CN103116155A

CN103116155A - Homotype radar same frequency interference suppression method used for ship formation condition

Info

Publication number: CN103116155A
Application number: CN2012103677039A
Authority: CN
Inventors: 陶然; 李元硕; 郇浩
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2012-09-28
Filing date: 2012-09-28
Publication date: 2013-05-22
Also published as: WO2014048193A1

Abstract

The invention relates to a method for suppressing same-frequency interference of same-type radars in the case of a naval formation, and belongs to the technical field of radar anti-jamming. In the present invention, under the condition that the working parameters are known when the radars in the formation work together, firstly, according to the fact that the LFM interference signal is focused in the fractional Fourier domain of its matching order and defocused in the fractional Fourier domain of other orders characteristics, using the method of successive filtering to eliminate the interference different from the modulation frequency of the radar transmission signal to be observed according to the interference energy from large to small; secondly, the signal processed in the frequency domain is inversely transformed into the time domain for matching filtering, and the time domain phase is adopted The adjacent cycle anti-asynchronous algorithm filters out the interference with the same modulation frequency as the echo signal. The invention effectively solves the same-frequency interference suppression problem that is different from the modulation frequency of the radar echo signal, further eliminates the same-frequency interference as the radar echo signal modulation frequency, and improves the anti-same-frequency interference capability and formation of the shipboard radar of the same type Networking capabilities.

Description

A Same-type Radar Same-frequency Interference Suppression Method Used in Ship Formation

技术领域 technical field

本发明属于雷达抗干扰技术领域，涉及一种用于舰艇编队情况下的同型雷达同频干扰抑制方法，具体涉及一种在舰艇编队情况下抑制线性调频脉冲体制雷达间同频干扰的方法，用于提高编队雷达组网能力。The invention belongs to the technical field of radar anti-jamming, and relates to a method for suppressing co-frequency interference of same-type radars in the case of a ship formation, in particular to a method for suppressing co-frequency interference between radars of a linear frequency modulation pulse system in the case of a ship formation. To improve the formation radar networking capability.

背景技术 Background technique

现役舰载雷达大多为LFM（Linear Frequency Modulation）脉冲体制雷达。该体制雷达在发射机峰值功率受限的条件下，充分利用发射机的平均功率，较好地解决了雷达作用距离与距离分辨率这一对在普通脉冲体制雷达中难以解决的矛盾，同时提高了信号的处理增益。Most of the shipboard radars in active service are LFM (Linear Frequency Modulation) pulse system radars. Under the condition that the peak power of the transmitter is limited, the radar of this system makes full use of the average power of the transmitter, which better solves the contradiction between the radar operating range and the distance resolution, which is difficult to solve in the ordinary pulse system radar, and improves the signal processing gain.

在舰艇编队作战时，因探测目标特性不同，探测距离、探测精度等要求也不尽相同，使得编队内部雷达工作在不同的发射参数下，例如脉冲重复周期、脉冲宽度、脉冲的调频率等，但往往都处于相同或相近的工作频段。随着水面舰艇编队的规模日益扩大，编队内部各舰艇间同型雷达的数量不断增多，使得同频干扰现象频繁发生。根据雷达重复周期的差异，同频干扰可分为同频同步干扰和同频异步干扰。当两部工作在相同载频的脉冲雷达，脉冲重复频率相同、接近或为整数倍关系时，两者间的同频干扰为同频同步干扰；反之，当脉冲重复频率相差大于某个值（对于确定的两部雷达，这个值是确定的），但不为整数倍关系时，两者间的同频干扰即为同频异步干扰。雷达同频干扰会大大降低雷达编队的组网能力，其对目标探测的影响是：1）造成大片虚警，特别是影响对导弹等小目标的探测；2）破坏雷达对目标的连续跟踪能力。目前，利用信号处理手段对同频干扰进行抑制的方法是通过改变雷达脉冲重复频率，将同频同步干扰变为同频异步干扰，利用干扰信号与目标回波间的脉冲重复频率差区分并滤除干扰，主要方法为陈正禄、许健的文献《舰载脉冲压缩体制雷达的抗同频干扰技术研究》中提到的相邻周期反异步算法及其改进算法和刘冬利、付建国、索继东的文献《时域多脉冲相关法抗雷达同频干扰》中提到的时域脉冲相关法。脉冲重复频率不同，导致不同周期的异步干扰出现在不同的距离单元，而回波信号出现在相同距离单元，因此可在脉冲压缩处理之后找到干扰所在距离单元，直接将其滤除。但两种方法均存在一定劣势：1、没有充分利用LFM脉冲体制雷达信号特征，而是对脉冲体制雷达一概而论，针对同频干扰数量较多时效果不好；2、匹配滤波器对与雷达回波信号调频率不同的干扰信号失配，造成输出峰值展宽，反异步的干扰抑制效果不好。When fighting in a ship formation, due to the different characteristics of the detection target, the requirements for detection distance and detection accuracy are also different, so that the radar within the formation works under different launch parameters, such as pulse repetition period, pulse width, pulse modulation frequency, etc. But they are often in the same or similar working frequency band. With the increasing scale of surface warship formations, the number of radars of the same type among ships within the formation is increasing, which leads to frequent occurrence of co-frequency interference. According to the difference of radar repetition period, co-frequency interference can be divided into co-frequency synchronous interference and co-frequency asynchronous interference. When two pulse radars working on the same carrier frequency have the same pulse repetition frequency, close to or an integer multiple, the same-frequency interference between the two is same-frequency synchronous interference; otherwise, when the pulse repetition frequency difference is greater than a certain value ( For two determined radars, this value is determined), but when the relationship is not an integer multiple, the same-frequency interference between the two is the same-frequency asynchronous interference. Radar co-frequency interference will greatly reduce the networking capability of the radar formation, and its impact on target detection is: 1) causing large areas of false alarms, especially affecting the detection of small targets such as missiles; 2) destroying the continuous tracking capability of radars to targets . At present, the method of using signal processing to suppress co-frequency interference is to change the same-frequency synchronous interference into co-frequency asynchronous interference by changing the radar pulse repetition frequency, and use the pulse repetition frequency difference between the interference signal and the target echo to distinguish and filter In addition to interference, the main method is the adjacent cycle anti-asynchronous algorithm and its improved algorithm mentioned in the document "Research on Anti-same-frequency Interference Technology of Shipborne Pulse Compression System Radar" by Chen Zhenglu and Xu Jian and Liu Dongli, Fu Jianguo, Suo Jidong The time-domain pulse correlation method mentioned in the document "Time-domain multi-pulse correlation method against radar co-frequency interference". The pulse repetition frequency is different, resulting in different periods of asynchronous interference appearing in different distance units, while the echo signal appears in the same distance unit, so the distance unit where the interference is located can be found after pulse compression processing and directly filtered out. However, both methods have certain disadvantages: 1. They do not make full use of the characteristics of the LFM pulse system radar signal, but generalize the pulse system radar, and the effect is not good when there is a large number of co-frequency interference; 2. The matched filter is compatible with the radar echo The mismatch of interference signals with different signal modulation frequencies causes the output peak to broaden, and the anti-asynchronous interference suppression effect is not good.

分数阶傅里叶变换（FRFT，Fractional Fourier Transform)是傅里叶变换的广义形式，它将信号分解到同一调频率、不同起始频率的线扫频正交基函数上。因此，分数阶傅里叶变换对线性调频信号具有良好的能量聚焦特性，是LFM信号检测和参数估计的有效工具。有很多文献论述其在对LFM脉冲信号的时延估计方面以及LFM脉冲信号初始频率与调频率二维分辨能力都具有很大的优势，并且其离散运算复杂度又和快速傅里叶变换（FFT）相当，易于工程实现。Fractional Fourier Transform (FRFT, Fractional Fourier Transform) is a generalized form of Fourier Transform, which decomposes the signal into line-sweep orthogonal basis functions with the same modulation frequency and different starting frequencies. Therefore, the fractional Fourier transform has good energy-focusing properties for LFM signals, and is an effective tool for LFM signal detection and parameter estimation. There are many literatures discussing that it has great advantages in the time delay estimation of LFM pulse signal and the two-dimensional resolution ability of the initial frequency and modulation frequency of LFM pulse signal, and its discrete operation complexity is comparable to that of fast Fourier transform (FFT ) is quite easy to implement in engineering.

本发明利用一种离散分数阶傅里叶变换对信号进行处理，其定义为：The present invention utilizes a kind of discrete fractional Fourier transform to process the signal, which is defined as:

${Y Y}_{P P} ((m m)) = = \sqrt{\frac{| | sin sin α α | | - - jsgn jsgn ((sin sin α α)) cos cos α α}{M m}} \cdot &Center Dot; {e e}^{\frac{j j}{22} cot cot α α \cdot &Center Dot; {m m}^{22} \cdot &Center Dot; Δ Δ {u u}^{22}} \cdot &Center Dot; {Σ Σ}_{n no = = - - N N}^{N N} {e e}^{- - j j \frac{22 π π \cdot &Center Dot; n no \cdot &Center Dot; m m}{M m}} \cdot &Center Dot; {e e}^{\frac{j j}{22} cot cot α α \cdot &Center Dot; {n no}^{22} \cdot &Center Dot; Δ Δ {t t}^{22}} \cdot &Center Dot; y the y ((n no))$

其中y(n)、Y_p(m)为分数阶傅里叶变换的输入输出序列，p为离散分数阶傅里叶变换的阶次，α＝pπ/2，Δt和Δu分别是时域和分数阶傅里叶域的采样间隔，满足

N和M分别是其输入和输出的点数。Among them, y(n), Y _p (m) are the input and output sequences of fractional Fourier transform, p is the order of discrete fractional Fourier transform, α=pπ/2, Δt and Δu are time domain and The sampling interval of the fractional Fourier domain satisfies

N and M are the number of its input and output points respectively.

发明内容 Contents of the invention

本发明针对舰载LFM脉冲体制雷达编队工作时产生的同频异步干扰，现有技术中对于干扰数量较多、干扰回波信号与接收匹配滤波器失配等情况下抑制效果不好的问题，提出了一种舰艇编队情况下，采用分数阶傅里叶变换域滤波处理与时域反异步处理相结合的方法来实现同型雷达同频干扰的抑制方法。The present invention is aimed at the same-frequency asynchronous interference generated when the shipboard LFM pulse system radar formation works. In the prior art, the suppression effect is not good when the interference amount is large, the interference echo signal and the receiving matching filter are mismatched, etc., In the case of a naval formation, a combination of fractional Fourier transform domain filter processing and time domain anti-asynchronous processing is proposed to achieve the same-type radar co-frequency interference suppression method.

本发明的基本原理是：在编队内部雷达协同工作时工作参数，如调频率、脉冲宽度均已知的条件下，首先，根据LFM干扰信号在其匹配阶次的分数阶傅里叶域聚焦而在其他阶次的分数阶傅里叶域散焦的特性，采用逐次滤波的方法，按干扰能量由大到小依次消除与待观测雷达发射信号调频率不同的干扰；其次，经过频域处理后的信号逆变换到时域进行匹配滤波，采用时域相邻周期反异步算法，滤除与回波信号调频率相同的干扰。The basic principle of the present invention is: when the internal radar of the formation cooperates to work, working parameters, such as under the condition that modulation frequency, pulse width are all known, at first, according to the fractional order Fourier domain focusing of LFM interference signal of its matching order and In other orders of fractional Fourier domain defocusing characteristics, the successive filtering method is used to eliminate the interference different from the modulation frequency of the transmitted signal of the radar to be observed according to the interference energy from large to small; secondly, after frequency domain processing The signal is inversely transformed to the time domain for matching filtering, and the adjacent cycle anti-asynchronous algorithm in the time domain is used to filter out the interference with the same modulation frequency as the echo signal.

本发明的目的是通过以下技术方案实现的。The purpose of the present invention is achieved through the following technical solutions.

本发明的一种用于舰艇编队情况下的同型雷达同频干扰抑制方法，其具体步骤如下：A kind of same-type radar same-frequency interference suppression method used in the situation of naval vessel formation of the present invention, its specific steps are as follows:

1）针对当前观测雷达，取其回波信号中K个雷达脉冲重复周期数据，对所取的每个雷达脉冲重复周期的回波信号以Δt＝1/Fs为时间间隔进行时域采样，得到脉冲重复周期的采样序列，其中第k个脉冲重复周期的采样序列x_k(n)表示为：1) For the current observation radar, take K radar pulse repetition period data in the echo signal, and perform time-domain sampling on the echo signal of each radar pulse repetition period taken at Δt=1/Fs as the time interval, and obtain The sampling sequence of the pulse repetition period, where the sampling sequence x _k (n) of the kth pulse repetition period is expressed as:

${x x}_{k k} ((n no)) = = {A A}_{k k} rect rect ((\frac{n no - - {n no}_{00,, k k}}{M m})) exp exp {((jπ jπ {μ μ}_{00} ((((n no - - {n no}_{00,, k k})) Δt Δt))))}^{22} exp exp ((j j 22 π π {f f}_{d d,, k k} nΔt nΔt))$

$+ + {Σ Σ}_{i i = = 11}^{Q Q} {A A}_{J J ((i i,, k k))} rect rect ((\frac{n no - - {n no}_{00_{J J} ((i i,, k k))}}{{M m}_{J J ((i i,, k k))}})) exp exp {((jπ jπ {μ μ}_{i i} ((((n no - - {n no}_{00_{J J} ((i i,, k k))})) Δt Δt))))}^{22} exp exp ((j j 22 π π {f f}_{{d d}_{J J} ((i i,, k k))} nΔt nΔt)) + + {w w}_{k k} ((n no)) - - - - - - ((11))$

所述x_k(n)的序列长度为N＝TΔt，n=1,2…N，其中T为发射信号的脉冲重复周期；K＝χ+1,其中χ为待观测LFM脉冲体制雷达脉冲个数；Fs为采样频率，且Fs取为大于回波信号带宽的2倍的数值；The sequence length of the x _k (n) is N=TΔt, n=1, 2...N, wherein T is the pulse repetition period of the transmitted signal; K=χ+1, wherein χ is the number of LFM pulse system radar pulses to be observed number; Fs is the sampling frequency, and Fs is taken as a value greater than twice the bandwidth of the echo signal;

式（1）中，k＝1,…,K；μ₀为已知的该观测雷达目标回波信号的调频率且其脉宽长度为M＝T₀/Δt，T₀为其脉冲宽度；μ_j为已知的第i个同频干扰信号的调频率且其脉宽长度

i＝1…I，

为其已知的脉冲宽度，I为编队内部可能产生同频干扰的雷达数目也即I＝Q-1，Q为编队内部同时工作LFM脉冲体制舰载雷达雷达数目；w_k(n)为零均值、方差为σ²的高斯白噪声；A_k、n_0，k、f_d,k和A_J(i，k)、

分别为接收到的第k个雷达脉冲重复周期的目标回波和第i个干扰的幅度、时延及多普勒频率；In formula (1), k=1,...,K; μ ₀ is the known modulation frequency of the radar target echo signal and its pulse width is M=T ₀ /Δt, and T ₀ is its pulse width; μ _j is the known modulation frequency of the i-th co-channel interference signal and its pulse width length

i=1...I,

Its known pulse width, I is the number of radars that may produce co-frequency interference within the formation, that is, I=Q-1, and Q is the number of shipboard radars with LFM pulse system working simultaneously within the formation; w _k (n) is zero Gaussian white noise with mean and variance σ ² ; A _k , n _0,k , f _d,k and A _J(i,k) ,

are the amplitude, time delay and Doppler frequency of the received target echo of the k-th radar pulse repetition period and the i-th interference, respectively;

2）判断干扰调频率μ_i能否与目标回波信号调频率μ₀进行分辨：当

时，认为该干扰的调频率可以与回波信号调频率进行分辨，此时将调频率记为μ₁,μ₂,…,μ_η，η≤I；当

时，认为该干扰的调频率不能与回波信号调频率进行分辨，此时认为μ_i＝μ₀，并将调频率近似标记为μ_η+1，μ_η+2，…,μ_I；2) Judging whether the interference modulation frequency μ _i can be distinguished from the target echo signal modulation frequency μ ₀ : when

, it is considered that the modulation frequency of the interference can be distinguished from the modulation frequency of the echo signal, at this time, the modulation frequency is recorded as μ ₁ , μ ₂ ,..., μ _η , η≤I; when

, it is considered that the modulation frequency of the interference cannot be distinguished from the modulation frequency of the echo signal, at this time it is considered that μ _i = μ ₀ , and the modulation frequency is approximately marked as μ _η+1 , μ _η+2 ,...,μ _I ;

上述ε＝6.9486；The above ε = 6.9486;

3）针对调频率为μ₁,μ₂,…,μ_η的干扰进行滤除，具体步骤如下：3) Filter out the interference with the modulation frequency of μ ₁ , μ ₂ ,…, μ _η , the specific steps are as follows:

S1）从μ₁,μ₂,…,μ_η中任意选中一个μ_i；S1) Randomly select one μ _i from μ ₁ , μ ₂ ,…, μ _η ;

S2）对当前选择的μ_i的K个脉冲周期采样序列x_k(n)，k＝1，2，…K，分别进行p_i阶的N点离散分数阶傅里叶变换，得到K个

k＝1，2，…K，m=1,2…N,即S2) For the K pulse period sampling sequence x _k (n) of the currently selected μ _i , k=1, 2, ... K, respectively perform N-point discrete fractional Fourier transform of p _i order to obtain K

k=1, 2,...K, m=1, 2...N, that is

${X x}_{{P P}_{i i},, k k} ((m m)) = = \sqrt{\frac{| | sin sin {α α}_{i i} | | - - jsgn jsgn ((sin sin {α α}_{i i})) cos cos {α α}_{i i}}{N N}} \cdot \cdot {e e}^{\frac{j j}{22} cot cot {α α}_{i i} \cdot \cdot {m m}^{22} \cdot \cdot Δ Δ {u u}_{i i}^{22}} \cdot \cdot {Σ Σ}_{n no = = 11}^{N N} {e e}^{- - j j \frac{22 π π \cdot \cdot n no \cdot \cdot m m}{N N}} \cdot \cdot {e e}^{\frac{j j}{22} cot cot {α α}_{i i} \cdot \cdot {n no}^{22} \cdot \cdot Δ Δ {t t}^{22}} \cdot \cdot {x x}_{k k} ((n no)) - - - - - - ((22))$

其中，p_i＝2·α_i/π，α_i＝arccot(2π·μ_i)且满足

Among them, p _i =2·α _i /π, α _i =arccot(2π·μ _i ) and satisfy

S3）在分数阶傅里叶域分别找到K个脉冲周期的调频率为μ_i的干扰所在单元并设计矩形陷波器，具体过程为：对第k个周期，k=I…K，利用常用单元平均的恒虚警处理方法，对步骤S2）得到的

的幅值即

进行单元搜索，找到第k个周期调频率为μ_i的干扰所在单元的坐标，记为m_(0，i),m_(1，i)…

P_k为该周期恒虚警检测单元数目；分别以这些坐标为中心设置矩形陷波器如下所示：S3) In the fractional-order Fourier domain, respectively find the units where the interference of K pulse periods with a modulation frequency of μ _i is located and design a rectangular notch filter. The specific process is: for the k-th period, k=I...K, using the commonly used The constant false alarm processing method of unit average, for the obtained in step S2)

The magnitude of

Carry out unit search, find the coordinates of the unit where the kth periodic modulation frequency is μ _i , which is recorded as m _{(0, i)} , m _{(1, i)} ...

P _k is the number of constant false alarm detection units in this period; set the rectangular notch filter with these coordinates as the center As follows:

其中，

为分数阶傅里叶域滤波点数；即根据第i个干扰的脉冲宽度

将干扰在匹配分数阶域的主瓣及第1、2个副瓣置零；in,

is the number of points for fractional Fourier domain filtering; that is, according to the pulse width of the i-th interference

Set the main lobe and the first and second side lobes of the interference in the matching fractional order domain to zero;

对

与选定的矩形陷波器

进行分数阶傅里叶域相乘，得到

X_{p_{1}}^{'} (m),

即：right

with the selected rectangular notch filter

Perform fractional Fourier domain multiplication to get

x_{p_{1}}^{'} (m),

Right now:

${X x}_{{p p}_{i i},, k k}^{' '} ((m m)) = = {X x}_{{p p}_{i i},, k k} ((m m)) \times \times {H h}_{{μ μ}_{i i}} ((m m)) - - - - - - ((44))$

如果利用常用单元平均的恒虚警处理方法在搜索过程中未检测到干扰，记录该调频率；If no interference is detected during the search using the constant false alarm processing method of common unit averaging, record the modulation frequency;

S4）对步骤S2）得到的每个

分别与步骤S3）得到的相应的也即与其具有相同k值的陷波器进行分数阶傅里叶域相乘，得到

然后对每个分别做-p_i阶次的离散分数阶傅里叶变换，得到K个周期去除调频率为μ_i的同频干扰的时域数据；S4) for each obtained in step S2)

Multiply with the corresponding notch filter obtained in step S3), that is, the notch filter with the same value of k, to perform fractional Fourier domain multiplication to obtain

then for each Perform the discrete fractional Fourier transform of -p _i order respectively to obtain the time-domain data of removing co-channel interference whose modulation frequency is μ _i for K cycles;

S5）如果此时μ₁,μ₂,…,μ_η中全部的值均被选中且执行过步骤S2）~S4），则转入步骤4），否则从μ₁,μ₂,…,μ_η中选定一个未被选中过的值，重复执行步骤S2）~S4）操作，并将步骤S4）的结果作为当前的K个脉冲周期采样序列x_k(n)代入步骤S2）；S5) If at this time all values in μ ₁ , μ ₂ ,…,μ _η are selected and steps S2)~S4) have been executed, then go to step 4), otherwise from μ ₁ , μ ₂ ,…,μ Select an unselected value in _η , repeat steps S2)~S4) operations, and substitute the result of step S4) into step S2) as the current sampling sequence x _k (n) of K pulse periods;

4）消除强信号对弱信号的遮蔽效应，具体过程为：4) Eliminate the masking effect of strong signals on weak signals, the specific process is:

对步骤3）的步骤S3）中记录的干扰的调频率，重复步骤3）的过程，以消除遮蔽效应影响，从而得到K个周期滤除调频率为μ_i的同频干扰的数据，其中i＝1,…,η；For the modulation frequency of the interference recorded in step S3) of step 3), repeat the process of step 3) to eliminate the influence of the shadowing effect, so as to obtain the data of the co-channel interference with the modulation frequency μ _i filtered out for K cycles, where i =1,...,η;

5）去除调频率与目标回波信号相同的干扰，即步骤2）中调频率为μ_η+1，μ_η+2，…,μ_I的干扰，具体过程为：5) Remove the interference whose modulation frequency is the same as the target echo signal, that is, the interference whose modulation frequency is μ _η+1 , μ _η+2 , …, μ _I in step 2), the specific process is:

对步骤4）所得的结果做调频率为μ_η的匹配滤波处理，对得到的K个脉压数据y_k(n)采用前后周期幅值相减的方法得到（K-1）个Δy_k(n)：The result obtained in step 4 ₎ is subjected to matched filter processing with a modulation frequency of μ _η , and (K-1) Δy _k ( n):

Δy_k(n)＝|y_k(n)|-|y_k+1(n)|,k＝1,2,…,K-1 (5)Δy _k (n)=|y _k (n)|-|y _k+1 (n)|, k=1,2,...,K-1 (5)

在每个Δy_k(n)中，大于门限U_T的单元认为该位置受到来自第k个周期的干扰；对每个k，将y_k(n)中这些大于门限U_T的单元的值用y_k+1(n)中对应下标的单元的值代替，从而滤除y_k(n)中前K-1个脉冲重复周期中调频率与目标回波信号相同的干扰，得到y′_k(n)，k＝1,2,…,K-1，即为经过分数阶傅里叶域和时域联合干扰抑制后的序列；其中门限U_T的选取方式为：设置一个范围为10^-3至10^-6之间的虚警概率P_fa，再根据步骤1）中接收回波信号中所混有噪声的方差σ²以及虚警概率P_fa确定判决门限U_T：In each Δy _k (n), the units greater than the threshold U _T consider that the position is disturbed by the kth period; for each k, the values of these units greater than the threshold U _T in y _k (n) are used by y _k+1 (n) to replace the value of the unit corresponding to the subscript, so as to filter out the interference of the same modulation frequency as the target echo signal in the first K-1 pulse repetition period of y _k (n), and obtain y′ _k ( n), k=1,2,...,K-1, which is the sequence after joint interference suppression in the fractional Fourier domain and time domain; the selection method of the threshold U _T is: set a range of 10 ^-3 The false alarm probability P _fa between 10 ^-6 and then according to the variance σ ² of the noise mixed in the received echo signal in step 1) and the false alarm probability P _fa determine the decision threshold U _T :

${U u}_{T T} = = \sqrt{- - {σ σ}^{22} ln ln {P P}_{fa fa}} - - - - - - ((66))$

有益效果Beneficial effect

本发明通过分数阶傅里叶域自适应滤波有效解决了与雷达回波信号调频率不同的同频干扰抑制问题，同时利用分数阶傅里叶变换的可逆性，逆变换到时域后结合传统反异步抗同频干扰方法进一步消除与雷达回波信号调频率相同的同频干扰，提高了舰载同型雷达的抗同频干扰能力和编队组网能力，具体优势如下：The present invention effectively solves the same-frequency interference suppression problem that is different from the modulation frequency of the radar echo signal through fractional-order Fourier domain adaptive filtering. The anti-asynchronous anti-co-frequency interference method further eliminates the co-frequency interference with the same modulation frequency as the radar echo signal, and improves the anti-co-frequency interference capability and formation networking capability of the shipboard radar of the same type. The specific advantages are as follows:

1）本发明提出的一种用于舰艇编队情况下的同型雷达同频干扰抑制方法可以抑制多个与发射信号调频率不同的同频干扰；1) A same-frequency interference suppression method for same-type radars proposed in the present invention can suppress multiple same-frequency interferences that are different from the modulation frequency of the transmitted signal;

2）本发明提出的一种用于舰艇编队情况下同型雷达同频干扰抑制方法，利用分数阶傅里叶变换对LFM信号的聚焦特性，可减少信噪比损失；2) The present invention proposes a same-frequency interference suppression method for same-type radars in the case of naval formations, which can reduce the loss of signal-to-noise ratio by using the focusing characteristics of the LFM signal by fractional Fourier transform;

3）本发明提出的一种用于舰艇编队情况下同型雷达同频干扰抑制方法可以通过快速傅里叶变换算法实现，计算复杂度低。3) A same-frequency interference suppression method for same-type radars proposed in the present invention can be realized by a fast Fourier transform algorithm with low computational complexity.

附图说明 Description of drawings

图1为本发明的一种用于舰艇编队情况下的同型雷达同频干扰抑制方法的实现流程图；Fig. 1 is a kind of implementation flowchart of the same-type radar same-frequency interference suppression method used in the situation of the ship formation of the present invention;

图2为使用不同干扰抑制方法的调频率区域分布；Figure 2 shows the regional distribution of frequency modulation using different interference suppression methods;

图3为变换域干扰抑制的简化流程图；Fig. 3 is a simplified flow chart of transform domain interference suppression;

图4为未经过同频异步干扰抑制处理，相参积累后的效果图；Figure 4 is an effect diagram after coherent accumulation without coherent and asynchronous interference suppression processing;

图5为经过同频异步干扰抑制处理，相参积累后的效果图；Figure 5 is an effect diagram after coherent accumulation after coherent and asynchronous interference suppression processing;

图6为SNR=-5dB、脉宽相同、带宽相差1MHz的单周期干扰信号与回波信号在时域完成重合时滤除不同点数时输入信干比与输出信干噪比的关系性能曲线。Figure 6 shows the performance curve of the relationship between input SIR and output SIR when different points are filtered out when SNR=-5dB, the same pulse width, and a bandwidth difference of 1MHz between the single-cycle interference signal and the echo signal are overlapped in the time domain.

具体实施方式 Detailed ways

下面结合附图和实施例对本发明作进一步说明。The present invention will be further described below in conjunction with drawings and embodiments.

首先对本发明的理论依据和推导过程进行说明如下。First, the theoretical basis and derivation process of the present invention are described as follows.

1、基于分数阶傅里叶变换的LFM信号调频率分辨率分析：1. Analysis of modulation frequency resolution of LFM signal based on fractional Fourier transform:

假设某一LFM信号表示为：Suppose an LFM signal is expressed as:

T为信号持续时间，f₀为信号初始频率，μ为调频率，A为信号的幅度。T is the duration of the signal, f ₀ is the initial frequency of the signal, μ is the modulation frequency, and A is the amplitude of the signal.

调频率分辨率定义为信号经分数阶傅里叶变换后，在匹配初始频率下变换阶次的-3dB宽度值。The modulation frequency resolution is defined as the -3dB width value of the transformation order at the matching initial frequency after the signal is subjected to fractional Fourier transformation.

对于公式(5)中的信号，匹配初始频率值如下：For the signal in formula (5), the matching initial frequency value is as follows:

u_p＝f₀sinα (6)u _p = f ₀ sinα (6)

那么在匹配初始频率值下LFM信号的分数阶傅里叶变换为：Then the fractional Fourier transform of the LFM signal at the matching initial frequency value is:

${X x}_{p p} (({u u}_{p p})) = = exp exp ((jπ jπ \overset{^^}{μ μ} {u u}^{22})) {&Integral; &Integral;}_{- - T T / / 22}^{T T / / 22} exp exp [[jπ jπ {t t}^{22} ((\overset{^^}{μ μ} - - {μ μ}_{00}))]] dt dt - - - - - - ((77))$

对(7)式进行计算，可得Calculate (7), we can get

${X x}_{p p} (({u u}_{p p})) = = \frac{Texp Texp ((jπ jπ \overset{^^}{μ μ} {u u}^{22})) ((C C ((ξ ξ)) + + jsign jsign ((\overset{^^}{μ μ} + + {μ μ}_{00})) S S ((ξ ξ))))}{ξ ξ} - - - - - - ((88))$

其中， $ξ = T \sqrt{| \hat{μ} + μ_{0} |} / \sqrt{2},$ in, $ξ = T \sqrt{| \hat{μ} + μ_{0} |} / \sqrt{2},$

其幅度为its amplitude is

$| | {X x}_{p p} (({u u}_{p p})) | | = = \frac{T T}{ξ ξ} \sqrt{{C C}^{22} ((ξ ξ)) + + {S S}^{22} ((ξ ξ))} - - - - - - ((99))$

由此可见，信号s(t)在其匹配初始频率下的FRFT为Fresnel函数形式。根据Fresnel函数的性质，得出其匹配初始调频率下调频率-3dB宽度为δ_μ为：It can be seen that the FRFT of the signal s(t) at its matching initial frequency is in the form of a Fresnel function. According to the nature of the Fresnel function, it is obtained that the width of the -3dB width of the matching initial tuning frequency down-tuning frequency is δ _μ as:

${δ δ}_{μ μ} = = \frac{6.9486 6.9486}{{T T}^{22}} - - - - - - ((1010))$

因此在进行同频干扰抑制时，对于可以与信号调频率进行分辨的干扰选择在其相应匹配分数阶域进行抑制；对于与信号调频率无法分辨的干扰，将其保护起来直至全部变换域滤波完成后，逆变换至时域再对这些干扰进行传统的反异步处理，具体流程及滤波区域如图1、图2所示；Therefore, when performing co-channel interference suppression, the interference that can be distinguished from the signal modulation frequency is selected to be suppressed in its corresponding matching fractional order domain; for the interference that cannot be distinguished from the signal modulation frequency, it is protected until all transform domain filtering is completed Afterwards, inverse transform to the time domain and then perform traditional anti-asynchronous processing on these interferences. The specific process and filtering area are shown in Figure 1 and Figure 2;

2、不同调频率信号在分数阶域的遮蔽效应分析：2. Analysis of the masking effect of signals with different modulation frequencies in the fractional order domain:

在舰艇编队情况下雷达同频干扰抑制前，首先要进行多分量LFM信号的检测，判断是否存在该调频率的干扰。但是由于强信号分量可能将弱信号分量遮蔽，因此，直接采用峰值检测的方法将难以实现对弱信号分量的可靠检测，需要采用逐次消去强信号分量的方法，提高对弱信号检测的可靠性。Before the same-frequency radar interference is suppressed in the case of a naval formation, multi-component LFM signal detection must be carried out first to determine whether there is interference with the modulation frequency. However, since the strong signal component may cover the weak signal component, it is difficult to achieve reliable detection of the weak signal component by directly using the peak detection method.

多分量LFM信号分数阶傅里叶谱的相互遮蔽是指某分量LFM信号在自身能量聚集性最好的分数阶傅里叶域中的峰值受到了其他分量LFM信号在该阶分数阶傅里叶域能量分布的遮蔽影响。在此引入遮蔽系数这一变量。以两分量LFM信号为例进行具体分析。设某分量LFM信号g(t)在α₀阶分数阶傅里叶域中实现最佳能量聚集，而某分量LFM信号h(t)在α₁阶分数阶傅里叶域中实现最佳能量聚集。定义遮蔽系数The mutual shadowing of fractional Fourier spectra of multi-component LFM signals means that the peak value of a certain component LFM signal in the fractional Fourier domain with the best self-energy aggregation is affected by the peak value of other component LFM signals in the fractional Fourier domain of this order. Shadowing effects on domain energy distribution. The variable shading coefficient is introduced here. Take the two-component LFM signal as an example for specific analysis. It is assumed that a certain component LFM signal g(t) realizes the best energy gathering in the α _0th order fractional Fourier domain, and a certain component LFM signal h(t) realizes the best energy accumulation in the α _1st order fractional Fourier domain gather. Define the shading factor

${ϵ ϵ}_{{α α}_{11}} = = {| | {G G}_{{α α}_{11}} ((m m)) | |}^{22} / / {| | {H h}_{{α α}_{11}} ((m m)) | |}^{22} = = \frac{{A A}_{g g}^{22} / / sin sin Δα Δα}{{A A}_{h h}^{22} {f f}_{s the s} {T T}_{d d} \sqrt{11 + + {μ μ}_{h h}^{22} {γ γ}^{44}}} - - - - - - ((1111))$

其中

α₀＝arccot(-μ_gγ²)，α₁＝arccot(-μ_hγ²)，A_g和μ_g为g(t)的幅度和调频率，A_h和μ_h为h(t)的幅度和调频率。γ为量纲归一化处理时引入的尺度因子，

T_d为信号持续时间，f_s为采样率。又因为in

α ₀ ＝arccot(-μ _g γ ² ), α ₁ ＝arccot(-μ _h γ ² ), A _g and μ _g are the amplitude and modulation frequency of g(t), A _h and μ _h are h(t) amplitude and modulation frequency. γ is the scale factor introduced during dimension normalization processing,

T _d is the signal duration, f _s is the sampling rate. also because

$Δα Δα = = \frac{| | {μ μ}_{h h} - - {μ μ}_{g g} | | {γ γ}^{22}}{\sqrt{11 + + {μ μ}_{h h}^{22} {γ γ}^{44}} \sqrt{11 + + {μ μ}_{g g}^{22} {γ γ}^{44}}} = = \sqrt{\frac{{(({μ μ}_{h h} - - {μ μ}_{g g}))}^{22} {f f}_{s the s}^{22} {T T}_{d d}^{22}}{(({f f}_{s the s}^{22} + + {μ μ}_{h h}^{22} {T T}_{d d}^{22})) (({f f}_{s the s}^{22} + + {μ μ}_{g g}^{22} {T T}_{d d}^{22}))}} - - - - - - ((1212))$

所以，式(11)可以化为Therefore, formula (11) can be transformed into

${ϵ ϵ}_{{α α}_{11}} = = \frac{{A A}_{g g}^{22}}{{A A}_{h h}^{22} {f f}_{s the s} {T T}_{d d}^{22}} \sqrt{\frac{(({f f}_{s the s}^{22} + + {μ μ}_{g g}^{22} {T T}_{d d}^{22}))}{{(({μ μ}_{h h} - - {μ μ}_{g g}))}^{22}}} - - - - - - ((1313))$

系数体现了分量g(t)对分量h(t)的分数阶傅里叶谱遮蔽程度，越小，遮蔽程度越小。从式(13)可以看出分数阶傅里叶域中LFM分量间的相互遮蔽取决于各自的幅度、调频率以及采样时间和采样频率。coefficient It reflects the fractional Fourier spectrum shielding degree of component g(t) to component h(t), The smaller the value, the less occlusion. It can be seen from formula (13) that the mutual shielding between LFM components in the fractional Fourier domain depends on their respective amplitudes, modulation frequencies, and sampling time and sampling frequency.

在检测多分量LFM干扰信号时，为了消除强干扰对弱干扰的遮蔽效应，在进行分数阶域干扰抑制时可以进行两次调频率遍历，具体流程如图3所示。When detecting multi-component LFM interference signals, in order to eliminate the masking effect of strong interference on weak interference, two frequency modulation traversals can be performed when performing fractional domain interference suppression. The specific process is shown in Figure 3.

3、分数阶傅里叶域最优滤波点数确定：3. Determine the optimal number of filtering points in the fractional Fourier domain:

当干扰在时域远离目标回波时，在匹配阶次分数阶傅里叶域滤波点数越多，被抑制的能量越多；当干扰与目标回波在时域接近时，干扰的存在严重影响信号检测，在分数阶域进行干扰滤波时，滤波点数越多，干扰能量减少的同时信号损失也会增大。因此在选择分数阶傅里叶域滤波点数时，需要对不同情况下干扰滤波点数进行折中考虑。When the interference is far away from the target echo in the time domain, the more points in the matching order fractional Fourier domain filter, the more energy is suppressed; when the interference is close to the target echo in the time domain, the presence of interference has a serious impact For signal detection, when performing interference filtering in the fractional order domain, the more filtering points are, the less the interference energy will be and the greater the signal loss will be. Therefore, when selecting the number of filtering points in the fractional Fourier domain, it is necessary to consider the compromise of the number of interference filtering points in different situations.

对于公式(5)的信号，匹配分数阶傅里叶变化的旋转角度为：For the signal of equation (5), the rotation angle to match the fractional Fourier transform is:

${p p}_{00} = = - - \frac{22}{π π} {cot cot}^{- - 11} {μ μ}_{00} - - - - - - ((1414))$

得信号s(t)在匹配变换阶次下的FRFT为：The FRFT of the obtained signal s(t) under the matching transformation order is:

${X x}_{{p p}_{00}} ((u u)) = = T T sin sin c c ((πT πT ((u u csc csc {α α}_{00} - - {f f}_{00})))) exp exp ((jπ jπ {u u}^{22} cot cot {α α}_{00})) - - - - - - ((1515))$

可见信号在其匹配变换阶次下的分数阶傅里叶变换为sinc函数形式，其-3dB宽度δ_u为：原信号能量集中在主瓣，占原信号总能量的90%左右，当包含3个副瓣，能量可达到97.5%，包含6个副瓣，能量达到98.5%，而包含9个副瓣，能量可达到99%。通过仿真寻求最佳滤波点数发现：当干扰与回波信号脉宽相同，带宽相差1MHz时，在干扰匹配阶次的分数阶傅里叶域滤除主瓣加上左右2个副瓣时，检测性能最佳，如图6。It can be seen that the fractional Fourier transform of the signal under its matching transformation order is in the form of a sinc function, and its -3dB width δ _u is: The energy of the original signal is concentrated in the main lobe, accounting for about 90% of the total energy of the original signal. When it contains 3 side lobes, the energy can reach 97.5%, if it contains 6 side lobes, the energy can reach 98.5%, and if it contains 9 side lobes, the energy can reach 98.5%. It can reach 99%. Find the best number of filtering points through simulation: When the pulse width of the interference and the echo signal are the same, and the bandwidth difference is 1MHz, when the main lobe plus the left and right side lobes are filtered out in the fractional Fourier domain of the interference matching order, the detection The performance is the best, as shown in Figure 6.

实施例Example

针对LFM脉冲体制雷达信号，接收机的输入信号带宽大约为5MHz，以10MHz的采样率对信号进行采样。目标回波与干扰的参数如表1所示。For the LFM pulse system radar signal, the input signal bandwidth of the receiver is about 5MHz, and the signal is sampled at a sampling rate of 10MHz. The parameters of target echo and interference are shown in Table 1.

表1时延仿真参数Table 1 Latency simulation parameters

假设噪声的功率为σ²，则可以根据回波信号功率和噪声功率得出信噪比，此处信噪比指以回波信号带宽为参考的输入信噪比，设定信号的信噪比为SNR。Assuming that the power of the noise is σ ² , the signal-to-noise ratio can be obtained according to the echo signal power and the noise power. Here, the signal-to-noise ratio refers to the input signal-to-noise ratio with the echo signal bandwidth as a reference. is the SNR.

一种用于舰艇编队情况下同型雷达同频异步干扰抑制方法，具体实现步骤如下：A same-frequency and asynchronous interference suppression method for same-type radars in the case of a naval formation, the specific implementation steps are as follows:

1）选取11个脉冲重复周期数据，采样率为10MHz/s，每个周期10000个点，对这些数据进行传统的脉冲压缩处理及MTD处理，处理结果如附图4所示；1) Select 11 pulse repetition cycle data, the sampling rate is 10MHz/s, and each cycle has 10,000 points, and perform traditional pulse compression processing and MTD processing on these data, and the processing results are shown in Figure 4;

2）计算

可见|μ_i-μ₀|＞δ_μ，i＝1,2,…,8，|μ₉-μ₀|＜δ_μ，将调频率为μ_i,i＝1,2,…,8的干扰按能量由大到小排列，调频率分别记为μ₁,μ₂,…,μ₈，μ₉近似为μ₀。根据公式p＝2·arccot(2π·μ)/π，计算调频率μ₁,μ₂,…,μ₈所对应的匹配变换阶次p₁,p₂,…,p₈；2) calculate

It can be seen that |μ _i -μ ₀ |＞δ _μ , i=1,2,…,8, |μ ₉ -μ ₀ |<δ _μ , the modulation frequency is μ _i ,i=1,2,…,8 The interference is arranged in descending order of energy, and the modulation frequencies are recorded as μ ₁ , μ ₂ ,…, μ ₈ , and μ ₉ is approximately μ ₀ . According to the formula p=2·arccot(2π·μ)/π, calculate the matching transformation order _p ₁ , p ₂ ,...,p ₈ corresponding to the modulation frequency μ 1 , μ ₂ ,…, μ ₈ ;

3）根据公式(2)对各个周期数据做p₁阶次的离散分数阶傅里叶变换，然后利用恒虚警检测处理，找到干扰所在单元的坐标，将包括其主瓣和第1、2副瓣在内的所有点置零处理；对经滤波后的数据做-p₁阶次的离散分数阶傅里叶变换；3) According to formula (2), do discrete fractional Fourier transform of order p ₁ for each cycle data, and then use constant false alarm detection processing to find the coordinates of the unit where the interference is located, including its main lobe and the first and second All points including the sidelobe are set to zero; perform -p ₁ order discrete fractional Fourier transform on the filtered data;

4）针对调频率为μ₂,…,μ₈的干扰，对步骤3）所得的数据重复步骤3）中的滤波过程，分数阶傅里叶变换阶次依次为p₂,…,p₈，得到滤除调频率为μ₂,…,μ₈的干扰后的时域数据；4) For the interference whose modulation frequency is μ ₂ ,…, μ ₈ , repeat the filtering process in step 3) for the data obtained in step 3), the order of fractional Fourier transform is p ₂ ,…, p ₈ in turn, Obtain the time-domain data after filtering out the interference with the modulation frequency of μ ₂ ,…, μ ₈ ;

5）对步骤4）所得的各个周期数据做匹配滤波；第k周期与第k+1周期幅值相减，k＝1,…,10；设置虚警概率P_fa=10^-3，根据信号中所混有噪声的分布特性，求得判决门限值

其中σ²是噪声的功率，可根据信噪比得出；差值大于U_T的单元是第k个周期干扰所在单元，将这些单元数值用第k+1个周期对应单元的数值代替，取替换后的前10个周期数据，进行相参积累处理，处理结果如附图5所示。5) Perform matched filtering on the data of each cycle obtained in step 4); subtract the amplitude of the kth cycle from the k+1th cycle, k=1,...,10; set the false alarm probability P _fa =10 ^-3 , according to the signal The distribution characteristics of the noise mixed in, and the decision threshold value is obtained

Where σ ² is the power of the noise, which can be obtained according to the signal-to-noise ratio; the unit whose difference is greater than U _T is the unit where the interference of the kth period is located, and the value of these units is replaced by the value of the corresponding unit of the k+1th period, taking The data of the first 10 cycles after replacement are processed by coherent accumulation, and the processing results are shown in Figure 5.

表2是单周期对于调频率不同的干扰基于FRFT的处理增益仿真结果。Table 2 shows the FRFT-based processing gain simulation results for interference with different modulation frequencies in a single cycle.

表2不同调频率的干扰抑制增益Table 2 Interference suppression gain for different tuning frequencies

从表2可知，在干扰与目标回波在时域完全重合，即对检测影响最恶劣的情况下，当干扰与回波信号的调频率相差1M时，系统的抗干扰容限可以达到-30dB左右；当调频率相差为2M时，由于信号在干扰匹配阶次的分数阶域展宽程度加大，各点平均功率减小，系统本身的抗干扰能力增强，适当增加滤波点数，抗干扰容限略有提高。需注意的是当干扰能量继续增大，此时sinc函数旁瓣能量也较大，在分数阶傅里叶域难以完全抑制，故逆变换后在时域将残留大的干扰信号，影响目标检测。It can be seen from Table 2 that when the interference and the target echo completely overlap in the time domain, that is, the worst impact on detection, when the modulation frequency difference between the interference and the echo signal is 1M, the anti-interference tolerance of the system can reach -30dB Left and right; when the modulation frequency difference is 2M, because the signal broadens in the fractional domain of the interference matching order, the average power of each point decreases, and the anti-interference ability of the system itself is enhanced. slightly improved. It should be noted that when the interference energy continues to increase, the side lobe energy of the sinc function is also large, and it is difficult to completely suppress it in the fractional Fourier domain. Therefore, after the inverse transformation, a large interference signal will remain in the time domain, which will affect the target detection. .

以上所述的具体描述，对发明的目的、技术方案和有益效果进行了进一步详细说明，所应理解的是，以上所述仅为本发明的具体实例而已，并不用于限定本发明的保护范围，凡在本发明的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The specific description above has further described the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific example of the present invention and is not intended to limit the protection scope of the present invention. , Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. homotype radar co-channel interference method of inhibitioning that is used in the fleet situation is applicable to when the inner radar collaborative work of formation frequency modulation rate, pulse width all under known condition, it is characterized in that, concrete steps are as follows:

1) for current observation radar, get K radar pulse repetition period data in its echoed signal, echoed signal to each radar pulse repetition period of getting is carried out time-domain sampling take Δ t=1/Fs as the time interval, obtain the sample sequence of pulse repetition time, wherein the sample sequence x of k pulse repetition time _k(n) be expressed as:

x_{k} (n) = A_{k} rect (\frac{n - n_{0, k}}{M}) \exp {(jπ μ_{0} ((n - n_{0, k}) Δt))}^{2} \exp (j 2 π f_{d, k} nΔt)

+ Σ_{i = 1}^{Q} A_{J (i, k)} rect (\frac{n - n_{0_{J} (i, k)}}{M_{J (i, k)}}) \exp {(jπ μ_{i} ((n - n_{0_{J} (i, k)}) Δt))}^{2} \exp (j 2 π f_{d_{J} (i, k)} nΔt) + w_{k} (n) - - - (1)

Described x _k(n) sequence length is N=T Δ t, n=1,2 ... N, wherein T is the pulse repetition time that transmits; K=χ+1, wherein χ is LFM pulse radar pulse number to be observed; Fs is sample frequency, and Fs is taken as the numerical value of 2 times greater than the echoed signal bandwidth;

In formula (1), k=1 ..., K; μ ₀For frequency modulation rate and its pulsewidth length of this known observation radar target echo signal is M=T ₀/ Δ t, T ₀Be its pulse width; μ _jFrequency modulation rate and its pulsewidth length for i known co-channel interference signal

I=1 ... I,

Be its known pulse width, I is also I=Q-1 for the inner radar number that may produce co-channel interference of forming into columns, and Q is the formation inside LFM pulse system shipborne radar radar number of working simultaneously; w _k(n) be σ for zero-mean, variance ²White Gaussian noise; A _k, n _{0, k}, f _d,kAnd A _{J (i, k)},

Be respectively target echo and i amplitude, time delay and the Doppler frequency of disturbing of k the radar pulse repetition period that receives;

2) frequency modulation rate μ is disturbed in judgement _iCan with target echo signal frequency modulation rate μ ₀Differentiate: when

The time, think that the frequency modulation rate of this interference can be differentiated with echoed signal frequency modulation rate, be designated as μ with the frequency modulation rate this moment ₁, μ ₂..., μ _η, η≤I; When

The time, think that the frequency modulation rate of this interference can not be differentiated with echoed signal frequency modulation rate, think μ this moment _i=μ ₀, and be μ with frequency modulation rate approximate marker _η+1, μ _η+2..., μ _IAbove-mentioned ε=6.9486;

3) be μ for the frequency modulation rate ₁, μ ₂..., μ _ηInterference carry out filtering, concrete steps are as follows:

S1) from μ ₁, μ ₂..., μ _ηIn choose arbitrarily a μ _i

S2) to the μ of current selection _iK recurrence interval sample sequence x _k(n), k=1,2 ... K carries out respectively p _iThe N point Discrete Fractional Fourier transform on rank obtains K

K1,2 ... K, m=1,2 ... N. be

X_{P_{i}, k} (m) = \sqrt{\frac{| \sin α_{i} | - jsgn (\sin α_{i}) \cos α_{i}}{N}} \cdot e^{\frac{j}{2} \cot α_{i} \cdot m^{2} \cdot Δ u_{i}^{2}} \cdot Σ_{n = 1}^{N} e^{- j \frac{2 π \cdot n \cdot m}{N}} \cdot e^{\frac{j}{2} \cot α_{i} \cdot n^{2} \cdot Δ t^{2}} \cdot x_{k} (n) - - - (2)

Wherein, p _i=2 α _i/ π, α _i=arccot (2 π μ _i) and satisfy

S3) finding respectively the frequency modulation rate of K recurrence interval at fractional number order Fourier is μ _iUnit, interference place and design the rectangle trapper, detailed process is: to k cycle, k=1 ... K utilizes the average CFAR disposal route of common elements, to step S2) obtain

Amplitude namely

Carry out unit searches, finding k cycle frequency modulation rate is μ _iThe coordinate of unit, interference place, be designated as m _{(0, i)}, m _{(1, i)}

P _kBe this cycle CFAR detection number of unit; The rectangle trapper is set centered by these coordinates respectively

As follows:

Wherein,

For fractional order Fourier domain filter is counted; Namely according to i the pulse width of disturbing

With main lobe and the 1st, 2 secondary lobe zero setting of disturbing in coupling fractional order territory;

Right

With selected rectangle trapper

Carry out fractional number order Fourier and multiply each other, obtain

X_{p_{1}}^{'} (m),

That is:

X_{p_{i}, k}^{'} (m) = X_{p_{i}, k} (m) \times H_{μ_{i}} (m) - - - (4)

If utilize the average CFAR disposal route of common elements interference not detected in search procedure, record this frequency modulation rate;

S4) to step S2) obtain each

Respectively with step S3) the corresponding trapper that also namely has identical k value with it that obtains carries out fractional number order Fourier and multiplies each other, obtain

Then to each

Do respectively-p _iThe Discrete Fractional Fourier transform of order, obtaining K cycle removal frequency modulation rate is μ _iThe time domain data of co-channel interference;

S5) if this moment μ ₁, μ ₂..., μ _ηIn whole value all selected and carried out step S2) ~ S4), change step 4) over to, otherwise from μ ₁, μ ₂..., μ _ηIn the selected value of selected mistake not, repeated execution of steps S2) ~ S4) operation, and with step S4) result as current K recurrence interval sample sequence x _k(n) substitution step S2);

4) eliminate strong signal to the capture-effect of weak signal, detailed process is:

Step S3 to step 3)) the process frequency modulation rate of interference of record in, repeating step 3) to eliminate the capture-effect impact, is μ thereby obtain K cycle filtering frequency modulation rate _iThe data of co-channel interference, i=1 wherein ..., η;

5) remove the interference identical with target echo signal of frequency modulation rate, i.e. step 2) middle frequency modulation rate is μ _η+1, μ _η+2..., μ _iInterference, detailed process is:

It is μ that the result of step 4) gained is done the frequency modulation rate ₀Matched filtering process, to K the pulse pressure data y that obtains _k(n) method that adopts front and back cycle amplitude to subtract each other obtains (k-1) individual Δ _k(n):

Δy _k(n)＝|y _k(n)|-|y _k+1(n)|,k＝1,2,…,K-1 (5)

At each Δ y _k(n) in, greater than thresholding U _TThe unit think that this position is subject to the interference from k cycle; To each k, with y _k(n) in, these are greater than thresholding U _TThe value y of unit _k+1(n) in, the value of corresponding lower target unit replaces, thus filtering y _k(n) in, the frequency modulation rate interference identical with target echo signal in front K-1 the pulse repetition time, obtain y ' _k(n), k=1,2 ..., K-1 is through the sequence after fractional number order Fourier and time domain combined interference inhibition; Thresholding U wherein _TThe mode of choosing be: it is 10 that a scope is set ^-3To 10 ^-6Between false-alarm probability P _fa, then according to receiving the noisy variances sigma of mixing in echoed signal in step 1) ²And false-alarm probability P _faDetermine decision threshold U _T:

U_{T} = \sqrt{- σ^{2} \ln P_{fa}} - - - (6) .