velocity of the particle at iteration .

46)按照步骤42)-45)的操作进行迭代更新，直至达到最大迭代次数，并输出群体历史最优适应值和位置，以得到脉压后的回波信号的最小峰值旁瓣比及其对应的频率编码。46) Perform iterative updates according to the operations of steps 42)-45) until the maximum number of iterations is reached, and output the group's historical optimal fitness value and position to obtain the minimum peak-to-sidelobe ratio of the echo signal after pulse compression and its corresponding frequency coding.

本发明提供的低峰值旁瓣频率编码雷达波形设计方法选用了脉内频率编码雷达波形并采用了粒子群优化算法进行波形优化，与传统方法相比，该方法具有更好的测距精度与测距分辨率，优化后的频率编码波形相对于未经优化的频率编码波形具有更低的峰值旁瓣比，使得雷达在具备优良抗干扰性能的同时，还提升了复杂场景中对小目标的检测能力。此外，粒子群PSO算法的收敛速度快，可以高效率完成优化波形的任务。The low peak sidelobe frequency coded radar waveform design method provided by the present invention selects the intra-pulse frequency coded radar waveform and adopts the particle swarm optimization algorithm for waveform optimization. Compared with the traditional method, this method has better ranging accuracy and ranging resolution. The optimized frequency coded waveform has a lower peak sidelobe ratio than the unoptimized frequency coded waveform, so that the radar has excellent anti-interference performance while also improving the detection ability of small targets in complex scenes. In addition, the particle swarm PSO algorithm has a fast convergence speed and can efficiently complete the task of optimizing the waveform.

实施例二Embodiment 2

下面通过仿真试验对本发明的有益效果进行验证说明。The beneficial effects of the present invention are verified and explained below through simulation experiments.

1、仿真条件：1. Simulation conditions:

输入脉冲宽度10μs，脉冲带宽40MHZ，采样频率80MHZ，频率编码个数10个，1~10随机频率编码，选取M=9个子脉冲段发射，每个子脉冲脉宽为1μs，子脉冲带宽为4MHZ，发射信号总脉宽为9μs，总带宽为36 MHz，在快时间采样序列中生成脉内频率编码雷达信号。对各个子脉冲分别做脉压处理后累加起来，设置权重系数

Figure SMS_185
、学习因子
Figure SMS_186
和
Figure SMS_187
都等于1，粒子维度为10，最大迭代次数设置为200。粒子速度上下界取[-1,1]，粒子位置限制在频率编码范围内[1,10]，且保证随机编码序列的十个数字各不相同。Input pulse width 10μs, pulse bandwidth 40MHZ, sampling frequency 80MHZ, frequency coding number 10, 1~10 random frequency coding, select M=9 sub-pulse segments for transmission, each sub-pulse pulse width is 1μs, sub-pulse bandwidth is 4MHZ, the total pulse width of the transmitted signal is 9μs, the total bandwidth is 36 MHz, and the intra-pulse frequency coded radar signal is generated in the fast time sampling sequence. Perform pulse compression processing on each sub-pulse and add them up, and set the weight coefficient
Figure SMS_185
, learning factor
Figure SMS_186
and
Figure SMS_187
All are equal to 1, the particle dimension is 10, and the maximum number of iterations is set to 200. The upper and lower bounds of the particle velocity are [-1, 1], the particle position is limited to the frequency encoding range [1, 10], and the ten numbers of the random encoding sequence are guaranteed to be different.

2、仿真内容及结果分析：2. Simulation content and result analysis:

利用上述一种低峰值旁瓣频率编码雷达波形设计方法可以得到一次整个过程的仿真结果。本次试验采用的脉内频率编码雷达回波仿真如图3所示。The above-mentioned low peak sidelobe frequency coded radar waveform design method can obtain the simulation result of the whole process. The intra-pulse frequency coded radar echo simulation used in this experiment is shown in Figure 3.

请参见图4-5，图4是仿真实验中频率编码优化前的脉压结果示意图，图5是仿真实验中频率编码优化后的脉压结果示意图。对比图4和图5可以明显看出，优化后的最大旁瓣值降低了不少。Please refer to Figures 4-5. Figure 4 is a schematic diagram of the pulse pressure results before frequency coding optimization in the simulation experiment, and Figure 5 is a schematic diagram of the pulse pressure results after frequency coding optimization in the simulation experiment. By comparing Figures 4 and 5, it can be clearly seen that the maximum sidelobe value after optimization is reduced a lot.

本次仿真试验还对优化前后的脉冲压缩结果做一个dB换算，请参见图6-7，图6是仿真实验中优化前脉冲压缩旁瓣比示意图，图7是仿真实验中优化后脉冲压缩旁瓣比示意图。经过多次试验取平均，可以得出优化后的峰值旁瓣比降低了5dB左右这个结论，从-12dB到-17dB左右。This simulation experiment also makes a dB conversion of the pulse compression results before and after optimization, see Figures 6-7, Figure 6 is a schematic diagram of the pulse compression sidelobe ratio before optimization in the simulation experiment, and Figure 7 is a schematic diagram of the pulse compression sidelobe ratio after optimization in the simulation experiment. After taking the average of multiple tests, it can be concluded that the peak sidelobe ratio after optimization is reduced by about 5dB, from -12dB to about -17dB.

图8是仿真实验中基于PSO算法的仿真迭代示意图，可以看到经过100次左右的迭代，就可以达到最终的收敛值，并且仿真图的起始和终止位置也分别与图6的图7中的峰值旁瓣比能够对应上，可以证明该仿真的正确性。FIG8 is a schematic diagram of the simulation iteration based on the PSO algorithm in the simulation experiment. It can be seen that after about 100 iterations, the final convergence value can be reached, and the starting and ending positions of the simulation diagram can correspond to the peak sidelobe ratios in FIG6 and FIG7 respectively, which can prove the correctness of the simulation.

经过多次仿真试验可以得出结论，每一次迭代的结果都能对波形起到优化的目的，且收敛速度快(多数情况在100次迭代内完成收敛)，可以高效率实现波形优化，在可接受的优化范围内，本算法成功实现了对信号波形的优化，达到了降低旁瓣的最终目的。After many simulation tests, it can be concluded that the result of each iteration can optimize the waveform, and the convergence speed is fast (in most cases, convergence is completed within 100 iterations), and the waveform optimization can be realized efficiently. Within the acceptable optimization range, this algorithm successfully realizes the optimization of the signal waveform and achieves the ultimate goal of reducing the sidelobes.

此外，为验证本发明对小目标的检测能力是否有提高，设置两个目标分别为强目标在1000m距离外和弱目标在1100m距离外，并在速度均相等的情况下，进行两次相参积累仿真，结果如图9和图10所示，其中，图9是优化前相参积累俯视图，图10是优化后相参积累俯视图。根据仿真结果图容易得出结论：优化前的弱目标容易被强目标的旁瓣影响，造成漏判，而经过本发明优化后的相参积累仿真，可以清晰明了的把弱目标的位置也确定下来。因此本发明也具备提高对小目标的检测能力的这个优点。In addition, in order to verify whether the present invention has improved the detection capability of small targets, two targets are set, namely, a strong target at a distance of 1000m and a weak target at a distance of 1100m, and two coherent accumulation simulations are performed under the condition that the speeds are equal. The results are shown in Figures 9 and 10, wherein Figure 9 is a top view of the coherent accumulation before optimization, and Figure 10 is a top view of the coherent accumulation after optimization. It is easy to draw a conclusion based on the simulation result diagram: the weak target before optimization is easily affected by the side lobes of the strong target, resulting in missed judgment, and the coherent accumulation simulation after optimization by the present invention can clearly determine the position of the weak target. Therefore, the present invention also has the advantage of improving the detection capability of small targets.

以上内容是结合具体的优选实施方式对本发明所作的进一步详细说明，不能认定本发明的具体实施只局限于这些说明。对于本发明所属技术领域的普通技术人员来说，在不脱离本发明构思的前提下，还可以做出若干简单推演或替换，都应当视为属于本发明的保护范围。The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the scope of protection of the present invention.

Claims (4)

1.一种低峰值旁瓣频率编码雷达波形设计方法，其特征在于，包括：1. A low peak sidelobe frequency coded radar waveform design method is characterized in that, comprising: 步骤1：脉内捷变雷达发射信号并接收回波信号，并将所述回波信号与对应的发射载频依次进行混频处理和分段脉冲压缩处理，得到脉压后的回波信号；包括：Step 1: The intra-pulse agile radar transmits signals and receives echo signals, and performs frequency mixing processing and segmental pulse compression processing on the echo signals and corresponding transmitting carrier frequencies in sequence to obtain pulse-compressed echo signals; include: 11)将每个脉冲等分成Q个子脉冲，子脉冲之间频率捷变，并从中随机选取M个子脉冲进行发射，则第n个脉冲的第m个子脉冲的发射信号为：11) Each pulse is equally divided into Q sub-pulses, and the frequency between the sub-pulses is agile, and M sub-pulses are randomly selected for transmission, then the transmission signal of the m-th sub-pulse of the n-th pulse is:
Figure FDA0004221763430000011
Figure FDA0004221763430000011
 其中，t表示时间，rect(·)表示矩形窗函数，κ表示线性调频信号的斜率，Tr表示脉冲重复周期，Tsub表示每个子脉冲的脉宽，j表示虚数单位；Among them, t represents the time, rect( ) represents the rectangular window function, κ represents the slope of the chirp signal, T r represents the pulse repetition period, T sub represents the pulse width of each sub-pulse, and j represents the imaginary number unit; fm为第n个脉冲的第m个子脉冲的载频，其表达式为：f m is the carrier frequency of the mth sub-pulse of the nth pulse, and its expression is:
Figure FDA0004221763430000012
Figure FDA0004221763430000012
 其中，cm∈[1,2,…,Q]，m＝[1,2,…,M]表示脉内跳频编码，fn＝f0+anΔf表示第n个脉冲的载频，f0为初始载频，an为脉间跳频编码，Δf为跳频带宽，Bsub为每个子脉冲的带宽；Among them, c m ∈ [1,2,…,Q], m=[1,2,…,M] means intra-pulse frequency hopping code, f n =f 0 +a n Δf means the carrier frequency of the nth pulse , f 0 is the initial carrier frequency, a n is the inter-pulse frequency hopping code, Δf is the frequency hopping bandwidth, and B sub is the bandwidth of each sub-pulse; 12)接收第n个脉冲的第m个子脉冲的发射信号对应的回波信号，其表达式为：12) Receive the echo signal corresponding to the transmitted signal of the mth sub-pulse of the nth pulse, whose expression is:
Figure FDA0004221763430000013
Figure FDA0004221763430000013
 其中，N表示脉冲总数，K表示目标总数，
Figure FDA0004221763430000014
为第k个目标的第n个脉冲回波信号与发射信号之间的时延，c为光速，rk为第k个目标的距离，vk为第k个目标的速度，σk为第k个目标的散射系数；Among them, N represents the total number of pulses, K represents the total number of targets,
Figure FDA0004221763430000014
is the time delay between the nth pulse-echo signal of the kth target and the transmitted signal, c is the speed of light, r k is the distance of the kth target, v k is the speed of the kth target, σ k is the Scatter coefficients of k targets; 13)对第n个脉冲的第m个子脉冲进行分段脉压处理，公式表示为：13) Perform segmental pulse pressure processing on the mth sub-pulse of the nth pulse, the formula is expressed as:
Figure FDA0004221763430000021
Figure FDA0004221763430000021
 其中，sr(n,t)表示脉内频率编码雷达接收的第n个脉冲的回波信号；
Figure FDA0004221763430000022
表示sr(n,t)对应的每个子脉冲的匹配滤波函数，其为sref(n,m,-t)的共轭函数；Among them, s r (n, t) represents the echo signal of the nth pulse received by the intra-pulse frequency coded radar;
Figure FDA0004221763430000022
Indicates the matched filter function of each sub-pulse corresponding to s r (n, t), which is the conjugate function of s ref (n, m, -t);
Figure FDA0004221763430000023
Figure FDA0004221763430000023
 14)将一个脉冲内M个子脉冲的分段脉压结果相加，得到该脉冲脉压后的回波信号，其表达式为：14) Add the segmented pulse pressure results of M sub-pulses in one pulse to obtain the echo signal after the pulse pressure, the expression of which is:
Figure FDA0004221763430000024
Figure FDA0004221763430000024
 其中，y(n,t)表示脉压后的回波信号，Ak表示第k个目标脉压后的幅值，k＝[1,2,…,K]，K为目标总数，sinc()表示每个子脉冲经过脉压处理后累加形成的包络，β(t)表示噪声；Among them, y(n,t) represents the echo signal after the 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 the accumulation of each sub-pulse after pulse pressure processing, and β(t) represents noise; 步骤2：基于脉压后的回波信号建立频率编码优化模型；Step 2: Establish a frequency encoding optimization model based on the echo signal after the pulse pressure; 步骤3：根据脉压后的回波信号，随机出一组频率编码，并把初始值作为当前个体最优适应值和全局最优适应值；Step 3: Randomly generate a set of frequency codes according to the echo signal after the pulse pressure, and use the initial value as the current individual optimal fitness value and the global optimal fitness value; 步骤4：基于粒子群PSO算法对所述频率编码优化模型进行求解，得到脉压后的回波信号的最小峰值旁瓣比及其对应的频率编码。Step 4: Solve the frequency encoding optimization model based on the particle swarm optimization PSO algorithm to obtain the minimum peak-to-sidelobe ratio of the echo signal after the pulse pressure and the corresponding frequency encoding. 2.根据权利要求1所述的低峰值旁瓣频率编码雷达波形设计方法，其特征在于，步骤2包括：2. the low peak sidelobe frequency coded radar waveform design method according to claim 1, is characterized in that, step 2 comprises: 对脉压后的回波信号取模值，并基于函数中每个点对应峰值的dB值，构建一个以频率编码为自变量的优化模型，该优化模型的目标函数为：Take the modulus value of the echo signal after the pulse pressure, and based on the dB value corresponding to the peak value of each point in the function, construct an optimization model with frequency code as the independent variable. The objective function of the optimization model is:
Figure FDA0004221763430000031
Figure FDA0004221763430000031
 3.根据权利要求2所述的低峰值旁瓣频率编码雷达波形设计方法，其特征在于，步骤4包括：3. the low peak sidelobe frequency coded radar waveform design method according to claim 2, is characterized in that, step 4 comprises: 41)初始化粒子群PSO算法参数；41) Initialize the parameters of the particle swarm PSO algorithm; 42)计算每个粒子的当前位置和速度的最优适应值；42) Calculate the optimal fitness value of the current position and velocity of each particle; 43)将每个粒子的当前位置和速度的最优适应值分别与每个粒子的个体历史最优适应值进行比较判断，并更新每个粒子的历史最优适应值和位置；43) comparing and judging the optimal fitness value of the current position and speed of each particle with the individual historical optimal fitness value of each particle, and updating the historical optimal fitness value and position of each particle; 44)将当前次迭代的群体最优适应值与群体历史最优适应值进行比较判断，并更新群体历史最优适应值和位置；44) Compare and judge the optimal fitness value of the current iteration with the optimal fitness value of the group history, and update the optimal fitness value and position of the group history; 45)更新粒子的速度与位置；45) Update the speed and position of the particles; 46)按照步骤42)-45)的操作进行迭代更新，直至达到最大迭代次数，并输出群体历史最优适应值和位置，以得到脉压后的回波信号的最小峰值旁瓣比及其对应的频率编码。46) Perform iterative update according to steps 42)-45) until the maximum number of iterations is reached, and output the historical optimal fitness value and position of the group to obtain the minimum peak side lobe ratio of the echo signal after the pulse pressure and its corresponding frequency code. 4.根据权利要求3所述的低峰值旁瓣频率编码雷达波形设计方法，其特征在于，在步骤45)中，更新粒子的速度与位置的公式为：4. the low peak side lobe frequency coded radar waveform design method according to claim 3 is characterized in that, in step 45), the formula of updating the speed and position of particle is:
Figure FDA0004221763430000041
Figure FDA0004221763430000041
 其中，ω为权重系数，c1和c2为学习因子，r1和r2为[0,1]之间的随机值，Pbest和Gbest分别为个体最优适应值和全局最优适应值，Piter和Viter分别为第iter次迭代时粒子的最新位置和速度，Piter+1和Viter+1分别为第iter+1次迭代时粒子的最新位置和速度。Among them, ω is the weight coefficient, c 1 and c 2 are the learning factors, r 1 and r 2 are random values between [0,1], P best and G best are the individual optimal fitness value and the global optimal fitness value respectively value, P iter and V iter are the latest position and velocity of the particle at the iter iteration, and P iter+1 and V iter+1 are the latest position and velocity of the particle at the iter+1 iteration.
CN202310327419.7A 2023-03-30 2023-03-30 Low peak sidelobe frequency coding radar waveform design method Active CN116027280B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202310327419.7A CN116027280B (en) 2023-03-30 2023-03-30 Low peak sidelobe frequency coding radar waveform design method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202310327419.7A CN116027280B (en) 2023-03-30 2023-03-30 Low peak sidelobe frequency coding radar waveform design method

Publications (2)

Publication Number Publication Date
CN116027280A CN116027280A (en) 2023-04-28
CN116027280B true CN116027280B (en) 2023-06-09

Family

ID=86074478

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202310327419.7A Active CN116027280B (en) 2023-03-30 2023-03-30 Low peak sidelobe frequency coding radar waveform design method

Country Status (1)

Country Link
CN (1) CN116027280B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116774165B (en) * 2023-08-25 2023-11-10 西安电子科技大学 Multi-radar cooperative anti-interference signal waveform design method and device
CN118642185B (en) * 2024-08-15 2024-11-22 吉林大学 Ocean electromagnetic emission control waveform optimization method

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105137398A (en) * 2015-07-24 2015-12-09 西安电子科技大学 Genetic algorithm-based radar anti-forwarding-type interference pulse compression filter optimization method

Family Cites Families (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5347283A (en) * 1989-06-14 1994-09-13 Hughes Aircraft Company Frequency agile radar
CA2723754C (en) * 2008-05-07 2013-10-08 Colorado State University Research Foundation Networked waveform system
US10725175B2 (en) * 2018-10-30 2020-07-28 United States Of America As Represented By The Secretary Of The Air Force Method, apparatus and system for receiving waveform-diverse signals
CN114764136A (en) * 2021-01-11 2022-07-19 江苏云禾峰智能科技有限公司 Radar anti-interference waveform generation method based on multi-time scale coupling network
CN112965037B (en) * 2021-02-10 2023-06-02 西南电子技术研究所（中国电子科技集团公司第十研究所） Radar signal waveform uncertainty test system
CN113655446B (en) * 2021-03-17 2024-09-13 南京航空航天大学 Frequency-code pattern combined agile waveform design method based on alternate direction multiplier method
CN113075635B (en) * 2021-03-30 2024-04-12 南京航空航天大学 Method for reconstructing target information of frequency agile radar based on coherent accumulation
CN113376601B (en) * 2021-05-10 2022-11-01 西安电子科技大学 Sidelobe Suppression Method for Frequency-Agile Radar Based on CLEAN Algorithm
CN113298901B (en) * 2021-05-13 2022-12-06 中国科学院深圳先进技术研究院 Method for reconstructing magnetic resonance image in convoluted field of view, computer device and storage medium
CN113721216B (en) * 2021-08-30 2024-05-17 西安电子科技大学 Target detection waveform optimization and processing method of agile coherent radar
CN113884992B (en) * 2021-10-20 2024-10-29 西安电子科技大学 Self-adaptive anti-interference method of frequency agile radar
CN115825953B (en) * 2023-02-16 2023-06-16 西安电子科技大学 A forward-looking super-resolution imaging method based on random frequency coded signals

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105137398A (en) * 2015-07-24 2015-12-09 西安电子科技大学 Genetic algorithm-based radar anti-forwarding-type interference pulse compression filter optimization method

Also Published As

Publication number Publication date
CN116027280A (en) 2023-04-28

Similar Documents

Publication Publication Date Title
CN116027280B (en) Low peak sidelobe frequency coding radar waveform design method
CN108415010B (en) A radar multi-target detection method based on trapezoidal LFMCW modulation
US7463181B2 (en) Method of suppressing interferences in systems for detecting objects
CN109061589B (en) Target motion parameter estimation method of random frequency hopping radar
CN113759321B (en) Sectional pulse pressure intermittent sampling forwarding interference resisting method based on agile radar
CN110161472B (en) A method for de-ambiguating velocity of broadband vehicle-mounted millimeter-wave radar based on signal multiplexing
CN113341383B (en) Anti-interference intelligent decision method for radar based on DQN algorithm
CN105891831A (en) Rapid scanning method for Doppler weather radar
GB2632067A (en) Singular value decomposition-improved sea clutter suppression algorithm
CN109061626B (en) Method for detecting low signal-to-noise ratio moving target by step frequency coherent processing
CN113640752A (en) A Waveform Design Method Based on Interpulse Phase and Spectrum Double Agility
CN112034434A (en) Radar radiation source identification method based on sparse time-frequency detection convolutional neural network
CN116299427A (en) Attention mechanism-based lightweight ultra-wideband radar gesture recognition method
CN105137398A (en) Genetic algorithm-based radar anti-forwarding-type interference pulse compression filter optimization method
CN113238194B (en) Broadband phased array radar anti-decoy interference method based on fractional domain-frequency domain processing
CN114384477A (en) An integrated waveform generation method for detection and interference based on intermittent sampling
CN117269897A (en) Radar intelligent interference waveform design optimization method and system based on cross-correlation function and genetic algorithm
CN112881984A (en) Radar signal anti-interference processing method and device and storage medium
CN115856813B (en) Radar target sidelobe suppression method based on cascade processing of APC and IARFT
CN117834360A (en) Low sidelobe pulse compression processing method based on step frequency MSK signal
CN114488054B (en) Computationally efficient synthetic aperture radar ground moving target focusing method
CN115453471A (en) An Integrated Waveform Design Method for Interference Detection Based on Sparrow Search Algorithm
CN110673118A (en) Active sonar single-frequency pulse train waveform design and detection algorithm
CN115184876A (en) 2FSK signal parameter estimation method based on wavelet transformation and waveform shaping
CN112986989B (en) Method of Suppressing Range Ambiguity of Quadrature Phase Encoded Signal Based on Genetic Algorithm

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant