Dynamic digital channelization blind sub-band detection method based on characteristic value difference

Abstract

The invention relates to a dynamic digital channelization blind sub-band detection method based on eigenvalue difference, which is characterized in that a decision rule is designed by utilizing the ratio of the difference between the maximum eigenvalue and the minimum eigenvalue of a sub-band signal sampling covariance matrix to the harmonic average of all eigenvalues: firstly, receiving a signal sequence x (n) based on a sub-band by utilizing a resampling technology; n is greater than or equal to 0 and less than or equal to MN-1, and constructing an M * N-dimensional observation data matrix X of the M virtual channels; then, calculating a sampling covariance matrix # imgabs0 # of a sub-band receiving signal by using the observation data matrix, calculating all eigenvalues lambda i (i = 1, 2,..., M) of # imgabs1 #, and setting lambda 1 > lambda 2 >... > lambda M; secondly, using the difference between the maximum and minimum characteristic values and the harmonic average ratio of all the characteristic values to construct and calculate a test judgment quantity lambda, and calculating a judgment threshold tau according to a target false alarm probability Pf; and finally, implementing detection judgment: if lambda is greater than tau, judging that the sub-band signal exists; and if lambda is less than tau, judging that the sub-band signal does not exist. The method has the advantage of total blind detection, and can effectively improve the detection performance under the condition of low signal-to-noise ratio.

Description

Technical Field

[0001] The invention relates to a dynamic digital channelization blind subband detection method based on eigenvalue difference, belonging to the technical field of radar signal detection and processing. Background Art

[0002] Dynamic digital channelized receivers are important equipment in electronic warfare, and reliable sub-band signal detection technology is the key technology to realize dynamic digital channelized receivers. However, in the process of sub-band signal detection, the signals received by the receiver often have the characteristics of non-cooperation, low signal-to-noise ratio, and lack of statistical prior information. Therefore, it is of great value to effectively utilize the characteristics of sub-band received signals and develop effective blind sub-band detection algorithms.

[0003] Blind detection methods usually use the sampling covariance matrix to construct the test decision quantifier. Classic blind detection based on the sampling covariance matrix includes the covariance absolute value detection method, which uses the ratio of the absolute value sum of the non-diagonal elements of the sampling covariance matrix to the absolute value sum of the diagonal elements as the test decision quantifier, and can well detect high-correlation subband signals. With the development of random matrix theory, blind signal detection methods based on the eigenvalues ​​of the sampling covariance matrix have attracted widespread attention. Among them, the detection methods based on the difference between the maximum and minimum eigenvalues ​​and the ratio of the maximum and minimum eigenvalues ​​use the extreme eigenvalues ​​of the sampling covariance matrix to construct the test decision quantifier, and show good detection performance in the detection of low signal-to-noise ratio and high-correlation received signals. However, these two methods only use the information of the extreme eigenvalues ​​of the sampling covariance matrix, while ignoring the use of other eigenvalues. In order to better utilize the information of the eigenvalues ​​of the sampling covariance matrix, researchers further proposed three types of detection methods based on the ratio of the maximum (or minimum) eigenvalue to the arithmetic mean, the ratio of the maximum (or minimum) eigenvalue to the geometric mean, and the ratio of the difference between the maximum / minimum eigenvalues ​​to the arithmetic mean. These methods have improved the detection performance to a certain extent, but they have not fully exploited the information of all eigenvalues ​​of the sampling covariance matrix, and thus have not achieved the best blind detection effect. The reasons are as follows: (1) The first two detection methods based on the ratio of the maximum (or minimum) eigenvalue to the arithmetic mean and the ratio of the maximum (or minimum) eigenvalue to the geometric mean ignore the use of the minimum eigenvalue information, which limits the improvement of detection performance under low signal-to-noise conditions to a certain extent; (2) In addition to making full use of the information of all eigenvalues, more importantly, the test judgment quantity constructed based on the eigenvalue needs to maximize the difference between the signal (H1 state) and the signal-free (H0 state) states as much as possible. However, the above three methods use the arithmetic mean or geometric mean to measure the degree of change of all eigenvalues, and do not maximize the difference between the H1 and H0 states, which further limits the improvement of detection performance.

[0004] In view of this, the present invention proposes an effective dynamic digital channelized blind sub-band signal detection method by simultaneously utilizing the information of extreme eigenvalues ​​and all other eigenvalues ​​and maximizing the difference in eigenvalue changes between the signal and no signal states in the process of test decision quantity design. Summary of the invention

[0005] Technical problem: The present invention proposes a dynamic digital channelized blind sub-band detection method based on eigenvalue difference analysis. The method uses the difference between extreme eigenvalues ​​and the harmonic mean of eigenvalues ​​to design a test decision quantifier. It does not require any prior information about noise and signals and is a blind detection method with wide applicability. The test decision quantifier uses the information of all eigenvalues ​​of the sampling covariance matrix and well characterizes the differences between the eigenvalues, effectively improving the detection performance under low signal-to-noise ratio conditions.

[0006] Technical solution: The present invention proposes a dynamic digital channelized blind sub-band detection method based on eigenvalue difference analysis, which designs a decision rule by using the ratio of the difference between the maximum and minimum eigenvalues ​​of the sub-band signal sampling covariance matrix and the harmonic mean of all eigenvalues: First, based on the sub-band received signal sequence x(n), 0≤n≤Q-1, an M×N-dimensional observation data matrix X of M virtual channels is constructed by using the resampling technology, where Q=MN; then, the sampling covariance matrix of the sub-band received signal is calculated using the observation data matrix And calculate all eigenvalues ​​λ of the sampling covariance matrix i (i=1,2,…,M), and let λ1>λ2>…>λ M ; Secondly, the test decision quantity Λ is calculated using the ratio of the difference between the maximum and minimum eigenvalues ​​and the harmonic mean of all eigenvalues, and the target false alarm probability P is calculated according to the target false alarm probability P. f Calculate the decision threshold τ; finally, implement the detection decision: if Λ>τ, then it is determined that there is a signal in the sub-band; if Λ<τ, then it is determined that there is no signal in the sub-band. The specific steps of this method are:

[0007] 1) Sample the subband signal to be detected to obtain the received sequence x(n), 0≤n≤Q-1, and use the resampling technology to construct the observation data matrix of M virtual channels Here Q = MN;

[0008] 2) Calculate the sampling covariance matrix using the observation data matrix

[0009] 3) Calculate the sampling covariance matrix All eigenvalues ​​of and are labeled as λ1>λ2>…>λ M ;

[0010] 4) Calculate the difference between the maximum and minimum eigenvalues ​​α = λ1-λ Mand the harmonic mean of all eigenvalues On this basis, the test judgment amount is calculated

[0011] 5) According to the target false alarm probability P f Calculate the decision threshold:

[0012] Here F1 -1 () represents the inverse cumulative distribution function of the first-order Tracy-Widom distribution;

[0013] 6) Detection judgment: If Λ>τ, it is determined that there is a signal in the sub-band; if Λ<τ, it is determined that there is no signal in the sub-band.

[0014] All symbol annotations

[0015]

[0016]

[0017] Beneficial effects: The beneficial effects of the present invention are mainly reflected in the following three aspects:

[0018] 1) The method proposed in the present invention uses the difference between extreme eigenvalues ​​and the harmonic mean of the eigenvalues ​​to construct the test decision quantity. No prior information of noise and signal is required in the detection process. It is a blind subband detection method with wide applicability.

[0019] 2) The method proposed in the present invention can effectively improve the subband signal detection performance under low signal-to-noise ratio conditions by using the maximum / minimum extreme eigenvalue of the covariance matrix and all other eigenvalue information to design the test decision quantity by using the virtual channel;

[0020] 3) By adopting the harmonic mean technique to maximize the average change of all eigenvalues ​​in both signal and no-signal states, it is conducive to correct judgment, thereby further improving the sub-band signal detection performance under low signal-to-noise ratio conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 The invention is a flow chart for realizing a dynamic digital channelized blind sub-band detection method based on eigenvalue difference analysis.

[0022] Figure 2 It is a comparison chart of detection probability performance curves of the detection method proposed in the present invention and three classical detection methods: covariance absolute value detection, maximum and minimum eigenvalue ratio detection, and maximum / minimum eigenvalue difference and arithmetic mean ratio detection. DETAILED DESCRIPTION

[0023] The present invention proposes a dynamic digital channelized blind sub-band detection method based on eigenvalue difference analysis, which designs a decision rule by using the ratio of the difference between the maximum and minimum eigenvalues ​​of the sampling covariance matrix of the sub-band signal to the harmonic mean of all eigenvalues: first, the observation data matrix of the multi-virtual channel is constructed for the sub-band received signal sequence by using the resampling technology; then, the sampling covariance matrix of the sub-band received signal is calculated by using the observation data matrix, and all eigenvalues ​​of the sampling covariance matrix are calculated thereby; secondly, the inspection decision amount is calculated by using the ratio of the difference between the maximum and minimum eigenvalues ​​and the harmonic mean of all eigenvalues, and the decision threshold is calculated according to the target false alarm probability; finally, the detection decision is implemented: if the inspection decision amount is greater than the decision threshold, it is judged that there is a signal in the sub-band; if the inspection decision amount is less than the decision threshold, it is judged that there is no signal in the sub-band. The specific implementation method of the method is described as follows:

[0024] 1) Sample the subband signal to be detected to obtain the received sequence x(n), 0≤n≤Q-1. Here, we assume that the number of sampling points satisfies Q=MN. By resampling, we can construct the observation data matrix based on M virtual channels.

[0025] 2) Calculate the sampling covariance matrix using the observation data matrix

[0026] 3) Calculate the sampling covariance matrix All eigenvalues ​​of and are labeled as λ1>λ2>…>λ M ;

[0027] 4) Calculate the difference between the maximum and minimum eigenvalues ​​λ1-λ M and the harmonic mean of all eigenvalues And in using the ratio of the two to construct the test judgment

[0028] 5) According to the target false alarm probability P f Calculate the decision threshold:

[0029] Here F1 -1 () represents the inverse cumulative distribution function of the first-order Tracy-Widom distribution;

[0030] 6) Detection judgment: If Λ>τ, it is determined that there is a signal in the sub-band; if Λ<τ, it is determined that there is no signal in the sub-band.

[0031] The following is a detailed explanation from three aspects: sub-band signal detection model based on eigenvalue difference analysis, implementation method, and specific detection process.

[0032] 1. Detection Model

[0033] After analysis and filtering, the digital channelized receiving system converts the received broadband input signal into multiple narrow bandwidth sub-band signals. Assume that the received signal sequence obtained by sampling the sub-band output signal to be detected is x(n), 0≤n≤Q-1, s(n) represents the corresponding signal component in the sampled signal x(n) at the nth moment, and u(n) represents the Gaussian white noise component with zero mean and unknown noise variance. Then the sub-band signal detection problem can be modeled as the following binary hypothesis testing model:

[0034]

[0035] Here, H0 indicates that only noise exists in the sub-band without any signal component, and H1 indicates that a signal component exists in the sub-band.

[0036] (II) Implementation methods

[0037] The difficulty of the actual detection process lies in the lack of noise variance and signal prior information. To solve this problem, the present invention proposes a blind detection algorithm based on eigenvalue difference analysis. To this end, the observation data matrix of M virtual channels is obtained by resampling the received signal sequence:

[0038]

[0039] Here we may as well assume that Q = MN. On this basis, calculate the M×M sampling covariance matrix of the virtual channel signal:

[0040]

[0041] Note that when the sampling sequence length Q is sufficiently large, the sampling covariance matrix Approaching the statistical covariance matrix. Since the noise is Gaussian white noise, this means that when the subband signal does not exist (H0 state) Approaching an unknown diagonal matrix with equal diagonal elements; when the subband signal exists (H1 state), due to the influence of the analysis filter and oversampling, the virtual channel signals are no longer statistically independent. No longer tends to a diagonal matrix. Therefore, from the perspective of examining eigenvalues, in the H0 state All eigenvalues ​​of will tend to be equal (numerically equal to the unknown noise variance), while in the H1 state All eigenvalues ​​of will no longer be equal. Using this fact, we can test To determine whether the subband signal exists, we can calculate the sampling covariance matrix All eigenvalues ​​of and are labeled as λ1>λ2>…>λ M . It follows that the difference between the largest and smallest eigenvalues ​​and the harmonic mean of all eigenvalues ​​is:

[0042] α=λ1-λ M (4)

[0043]

[0044] Note that α represents the difference between the extreme eigenvalues ​​of the covariance matrix used by the M virtual channel signals, and also represents the maximum difference between all its eigenvalues; while β represents the average difference between all eigenvalues ​​of the covariance matrix used by the M virtual channel signals, and it is the smallest in the geometric mean, arithmetic mean, etc. Therefore, α / β measures the difference between the eigenvalues ​​caused by the existence of the signal as much as possible. To this end, the present invention proposes a new sub-band signal test decision metric:

[0045]

[0046] Note that when only noise is present, the sampling covariance matrix It obeys the central Wishart distribution, and when the number of columns N of the observation data matrix is ​​large enough, β can be approximated by the harmonic mean of the maximum and minimum eigenvalues. Therefore, using the results of random matrix theory, we can know that the following approximate relationship holds true:

[0047]

[0048] Therefore, when N is sufficiently large, the approximate distribution of the test decision quantity Λ is determined by the extreme eigenvalue distribution of the central Wishart matrix. According to the random matrix theory, the distribution of the maximum and minimum eigenvalues ​​of the central Wishart matrix is ​​Tracy-Widom distribution. Based on this, the present invention obtains the false alarm probability P of a given target by integrating the threshold analysis results of the maximum eigenvalue and the minimum eigenvalue distribution. f The calculation expression of the decision threshold is:

[0049]

[0050] Among them, F1 -1 () represents the inverse cumulative distribution function of the first-order Tracy-Widom distribution. Considering that in the actual detection process, the values ​​of M and N are very limited, the theoretical threshold represented by formula (8) usually has a certain deviation in practical applications. A large number of simulation experiments have shown that the theoretical decision threshold shown in formula (8) is usually higher than the actual value. In practical applications, it can be further corrected to the form shown in formula (9) to have a higher threshold approximation accuracy:

[0051]

[0052] From the above analysis and design process, it can be seen that the method proposed in the present invention utilizes the difference between extreme eigenvalues ​​and the harmonic mean of eigenvalues ​​to design the test decision amount, does not require any prior information about noise and signals, has blind detection characteristics, and has wide adaptability; the test decision amount utilizes the information of all eigenvalues ​​including the extreme eigenvalues ​​of the covariance matrix, and can effectively improve the subband detection performance under low signal-to-noise ratio conditions; compared with the classic subband detection method based on the ratio of the difference between extreme eigenvalues ​​and the mathematical mean, the use of harmonic mean can more obviously characterize the eigenvalue difference, which is conducive to correct judgment and improves the detection probability.

[0053] (III) Specific implementation steps

[0054] Here we combine the above analysis process and process Figure 1 , the implementation steps of a dynamic digital channelization blind sub-band detection method based on eigenvalue difference analysis involved in the present invention are further described:

[0055] (a) Oversample the subband signal to be detected to obtain the received signal sequence x(n), 0≤n≤Q-1. Here, we assume that Q=MN, then the observation data matrix of M virtual channels can be obtained by resampling technology:

[0056]

[0057] (b) Calculate the sampling covariance matrix of the received signal according to formula (3):

[0058] (c) Using eigenvalue decomposition to obtain the sampling covariance matrix All eigenvalues ​​of , and we may mark them as λ1>λ2>…>λ M ;

[0059] (d) Calculate the difference between the maximum and minimum eigenvalues ​​and the harmonic mean of all eigenvalues, and use the ratio of the two to calculate the test decision quantile

[0060] (e) Calculate the decision threshold τ according to formula (9);

[0061] (f) Implement detection judgment: if Λ>τ, it is determined that there is a signal in the sub-band; if Λ<τ, it is determined that there is no signal in the sub-band.

[0062] Finally, numerical simulation is performed to verify the beneficial effect of the blind subband detection method proposed in the present invention. f =0.1, received signal sequence length Q=1000, number of virtual channels M=10. Figure 2The performance comparison between the detection method proposed in the present invention and the three most representative detection methods, namely, the absolute value detection of covariance, the ratio detection of the maximum and minimum eigenvalues, and the ratio detection of the maximum / minimum eigenvalue difference and the arithmetic mean, is given. The simulation results clearly show that the detection performance of the subband signal under low signal-to-noise ratio conditions is significantly improved by the method proposed in the present invention.

Claims

1. A dynamic digital channelized all-blind sub-band detection method based on eigenvalue difference analysis, characterized in that: The method constructs a decision rule using the ratio of the difference between the maximum and minimum eigenvalues ​​of the subband signal sampling covariance matrix and the harmonic mean of all eigenvalues: First, the M×N dimensional observation data matrix X of M virtual channels is constructed based on the subband received signal sequence x(n), 0≤n≤Q-1 using the resampling technology, where Q=MN; then, the sampling covariance matrix of the subband received signal is calculated using the observation data matrix And calculate all eigenvalues ​​λ of the sampling covariance matrix i (i=1,2,…,M), and let λ1>λ2>…>λ M ; Secondly, the test decision quantity Λ is calculated using the ratio of the difference between the maximum and minimum eigenvalues ​​and the harmonic mean of all eigenvalues, and the target false alarm probability P is calculated based on the target false alarm probability P. f Calculate the decision threshold τ; finally, implement the detection decision: if Λ>τ, it is determined that there is a signal in the sub-band; if Λ>τ, it is determined that there is no signal in the sub-band.

2. The method for dynamic digital channelization blind sub-band detection based on eigenvalue difference analysis according to claim 1, characterized in that: This method uses the ratio of the difference between the maximum and minimum eigenvalues ​​of the subband signal sampling covariance matrix and the harmonic mean of all eigenvalues ​​to design the decision rule. The specific steps are: 1) Sample the subband signal to be detected to obtain the received sequence x(n), 0≤n≤Q-1, and use the resampling technology to construct the observation data matrix of M virtual channels Here Q = MN; 2) Calculate the sampling covariance matrix using the observation data matrix 3) Calculate the sampling covariance matrix All eigenvalues ​​of and are labeled as λ1>λ2>…>λ M ; 4) Calculate the difference between the maximum and minimum eigenvalues ​​α = λ1-λ M and the harmonic mean of all eigenvalues And calculate the test judgment amount 5) According to the target false alarm probability P f Calculate the decision threshold: Here F1 -1 () represents the inverse cumulative distribution function of the first-order Tracy-Widom distribution; 6) Detection judgment: If Λ>τ, it is determined that there is a signal in the sub-band; if Λ<τ, it is determined that there is no signal in the sub-band.

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