阅读说明：本技术 基于特征值的动态信道化子带频谱检测方法 (Dynamic channelization subband spectrum detection method based on characteristic value ) 是由 张春杰 周振宇 司伟建 邓志安 曲志昱 侯长波 汲清波 杨梦� 于 2019-08-26 设计创作，主要内容包括：本发明涉及雷达信号处理领域,具体涉及基于特征值的动态信道化子带频谱检测方法。根据信道化输出的第i路子带信号,经单通道信号的多通道转换,得到M×N维观测矩阵,构造采样协方差矩阵；根据采样协方差矩阵进行特征分解,得到相对应形式平均特征值和当前子带最小特征值,构造相应算法的检测统计量；根据实际情况通过虚警概率,得到相应算法检测门限的表达式；根据相应的检测算法的判决表达式,确定信号是否存在,即当α＞γ时,判断存在信号,否则不存在。相对于目前的经典频谱检测处理方法,本发明在低信噪比、低采样点的条件下,获得了更高的检测性能,提高了检测的精确程度,更加符合未来电子战中的信号电磁环境。(The present invention relates to radar signal processing fields, and in particular to the dynamic channelization subband spectrum detection method based on characteristic value.According to the i-th way band signal that channelizing exports, the multichannel conversion through single channel signal obtains M × N-dimensional observing matrix, constructs sample covariance matrix；Feature decomposition is carried out according to sample covariance matrix, corresponding form mean eigenvalue and current sub-band minimal eigenvalue is obtained, constructs the detection statistic of respective algorithms；According to the actual situation by false-alarm probability, the expression formula of respective algorithms detection threshold is obtained；According to the judgement expression formula of corresponding detection algorithm, determine that signal whether there is, i.e., as α > γ, there are signals for judgement, are otherwise not present.Relative to current classical frequency spectrum detection processing method, the present invention obtains higher detection performance under conditions of low signal-to-noise ratio, low sampled point, improves the levels of precision of detection, the signal electromagnet environment being more in line in future electronic war.)

1. the dynamic channelization subband spectrum detection method based on characteristic value characterized by comprising

Step 1: the i-th way band signal exported according to channelizing is converted by the multichannel of single channel signal, obtains M × N The observing matrix of dimension, and construct sample covariance matrix R_ix(N)；

Step 2: according to the sample covariance matrix R of each subband signal_ix(N), feature decomposition is carried out, corresponding form is obtained Mean eigenvalue and current sub-band minimal eigenvalue, and then construct respective algorithms detection statistic α；When in reception signal Only noise when, according to Random Matrices Theory, sample covariance matrix at this time is a Wishart random matrix；

Step 3: according to the actual situation, pass through the false-alarm probability P of setting_f, determine and obtain the table of the detection threshold γ of respective algorithms Up to formula；

Step 4: according to the judgement expression formula of corresponding detection algorithm, determine that signal whether there is, i.e., as α > γ, judgement is deposited In signal, otherwise as α < γ, signal is not present in judgement.

2. the dynamic channelization subband spectrum detection method according to claim 1 based on characteristic value, which is characterized in that institute It states in step 1, the process of the multichannel conversion of the single channel signal are as follows:

Assuming that the channel number of dynamic digital channelized receiver system is K, input signal x [n] is decomposed and is analyzed by whole band The output signal on the available road K after filter group, the output signal of i-th of subband can be expressed as x_i(n), i=0, 1 ..., K-1, and x_i(n) it is made of signal and noise two parts:

x_i(n)=s_i(n)+ω_i(n), i=0,1 ..., K-1

Wherein s_i(n) signal that the i-th subchannels are obtained in n-th of instance sample, ω are indicated_i(n) it represents in the i-th subchannels Gaussian noise, mean value 0, variance σ²；One two can be expressed as to the frequency spectrum detection of each subband of dynamic channelization First Hypothesis Testing Problem:

Wherein: H₀And H₁Respectively indicating in channel only includes the case where there are the mixed signals of signal and noise in noise and channel；

The output signal x of i-th of subband_i(n) observing matrix obtained after over-sampling is handled can indicate are as follows:

In formula above, x_im, m=1,2 ..., M respectively indicates the output signal of i-th of subband through the more of single channel signal The signal in each channel obtained after the conversion of channel, the signal in each channel contain N number of sampled point.

3. the dynamic channelization subband spectrum detection method according to claim 2 based on characteristic value, it is characterised in that: institute State the process of the construction sample covariance matrix in step 1 are as follows:

By subband output signal x_iIt (n), can be in the hope of the sampling covariance of i-th of subband output signal after over-sampling is handled Matrix are as follows:

Work as H₀Under conditions of establishment, receives in signal and only exist noise, then the sample covariance matrix for receiving signal can indicate Are as follows:

R_ix(N)=R_iω(N)=E [W_iW_i ^H]=W_iW_i ^H/N。

4. the dynamic channelization subband spectrum detection method according to claim 3 based on characteristic value, it is characterised in that: institute Stating step 2 includes:

(2.1) to the sample covariance matrix R of each subband signal_ix(N) feature decomposition is carried out, R is obtained_ix(N) M feature Value；Find out the average value of this M characteristic valueAnd geometrical meanWith minimal eigenvalue therein

(2.2) three kinds of corresponding detection statistics of algorithm are constructed according to the expression formula of detection statistic to be respectively as follows:

AEME algorithm:

IAEME algorithm:

GMEME algorithm:

5. the dynamic channelization subband spectrum detection method according to claim 4 based on characteristic value, it is characterised in that: step Detection threshold in rapid three is respectively as follows:

AEME algorithm:

IAEME algorithm:

GMEME algorithm:

Wherein F₁It (t) is 1 rank Tracy-Widom distribution function.

Technical field

The present invention relates to radar signal processing fields, and in particular to the dynamic channelization subband spectrum detection based on characteristic value Method, the subband spectrum detection that can be used in dynamic digital channelized receiver.

Background technique

With the development of technology, the signal electromagnet environment of modern electronic warfare becomes more complicated, and receiver is as electronic warfare The important system of middle reception of wireless signals, received signal often have non-cooperation, prior information it is unknown, receive signal in The unknown feature in subband signal number, bandwidth and the position for being included.

It, being capable of the big instant bandwidth of dynamically adapting since dynamic digital channelized receiver is as a kind of novel receiver Signal, overcome present in conventional uniform digital channelized receiver across channel situation, realize in broadband signal The extraction of multiple signals with separate.In dynamic digital channelized receiver, correctly the frequency spectrum of subband signal is detected, Judge in subchannel with the presence or absence of signal, then to there are the subchannels of signal to carry out comprehensive reconstructing corresponding original sub- letter Number, it is the key that dynamic digital channelization technique, there is important influence to subsequent signal processing.

Current classical frequency spectrum detection processing method mainly includes that energy measuring method, matching matrix and cyclo-stationary are special Levy detection method.The advantages of energy measuring method is that algorithm realizes simple, is not required to the prior information it is to be understood that signal.But need basis Noise estimates detection threshold, is affected by the uncertainty of noise；The advantages of matching matrix is detection accuracy height, certain Under the conditions of be optimum detection.But it should be understood that the prior information of signal and noise, this radar signal in modern electronic warfare It is difficult to accomplish in reception；And the advantages of cyclostationary characteristic detection method is that noiseproof feature is strong, but it realizes that process is complicated, The time for carrying out signal detection is longer, does not have real-time.In recent years, Random Matrices Theory is as a kind of new theory, hair Exhibition promotes research of the people to frequency spectrum detection technology.Frequency spectrum detecting method based on Random Matrices Theory receives letter by analysis Number the characteristic value of sample covariance matrix carry out frequency spectrum detection, have realize it is simple, do not need prior information and detection The good advantage of effect and the concern by scholars, and occur including the ratio between minimax characteristic value (Maximum-Minimum Eigenvalue, MME), the ratio between mean eigenvalue and maximum eigenvalue (Average-Maximum Eigenvalue, AME), most The difference (Different Between the Maximum and Minimun Eigenvalue, DMM) etc. of big minimal eigenvalue Outstanding algorithm and its it is correspondingly improved algorithm.However, the existing frequency spectrum detection algorithm based on characteristic value mostly uses maximum spy The APPROXIMATE DISTRIBUTION rule of value indicative, obtained thresholding precision in expression need to be further increased, and do not account for sampling association Influence of the inner link that all characteristic values of variance matrix include to frequency spectrum detecting result.At the same time, the difference one of characteristic value The final threshold judgement expression formula of class algorithm is related with noise, and testing result will receive the influence of noise.

Summary of the invention

The purpose of the present invention is to provide the dynamic channelization subband spectrum detection methods based on characteristic value, in low noise Than obtaining higher detection performance, improving the levels of precision of detection, be more in line with and do not send a telegram here under conditions of, low sampled point Signal electromagnet environment in son war.

The object of the present invention is achieved like this:

Step 1: the i-th way band signal exported according to channelizing is converted by the multichannel of single channel signal, obtains M The observing matrix of × N-dimensional, and construct sample covariance matrix R_ix(N)；

Step 2: according to the sample covariance matrix R of each subband signal_ix(N), feature decomposition is carried out, is obtained corresponding The mean eigenvalue of form and the minimal eigenvalue of current sub-band, and then construct the detection statistic α of respective algorithms；Believe when receiving When there was only noise in number, according to Random Matrices Theory, sample covariance matrix at this time is a Wishart random matrix；

Step 3: according to the actual situation, pass through the false-alarm probability P of setting_f, determining to obtain the detection threshold γ of respective algorithms Expression formula；

Step 4: it according to the judgement expression formula of corresponding detection algorithm, determines that signal whether there is, i.e., as α > γ, sentences Disconnected there are signals, and otherwise as α < γ, signal is not present in judgement.

The invention also includes structure features some in this way:

1. in the step 1, the process of the multichannel conversion of the single channel signal are as follows:

Assuming that the channel number of dynamic digital channelized receiver system be K, input signal x [n] by whole band decompose and The output signal on the available road K after analysis filter group, the output signal of i-th of subband can be expressed as x_i(n), i=0, 1 ..., K-1, and x_i(n) it is made of signal and noise two parts:

x_i(n)=s_i(n)+ω_i(n), i=0,1 ..., K-1

Wherein s_i(n) signal that the i-th subchannels are obtained in n-th of instance sample, ω are indicated_i(n) the i-th way letter is represented Gaussian noise in road, mean value 0, variance σ²；One can be expressed as to the frequency spectrum detection of each subband of dynamic channelization A binary hypothesis test problem:

Wherein: H₀And H₁It respectively indicates in channel only comprising there are the mixed signals of signal and noise in noise and channel Situation；

The output signal x of i-th of subband_i(n) observing matrix obtained after over-sampling is handled can indicate are as follows:

In formula above, x_im, m=1,2 ..., M respectively indicates the output signal of i-th of subband through single channel signal Multichannel conversion after the obtained signal in each channel, the signal in each channel contains N number of sampled point.

2. the process of the construction sample covariance matrix in the step 1 are as follows:

By subband output signal x_iIt (n), can be in the hope of the sampling association of i-th of subband output signal after over-sampling is handled Variance matrix are as follows:

Work as H₀It under conditions of establishment, receives in signal and only exists noise, then the sample covariance matrix for receiving signal can be with It indicates are as follows:

R_ix(N)=R_iω(N)=E [W_iW_i ^H]=W_iW_i ^H/N。

3. the step 2 includes:

(2.1) to the sample covariance matrix R of each subband signal_ix(N) feature decomposition is carried out, R is obtained_ix(N) M Characteristic value；Find out the average value of this M characteristic valueAnd geometrical meanWith minimal eigenvalue therein

(2.2) three kinds of corresponding detection statistics of algorithm are constructed according to the expression formula of detection statistic to be respectively as follows:

AEME algorithm:

IAEME algorithm:

GMEME algorithm:

4. detection threshold in step 3 is respectively as follows:

AEME algorithm:

IAEME algorithm:

GMEME algorithm:

Wherein F₁It (t) is 1 rank Tracy-Widom distribution function.

The beneficial effects of the present invention are:

Frequency spectrum is examined 1. the present invention has comprehensively considered the inner link that all characteristic values of sample covariance matrix are included The influence of result is surveyed, the Limit Distribution of the more accurate minimal eigenvalue of application, which is deduced, more accurately detects thresholding expression Formula improves detection performance；

2. detection threshold expression formula and false-alarm probability P of the invention_f, the sight that obtains after channelizing subband signal over-sampling The line number for surveying matrix is related with columns, unrelated with noise, does not need any prior information of known signal and noise when detecting Detection can be completed, overcome interference of the noise variation to detection performance, be a blind checking method；

3. the present invention can need to be adjusted false-alarm probability according to the actual situation obtains different detection decision thresholds, It is adapted to different application scenarios；

4. due to the characteristic value difference of signal and noise be all under any circumstance it is existing, no matter the letter of which kind of form Number, the differentiation between signal and noise can be carried out by characteristic value, therefore this method all has detection to multi-signal Can, have the advantages that be adapted to composite signal detection；

5. the present invention under conditions of low signal-to-noise ratio, low sampled point and low M value, all has more compared with existing algorithm The performance of high detection performance, especially IAEME algorithm is best, can play a role under the conditions of worse, has more preferable Adaptability；

6. the present invention obtains higher detection performance, improves detection under conditions of low signal-to-noise ratio, low sampled point Levels of precision, have many advantages, such as to realize it is simple, do not need prior information, be adaptable, detection performance it is good, be more in line with and do not send a telegram here Signal electromagnet environment in son war, has a good application prospect.

Detailed description of the invention

Fig. 1 is the structure principle chart of the dynamic channelization subband spectrum detection method based on characteristic value；

Fig. 2 is the general algorithm flow chart of 3 kinds of algorithms of the invention；

Fig. 3 is the amplitude-versus-frequency curve figure for 4 kinds of mixed signals that the present invention inputs；

Fig. 4 (a) is the schematic diagram of channelizing of the present invention treated time domain output result；

Fig. 4 (b) is the schematic diagram of channelizing of the present invention treated frequency domain output result；

Fig. 5 is 3 kinds of algorithms of the present invention and detection probability comparison diagram of other existing algorithms under signal-to-noise ratio different situations；

Fig. 6 is that the detection probability of 3 kinds of algorithms of the present invention and other existing algorithms under sampling number N different situations compares Figure；

Fig. 7 is the line number M different situations of 3 kinds of algorithms of the present invention and other existing algorithms in signal sampling covariance matrix Under detection probability comparison diagram；

Specific embodiment

In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing to the present invention It is described further:

Detection method includes the following steps for dynamic channelization subband spectrum based on characteristic value of the invention:

A. the sight of M × N-dimensional is obtained after the conversion of the multichannel of single channel signal to the i-th way band signal of channelizing output Matrix is surveyed, and constructs sample covariance matrix R_ix(N):

A1. the multichannel conversion process of single channel signal

Assuming that the channel number of dynamic digital channelized receiver system be K, input signal x [n] by whole band decompose and The output signal on the available road K after analysis filter group, the output signal of i-th of subband can be expressed as x_i(n), i=0, 1 ..., K-1, and x_i(n) it is made of signal and noise two parts:

x_i(n)=s_i(n)+ω_i(n), i=0,1 ..., K-1

Wherein s_i(n) signal that the i-th subchannels are obtained in n-th of instance sample, ω are indicated_i(n) the i-th way letter is represented Gaussian noise in road, mean value 0, variance σ².One can be expressed as to the frequency spectrum detection of each subband of dynamic channelization A binary hypothesis test problem:

H₀And H₁Respectively indicating in channel only includes the case where there are the mixed signals of signal and noise in noise and channel.

In dynamic digital channelization structure, each subband reception data to be dealt with are usually single channel form, The observation data vector of as one 1 × L.To obtain the sample covariance matrix that each subband receives signal, need single-pass Channel receiving signal is converted to the received form of multichannel, i.e., observation data vector is converted to the data matrix form of M × N.This Invention is handled the output data of each sub-channels using over-sampling method.

The output signal x of i-th of subband_i(n) observing matrix obtained after over-sampling is handled can indicate are as follows:

In formula above, x_im, m=1,2 ..., M respectively indicates the output signal of i-th of subband through single channel signal Multichannel conversion after the obtained signal in each channel, the signal in each channel contains N number of sampled point.

A2. sample covariance matrix is constructed

By subband output signal x_iIt (n), can be in the hope of the sampling association of i-th of subband output signal after over-sampling is handled Variance matrix are as follows:

Work as H₀It under conditions of establishment, receives in signal and only exists noise, then the sample covariance matrix for receiving signal can be with It indicates are as follows:

R_ix(N)=R_iω(N)=E [W_iW_i ^H]=W_iW_i ^H/N

B. to the sample covariance matrix R of each subband signal_ix(N) feature decomposition is carried out, the flat of corresponding form is found out The minimal eigenvalue of equal characteristic value and current sub-band, and then construct the detection statistic α of respective algorithms:

When receiving only noise in signal, according to Random Matrices Theory it is found that sample covariance matrix at this time is one A Wishart random matrix.The characteristic value of Wishart random matrix meets following several fundamental theorems:

Theorem 1: it assuming that noise is real signal, enables

Assuming thatEnable λ_min(A (N)) indicates random matrix A (N) corresponding minimal eigenvalue, thenObey 1 rank Tracy-Widom distribution F₁(t)。

Theorem 2: it assuming that noise is complex signal, enables

Assuming thatEnable λ_min(A (N)) is indicated with the corresponding minimal eigenvalue of matrix A (N), thenObey 2 rank Tracy-Widom distribution F₂(t)。

Theorem 3: whenWhen,

To the sample covariance matrix R of each subband signal of channelizing output_ix(N) Eigenvalues Decomposition is carried out, R is obtained_ix (N) M characteristic value is respectively λ₁,λ₂,...,λ_M.In H₀In the case where, its available M equal eigenvalue λs_i=σ²。 In H₁In the case where, each characteristic value can be expressed as λ_i=ρ_i+σ².Therefore, in the ideal case, H₀And H₁In the case of two kinds The average value of characteristic value of sample covariance matrix of reception signal be respectively σ²WithAnd minimal eigenvalue is to make an uproar Sound variances sigma².Therefore, the difference of the average value and minimal eigenvalue that can use characteristic value is united the ratio of the two as detection Metering carries out frequency spectrum detection.

B1. to AEME algorithm, work as H₀When establishment, the variance of noise can be indicated are as follows:

According to theorem 3 it is found that R_ix(N) average value of characteristic value can indicate are as follows:

The ratio between mean eigenvalue and minimal eigenvalue (AEME) algorithm are by the mean eigenvalue of subband to be detected and the subband The ratio between minimal eigenvalue be used as test statistics, be shown below:

B2. to IAEME algorithm, work as H₀When establishment, the variance of noise can be indicated are as follows:

Further, when signal is not present in subchannel, R_ix(N) mean eigenvalue can indicate are as follows:

According to theorem 3 it is found that R_ix(N) average value of characteristic value can indicate are as follows:

The ratio between improved mean eigenvalue and minimal eigenvalue (IAEME) algorithm by the mean eigenvalue of subband to be detected with The ratio between minimal eigenvalue of the subband is used as test statistics, is shown below:

B3. to GMEME algorithm, R_ix(N) geometrical mean of characteristic value can indicate are as follows:

When signal is not present in subchannel, R_ix(N) product of characteristic value can indicate are as follows:

Then R_ix(N) geometrical mean of characteristic value can indicate are as follows:

According to theorem 3 it is found that R_ix(N) geometrical mean of characteristic value can indicate are as follows:

The ratio between geometric average characteristic value and minimal eigenvalue (GMEME) algorithm are by the geometric average characteristic value of subband to be detected It is used as test statistics with the ratio between the minimal eigenvalue of the subband, is shown below:

C. the false-alarm probability P being set according to actual conditions_fDetermine the expression formula of the detection threshold γ of respective algorithms:

C1. to AEME algorithm, it is assumed that noise is real signal, enables γ₁To detect decision threshold, if α^AEME>γ₁, then show letter Number exist；Otherwise judge that signal is not present.According to false-alarm probability P_fDefinition can do following derivation:

The thus decision threshold of available AEME algorithm are as follows:

C2. to IAEME algorithm, it is assumed that noise is real signal, enables γ₂To detect decision threshold, if α^IAEME>γ₂, then show Signal exists；Otherwise judge that signal is not present.According to false-alarm probability P_fDefinition can do following derivation:

The thus decision threshold of available IAEME algorithm are as follows:

C3. to GMEME algorithm, it is assumed that noise is real signal, enables γ₃To detect decision threshold, if α^GMEME>γ₃, then show Signal exists；Otherwise judge that signal is not present.According to false-alarm probability P_fDefinition can do following derivation:

The thus decision threshold of available GMEME algorithm are as follows:

In the above decision threshold expression formula, the value of μ and υ can be obtained with reference to theorem 1.From the expression of each decision threshold Formula it can be concluded that, detection threshold is not affected by noise, and only with false-alarm probability P_fAnd the output signal warp of each subband The related conclusion of line number M and columns N of the observing matrix obtained after the multichannel conversion of single channel signal.

D. it determines that signal whether there is according to the judgement expression formula of corresponding detection algorithm, i.e., as α > γ, judges exist Signal, otherwise as α < γ, signal is not present in judgement.

In conjunction with example, the technical scheme of the present invention is realized as follows:

Setting system bandwidth is B=750MHz, can set f for the sample frequency of system according to bandpass sample theory_s =1500MHz will monitor that frequency band is divided into M=16 subband according to the dynamic digital channelization structure in Fig. 1.Input signal is set It is set to the mixed signal of linear frequency modulation (LFM) signal, bpsk signal, four kinds of signals of QPSK signal and normal signal composition.If Setting LFM signal initial frequency is 151MHz, and termination set of frequency is 319MHz.The parameter of bpsk signal is set as carrier frequency f₀= 522MHz, coding mode use 13 Barker code S_BPSK=[1,1,1,1,1,0,0,1,1,0,1,0,1].The parameter of QPSK signal It is set as carrier frequency f₀=363MHz, coding mode use 16 Frank code S_QPSK=[00,01,10,10,11,01,11,00, 01,10,01,00,11,00,10,11], the parameter of normal signal is set as carrier frequency f₀=100MHz.Data length is set as 56000 points, the data length corresponding to every sub-channels is 3500 points.SNR=13dB is set by signal-to-noise ratio.Input signal Amplitude-versus-frequency curve is as shown in Figure 3.Above-mentioned mixed signal is handled using dynamic digital channelization structure shown in FIG. 1 Afterwards, subband spectrum is detected using 3 kinds of algorithms in the present invention.