An array anti-jamming method applicable to large dynamic range desired signals

Abstract

The present invention discloses an array anti-jamming method applicable to large dynamic range desired signals, belonging to the technical field of array anti-jamming, and comprising the following steps: S1, performing FFT transformation on the received signal to obtain decomposed frequency domain sub-bands; S2, selecting sub-bands for interference estimation based on the spectral characteristics of the desired signal, and estimating the interference covariance matrix; S3, performing eigenvalue decomposition on the interference covariance matrix to estimate the number of interference sources and the DOA of the interference signals; S4, constructing an orthogonal space of the interference space on all sub-bands and performing orthogonal projection to eliminate interference. By adopting the above-mentioned array anti-jamming method applicable to large dynamic range desired signals, the present invention can effectively suppress interference signals while avoiding misidentifying the desired signal as interference, and can effectively reduce the loss of the desired signal.

Description

Technical Field

[0001] The present invention relates to the technical field of array anti-interference, and particularly to an array anti-interference method applicable to large dynamic range desired signals. Background Art

[0002] Adaptive array processing can effectively suppress interference signals in a certain direction and has been widely used in interference suppression of navigation receivers. However, when the dynamic range of the desired signal is large, the power of the desired signal may be higher than the power of the noise.

[0003] For the scenario where both the power of the interference signal and the power of the desired signal are higher than the power of the noise, the array anti-interference method based on power inversion will suppress the desired signal as interference, resulting in loss of the desired signal. To suppress interference from other directions in space while ensuring the gain of the desired signal, the Adaptive Digital Beamforming (ADBF) method is an option. However, this method requires the known Direction of Arrival (DOA) of the desired signal, and the prior knowledge of the DOA of the desired signal is usually difficult to obtain. Summary of the Invention

[0004] The object of the present invention is to provide an array anti-interference method applicable to large dynamic range desired signals. Based on the prior information that the desired signal is a spread spectrum signal with known spectral characteristics, this method utilizes the spectral characteristics of the desired signal, combines the idea of spatio-frequency adaptive processing, decomposes the received signal into frequency domain sub-bands through Fourier transform, estimates the interference by selecting the sub-bands corresponding to the "zero point" positions, and while effectively suppressing the interference signal, avoids misidentifying the desired signal as interference, and can effectively reduce the loss of the desired signal.

[0005] To achieve the above object, the present invention provides an array anti-interference method applicable to large dynamic range desired signals, including the following steps:

[0006] S1. Perform FFT transformation on the received signal to obtain the decomposed frequency domain sub-bands;

[0007] S2. Based on the spectral characteristics of the desired signal, select the sub-bands for interference estimation and estimate the covariance matrix;

[0008] The desired signal has a main lobe and side lobes within the sampling rate bandwidth. Among them, the amplitude of the main lobe is high, the amplitude of the side lobe is low, the connection between the main lobe and the side lobe is the frequency domain zero point, more than 95% of the energy of the desired signal is concentrated within the signal passband, and the power of the sub-band signal near the frequency domain zero point is low and only contains interference;

[0009] Select the sub-band corresponding to the zero point position in the frequency domain for interference estimation, avoid misidentifying the desired signal as interference, and reduce the impact on the desired signal;

[0010] S3. Perform eigenvalue decomposition on the covariance matrix to estimate the number of interference sources and the DOA of the interference signals;

[0011] S4. Construct the orthogonal space of the interference space on all sub-bands and perform orthogonal projection to eliminate the interference.

[0012] Preferably, in step S1, assume that the signal received by the m-th array element at time t is:

[0013]

[0014] where s0 is the desired signal received by the array, s1…s J are J interference signals; τ m,j is the time delay of the signal j on the m-th array element relative to the reference array element when receiving the signal from the incoming direction; n is Gaussian white noise; the range of m is 1 to M, and M is the number of array elements; Perform FFT transformation on the signal received by the m-th array element at time t to obtain:

[0015]

[0016]

[0017] where f n represents the frequency;

[0018] Merge the FFT results of the signals received by each array element and write them in matrix form to obtain:

[0019]

[0020] where,

[0021]

[0022]

[0023]

[0024]

[0025] and are the results after Fourier transformation of x m (t), s j (t) and n m (t) respectively; the elements in A(f n ) are the frequency domain representations of the time delays; L is the number of frequency domain snapshots; T represents transpose.

[0026] Preferably, in step S2, the estimated covariance matrix includes:

[0027] The covariance matrix of the array received signal at frequency f n is:

[0028]

[0029] where E represents the mean value and H represents the conjugate transpose;

[0030] The covariance matrix calculated using L frequency-domain snapshots is as:

[0031]

[0032] Denote the index corresponding to f n as N F , N F = 1, 2, …, N S , N S is the number of subbands after decomposition; the covariance matrix of the N F -th subband is expressed as:

[0033]

[0034] where is the steering vector of the signal, is the autocorrelation result of the signal, is the power of the frequency-domain noise signal, and I is the M-dimensional identity matrix.

[0035] Therefore, the present invention adopts the above-mentioned array anti-jamming method applicable to large dynamic range desired signals, and its technical effects are as follows:

[0036] (1) Overcome the drawback that the anti-jamming algorithm based on the Power Inverse criterion causes the loss of high signal-to-noise ratio desired signals and the limitation that the adaptive beamforming method requires the known arrival direction of the desired signal, and can suppress the interference from other directions in space while ensuring the gain of the desired signal.

[0037] (2) The method provided by the present invention can achieve the suppression of interference signals in the scenario of large dynamic range desired signals with limited improvement on the basis of the existing space-frequency anti-jamming technology.

[0038] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. Brief Description of the Drawings

[0039] Figure 1 It is a schematic diagram of the frequency-domain zero-point position of the spread spectrum signal;

[0040] Figure 2 The eigenvalue distribution under the selection of different sub - bands;

[0041] Figure 3 It is the variation of the eigenvalues of the desired signal with the input SNR under the selection of different sub - bands;

[0042] Figure 4 It is a schematic diagram of processing adjacent spectral peaks by selecting zero - point position data;

[0043] Figure 5 It is the FFT result in the frequency domain of each signal component before processing;

[0044] Figure 6 It is the FFT result in the frequency domain of each signal component after processing by the method of the present invention. Specific embodiments

[0045] The technical solution of the present invention will be further described below with reference to the drawings and embodiments.

[0046] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs.

[0047] Embodiment 1

[0048] As Figure 1 shown, since the desired signal is a direct - sequence spread - spectrum signal (hereinafter referred to as the spread - spectrum signal) and the spectral characteristics of the spread - spectrum signal are known information. According to the spectral characteristics of the spread - spectrum signal, it can be found that there are main lobes and side lobes in the sampling - rate bandwidth of the spread - spectrum signal. The main - lobe amplitude is relatively high, the side - lobe amplitude is relatively low, and the connection between the main lobe and the side lobe is the frequency - domain zero point. Considering that more than 95% of the energy of the desired signal is concentrated in the signal passband and the signal power in the sub - bands near the signal frequency - domain zero point is low, it can be approximately considered that only interference is included. We define these positions as "zero - point" positions, and select the sub - bands corresponding to these frequency - domain "zero - point" positions for interference estimation, which can avoid misidentifying the signal as interference, thereby reducing the impact on the desired signal.

[0049] Assume that the signal received by the m - th array element at time t is:

[0050]

[0051] where s0 is the desired signal received by the array, s1…s J are J interference signals; τ m,j is the time delay of the signal received by the m - th array element relative to the reference array element when the signal comes from the direction; n is Gaussian white noise. For the signal received by the m - th array element at time t, perform an FFT transformation to obtain:

[0052]

[0053]

[0054] The FFT results of the received signals of each array element are combined and written in the form of a matrix, obtaining:

[0055]

[0056] where

[0057]

[0058]

[0059]

[0060]

[0061] and are the results after Fourier transform of x m (t), s j (t) and n m (t) respectively; the elements in A(f n ) are the frequency-domain representations of time delays.

[0062] The covariance matrix of the array received signal at frequency f n is:

[0063]

[0064] The sampling covariance matrix is calculated using L frequency-domain snapshots and is:

[0065]

[0066] The index corresponding to f n is denoted as N F , N F = 1, 2, …, N S , and the covariance matrix of the N F -th subband is expressed as:

[0067]

[0068] where is the steering vector of the signal, is the autocorrelation result of the signal, is the power of the frequency-domain noise signal, and I is the M-dimensional identity matrix. The Gaussian white noise after FFT transformation still follows a uniform distribution in the frequency domain, and the frequency-domain amplitude becomes N s times the time-domain amplitude.

[0069] Perform eigen - decomposition on R(N F ), and the obtained eigenvalues are arranged in descending order as λ1≥λ2≥…≥λ M , and their corresponding eigen - vectors are v1, v2, …, v M , and we have:

[0070]

[0071] Select two sub - bands N1 and N2 for eigen - decomposition and compare and analyze the differences in their eigenvalues. N1 is the sub - band at the zero - point position, and N2 is the sub - band within the pass - band of the spread - spectrum signal. Assume that the incident signal includes two interference signals and one desired signal, the interference power is greater than the signal power, and the input SNR is 14 dB. Figure 2 For the eigenvalue distributions in different sub - band selection cases, it can be seen that the first two large eigenvalues come from two high - power interference signals, and the third eigenvalue comes from the desired signal. In the result of eigen - decomposition by selecting sub - band N2, the eigenvalue corresponding to the desired signal is significantly present, and then the corresponding eigen - vector will also be partitioned into the interference space, which will attenuate the desired signal in subsequent interference cancellation; compared with eigen - decomposition by selecting sub - band N2, when selecting sub - band N1 for eigen - decomposition, the component of the desired signal decreases, and its eigenvalue of the desired signal is close to the noise eigenvalue. Under the same desired - signal conditions, obviously, selecting sub - band N1 for interference estimation will obtain better results than selecting sub - band N2.

[0072] For further analysis, set the input SNR to vary in the range of 0 dB to 25 dB, and the two interference signals remain unchanged. Since the interference power is much greater than the desired - signal power, when the SNR varies within this range, λ3 always represents the eigenvalue of the desired signal. The variation of the eigenvalue λ3 corresponding to the desired signal with the input SNR in different sub - band selection cases is as Figure 2 shown. It can be seen that when selecting sub - band N2, the eigenvalue corresponding to the desired signal increases with the increase of the input SNR; when selecting sub - band N1, the eigenvalue corresponding to the desired signal changes little with the input SNR and is always less than the eigenvalue corresponding to the desired signal when selecting sub - band N2. Figure 3 shown, it can be seen that when selecting sub - band N2, the eigenvalue corresponding to the desired signal increases with the increase of the input SNR; when selecting sub - band N1, the eigenvalue corresponding to the desired signal changes little with the input SNR and is always less than the eigenvalue corresponding to the desired signal when selecting sub - band N2.

[0073] In the case of high SNR, to minimize the component of the desired signal in R(N F ), it is necessary to select the sub - band with the smallest amplitude in for interference estimation. By observing the spectrum of the spread - spectrum signal, these sub - bands are the sub - bands at the spread - spectrum zero - point positions. Numerically, the first zero - point frequency of the spread - spectrum signal in the single - side spectrum is equal to the reciprocal of the spread - spectrum code period 1 / T c , that is, the spread - spectrum code rate r c . Assume that there are a total of P zero - points, and the zero - point frequencies can be denoted as f ZP(p), there is

[0074] f ZP(p) = pr c p = 1, 2, …, P (12)

[0075] The sub - band containing the frequency - domain zero is denoted as N ZP(p) , because the sub - band needs to consider the bilateral spectrum, so in N ZP(p) p = ±1, ±2, …, ±P.

[0076] Within the sampling bandwidth, as long as the interference bandwidth covers the sub - band where the spread - spectrum zero is located, the covariance matrix calculated using this sub - band can contain the interference components, so as to correctly estimate the interference signal information. Using multiple spread - spectrum zero sub - bands for estimation can better capture the interference signal, thereby suppressing interference. Therefore, a covariance matrix can be constructed using multiple frequency - domain zero sub - bands within the receiver sampling rate range for source estimation and DOA estimation, and the data of the adjacent spectral peaks are processed with the results estimated at each zero position. The schematic diagram of selecting zero - position data to process adjacent spectral peaks is as Figure 4 shown. The horizontal axis of the coordinate axis represents the digital intermediate - frequency signal frequency. Interference estimation is performed at each zero point, and interference cancellation is performed on the sub - band between the two nearby peaks according to the obtained information, so that multi - frequency - point interference within the sampling bandwidth can be better processed.

[0077] Here, only one sub - band is used for interference signal estimation. Denote this sub - band as N ZP , and denote the corresponding covariance matrix as R ZP , there is:

[0078]

[0079] The estimate of the covariance matrix calculated using L snapshots is:

[0080]

[0081] For after performing eigen - decomposition, divide the eigen - space:

[0082]

[0083] The larger D eigenvalues and the corresponding eigen - vectors form Λ SI and U SI , Λ SI = diag(λ1, λ2, …, λ D ), U SI = [v1, v2, …, v D , representing the signal and interference space; the smaller M - D eigenvalues and the corresponding eigen - vectors form Λ N and U N , ΛN = diag(λ D+1 , …, λ M ), U N = [v D+1 , …, v M , representing the noise space. Determining the value of D is the process of partitioning the signal subspace and the noise subspace. Commonly used partitioning criteria include the Akaike information criterion or the minimum description length criterion. This step is called the number of sources estimation.

[0084] Apply the minimum description length criterion for the number of sources estimation, and find the D that minimizes the following formula. D is the number of sources:

[0085]

[0086] Next, use the MUSIC algorithm for two-dimensional DOA estimation. The MUSIC spectrum represents the orthogonality between the steering vector and the noise space, and its expression is:

[0087]

[0088] where is the search steering vector. When , the orthogonality with U N is maximized, obtains the maximum value, and thus the direction of arrival of the estimated signal However, MUSIC requires a full-dimensional search, and the computational complexity is too high. Root-MUSIC is a method that uses polynomial root finding to replace the search process. Compared with MUSIC, it can reduce the computational complexity by more than half. The root-finding formula of Root-MUSIC is:

[0089]

[0090] For the convenience of root-finding calculation, rewrite the steering vector to be found according to the X-axis direction and the Y-axis direction in the form of , and there is:

[0091]

[0092] Set the and terms in to v, and the term to u. The equivalent number of array elements in the X and Y axis directions are M X and M Y , respectively. Then the steering vectors in these two directions are respectively expressed as:

[0093]

[0094]

[0095] Let \(z_1 = e\) j2πdu / λ , \(z_2 = e\) j2πdv / λ , simplifying the quadratic formula gives:

[0096]

[0097]

[0098] Solving the above equation, the obtained estimates are respectively:

[0099]

[0100]

[0101] Since the order of the estimated and does not conform to the original angular relationship, matching is still required. The cost function \(\Theta\) is constructed as:

[0102]

[0103] where \(D\) and need to be substituted into \(a\) X and \(a\) Y in turn, and the cost function is calculated \(D\) 2 times. Taking the combination of the first \(D\) minimum values, the original and matching relationship is obtained. The obtained DOA results:

[0104]

[0105]

[0106] The incident directions of \(D\) signals are obtained through two-dimensional DOA estimation To suppress interference, the steering vectors corresponding to the sub-band frequencies are constructed according to the DOA estimation results on all sub-bands Then, take the of the \(D\) directions to be suppressed and construct There is:

[0107]

[0108] According to the properties of the eigen-space, the projection matrix of the orthogonal complement space of the interference subspace is expressed as:

[0109]

[0110] Then for After performing projection processing, we have:

[0111]

[0112] For Y f After performing IFFT processing, it is restored to the time-domain signal after interference suppression and then subsequent signal processing is carried out.

[0113] Next, the effectiveness of the method proposed in the present invention is verified by Matlab simulation. The array model uses a 4-element circular array with a radius of half a wavelength. The carrier frequency of the desired signal is 1575.42 MHz, the code rate is 10.23 Mcps, the incident azimuth angle and elevation angle are both 10°, and the signal-to-noise ratio is 20 dB. A single-interference incident scenario is set, the interference signal is a random phase-modulated broadband interference with a center frequency of 1575.42 MHz, and the incident direction θ = 25°, and the interference-to-noise ratio is 100 dB. Figure 5 The frequency-domain FFT results of each signal component before processing are given. Figure 6 The frequency-domain FFT results of each signal component after being processed by the present method are given.

[0114] It can be seen that after anti-interference processing, the interference signal is effectively suppressed, and at the same time, the desired signal still maintains a high signal-to-noise ratio.

[0115] Therefore, the present invention adopts the above-mentioned array anti-interference method applicable to desired signals with a large dynamic range. Based on the prior information that the desired signal is a spread-spectrum signal with known spectral characteristics, this method utilizes the spectral characteristics of the desired signal, combines the idea of space-frequency adaptive processing, decomposes the received signal into frequency-domain sub-bands through Fourier transform, estimates the interference by selecting the sub-bands corresponding to the "zero point" positions, and while effectively suppressing the interference signal, avoids misidentifying the signal as interference, and can effectively reduce the loss of the desired signal.

[0116] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An array anti-interference method applicable to large dynamic range desired signals, characterized in that, It includes the following steps: S1. Perform FFT transformation on the received signal to obtain the decomposed frequency-domain subbands; S2. Based on the spectral characteristics of the desired signal, select the subbands for interference estimation and estimate the covariance matrix; The desired signal has a main lobe and side lobes within the sampling rate bandwidth. Among them, the main lobe has a high amplitude and the side lobe has a low amplitude. The connection between the main lobe and the side lobe is the frequency-domain zero point. More than 95% of the energy of the desired signal is concentrated within the signal passband. The power of the subband signal near the frequency-domain zero point is low and only contains interference; Select the subband corresponding to the frequency-domain zero point position for interference estimation to avoid misidentifying the desired signal as interference and reduce the impact on the desired signal; S3. Perform eigenvalue decomposition on the covariance matrix to estimate the number of interference sources and the DOA of the interference signal; S4. Construct the orthogonal space of the interference space on all subbands and perform orthogonal projection to eliminate the interference; In step S1, assume that the signal received by the m th array element at t moment is: ； Among them, is the desired signal received by the array, is interference signals; is the signal received from the direction of arrival at the th array element time delay relative to the reference array element; is Gaussian white noise; m ranges from 1 to M , M is the number of array elements; Perform FFT transformation on the signal received by the th array element at time, and obtain: ； Among them, represents the frequency; Merge the FFT results of the received signals of each array element and write them in matrix form to obtain: ； Where, ； ； ； ； , and are respectively , and after Fourier transform; The elements in are the frequency domain representation of time delay; L is the number of frequency domain snapshots; T represents transpose; In step S2, estimating the covariance matrix includes: The covariance matrix of the array received signal at the frequency is as follows: ； Among them, represents the mean value, represents the conjugate transpose; Utilize frequency-domain snapshots to calculate the covariance matrix as follows: ； Denote the corresponding index as , , where is the number of subbands after decomposition; the covariance matrix of the ； Among them, is the steering vector of the desired signal or interference signal, is the autocorrelation result of the signal, is the power of the frequency-domain noise signal, is an identity matrix of dimension.

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