Virtual multi-channel interference suppression method for antenna array

Abstract

The invention discloses a virtual multi-channel interference suppression method for an antenna array, and belongs to the field of array signal processing. According to the invention, the problem that the interference suppression capability is reduced when a traditional method faces a novel interference scene is solved. The method comprises the following steps: firstly, analyzing a received signal by using a MUSIC algorithm to obtain an interference number, and estimating an angle of arrival of an expected signal and an interference signal; secondly, generating weights of each interference channel and each auxiliary channel, and obtaining a cancellation angle iteration initial value on the basis; using a Newton method to iteratively update cancellation angles of all interferences at all sampling points and refine an angle of arrival of a desired signal; and finally, calculating cancellation factors of all interferences at all sampling points to complete interference cancellation. The method has the capability of suppressing related interference, can adapt to interference of different intensities, can tolerate angle estimation errors of the MUSIC algorithm, and can calculate offset factors at all sampling moments through a few parameters so as to resist mobile interference. The method can be applied to suppression of interference signals.

Description

Technical Field

[0001] The present invention belongs to the field of array signal processing, and particularly relates to a method for suppressing interference in virtual multi-channels of an antenna array. Background Art

[0002] As a milestone in the development of spatial domain adaptive anti-jamming technology, Capon beamforming defines the upper bound of the interference suppression ability of multi-antenna receivers. However, due to its dependence on statistical characteristics, it cannot be realized in actual scenarios. The sampling matrix inversion method uses the outer product matrix of the received signals to approximate the autocorrelation matrix, completing the transformation from theory to application. However, when there is a model mismatch, the performance will decline. On this basis, a series of interference suppression methods based on the reconstruction of the interference-noise covariance matrix have emerged one after another. Combining subspace projection and steering vector estimation technologies, etc., has greatly improved the robustness in the case of interference parameter estimation errors. However, its processing logic centered on the covariance matrix makes the suppression ability poor in the face of multiple interferences and strong interferences. Null broadening and its extended methods form nulls within a certain spatial range to effectively resist moving interferences, but at the cost of more degrees of freedom. When there are multiple interference sources in space, a larger-scale array needs to be used for suppression, increasing the economic burden. The subsequent development of 5G and 6G related technologies has made the interferences faced by communication systems present new characteristics such as complexity, dynamics, and unknownness. Traditional beamforming anti-jamming methods show a large decline in performance in the face of new interference scenarios. Summary of the Invention

[0003] The purpose of the present invention is to solve the problem of the decline in interference suppression ability of traditional methods in the face of new interference scenarios, and a method for suppressing interference in virtual multi-channels of an antenna array is proposed.

[0004] The technical solution adopted by the present invention to solve the above technical problems is:

[0005] Based on one aspect of the present invention, a method for suppressing interference in virtual multi-channels of an antenna array, the method specifically includes the following steps:

[0006] Step 1: N receiving antennas in the antenna array are arranged in a uniform linear array. The N receiving antennas respectively receive analog signals from free space, and the received signals respectively pass through each radio frequency processing link to form N digital sequences.

[0007] Step 2: Integrate the N digital sequences formed in Step 1: Summarize the data of the N receiving antennas at L consecutive sampling points into a received data unit matrix r with N rows and L columns.

[0008] Step 3: Use the multiple signal classification algorithm to analyze the received data unit matrix r to obtain the number of signals M total existing in space, the intensity of each signal, and the arrival angle of each signal;

[0009] Step 4: Consider the signal with the weakest strength in the space as the desired signal, and consider the remaining signals in the space as interference signals, that is, the number of interference signals M = M total – 1. Denote the arrival angle of the desired signal estimated by the multiple signal classification algorithm as Denote the arrival angles of each interference signal estimated by the multiple signal classification algorithm as

[0010] Step 5: Obtain the angle ambiguity region Θ of the desired signal according to the empirical value Δ of the arrival angle estimation error and the arrival angle of the desired signal estimated by the multiple signal classification algorithm s , and obtain the angle ambiguity region Θ of the interference signal according to the empirical value Δ of the arrival angle estimation error and the arrival angles of each interference signal estimated by the multiple signal classification algorithm j ;

[0011] Step 6: Determine the number of processing channels M p = 2M + 1. The processing channels include 1 desired signal channel, M interference channels and M auxiliary channels;

[0012] Step 7: Initialize the calculation dimension U of the steering vector d = N, and set the maximum deviation factor f of the auxiliary channel p ;

[0013] Step 8: Initialize the deviation factor C of the current auxiliary channel p = 0;

[0014] Step 9: Initialize the processing angles θ f1 , θ f2 , …, θ fM of the M auxiliary channels as:

[0015]

[0016] Step 10: Set the index i of the current interference channel and the auxiliary channel to 1;

[0017] Step 11: Modify the processing angle of the i-th auxiliary channel to:

[0018] θ fi = θ fi + ε

[0019] where ε represents the angle step of the auxiliary channel;

[0020] Step 12: Divide the U d -dimensional steering vector of the arrival angle of the i-th interference signal estimated by the multiple signal classification algorithm by U d , and use the obtained quotient as the weight w ji of the i-th interference channel;

[0021]

[0022] Among them, the superscript "T" represents matrix transpose, e is the base of the natural logarithm, j in the exponent of e is the imaginary unit, and π is the circumference ratio;

[0023] Step thirteen: Divide the U-dimensional steering vector of the processed angle of the i-th auxiliary channel by U d and use the obtained quotient as the weight w of the i-th auxiliary channel d ; fi

[0024]

[0025] Step fourteen: Compare the relative magnitudes of U d and N;

[0026] If U d = N, then execute step fifteen;

[0027] Otherwise, execute step sixteen;

[0028] Step fifteen: Store the weight of the i-th interference channel calculated in step twelve, and then execute step sixteen;

[0029] Step sixteen: Calculate and store the output signal r of the current i-th interference channel and the output signal r of the i-th auxiliary channel according to the weight of the i-th interference channel calculated in step twelve, the weight of the i-th auxiliary channel calculated in step thirteen, and the received data unit matrix r ji and the output signal r of the i-th auxiliary channel fi ;

[0030] Step seventeen: Compare the magnitudes of i and the number of interference signals M;

[0031] If i = M, execute step eighteen, otherwise let i = i + 1 and return to execute step eleven;

[0032] Step eighteen: Calculate the feasible solution of the initial value of the cancellation angle according to r ji and r fi ;

[0033] If the number of feasible solutions is equal to M, then directly use the feasible solutions as the iterative initial values of the M interference center angles to execute step twenty-three;

[0034] If the number of feasible solutions is greater than M, then screen the feasible solutions, and the selected feasible solutions form the optional set Θ of the initial values of the cancellation angles D , and then execute step nineteen;

[0035] Step nineteen: Judge the optional set Θ of the initial values of the cancellation angles D ​Whether the number of elements in it is equal to M;

[0036] If the optional set Θ of the initial cancellation angle D in which the number of elements is equal to M, then the optional set Θ of the initial cancellation angle D in which the elements are the initial iteration values of the M interference center angles Then execute Step 23;

[0037] Otherwise, if the optional set Θ of the initial cancellation angle D in which the number of elements is not equal to M, then execute Step 20;

[0038] Step 20. Let the current auxiliary channel deviation factor C p = C p + 1;

[0039] Step 21. Judge the magnitude relationship between C p and f p – 1;

[0040] If C p > f p – 1, then execute Step 22;

[0041] Otherwise, return to execute Step 10;

[0042] Step 22. Let the steering vector calculation dimension U d = U d – 1, and return to execute Step 8;

[0043] Step 23. Read the output signals of the M interference channels and the output signals of the M auxiliary channels stored, and combine the initial iteration values to calculate the center angle θ of each interference j1 , θ j2 , …, θ jM and the angular velocities ω1, ω2, …, ω M ;

[0044] Step 24. Based on the center angle θ of each interference j1 , θ j2 , …, θ jM and the angular velocities ω1, ω2, …, ω M calculate the cancellation angle matrix of all interferences at L sampling moments;

[0045]

[0046] Among them, the cancellation angle θ of the mth interference at the lth sampling moment jm,l is:

[0047] θ jm,l = θ jm+ω m l, m = 1, 2, …, M, l = 1, 2, …, L

[0048] Step twenty-five: Read the weights of the M interference channels stored and the arrival angle of the desired signal estimated by the multiple signal classification algorithm in Step four Use the received data unit matrix r in Step two and the cancellation angles at L sampling moments to calculate the refined arrival angle of the desired signal

[0049] Step twenty-six: Use the refined arrival angle of the desired signal Divide the N-dimensional steering vector by N, and use the obtained quotient as the weight w of the desired signal channel s ;

[0050]

[0051] Step twenty-seven: Calculate the cancellation factors of each interference at L sampling points according to the cancellation angles at L sampling moments in Step twenty-four, the weight of the desired signal channel in Step twenty-six, and the weights of the interference channels stored in Step fifteen

[0052] Step twenty-eight: Output the signal y after interference cancellation according to the cancellation factors obtained in Step twenty-seven, the weight of the desired signal channel in Step twenty-six, the weights of the interference channels stored in Step fifteen, and the received data unit matrix r in Step two

[0053] Based on another aspect of the present invention, an antenna array virtual multi-channel interference suppression method, the method specifically includes the following steps:

[0054] Step one: N receiving antennas in the antenna array are arranged in a uniform linear array. The N receiving antennas respectively receive analog signals from free space, and the received signals respectively pass through each radio frequency processing link to form N digital sequences

[0055] The radio frequency processing link includes a low-noise amplifier, a down-converter, and an analog-to-digital converter

[0056] Step two: Integrate the N digital sequences formed in Step one: Summarize the data of the N receiving antennas at L consecutive sampling points into a received data unit matrix r with N rows and L columns

[0057] Step three: Use the multiple signal classification algorithm to analyze the received data unit matrix r to obtain the number M of signals existing in space total , the intensity of each signal and the arrival angle of each signal

[0058] Step four: Regard the signal with the weakest intensity in space as the desired signal, and regard the remaining signals in space as interference signals, that is, the number of interference signals M = M total–1, denote the arrival angle of the desired signal estimated by the multiple signal classification algorithm as Denote the arrival angles of each interfering signal estimated by the multiple signal classification algorithm as

[0059] Step Five: Obtain the angle ambiguity region Θ of the desired signal according to the empirical value Δ of the arrival angle estimation error and the arrival angle of the desired signal estimated by the multiple signal classification algorithm s , and obtain the angle ambiguity region Θ of the interfering signal according to the empirical value Δ of the arrival angle estimation error and the arrival angles of the interfering signals estimated by the multiple signal classification algorithm j ;

[0060]

[0061] Step Six: Determine the number of processing channels M according to the number of interfering signals M p = 2M + 1, and the processing channels include 1 desired signal channel, M interfering channels, and M auxiliary channels;

[0062] Step Seven: Initialize the dimension U for calculating the steering vector d = N, and set the maximum deviation factor f of the auxiliary channels p ;

[0063] Step Eight: Initialize the deviation factor C of the current auxiliary channel p = 0;

[0064] Step Nine: Initialize the processing angles θ of the M auxiliary channels f1 , θ f2 , …, θ fM are:

[0065]

[0066] Step Ten: Set the index i of the current interfering channel and the auxiliary channels to 1;

[0067] Step Eleven: Modify the processing angle of the i-th auxiliary channel to:

[0068] θ fi = θ fi + ε

[0069] where ε represents the angle step of the auxiliary channel;

[0070] Step Twelve: Divide the U d -dimensional steering vector of the arrival angle of the i-th interfering signal estimated by the multiple signal classification algorithm by U d , and use the obtained quotient as the weight w of the i-th interfering channel ji ;

[0071]

[0072] Among them, the superscript "T" represents matrix transpose, e is the base of the natural logarithm, j in the exponent of e is the imaginary unit, and π is the circumference ratio;

[0073] Step Thirteen: Divide the modified U of the processing angle of the i-th auxiliary channel by U d and use the obtained quotient as the weight w of the i-th auxiliary channel d ; fi ;

[0074]

[0075] Step Fourteen: Compare the relative magnitudes of U d and N;

[0076] If U d = N, then execute Step Fifteen;

[0077] Otherwise, execute Step Sixteen;

[0078] Step Fifteen: Store the weight of the i-th interference channel calculated in Step Twelve, and then execute Step Sixteen;

[0079] Step Sixteen: Calculate and store the output signal r of the current i-th interference channel and the output signal r of the i-th auxiliary channel according to the weight of the i-th interference channel calculated in Step Twelve, the weight of the i-th auxiliary channel calculated in Step Thirteen, and the received data unit matrix r ji and the output signal r of the i-th auxiliary channel fi ;

[0080] Step Seventeen: Compare the magnitudes of i and the number of interference signals M;

[0081] If i = M, execute Step Eighteen, otherwise let i = i + 1 and return to execute Step Eleven;

[0082] Step Eighteen: Calculate the feasible solution of the initial value of the cancellation angle according to r ji and r fi ;

[0083] If the number of feasible solutions is equal to M, directly use the feasible solutions as the iterative initial values of the M interference center angles to execute Step Twenty-three;

[0084] If the number of feasible solutions is greater than M, screen the feasible solutions, and the selected feasible solutions form the optional set Θ of the initial values of the cancellation angles D , and then execute Step Nineteen;

[0085] Step Nineteen: Determine whether the number of elements in the optional set Θ of the initial values of the cancellation angles D is equal to M;

[0086] If the number of elements in the optional set Θ of the cancellation angle initial value is equal to M, output M interference center angles θ D , θ j1 , θ j2 , …, θ jM , and then execute Step 23;

[0087] Otherwise, execute Step 20;

[0088] Step 20: Let the current auxiliary channel deviation factor C p = C p + 1;

[0089] Step 21: Judge the magnitude relationship between C p and f p – 1;

[0090] If C p > f p – 1, then execute Step 22;

[0091] Otherwise, return to Step 10;

[0092] Step 22: Let the steering vector calculation dimension U d = U d – 1, and return to execute Step 8;

[0093] Step 23: Set the angular velocities ω1, ω2, …, ω of each interference M to be all 0;

[0094] Step 24: Based on each interference center angle output in Step 19 and the angular velocities of each interference set in Step 23, obtain the cancellation angle matrix of all interferences at L sampling moments:

[0095]

[0096] Where:

[0097] θ jm,l = θ jm + ω m l, m = 1, 2, …, M; l = 1, 2, …, L

[0098] Step 25: Read the weights of the M interference channels stored and the arrival angle of the desired signal estimated by the multiple signal classification algorithm in Step 4 Use the received data unit matrix r in Step 2 and the cancellation angles at L sampling moments to calculate the refined arrival angle of the desired signal

[0099] Step 26: Divide the N-dimensional steering vector of the refined arrival angle of the desired signal by N, and use the obtained quotient as the weight w of the desired signal channels ;

[0100]

[0101] Step twenty-seven: Calculate the cancellation factor of each interference at L sampling points according to the cancellation angles at L sampling moments in Step twenty-four, the desired signal channel weights in Step twenty-six, and the interference channel weights stored in Step fifteen.

[0102] Step twenty-eight: Output the signal y after interference cancellation according to the cancellation factors obtained in Step twenty-seven, the desired signal channel weights in Step twenty-six, the interference channel weights stored in Step fifteen, and the received data unit matrix r in Step two.

[0103] The beneficial effects of the present invention are as follows:

[0104] The present invention first uses the MUSIC algorithm to analyze the received signal to obtain the number of interferences and estimate the arrival angles of the desired signal and the interference signals; secondly, generate the weights of each interference channel and the auxiliary channel, and on this basis, obtain the initial value of the cancellation angle iteration; then use the Newton method to iteratively update the cancellation angles of all interferences at all sampling points and refine the arrival angle of the desired signal; finally, calculate the cancellation factors of all interferences at all sampling points to complete the interference cancellation. The method of the present invention decouples the signal from the interference and has the ability to suppress relevant interferences; at the same time, it does not use the statistical property of the autocorrelation matrix to achieve superior suppression performance with a small number of sampling points; in addition, the present invention includes a cancellation factor calculation process with controllable precision and a desired signal arrival angle refinement process, which can adapt to different intensity interferences and tolerate the angle estimation error of the MUSIC algorithm; the method of the present invention uses a suitable motion model to calculate the cancellation factors at each sampling moment through a small number of parameters, thereby counteracting the moving interference. The method of the present invention can construct a multi-channel parallel digital processing channel for joint processing by utilizing the increasingly rich computing power resources on the premise of keeping the original hardware configuration unchanged, and has the characteristic of maintaining the adaptive robust suppression effect in complex and dynamic interference scenarios, and is applicable to the new interference situation in the post-5G and 6G eras. Description of the Drawings

[0105] Figure 1 is a schematic diagram of the signal model of an antenna array virtual multi-channel interference suppression method of the present invention;

[0106] Figure 2 is a functional block diagram of an antenna array virtual multi-channel interference suppression method of the present invention;

[0107] Figure 3 is a working flowchart of an antenna array virtual multi-channel interference suppression method of the present invention;

[0108] Figure 4It is the flow chart of the iterative solution of the interference center angle and angular velocity in the present invention;

[0109] Figure 5 It is the flow chart of the iterative refinement of the arrival angle of the desired signal in the present invention;

[0110] Figure 6 It is the simulation performance diagram of the first specific implementation manner of the virtual multi-channel interference suppression method for an antenna array in the present invention;

[0111] Among them, the arrival angle of the desired signal is 0°, the number of interferences is 4, the arrival angles of the interference signals are 25°, -30°, 35° and -50° respectively, the moving speeds are 0.002° / sampling point, -0.001° / sampling point, 0.0006° / sampling point and 0.0008° / sampling point respectively, and each interference is 40 dB stronger than the desired signal;

[0112] Figure 7 It is the simulation performance diagram of the tenth specific implementation manner of the virtual multi-channel interference suppression method for an antenna array in the present invention;

[0113] Among them, the arrival angle of the desired signal is 0°, the number of interferences is 2, the arrival angles of the interference signals are 25° and -30° respectively, both of which are static interferences and both are 40 dB stronger than the desired signal. Specific implementation manner

[0114] Specific implementation manner one: Combine Figures 1 to 3 to illustrate this implementation manner. The virtual multi-channel interference suppression method for an antenna array described in this implementation manner specifically includes the following steps:

[0115] Step one: As Figure 1 shown, N receiving antennas in the antenna array are arranged in a uniform linear array (N>1, the spacing between adjacent two receiving antennas is λ / 2, λ represents the wavelength of the electromagnetic wave used for communication), select element 1 as the reference element, stipulate that the incident angle on the right side of the normal is positive and the incident angle on the left side of the normal is negative, and N receiving antennas respectively receive analog signals from free space. The received signals respectively pass through each radio frequency processing link to form N digital sequences;

[0116] Step two: Integrate the N digital sequences formed in step one: Summarize the data of N receiving antennas at consecutive L sampling points into a received data unit matrix r with N rows and L columns. Among them, the element in the nth row and the lth column of the received data unit matrix r represents the received data of the nth receiving antenna at the lth sampling point (1≤n≤N, 1≤l≤L);

[0117] The data of N receiving antennas continuously enter. The receiving end divides every L sampling points into a received data unit matrix, and the same processing method is adopted for each received data unit matrix;

[0118] Step 3. Analyze the received data unit matrix r using the Multiple Signal Classification (MUSIC) algorithm to obtain the number of signals M existing in the space total , the intensity of each signal, and the arrival angle of each signal; the present invention is applicable to the case where M total does not exceed N;

[0119] Step 4. Regard the signal with the weakest intensity in the space as the Signal Of Interest (SOI), and regard the remaining signals in the space as interference signals, that is, the number of interference signals M = M total –1, denote the arrival angle of the desired signal estimated by the multiple signal classification algorithm as Denote the arrival angles of each interference signal estimated by the multiple signal classification algorithm as The present invention is applicable to the case where the number of desired signals is 1;

[0120] Step 5. Obtain the angle ambiguity region Θ of the desired signal according to the empirical value Δ of the arrival angle estimation error and the arrival angle of the desired signal estimated by the multiple signal classification algorithm s , and obtain the angle ambiguity region Θ of the interference signal according to the empirical value Δ of the arrival angle estimation error and the arrival angles of each interference signal estimated by the multiple signal classification algorithm j ;

[0121] Step 6. Determine the number of processing channels M p = 2M + 1, the processing channels include 1 desired signal channel, M interference channels, and M auxiliary channels;

[0122] Step 7. Initialize the guiding vector calculation dimension U d = N, set the maximum deviation factor f of the auxiliary channel p (f p is an integer not less than 1);

[0123] Step 8. Initialize the deviation factor C of the current auxiliary channel p = 0;

[0124] Step 9. Initialize the processing angles θ of M auxiliary channels f1 , θ f2 , …, θ fM are:

[0125]

[0126] Step 10. Set the current interference channel and auxiliary channel index i = 1;

[0127] Step 11. Modify the processing angle of the i-th auxiliary channel to:

[0128] θ fi = θ fi + ε

[0129] where ε represents the angular step of the auxiliary channel;

[0130] Step Twelve: Divide the U-dimensional steering vector of the arrival angle of the i-th interference signal estimated by the multiple signal classification algorithm by U d and use the obtained quotient as the weight w of the i-th interference channel d , and the dimension of w ji is U ji × 1; d ×1;

[0131]

[0132] where the superscript "T" represents matrix transpose, e is the base of the natural logarithm, j in the exponent of e is the imaginary unit, and π is the circumference ratio;

[0133] Step Thirteen: Divide the U-dimensional steering vector of the processed angle of the i-th auxiliary channel after modification by U d and use the obtained quotient as the weight w of the i-th auxiliary channel d , and the dimension of w fi is U fi × 1; d ×1;

[0134]

[0135] Step Fourteen: Compare the relative magnitudes of U d and N;

[0136] If U d = N, then execute Step Fifteen;

[0137] Otherwise, execute Step Sixteen;

[0138] Step Fifteen: Store the weight of the i-th interference channel calculated in Step Twelve (if there is already relevant storage, update the stored result), and then execute Step Sixteen;

[0139] Step Sixteen: Calculate and store the output signal r of the current i-th interference channel and the output signal r of the i-th auxiliary channel based on the weight of the i-th interference channel calculated in Step Twelve, the weight of the i-th auxiliary channel calculated in Step Thirteen, and the received data unit matrix r ji and the output signal r of the i-th auxiliary channel fi ;

[0140] Step Seventeen: Compare the magnitudes of i and the number of interference signals M;

[0141] If i = M, execute Step Eighteen; otherwise, let i = i + 1 and return to execute Step Eleven.

[0142] Step Eighteen: Calculate the feasible solutions for the initial value of the cancellation angle according to r ji and r fi .

[0143] If the number of feasible solutions is equal to M, directly use the feasible solutions as the iterative initial values of the M interference center angles to execute Step Twenty - Three.

[0144] If the number of feasible solutions is greater than M, screen the feasible solutions, and the screened feasible solutions form the optional set Θ of the initial value of the cancellation angle D , and then execute Step Nineteen.

[0145] Step Nineteen: Determine whether the number of elements in the optional set Θ of the initial value of the cancellation angle D is equal to M.

[0146] If the number of elements in the optional set Θ of the initial value of the cancellation angle D is equal to M, the elements in the optional set Θ of the initial value of the cancellation angle D are the iterative initial values of the M interference center angles and then execute Step Twenty - Three.

[0147] Otherwise, if the number of elements in the optional set Θ of the initial value of the cancellation angle D is not equal to M, execute Step Twenty.

[0148] Step Twenty: Let the current auxiliary channel deviation factor C p = C p + 1.

[0149] Step Twenty - One: Determine the magnitude relationship between C p and f p – 1.

[0150] If C p > f p – 1, execute Step Twenty - Two.

[0151] Otherwise, return to execute Step Ten.

[0152] Step Twenty - Two: Let the steering vector calculation dimension U d = U d – 1, and return to execute Step Eight.

[0153] Step Twenty - Three: Read the output signals of the M interference channels and the output signals of the M auxiliary channels stored, and combine the iterative initial values to calculate the central angle θ j1 of each interference, θ j2,…, θ jM with angular velocities ω1, ω2, …, ω M ;

[0154] Step Twenty - Four: Based on the central angles θ j1 , θ j2 , …, θ jM with angular velocities ω1, ω2, …, ω M Calculate the cancellation angle matrix of all interferences at L sampling moments;

[0155]

[0156] where the cancellation angle θ jm,l for the m - th interference at the l - th sampling moment is:

[0157] θ jm,l = θ jm + ω m l, m = 1, 2, …, M, l = 1, 2, …, L

[0158] Step Twenty - Five: Read the weights of the M interference channels stored and the arrival angle of the desired signal estimated by the multi - signal classification algorithm in Step Four Use the received data unit matrix r in Step Two and the cancellation angles at L sampling moments to calculate the refined arrival angle of the desired signal

[0159] Step Twenty - Six: Divide the N - dimensional steering vector of the refined arrival angle of the desired signal by N, and use the obtained quotient as the weight w of the desired signal channel , w s , w s whose dimension is N×1;

[0160]

[0161] Step Twenty - Seven: Calculate the cancellation factor of each interference at L sampling points according to the cancellation angles at L sampling moments in Step Twenty - Four, the weight of the desired signal channel in Step Twenty - Six, and the weights of the interference channels stored in Step Fifteen;

[0162] Step Twenty - Eight: Output the signal y after interference cancellation according to the cancellation factors obtained in Step Twenty - Seven, the weight of the desired signal channel in Step Twenty - Six, the weights of the interference channels stored in Step Fifteen, and the received data unit matrix r in Step Two.

[0163] The interference suppression method of this embodiment can combat dynamic interferences or scenarios where it is unknown whether the interference is dynamic.

[0164] Embodiment 2: The difference between this embodiment and Embodiment 1 is that a low-noise amplifier, a downconverter, and an analog-to-digital converter are included in the radio frequency processing link.

[0165] Other steps and parameters are the same as those in Embodiment 1.

[0166] The radio frequency processing link is used to perform low-noise amplification, downconversion, and analog-to-digital conversion on the received signal in sequence.

[0167] Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is that the specific process of Step 5 is as follows:

[0168]

[0169] Other steps and parameters are the same as those in Embodiment 1 or 2.

[0170] Embodiment 4: The difference between this embodiment and any one of Embodiments 1 to 3 is that the specific process of Step 16 is as follows:

[0171]

[0172] Among them, the superscript "H" represents the conjugate transpose of the matrix.

[0173] Other steps and parameters are the same as any one of Embodiments 1 to 3.

[0174] The output signals of the current i-th interference channel and the output signals of the i-th auxiliary channel are both 1×L in dimension. If there is relevant storage, update the storage result.

[0175] Embodiment 5: The difference between this embodiment and any one of Embodiments 1 to 4 is that the specific process of Step 18 is as follows:

[0176] Step A1: Read the output signals of the stored M interference channels and construct an interference channel waveform correlation matrix R of M rows and M columns:

[0177]

[0178] Step A2: Read the output signals of the stored M interference channels and the output signals of the M auxiliary channels, and construct an auxiliary channel waveform and interference channel waveform correlation vector R of M rows and 1 column f :

[0179]

[0180] Step A3: Calculate M initial auxiliary cancellation factors k according to the matrix R and the vector R f : fm :

[0181]

[0182] Among them, R m is the new matrix formed by replacing the m-th column of matrix R with vector R f ; det(·) represents calculating the determinant of the matrix.

[0183] Step A4: Construct an equation about the initial value θ of the cancellation angle according to the initial auxiliary cancellation factor:

[0184]

[0185] In the formula, the superscript "n" represents the n-th power of the value, and there is:

[0186]

[0187] Solve the equation about the initial value θ of the cancellation angle to obtain all U d -1 feasible solutions of the initial value of the cancellation angle;

[0188] If U d -1 is equal to M, directly execute Step Twenty-three;

[0189] If U d -1 is greater than M, execute Step A5;

[0190] Step A5: Screen out the initial values of the cancellation angles within the interference angle ambiguity region Θ j from all the feasible solutions calculated in Step A4. The screened initial values of the cancellation angles form an optional set Θ D .

[0191] Other steps and parameters are the same as those in any one of the specific embodiments one to four.

[0192] Specific Embodiment Six: Combine Figure 4 to illustrate this embodiment. The difference between this embodiment and any one of the specific embodiments one to five is that Step Twenty-three adopts Newton's method for iterative calculation, and the specific process is as follows:

[0193] Step 1: Initialize the current iteration number i = 0, and initialize the initial values of the angular velocity iteration to be all 0, set the expected suppression capabilities for M interference signals to be x1dB, x2dB,..., x M dB respectively, set the stop angle threshold thre and the maximum iteration number iter1;

[0194] Step 2: Solve the instantaneous angles of each interference signal at L sampling point moments by using the uniform angular velocity change model:

[0195]

[0196] where, θ jml represents the instantaneous angle of the m-th interference signal at the l-th sampling point time;

[0197] Step 3: Based on the arrival angles of each interference signal estimated by the multiple signal classification algorithm in Step 4 and the instantaneous angle θ of each interference signal at L sampling point times jml , construct the zero-order matrix of the interference channel at L sampling point times, and the dimension of the zero-order matrix of the interference channel at each sampling time among the L sampling point times is M×M;

[0198]

[0199] where, represents the zero-order matrix of the interference channel at the l-th sampling point time;

[0200] The intermediate variable q jαβ,l is:

[0201]

[0202] Step 4: Based on the updated processing angles of each auxiliary channel in Step 11 and the instantaneous angle θ of each interference signal at L sampling point times jml , construct the zero-order vector of the auxiliary channel at L sampling point times, and the dimension of the zero-order vector of the auxiliary channel at each sampling time among the L sampling point times is M×1;

[0203]

[0204] where, represents the zero-order vector of the auxiliary channel at the l-th sampling point time;

[0205] The intermediate variable q fαβ,l is:

[0206]

[0207] Step 5: Based on the zero-order matrix of the interference channel at L sampling point times and the zero-order vector of the auxiliary channel at L sampling point times, solve the zero-order cancellation factor at L sampling point times, and the dimension of the zero-order cancellation factor at each sampling time among the L sampling point times is M×1;

[0208]

[0209] where, m = 1, 2, …, M represents the new matrix formed by replacing the m-th column of the matrix with ;

[0210] Step 6: Based on the arrival angles of each interference signal estimated by the multiple signal classification algorithm in Step 4 and the instantaneous angle θ of each interference at L sampling points, jml construct the first-order matrix of the interference channel at L sampling points, and the dimension of the first-order matrix of the interference channel at each sampling time among the L sampling points is M×M;

[0211]

[0212] The element in the matrix is:

[0213]

[0214] Step 7: Based on the updated processing angles of each auxiliary channel in Step 11 and the instantaneous angle θ of each interference signal at L sampling points, jml construct the first-order vector of the auxiliary channel at L sampling points, and the dimension of the first-order vector of the auxiliary channel at each sampling time among the L sampling points is M×1;

[0215]

[0216] The intermediate variable is:

[0217]

[0218] Step 8: Based on the results of Steps 3 to 7, solve the first-order cancellation factors at L sampling points The dimension of the first-order cancellation factor at each sampling time among the L sampling points is M×M;

[0219]

[0220] The element in

[0221]

[0222] is: where denotes the new matrix formed by replacing the β-th row of the matrix with the β-th row of the matrix ; denotes the new matrix formed by replacing the β-th row of the matrix with the β-th row of the matrix and then replacing the element in the α-th column of the β-th row with the β-th element of the vector ; denotes the new matrix formed by replacing the α-th column of the matrix with

[0223] Step 9: Based on the arrival angles of each interference signal estimated by the multiple signal classification algorithm in Step 4 and the instantaneous angle θ of each interference signal at L sampling points, jml construct a second-order matrix of the interference channel at L sampling points The dimension of the second-order matrix of the interference channel at each sampling time among the L sampling points is M×M;

[0224]

[0225] The matrix The element in is:

[0226]

[0227] where N1 = N–1;

[0228] Step 10: Based on the processed angles of each auxiliary channel updated in Step 11 and the instantaneous angle θ of each interference signal at L sampling points jml construct a second-order vector of the auxiliary channel at L sampling points The dimension of the second-order vector of the auxiliary channel at each sampling time among the L sampling points is M×1;

[0229]

[0230] The intermediate variable is:

[0231]

[0232] Step 11: Based on the zero-order matrix of the interference channel, the zero-order vector of the auxiliary channel, the first-order matrix of the interference channel, the first-order vector of the auxiliary channel, the second-order matrix of the interference channel, and the second-order vector of the auxiliary channel at L sampling points, solve the second-order cancellation factor of each interference at L sampling points The dimension of the second-order cancellation factor of each interference at each sampling time among the L sampling points is M×M;

[0233]

[0234] The element in is:

[0235]

[0236] where represents the new matrix formed by replacing the α-th row of the matrix with the α-th row of the matrix ; Denote replacing the β-th row of matrix with the β-th row of matrix and then replacing the element in the m-th column of the β-th row with the β-th element of vector to form a new matrix; Denote replacing the α-th row of matrix with the α-th row of matrix and then replacing the element in the m-th column of the α-th row with the α-th element of vector to form a new matrix;

[0237] When α = β, Denote replacing the α-th row of matrix with the α-th row of matrix to form a new matrix; Denote replacing the α-th row of matrix with the α-th row of matrix and then replacing the element in the m-th column of the α-th row with the α-th element of vector to form a new matrix; when α ≠ β, Denote replacing the α-th row and the β-th row of matrix with the α-th row and the β-th row of matrix to form a new matrix; Denote replacing the α-th row and the β-th row of matrix with the α-th row and the β-th row of matrix and then replacing the element in the m-th column of the α-th row with the α-th element of vector and the element in the m-th column of the β-th row with the β-th element of vector to form a new matrix;

[0238] Step 12. Read the M interference channel output signals and M auxiliary channel output signals stored in Step 16, and calculate the power of the original cancellation signal at the i-th iteration by using the zero-order cancellation factors at L sampling point moments:

[0239]

[0240] where 1 ≤ m ≤ M, is an L×L matrix with non-zero elements only on the main diagonal line, the l-th element on the main diagonal line of is the m-th element of the cancellation factor

[0241] Step 13. Based on the angles and angular velocities of the interference signals and the power of the original cancellation signal at the i-th iteration during the i-th iteration process, calculate the gradient of the power of the original cancellation signal at the i-th iteration whose dimension is 2M×1;

[0242]

[0243] Among them:

[0244]

[0245] In the formula, is an L×L matrix with non-zero elements only on the main diagonal line, and the l-th element on the main diagonal line of is the element in the m-th row and α-th column of ; V is an L×L matrix with non-zero elements only on the main diagonal line, and the element in the l-th row and l-th column of V is l–(L–1) / 2, 1≤l≤L;

[0246] Step 14: Calculate the Hessian matrix G 11 (P (i) ) of the power of the i-th iteration original cancellation signal with respect to the angles and angular velocities of the interference signals in the i-th iteration process, and its dimension is M×M;

[0247]

[0248] Among them:

[0249]

[0250] In the formula, is an L×L matrix with non-zero elements only on the main diagonal line, and the l-th element on the main diagonal line of is the element in the m-th row and β-th column of ; is an L×L matrix with non-zero elements only on the main diagonal line, the l-th element on the main diagonal line of is the element in the α-th row and β-th column of , 1≤l≤L, 1≤m≤M;

[0251] Step 15: Calculate the joint Hessian matrix G 12 (P (i) ) of the power of the i-th iteration original cancellation signal with respect to the central angles and angular velocities of the interference signals in the i-th iteration process, and its dimension is M×M:

[0252]

[0253] Among them:

[0254]

[0255] Step 16: Calculate the joint Hessian matrix G of the original cancellation signal power at the i-th iteration with respect to the current angular velocities and central angles of each interference signal based on the central angles, angular velocities of each interference signal, and the original cancellation signal power at the i-th iteration 21 (P (i) ), whose dimension is M×M;

[0256]

[0257] Where:

[0258]

[0259] Step 17: Calculate the Hessian matrix G of the original cancellation signal power at the i-th iteration with respect to the current angular velocities of each interference signal based on the central angles, angular velocities of each interference signal, and the original cancellation signal power at the i-th iteration 22 (P (i) ), whose dimension is M×M;

[0260]

[0261] Where:

[0262]

[0263] Step 18: Construct the overall Hessian matrix G(P of the original cancellation signal power at the i-th iteration based on the Hessian matrix of the original cancellation signal power at the i-th iteration with respect to the current central angles of each interference signal, the joint Hessian matrix of the original cancellation signal power at the i-th iteration with respect to the current central angles and angular velocities of each interference signal, the joint Hessian matrix of the original cancellation signal power at the i-th iteration with respect to the current angular velocities and central angles of each interference signal, and the Hessian matrix of the original cancellation signal power at the i-th iteration with respect to the current angular velocities of each interference signal (i) ), whose dimension is 2M×2M;

[0264]

[0265] Step 19: Construct a zero-order matrix of the central angles of the interference signals based on the central angles of each interference signal in the i-th iteration and the arrival angles of each interference signal estimated by the multi-signal classification algorithm in Step 4 whose dimension is M×M;

[0266]

[0267] Intermediate variable q jαβ is:

[0268]

[0269] Step 20: Based on the central angles of each interference signal and the arrival angle of the desired signal estimated by the multiple signal classification algorithm in Step 4 during the i-th iteration, construct the zero-order vector of the desired signal channel The dimension of is M×1;

[0270]

[0271] Intermediate variable q sα is:

[0272]

[0273] Step 21: Based on the zero-order matrix of the central angles of the interference signals and the zero-order vector of the desired signal channel, solve the zero-order cancellation factor k of the desired signal (0) , k (0) The dimension of is M×1;

[0274]

[0275] where m = 1, 2, …, M represents the new matrix formed by replacing the m-th column of the matrix with ;

[0276] Step 22: Based on the central angles of each interference signal and the arrival angles of each interference signal estimated by the multiple signal classification algorithm in Step 4 during the i-th iteration, construct the first-order matrix of the central angles of the interference signals The dimension of is M×M;

[0277]

[0278] Matrix The element in is:

[0279]

[0280] Step 23: Based on the central angles of each interference signal and the arrival angle of the desired signal estimated by the multiple signal classification algorithm in Step 4 during the i-th iteration, construct the first-order vector of the desired signal channel The dimension of is M×1;

[0281]

[0282] Vector The element in is:

[0283]

[0284] Step 24. Solve the first-order cancellation factor \(k( 1 )\) of the desired signal based on the zero-order matrix of the interference signal center angle, the zero-order vector of the desired signal channel, the first-order matrix of the interference signal center angle, and the first-order vector of the desired signal channel. The dimension of \(k( 1 )\) is \(M\times M\);

[0285]

[0286] The elements (1) in \(k are as follows:

[0287]

[0288] In the formula, represents the new matrix formed by replacing the \(\beta\)-th row of the matrix with the \(\beta\)-th row of the matrix ; represents the new matrix formed by replacing the \(\beta\)-th row of the matrix with the \(\beta\)-th row of the matrix , and then replacing the element in the \(\alpha\)-th column of the \(\beta\)-th row with the \(\beta\)-th element of the vector ; \(|\cdot|\) represents taking the complex modulus value; represents the new matrix formed by replacing the \(\alpha\)-th column of the matrix with ;

[0289] Step 25. Obtain the allowable deviation vector \(\Delta k( 0 )\) of the zero-order cancellation factor of the desired signal according to the desired suppression capabilities of \(M\) interferences. The dimension of \(\Delta k(

[0290]

[0291] is \(M\times1\); i Step 26. Solve the allowable deviation vector \(\Delta\theta(

[0292]

[0293] of the current cancellation angle based on the first-order cancellation factor of the desired signal and the allowable deviation vector of the zero-order cancellation factor of the desired signal. The dimension of \(\Delta\theta( (i) )\) is \(M\times1\); The elements

[0294]

[0295] In the formula, is the new matrix formed by replacing the \(m\)-th column of the matrix \(k (1) with \(\Delta k (0) ;

[0296] Step 27: Take the minimum element in the vector Δθ (i) as the stop angle

[0297] Step 28: Calculate the iterative update step ξ based on the overall Hessian matrix of the original cancellation signal power at the i-th iteration and the gradient of the original cancellation signal power at the i-th iteration s , with a dimension of 2M×1;

[0298]

[0299] where G -1 (P (i) ) represents the inverse matrix of G(P (i) );

[0300] Step 29: Obtain the center angles and angular velocities of each interference signal in the (i + 1)-th iteration according to the iterative update step

[0301]

[0302] where:

[0303]

[0304] Step 30: Calculate the actual maximum error δθ of each interference angle at the current time according to the iterative update step (i) , with a dimension of M×1;

[0305]

[0306] The elements in δθ (i) are:

[0307]

[0308] where ξ s,m and ξ s,m+M represent the m-th and (m + M)-th elements of the iterative update step respectively;

[0309] Step 31: Determine whether each element in δθ (i) does not exceed

[0310] If each element in δθ (i) does not exceed , then execute Step 33; otherwise, execute Step 32;

[0311] Step 32: Determine whether the current iteration number i is equal to the maximum iteration number iter1–1;

[0312] ​If the current iteration number i is equal to the maximum iteration number iter1 - 1, then execute step 33;

[0313] Otherwise, let i = i + 1 and return to execute step 2;

[0314] Step 33: Output the central angle θ of each interference signal j1 , θ j2 , …, θ jM and angular velocities ω1, ω2, …, ω M :

[0315]

[0316] Other steps and parameters are the same as those in any one of the first to fifth specific embodiments.

[0317] Specific embodiment seven: Combine Figure 5 to illustrate this embodiment. The difference between this embodiment and any one of the first to sixth specific embodiments is that the specific process of step twenty-five is as follows:

[0318] Step B1: Set the maximum iteration number to iter2 (the value of iter2 set in the present invention is 1000), set the stop threshold ε s = 10 -8 , set the initial iteration value to

[0319] Initialize the current iteration number i = 0;

[0320] Step B2: Initialize the current sampling point index l = 1;

[0321] Step B3: Based on the cancellation angles at L sampling moments and the arrival angles of each interference signal estimated by the multiple signal classification algorithm in step four, construct the zero-order matrix of the refined expected signal angle of the current sampling point index with dimensions M × M;

[0322]

[0323] Among them, the intermediate variable q xαβ,l is:

[0324]

[0325] Among them, θ jβ,l represents the cancellation angle of the βth interference at the lth sampling moment;

[0326] Step B4: Based on the refined expected signal arrival angle at the i-th iteration and the cancellation angle at the lth sampling moment in step twenty-four, construct the zero-order vector of the refined expected signal angle of the current sampling point index The dimension is M×1;

[0327]

[0328] where: the intermediate variable q xsα,l is:

[0329]

[0330] where, θ jα,l represents the cancellation angle of the α-th interference at the l-th sampling moment;

[0331] Step B5: Refine the zero-order matrix of the desired signal angle based on the current sampling point index and the zero-order vector of the desired signal angle of the current sampling point index, and solve the zero-order refinement factor of the current sampling point index The dimension is M×1;

[0332]

[0333] where, represents replacing the m-th column of with

[0334] to form a new matrix; Step B6: Based on the refined arrival angle of the desired signal at the i-th iteration and the cancellation angle at the l-th sampling moment in step twenty-four, construct the first-order vector of the refined desired signal angle of the current sampling point index

[0335]

[0336] where, the element in the vector is:

[0337]

[0338] Step B7: Based on the first-order vector of the refined desired signal angle of the current sampling point index and the zero-order matrix of the refined desired signal angle of the current sampling point index, solve the first-order refinement factor of the current sampling point index The dimension is M×1;

[0339]

[0340] where, represents replacing the m-th column of with

[0341] Step B8. Based on the refined desired signal arrival angle at the $i$-th iteration and the cancellation angle at the $l$-th sampling moment in step 24, construct the refined second-order vector of the desired signal angle for the current sampling point index The dimension is $M\times1$;

[0342]

[0343] where the vector The element in is:

[0344] When $q$ xsα,l is 1, there is:

[0345]

[0346] Otherwise, there is:

[0347]

[0348] Step B9. Based on the refined second-order vector of the desired signal angle for the current sampling point index and the refined zero-order matrix of the desired signal angle for the current sampling point index, solve the second-order refinement factor for the current sampling point index The dimension is $M\times1$;

[0349]

[0350] where means the new matrix formed by replacing the $m$-th column of with ;

[0351] Step B10. Calculate the $N$-dimensional weights of the desired signal channel at the $i$-th iteration based on the refined desired signal arrival angle at the $i$-th iteration The dimension is $N\times1$;

[0352]

[0353] Step B11. Based on the $N$-dimensional weights of the desired signal channel at the $i$-th iteration, the zero-order refinement factor for the current sampling point index, the interference channel weights stored in step 15, and the received data unit matrix in step 2, calculate the $l$-th sampling point $r$ of the desired waveform at the $i$-th iteration l (i) ;

[0354]

[0355] where represents the $m$-th element of the vector , and $r$ [:,l] represents the column vector formed by all the elements in the $l$-th column of the matrix $r$.

[0356] Step B12: Calculate the first derivative of the \(l\)th sample point of the desired waveform in the \(i\)th iteration based on the refined desired signal arrival angle in the \(i\)th iteration, the \(N\)-dimensional weights of the desired signal channel in the \(i\)th iteration, the first-order refinement factor of the current sample point index, the interference channel weights stored in Step 15, and the received data unit matrix in Step 2;

[0357]

[0358] Among them, matrix \(A\) is a matrix with non-zero elements only on the main diagonal. The dimension of matrix \(A\) is \(N\times N\), and the element in the \(u\)th row and \(u\)th column of matrix \(A\) is \(u - 1\). Denote the \(m\)th element of vector , where \(1\leq m\leq M\) and \(1\leq u\leq N\);

[0359] Step B13: Calculate the second derivative of the \(l\)th sample point of the desired waveform in the \(i\)th iteration based on the refined desired signal arrival angle in the \(i\)th iteration, the \(N\)-dimensional weights of the desired signal channel in the \(i\)th iteration, the second-order refinement factor of the current sample point index, the interference channel weights stored in Step 15, and the received data unit matrix in Step 2:

[0360]

[0361] In the formula, Denote the \(m\)th element of vector ;

[0362] Step B14: Compare the magnitude relationship between \(l\) and \(L\);

[0363] If \(l = L\), then execute Step B15;

[0364] Otherwise, let \(l=l + 1\), and then return to Step B3;

[0365] Step B15: Construct the first derivative of the desired waveform power in the \(i\)th iteration based on the \(l\)th sample point of the desired waveform in the \(i\)th iteration and the first derivative of the \(l\)th sample point of the desired waveform in the \(i\)th iteration:

[0366]

[0367] Among them, \(r( i )\) represents the desired waveform in the \(i\)th iteration, with a dimension of \(1\times L\);

[0368]

[0369] Step B16. Based on the l-th sampling point of the expected waveform in the i-th iteration, the first derivative of the l-th sampling point of the expected waveform in the i-th iteration, and the second derivative of the l-th sampling point of the expected waveform in the i-th iteration, construct the second derivative of the power of the expected waveform in the i-th iteration:

[0370]

[0371] Where:

[0372]

[0373] Step B17. Based on the first derivative of the power of the expected waveform in the i-th iteration and the second derivative of the power of the expected waveform in the i-th iteration, calculate the update step in the i-th iteration:

[0374]

[0375] Step B18. Based on the refined expected signal arrival angle in the i-th iteration and the update step in the i-th iteration, obtain the refined expected signal arrival angle in the (i + 1)-th iteration

[0376]

[0377] Step B19. Determine whether the absolute value of ξ (i) exceeds the set stop threshold ε s ,

[0378] If it does not exceed, execute Step B21; otherwise, execute Step B20;

[0379] Step B20. Determine whether the current iteration number i is equal to the set maximum iteration number iter2 – 1;

[0380] If so, execute Step B21;

[0381] Otherwise, let i = i + 1 and return to Step B2;

[0382] Step B21. Based on the refined expected signal arrival angle in the i-th iteration, the expected signal angle ambiguity region in Step 5, and the expected signal arrival angle estimated by the multiple signal classification algorithm in Step 4, output the refined expected signal arrival angle

[0383]

[0384] Other steps and parameters are the same as those in any one of the first to sixth specific embodiments.

[0385] Specific Embodiment 8: The difference between this embodiment and any one of the first to seventh specific embodiments is that the specific process of Step 27 is as follows:

[0386] Step C1: Initialize the current sampling point index \(l = 1\);

[0387] Step C2: Based on the cancellation angle at the \(l\)-th sampling moment and the interference channel weights stored in Step 15, construct the cancellation factor interference matrix \(S\), where the dimension of \(S\) is \(M\times M\);

[0388]

[0389] where: the element \(S\) in matrix \(S\) αβ,l is:

[0390]

[0391] In the formula, \(a(\theta\) jβ,l ) represents the \(N\)-dimensional steering vector of \(\theta\) jβ,l , and the dimension of \(a(\theta\) jβ,l ) is \(N\times1\);

[0392]

[0393] Step C3: Based on the cancellation angle at the \(l\)-th sampling moment in Step 24 and the desired signal channel weights in Step 26, construct the cancellation factor desired signal vector \(s\), where the dimension of \(s\) is \(M\times1\);

[0394] \(s = [s\) 1,l \(s\) 2,l \(\cdots s\) M,l T

[0395] where, the element \(s\) in vector \(s\) α,l is:

[0396]

[0397] Step C4: Based on the cancellation factor interference matrix and the cancellation factor desired signal vector, calculate the cancellation factor vector \(k\) (l) , where the dimension of \(k\) (l) is \(M\times1\);

[0398] \(k\) (l) = [k\) 1,l \(k\) 2,l \(\cdots k\) M,l T

[0399] where, the element \(k\) in \(k\) (l) is: α,l as:

[0400]

[0401] In the formula, \(S\)​​α Denotes a new matrix formed by replacing the α-th column of matrix S with s;

[0402] Step C5: Compare the magnitude relationship between l and L;

[0403] If l = L, then execute Step C6;

[0404] Otherwise, set l = l + 1 and return to Step C2;

[0405] Step C6: Output the final cancellation factor matrix k based on the cancellation factor vectors at each sampling point, where the dimension of k is M × L;

[0406] k = [k (1) k (2) … k (L)

[0407] Other steps and parameters are the same as those in any one of the first to seventh specific embodiments.

[0408] Specific Embodiment Nine: The difference between this embodiment and any one of the first to eighth specific embodiments is that the specific process of Step Twenty-Eight is as follows:

[0409] Step D1: Initialize the current sampling point index l = 1;

[0410] Step D2: Calculate the cancellation signal y at the current sampling point according to the cancellation factors obtained in Step Twenty-Seven, the desired signal channel weight in Step Twenty-Six, the interference channel weight stored in Step Fifteen, and the received data unit matrix in Step Two l ;

[0411]

[0412] where k m,l represents the m-th element in the cancellation factor vector k (l) at the l-th sampling point;

[0413] Step D3: Compare the magnitude relationship between l and L;

[0414] If l = L, then execute Step D4;

[0415] Otherwise, set l = l + 1 and return to execute Step D2;

[0416] Step D4: Construct and output the signal y after interference cancellation based on the cancellation signals at each sampling point to complete the interference cancellation process. The signal after interference cancellation is expressed as:

[0417] y = [y1 y2…y L

[0418] Other steps and parameters are the same as those in any one of the first to eighth specific embodiments.

[0419] Embodiment Ten: For an antenna array virtual multi-channel interference suppression method described in this embodiment, the method specifically includes the following steps:

[0420] Step 1: As shown in Figure 1 , N receiving antennas in the antenna array are arranged in a uniform linear array (N>1, the spacing between adjacent two receiving antennas is λ / 2, where λ represents the wavelength of the electromagnetic wave used for communication). Select element 1 as the reference element. It is stipulated that the incident angle on the right side of the normal is positive and the incident angle on the left side of the normal is negative. The N receiving antennas respectively receive analog signals from free space, and the received signals respectively pass through each radio frequency processing link to form N digital sequences;

[0421] The radio frequency processing link includes a low-noise amplifier, a down-converter, and an analog-to-digital converter;

[0422] Step 2: Integrate the N digital sequences formed in Step 1: Summarize the data of the N receiving antennas at consecutive L sampling points into a received data unit matrix r with N rows and L columns. Among them, the element in the nth row and the lth column of the received data unit matrix r represents the received data of the nth receiving antenna at the lth sampling point (1≤n≤N, 1≤l≤L, in this invention, L = 50);

[0423] The data of the N receiving antennas continuously enters. The receiving end divides every L sampling points into a received data unit matrix, and the same processing method is adopted for each received data unit matrix;

[0424] Step 3: Use the Multiple Signal Classification (MUSIC) algorithm to analyze the received data unit matrix r to obtain the number M of signals existing in space total , the intensity of each signal, and the arrival angle of each signal; This invention is applicable to the case where M total does not exceed N;

[0425] Step 4: Regard the signal with the weakest intensity in space as the Signal Of Interest (SOI), and regard the remaining signals in space as interference signals, that is, the number of interference signals M = M total –1, denote the arrival angle of the desired signal estimated by the multi-signal classification algorithm as Denote the arrival angles of each interference signal estimated by the multi-signal classification algorithm as This invention is applicable to the case where the number of desired signals is 1;

[0426] Step 5: Obtain the desired signal angle ambiguity region Θ according to the empirical value Δ of the arrival angle estimation error and the arrival angle of the desired signal estimated by the multi-signal classification algorithm s, obtain the interference signal angle ambiguity region Θ according to the empirical value Δ of the angle of arrival estimation error and the angles of arrival of each interference signal estimated by the multiple signal classification algorithm j ;

[0427]

[0428] Step Six: Determine the number of processing channels M according to the number of interference signals M p = 2M + 1, and the processing channels include 1 desired signal channel, M interference channels, and M auxiliary channels;

[0429] Step Seven: Initialize the dimension U for calculating the steering vector d = N, and set the maximum deviation factor f of the auxiliary channel p (f p is an integer not less than 1);

[0430] Step Eight: Initialize the deviation factor C of the current auxiliary channel p = 0;

[0431] Step Nine: Initialize the processing angles θ of the M auxiliary channels f1 , θ f2 , …, θ fM are:

[0432]

[0433] Step Ten: Set the index i of the current interference channel and auxiliary channel to 1;

[0434] Step Eleven: Modify the processing angle of the i-th auxiliary channel to:

[0435]

[0436] where ε represents the angle step of the auxiliary channel;

[0437] Step Twelve: Divide the U-dimensional steering vector of the angle of arrival of the i-th interference signal estimated by the multiple signal classification algorithm by U d , and use the obtained quotient as the weight w of the i-th interference channel d , and the dimension of w ji is U ji × 1; d × 1;

[0438]

[0439] where the superscript "T" represents matrix transpose, e is the base of the natural logarithm, j in the e exponent is the imaginary unit, and π is the circumference ratio;

[0440] Step Thirteen: The U of the modified processing angle of the i-th auxiliary channel dThe i-th auxiliary channel weight w is obtained by dividing the i-th steering vector by U d , and the resulting quotient is used as the weight w of the i-th auxiliary channel fi , w fi has the dimension of U d ×1;

[0441]

[0442] Step Fourteen: Compare the relative magnitudes of U d and N;

[0443] If U d = N, then proceed to Step Fifteen;

[0444] Otherwise, proceed to Step Sixteen;

[0445] Step Fifteen: Store the weight of the i-th interference channel calculated in Step Twelve (update the stored result if there is already relevant storage), and then proceed to Step Sixteen;

[0446] Step Sixteen: Based on the weight of the i-th interference channel calculated in Step Twelve, the weight of the i-th auxiliary channel calculated in Step Thirteen, and the received data unit matrix r, calculate and store the output signal r ji of the current i-th interference channel and the output signal r fi of the i-th auxiliary channel;

[0447] Step Seventeen: Compare the magnitudes of i and the number of interference signals M;

[0448] If i = M, proceed to Step Eighteen; otherwise, set i = i + 1 and return to execute Step Eleven;

[0449] Step Eighteen: Calculate the feasible solutions for the initial value of the cancellation angle based on r ji and r fi ;

[0450] If the number of feasible solutions is equal to M, then directly use the feasible solutions as the iterative initial values of the M interference center angles to execute Step Twenty-Three;

[0451] If the number of feasible solutions is greater than M, then screen the feasible solutions, and the selected feasible solutions form the optional set Θ D of the initial values of the cancellation angle, and then proceed to Step Nineteen;

[0452] Step Nineteen: Determine whether the number of elements in the optional set Θ D of the initial values of the cancellation angle is equal to M;

[0453] If the number of elements in the optional set Θ D of the initial values of the cancellation angle is equal to M, then output the M interference center angles θ j1 , θj2 ,…, θ jM , then execute Step 23;

[0454] Otherwise, execute Step 20;

[0455] Step 20. Let the current auxiliary channel deviation factor C p = C p + 1;

[0456] Step 21. Judge the magnitude relationship between C p and f p – 1;

[0457] If C p > f p – 1, then execute Step 22;

[0458] Otherwise, return to Step 10;

[0459] Step 22. Let the steering vector calculation dimension U d = U d – 1, and return to execute Step 8;

[0460] Step 23. Set the angular velocities ω1, ω2, …, ω of each interference M to be all 0;

[0461] Step 24. Based on each interference center angle output in Step 19 and the angular velocities of each interference set in Step 23, obtain the cancellation angle matrix of all interferences at L sampling moments:

[0462]

[0463] where:

[0464] θ jm,l = θ jm + ω m l, m = 1, 2, …, M; l = 1, 2, …, L

[0465] Step 25. Read the weights of the M interference channels stored and the arrival angle of the desired signal estimated by the multiple signal classification algorithm in Step 4 Use the received data unit matrix r in Step 2 and the cancellation angles at L sampling moments to calculate the refined arrival angle of the desired signal

[0466] Step 26. Divide the N-dimensional steering vector of the refined arrival angle of the desired signal by N, and use the obtained quotient as the weight w of the desired signal channel s , w s has a dimension of N × 1;

[0467]

[0468] Step twenty-seven: Calculate the cancellation factor of each interference at L sampling points according to the cancellation angles at L sampling moments in Step twenty-four, the desired signal channel weights in Step twenty-six, and the interference channel weights stored in Step fifteen.

[0469] Step twenty-eight: Output the interference-cancelled signal y according to the cancellation factors obtained in Step twenty-seven, the desired signal channel weights in Step twenty-six, the interference channel weights stored in Step fifteen, and the received data unit matrix r in Step two.

[0470] The interference suppression method of this embodiment is applicable to static interference. Steps seven to eighteen are the same as those in the first specific embodiment, and the processes of steps twenty-five to twenty-eight are exactly the same as those in the first specific embodiment.

[0471] Experimental part

[0472] The parameter settings of the interference suppression method in the first specific embodiment are as follows: Set a multi-antenna receiver equipped with N = 8 receiving antennas, with each receiving antenna arranged uniformly along a straight line, the antenna spacing is λ / 2, and each antenna has a dedicated radio frequency chain. Use the MUSIC algorithm to analyze the integrated received data unit matrix r to obtain the number of signals M existing in space total = 5, the number of interference signals M = M total –1 = 4, estimate the arrival angle of the desired signal Estimate the arrival angles of each interference signal The empirical value of the arrival angle estimation error Δ = 5°, the number of processing channels M p = 2M + 1 = 9, including a total of 1 desired signal channel, 4 interference channels, and 4 auxiliary channels. Set the maximum deviation factor f of the auxiliary channels p to 10. The angle step ε of the auxiliary channels is taken as 0.5°. Set the desired suppression capabilities of M interferences to x1 = x2 = x3 = x4 = 60 dB, set the stop angle threshold thre = 100, and set the maximum number of iterations to iter1 = 1000. The obtained performance graph is as Figure 6 shown.

[0473] The parameter settings of the interference suppression method in the tenth specific embodiment are as follows: Set a multi-antenna receiver equipped with N = 8 receiving antennas, with each receiving antenna arranged uniformly along a straight line, the antenna spacing is λ / 2, and each antenna has a dedicated radio frequency chain. Use the MUSIC algorithm to analyze the integrated received data unit matrix r to obtain the number of signals M existing in space total = 3, the number of interference signals M = M total –1 = 2, estimate the arrival angle of the desired signal Estimate the arrival angles of each interference signal The empirical value of the arrival angle estimation error Δ = 5°, and determine the number of processing channels M according to the number of interference signals M p = 2M + 1 = 5, including a total of 1 desired signal channel, M = 2 interference channels, and M = 2 auxiliary channels. The obtained performance diagram is as Figure 7 shown

[0474] The above numerical examples of the present invention are only for illustrating in detail the calculation model and calculation process of the present invention, rather than limiting the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is impossible to enumerate all the implementation manners here. Any obvious changes or variations derived from the technical solutions of the present invention still fall within the protection scope of the present invention

Claims

1. A method for virtual multi-channel interference suppression of an antenna array, characterized in that The method specifically includes the following steps: Step 1: N receiving antennas in the antenna array are arranged in a uniform linear array. The N receiving antennas respectively receive analog signals from free space, and the received signals respectively pass through each radio frequency processing link to form N digital sequences; Step 2: Integrate the N digital sequences formed in Step 1: Summarize the data of the N receiving antennas at L consecutive sampling points into a received data unit matrix r of N rows and L columns; Step 3: Analyze the received data unit matrix r using the multiple signal classification algorithm to obtain the number of signals M existing in the space total , the intensity of each signal, and the arrival angle of each signal; Step 4: Consider the signal with the weakest strength in the space as the desired signal, and consider the remaining signals in the space as interference signals, that is, the number of interference signals M = M total – 1, denote the arrival angle of the desired signal estimated by the multiple signal classification algorithm as Denote the arrival angles of each interference signal estimated by the multiple signal classification algorithm as Step 5: Obtain the expected signal angle ambiguity region Θ based on the arrival angle estimation error empirical value Δ and the expected signal arrival angle estimated by the multiple signal classification algorithm s , and obtain the interference signal angle ambiguity region Θ based on the arrival angle estimation error empirical value Δ and the arrival angles of each interference signal estimated by the multiple signal classification algorithm j ; Step 6. Determine the number of processing channels M according to the number of interference signals M p = 2M + 1. The processing channels include 1 desired signal channel, M interference channels, and M auxiliary channels; Step 7: Initialize the dimension U for calculating the steering vector d = N, and set the maximum deviation factor f of the auxiliary channel p ; Step Eight: Initialize the deviation factor C of the current auxiliary channel p = 0; Step Nine: Initialize the processing angles θ of M auxiliary channels f1 , θ f2 , …, θ fM as follows: Step 10: Set the index i of the current interference channel and the auxiliary channel to i = 1; Step 11: Modify the processing angle of the i-th auxiliary channel to: θ fi = θ fi + ε where ε represents the auxiliary channel angle step; Step Twelve: Divide the U-dimensional steering vector of the arrival angle of the i-th interference signal estimated by the multiple signal classification algorithm by U d and use the resulting quotient as the weight w of the i-th interference channel d ; ji ​ where the superscript "T" represents matrix transpose, e is the base of the natural logarithm, j in the e exponent is the imaginary unit, and π is the pi; Step Thirteen: Divide the U of the processed angle of the i-th auxiliary channel after modification d by U d , and use the obtained quotient as the weight w of the i-th auxiliary channel fi ; Step Fourteen: Compare the relative magnitudes of U d and N; If U d = N, then perform Step 15; Otherwise, execute Step 16; Step 15: Store the weight of the i-th interference channel calculated in Step 12, and then execute Step 16; Step Sixteen: Calculate and store the output signal r of the current ith interference channel and the output signal r of the ith auxiliary channel based on the weight of the ith interference channel calculated in Step Twelve, the weight of the ith auxiliary channel calculated in Step Thirteen, and the received data unit matrix r ji ; fi ; Step 17: Compare the size of i and the number of interference signals M; If i = M, execute Step 18, otherwise let i = i + 1, and return to execute Step 11; Step Eighteen: Calculate the feasible solution of the initial value of the cancellation angle according to r ji and r fi Calculate the feasible solution of the initial value of the cancellation angle; If the number of feasible solutions is equal to M, directly use the feasible solutions as the initial values for the iteration of the angles of the M interference centers to execute Step 23; If the number of feasible solutions is greater than M, then the feasible solutions are screened, and the selected feasible solutions form an optional set Θ for the initial value of the cancellation angle, D and then step XIX is executed; Step Nineteen: Determine whether the number of elements in the optional set Θ of the cancellation angle initial values D is equal to M; If the number of elements in the optional set Θ of the cancellation angle initial values D is equal to M, then the elements in the optional set Θ D of the cancellation angle initial values are the M initial values for iterating the interference center angles Then step twenty-three is executed; Otherwise, if the number of elements in the optional set Θ D of the cancellation angle initial values is not equal to M, then step twenty is executed; Step Twenty: Set the current auxiliary channel deviation factor C p = C p + 1; Step 21, determine the magnitude relationship between C p and f p – 1; If C p > f p – 1, then perform Step Twenty-Two; Otherwise, return to execute Step 10; Step 22: Let the dimension of the steering vector calculation be U d = U d – 1, and return to execute Step 8; Step twenty-three: Read the output signals of the M interference channels and the output signals of the M auxiliary channels stored, and combine the iterative initial values Calculate the central angle θ of each interference j1 , θ j2 , …, θ jM And the angular velocities ω1, ω2, …, ω M ; Step 24: Based on the central angle θ of each interference j1 , θ j2 , …, θ jM and angular velocities ω1, ω2, …, ω M calculate the cancellation angle matrix of all interferences at L sampling moments; where the cancellation angle θ of the m-th interference at the l-th sampling moment is jm,l as follows: θ jm,l = θ jm + ω m l, m = 1, 2, …, M, l = 1, 2, …, L Step 25: Read the weights of the M interference channels stored and the arrival angle of the desired signal estimated by the multiple signal classification algorithm in Step 4 Calculate the refined arrival angle of the desired signal by using the received data unit matrix r in Step 2 and the cancellation angles at L sampling instants Step twenty-six: Divide the N-dimensional steering vector of the refined expected signal arrival angle by N, and use the resulting quotient as the weight w of the expected signal channel s ; Step 27: Calculate the cancellation factor of each interference at L sampling points according to the cancellation angles at L sampling moments in Step 24, the weight of the desired signal channel in Step 26, and the weights of the interference channels stored in Step 15; Step 28: Output the signal y after interference cancellation according to the cancellation factors obtained in Step 27, the weight of the desired signal channel in Step 26, the weights of the interference channels stored in Step 15, and the received data unit matrix r in Step 2; 2. The virtual multi-channel interference suppression method for an antenna array according to claim 1, characterized in that The radio frequency processing link includes a low-noise amplifier, a down-converter, and an analog-to-digital converter.

3. A method for suppressing virtual multi-channel interference of an antenna array according to claim 2, characterized in that The specific process of Step 5 is:

4. A method for suppressing virtual multi-channel interference of an antenna array according to claim 3, characterized in that The specific process of Step 16 is: where the superscript "H" represents the conjugate transpose of the matrix.

5. A method for virtual multi-channel interference suppression of an antenna array according to claim 4, characterized in that The specific process of Step 18 is: Step A1: Read the output signals of the stored M interference channels and construct an interference channel waveform correlation matrix R of M rows and M columns: Step A2: Read the output signals of the stored M interference channels and the output signals of the M auxiliary channels, and construct an M-row and 1-column correlation vector R of the auxiliary channel waveforms and the interference channel waveforms f : Step A3. Calculate M initial auxiliary cancellation factors k according to matrix R and vector R f fm :​ where R m is the new matrix formed by replacing the m-th column of matrix R with vector R f , and det(·) represents calculating the determinant of a matrix; Step A4: Construct an equation about the initial value θ of the cancellation angle according to the initial auxiliary cancellation factor: In the formula, the superscript "n" represents the nth power of the value, and there is: Solve the equation for the initial value θ of the cancellation angle to obtain all U d -1 feasible solutions for the initial value of the cancellation angle; If U d - 1 is equal to M, directly execute Step 23; If U d - 1 is greater than M, then perform step A5; Step A5: Screen out the initial cancellation angle values within the interference angle ambiguity region Θ from all the feasible solutions calculated in Step A4, and the selected initial cancellation angle values form an optional set Θ j D .​ 6. A method for virtual multi-channel interference suppression of an antenna array according to claim 5, characterized in that The specific process of Step 23 uses Newton's method for iterative calculation: Step 1. Initialize the current iteration number \(i = 0\), and initialize the initial values of angular velocity iteration both to 0, and set the expected suppression capabilities for \(M\) interference signals to \(x_1\mathrm{dB}\), \(x_2\mathrm{dB}\), \(\cdots\), \(x\) M \(\mathrm{dB}\) respectively, and set the stop angle threshold \(\mathrm{thre}\) and the maximum iteration number \(\mathrm{iter}1\); Step 2: Use a uniform angular velocity change model to solve the instantaneous angles of each interference signal at L sampling point moments: where θ jml represents the instantaneous angle of the m-th interference signal at the l-th sampling point moment; Step 3: Based on the arrival angles of each interference signal estimated by the multiple signal classification algorithm in Step 4 and the instantaneous angle θ of each interference signal at L sampling points, jml construct a zero-order matrix of the interference channel at L sampling points; Among them, represents the zero-order matrix of the interference channel at the l-th sampling point moment; Intermediate variable q jαβ,l is as follows: Step 4. Based on the processed angles of each auxiliary channel updated in Step Eleven and the instantaneous angles θ of each interference signal at L sampling points, construct the zero-order vectors of the auxiliary channels at L sampling points; jml , and construct the zero-order vectors of the auxiliary channels at L sampling points; Among them, represents the zero-order vector of the auxiliary channel at the l-th sampling point moment; Intermediate variable q fαβ,l is as follows: Step 5: Solve the zero-order cancellation factors at L sampling point moments based on the zero-order matrix of the interference channel and the zero-order vector of the auxiliary channel at L sampling point moments; Among them, m = 1, 2, …, M represents the new matrix formed by replacing the m-th column of the matrix with ; Step 6. Based on the arrival angles of each interference signal estimated by the multiple signal classification algorithm in Step 4 and the instantaneous angles θ of each interference at L sampling instants, construct a first-order matrix of the interference channels at L sampling instants; jml , and construct a first-order matrix of the interference channels at L sampling instants; Matrix The elements in are as follows: α = 1, 2,..., M; β = 1, 2,..., M; l = 1, 2,..., L Step 7. Based on the processed angles of each auxiliary channel updated in Step 11 and the instantaneous angles θ of each interference signal at L sampling points, construct the first-order vectors of the auxiliary channels at L sampling points; jml , and construct the first-order vectors of the auxiliary channels at L sampling points; Intermediate variable is as follows: α = 1, 2,..., M; β = 1, 2,..., M; l = 1, 2,..., L Step 8: Based on the results of Steps 3 to 7, solve for the first-order cancellation factors at L sampling point times The elements in are as follows: α = 1, 2, …, M; β = 1, 2, …, M; l = 1, 2, …, L Among them, represents the new matrix formed by replacing the β-th row of matrix with the β-th row of matrix ; represents the new matrix formed by replacing the β-th row of matrix with the β-th row of matrix and then replacing the element in the α-th column of the β-th row with the β-th element of vector ; represents the new matrix formed by replacing the α-th column of matrix with ; Step 9: Based on the arrival angles of each interference signal estimated by the multiple signal classification algorithm in Step 4 and the instantaneous angles θ of each interference signal at L sampling points, construct the second-order matrix of the interference channel at L sampling points jml , and construct the second-order matrix of the interference channel at L sampling points Matrix The elements in are as follows: α = 1, 2,..., M; β = 1, 2,..., M; l = 1, 2,..., L In the formula, N1 = N – 1; Step 10. Based on the processed angles of each auxiliary channel updated in Step Eleven and the instantaneous angles θ of each interference signal at L sampling points, construct the second-order vectors of the auxiliary channels at L sampling points jml , and construct the second-order vectors of the auxiliary channels at L sampling points Intermediate variable is: α = 1, 2,..., M; β = 1, 2,..., M; l = 1, 2,..., L Step 11: Solve the second-order cancellation factor of each interference at L sampling point moments based on the zero-order matrix of the interference channel, the zero-order vector of the auxiliary channel, the first-order matrix of the interference channel, the first-order vector of the auxiliary channel, the second-order matrix of the interference channel, and the second-order vector of the auxiliary channel The elements in are as follows: α = 1, 2,..., M; β = 1, 2,..., M; m = 1, 2,..., M; l = 1, 2,..., L Among them, represents the new matrix formed by replacing the α-th row of matrix with the α-th row of matrix ; represents the new matrix formed by replacing the β-th row of matrix with the β-th row of matrix , and then replacing the element in the m-th column of the β-th row with the β-th element of vector ; represents the new matrix formed by replacing the α-th row of matrix with the α-th row of matrix , and then replacing the element in the m-th column of the α-th row with the α-th element of vector ; When α = β, represents the new matrix formed by replacing the α-th row of matrix with the α-th row of matrix ; represents the new matrix formed by replacing the α-th row of matrix with the α-th row of matrix and then replacing the element in the m-th column of the α-th row with the α-th element of vector ; when α ≠ β, represents the new matrix formed by replacing the α-th row and the β-th row of matrix with the α-th row and the β-th row of matrix ; represents the new matrix formed by replacing the α-th row and the β-th row of matrix with the α-th row and the β-th row of matrix and then replacing the element in the m-th column of the α-th row with the α-th element of vector and the element in the m-th column of the β-th row with the β-th element of vector ; Step 12: Read the output signals of the M interference channels and the output signals of the M auxiliary channels stored in Step 16, and calculate the power of the original cancellation signal for the i-th iteration using the zero-order cancellation factors at L sampling points: where 1 ≤ m ≤ M, is an L×L matrix with non-zero elements only on the main diagonal, the l-th element on the main diagonal of is the m-th element of, 1 ≤ l ≤ L; Step 13: Calculate the gradient of the original cancellation signal power at the i-th iteration based on the angles and angular velocities of the interference signals and the original cancellation signal power at the i-th iteration Where: α＝1,2,…,M In the formula, is an L×L matrix with non-zero elements only on the main diagonal, and the l-th element on the main diagonal of is the element in the m-th row and α-th column of ; V is an L×L matrix with non-zero elements only on the main diagonal, and the element in the l-th row and l-th column of V is l–(L–1) / 2, where 1 ≤ l ≤ L; Step 14: Calculate the Hessian matrix G of the original cancellation signal power at the i-th iteration with respect to the angles of the current interference signals based on the angles, angular velocities of the interference signals, and the original cancellation signal power at the i-th iteration 11 (P (i) ); Where: α = 1, 2, …, M; β = 1, 2, …, M In the formula, is an L×L matrix with non-zero elements only on the main diagonal, and the l-th element on the main diagonal of is the element in the m-th row and β-th column of is an L×L matrix with non-zero elements only on the main diagonal, the l-th element on the main diagonal of is the element in the α-th row and β-th column of , where 1 ≤ l ≤ L and 1 ≤ m ≤ M; Step 15: Calculate the joint Hessian matrix \(G\) of the original cancellation signal power at the \(i\)-th iteration with respect to the central angles and angular velocities of the current interference signals based on the central angles, angular velocities of the interference signals, and the original cancellation signal power at the \(i\)-th iteration 12 (P (i) ): Where: α = 1, 2, …, M; β = 1, 2, …, M Step 16: Calculate the joint Hessian matrix G of the original cancellation signal power at the i-th iteration with respect to the angular velocity and central angle of each interference signal based on the central angle, angular velocity of each interference signal, and the original cancellation signal power in the i-th iteration process 21 (P (i) ); Where: α = 1, 2, …, M; β = 1, 2, …, M Step 17: Calculate the Hessian matrix \(G\) of the power of the \(i\)-th iteration original cancellation signal with respect to the angular velocities of the current interference signals based on the central angles, angular velocities of the interference signals, and the power of the \(i\)-th iteration original cancellation signal in the \(i\)-th iteration process 22 (P (i) ); Where: α = 1, 2, …, M; β = 1, 2, …, M Step 18: Based on the Hessian matrix of the original cancellation signal power in the \(i\)-th iteration with respect to the central angles of the current interference signals, the joint Hessian matrix of the original cancellation signal power in the \(i\)-th iteration with respect to the central angles and angular velocities of the current interference signals, the joint Hessian matrix of the original cancellation signal power in the \(i\)-th iteration with respect to the angular velocities and central angles of the current interference signals, and the Hessian matrix of the original cancellation signal power in the \(i\)-th iteration with respect to the angular velocities of the current interference signals, construct the overall Hessian matrix \(G(P (i) ) Step 19: Based on the central angles of each interference signal in the i-th iteration process and the arrival angles of each interference signal estimated by the multiple signal classification algorithm in Step 4, construct a zero-order matrix of the central angles of the interference signals Intermediate variable q jαβ is as follows: Step 20: Based on the central angles of each interference signal and the arrival angle of the desired signal estimated by the multiple signal classification algorithm in Step 4 during the i-th iteration, construct the zero-order vector of the desired signal channel Intermediate variable q sα is as follows: Step 21. Solve the zero-order cancellation factor k( 0 ) of the desired signal based on the zero-order matrix of the interference signal center angle and the zero-order vector of the desired signal channel; where m = 1, 2, …, M represents the new matrix formed by replacing the m-th column of the matrix with Step 22: Based on the central angles of each interference signal in the i-th iteration process and the arrival angles of each interference signal estimated by the multiple signal classification algorithm in Step 4, construct a first-order matrix of the central angles of the interference signals Matrix The elements in are as follows: α = 1, 2, …, M; β = 1, 2, …, M Step 23: Based on the central angles of the interference signals and the arrival angle of the desired signal estimated by the multiple signal classification algorithm in Step 4 during the i-th iteration, construct the first-order vector of the desired signal channel Vector The elements in are as follows: α＝1,2,…,M Step 24: Solve for the first-order cancellation factor k( 1 ) of the desired signal based on the zero-order matrix of the interference signal center angle, the zero-order vector of the desired signal channel, the first-order matrix of the interference signal center angle, and the first-order vector of the desired signal channel; k (1) The elements in are as follows: In the formula, represents the new matrix formed by replacing the β-th row of matrix with the β-th row of matrix ; represents the new matrix formed by replacing the β-th row of matrix with the β-th row of matrix and then replacing the element in the α-th column of the β-th row with the β-th element of vector ; |·| represents taking the complex modulus value; represents the new matrix formed by replacing the α-th column of matrix with ; Step 25. Obtain the allowable deviation vector Δk( 0 ) of the desired signal zero-order cancellation factor according to the desired signal suppression capabilities of M interferences; Step 26. Solve the allowable deviation vector Δθ( i ) of the current cancellation angle based on the allowable deviation vectors of the first-order cancellation factor and the zero-order cancellation factor of the desired signal; Δθ (i) The elements in are as follows: In the formula, is the new matrix formed by replacing the m-th column of matrix k (1) with Δk (0) ; Step 27, take the minimum element in the vector Δθ (i) as the stop angle Step 28: Calculate the iterative update step ξ based on the overall Hessian matrix of the original cancellation signal power at the i-th iteration and the gradient of the original cancellation signal power at the i-th iteration s ; where G -1 (P (i) ) represents the inverse matrix of G(P (i) ); Step 29: Obtain the central angles and angular velocities of the interference signals in the (i + 1)-th iteration according to the iterative update step size: Where: Step 30: Calculate the actual maximum error δθ of each interference angle currently according to the iterative update step (i) ; δθ (i) The elements in are as follows: where ξ s,m and ξ s,m+M represent the m-th and (m + M)-th elements of the iterative update step respectively; Step 31, determine whether each element in δθ (i) is not more than / thre; If δθ (i) each element in / thre, then step 33 is executed; otherwise, step 32 is executed; Step 32: Determine whether the current iteration number i is equal to the maximum iteration number iter1 – 1; If the current iteration number i is equal to the maximum iteration number iter1 – 1, then execute Step 33; Otherwise, let i = i + 1, and return to execute Step 2; Step 33, output the central angle θ of each interference signal j1 , θ j2 , …, θ jM and angular velocities ω1, ω2, …, ω M :

7. A method for virtual multi-channel interference suppression of an antenna array according to claim 6, characterized in that The specific process of the said Step 25 is as follows: Step B1: Set the maximum number of iterations as iter2 and set the stopping threshold ε s = 10 -8 , and set the initial value of iteration as Initialize the current iteration number i = 0; Step B2: Initialize the current sampling point index l = 1; Step B3: Based on the cancellation angles at L sampling moments and the arrival angles of each interference signal estimated by the multi-signal classification algorithm in Step 4, construct the desired signal angle refinement zero-order matrix of the current sampling point index where the intermediate variable q xαβ,l is: where θ jβ,l represents the cancellation angle of the β-th interference at the l-th sampling moment; Step B4. Based on the refined expected signal arrival angle at the $i$-th iteration and the cancellation angle at the $l$-th sampling moment in Step 24, construct the zero-order vector for refining the expected signal angle of the current sampling point index where: intermediate variable q xsα,l is: where, θ jα,l represents the cancellation angle of the α-th interference at the l-th sampling moment; Step B5: Refine the zero-order matrix of the desired signal angle based on the current sampling point index and the zero-order vector of the desired signal angle of the current sampling point index, and solve the zero-order refinement factor of the current sampling point index Among them, represents the new matrix formed after replacing the m-th column of with ; Step B6. Refine the expected signal arrival angle at the $i$-th iteration and the cancellation angle at the $l$-th sampling moment in step 24 to construct the first-order vector for refining the expected signal angle of the current sampling point index Among them, the vector The elements in are as follows: α＝1,2,…,M Step B7: Based on the first-order vector of the desired signal angle refinement and the zero-order matrix of the desired signal angle refinement at the current sampling point index, solve the first-order refinement factor at the current sampling point index Among them, represents the new matrix formed after replacing the m-th column of with ; Step B8. Based on the refined expected signal arrival angle at the $i$-th iteration and the cancellation angle at the $l$-th sampling moment in step 24, construct the second-order vector for refining the expected signal angle of the current sampling point index Among them, the vector The elements in are as follows: When q xsα,l is 1, there is: α＝1,2,…,M Otherwise, there is: α＝1,2,…,M Step B9: Solve the second-order refinement factor of the current sampling point index based on the expected signal angle-refined second-order vector of the current sampling point index and the expected signal angle-refined zero-order matrix of the current sampling point index Among them, represents the new matrix formed after replacing the m-th column of with ; Step B10: Calculate the N-dimensional weights of the desired signal channel at the i-th iteration based on the refined desired signal arrival angle at the i-th iteration Step B11: Calculate the l-th sampling point of the desired waveform in the i-th iteration based on the N-dimensional weights of the desired signal channel in the i-th iteration, the zero-order refinement factor of the current sampling point index, the interference channel weights stored in Step 15, and the received data unit matrix in Step 2 Among them, represents the m-th element of the vector , and r [:,l] represents the column vector formed by all the elements in the l-th column of the matrix r; Step B12: Based on the refined arrival angle of the desired signal in the i-th iteration, the N-dimensional weights of the desired signal channel in the i-th iteration, the first-order refinement factor of the current sampling point index, the interference channel weights stored in Step 15, and the received data unit matrix in Step 2, calculate the first derivative of the l-th sampling point of the desired waveform in the i-th iteration; Among them, matrix A is a matrix with non-zero elements only on the main diagonal. The dimension of matrix A is N×N, and the element in the u-th row and u-th column of matrix A is u - 1. denotes the m-th element of the vector, where 1 ≤ m ≤ M and 1 ≤ u ≤ N; Step B13: Based on the refined arrival angle of the desired signal in the i-th iteration, the N-dimensional weights of the desired signal channel in the i-th iteration, the second-order refinement factor of the current sampling point index, the interference channel weights stored in Step 15, and the received data unit matrix in Step 2, calculate the second derivative of the l-th sampling point of the desired waveform in the i-th iteration: In the formula, represents the m-th element of the vector; Step B14: Compare the magnitude relationship between l and L; If l = L, then execute Step B15; Otherwise, let l = l + 1, and then return to Step B3; Step B15: Based on the l-th sampling point of the desired waveform in the i-th iteration and the first derivative of the l-th sampling point of the desired waveform in the i-th iteration, construct the first derivative of the desired waveform power in the i-th iteration: where r( i ) represents the expected waveform of the i-th iteration; Step B16: Based on the l-th sampling point of the desired waveform in the i-th iteration, the first derivative of the l-th sampling point of the desired waveform in the i-th iteration, and the second derivative of the l-th sampling point of the desired waveform in the i-th iteration, construct the second derivative of the desired waveform power in the i-th iteration: Where: Step B17: Based on the first derivative of the desired waveform power in the i-th iteration and the second derivative of the desired waveform power in the i-th iteration, calculate the update step size in the i-th iteration: Step B18: Based on the refined expected signal arrival angle at the $i$-th iteration and the update step at the $i$-th iteration, obtain the refined expected signal arrival angle at the $(i + 1)$-th iteration : Step B19, determine whether ξ (i) exceeds the set stop threshold ε s , If it does not exceed, then execute Step B21, otherwise, execute Step B20; Step B20: Determine whether the current iteration number i is equal to the set maximum iteration number iter2 – 1; If so, then execute Step B21; Otherwise, let i = i + 1, and return to Step B2; Step B21: Based on the refined angle of arrival of the desired signal at the i-th iteration, the angle ambiguity region of the desired signal in Step 5, and the angle of arrival of the desired signal estimated by the multiple signal classification algorithm in Step 4, output the refined angle of arrival of the desired signal :

8. A method for suppressing virtual multi-channel interference of an antenna array according to claim 7, characterized in that, The specific process of the said Step 27 is as follows: Step C1: Initialize the current sampling point index l = 1; Step C2: Based on the cancellation angle at the l-th sampling moment and the interference channel weights stored in Step 15, construct the cancellation factor interference matrix S; where: the element S in matrix S αβ,l is: where \(a(\theta jβ,l )\) represents the \(N -\)dimensional steering vector of \(\theta jβ,l ; Step C3: Based on the cancellation angle at the l-th sampling moment in Step 24 and the desired signal channel weights in Step 26, construct the cancellation factor desired signal vector s; Among them, the element s in the vector s α,l is as follows: Step C4: Calculate the cancellation factor vector k of the current sampling point based on the cancellation factor interference matrix and the cancellation factor desired signal vector (l) ; k (l) = [k 1,l k 2,l … k M,l T ​ Among them, k (l) The element k in α,l is as follows: where S α represents a new matrix formed by replacing the α-th column of matrix S with s; Step C5: Compare the magnitude relationship between l and L; If l = L, then execute Step C6; Otherwise, let l = l + 1 and return to Step C2; Step C6: According to the cancellation factor vectors at each sampling point, output the final cancellation factor matrix k; k = [k (1) k (2) … k (L) 。 9. The virtual multi-channel interference suppression method for an antenna array according to claim 8, characterized in that, The specific process of Step 28 is as follows: Step D1: Initialize the current sampling point index l = 1; Step D2: Calculate the cancellation signal y at the current sampling point based on the cancellation factor obtained in Step 27, the desired signal channel weights in Step 26, the interference channel weights stored in Step 15, and the received data unit matrix in Step 2 l ; where k m,l represents the m-th element in the cancellation factor vector k (l) for the l-th sampling point; Step D3: Compare the magnitude relationship between l and L; If l = L, then execute Step D4; Otherwise, let l = l + 1 and return to execute Step D2; Step D4: Construct and output the interference-cancelled signal y based on the cancellation signals at each sampling point, completing the interference cancellation process. The interference-cancelled signal is expressed as: y = [y1 y2 … y L .

10. A method for virtual multi-channel interference suppression of an antenna array, characterized in that, The method specifically includes the following steps: Step 1: The N receiving antennas in the antenna array are arranged in a uniform linear array. The N receiving antennas respectively receive analog signals from free space, and the received signals respectively pass through each radio frequency processing link to form N digital sequences; The radio frequency processing link includes a low-noise amplifier, a down-converter, and an analog-to-digital converter; Step 2: Integrate the N digital sequences formed in Step 1: Summarize the data of the N receiving antennas at L consecutive sampling points into a received data unit matrix r of N rows and L columns; Step 3: Analyze the received data unit matrix r using the multiple signal classification algorithm to obtain the number of signals M existing in the space total , the intensity of each signal, and the arrival angle of each signal; Step 4: Regard the signal with the weakest intensity in the space as the desired signal, and regard the remaining signals in the space as interference signals, that is, the number of interference signals M = M total – 1, denote the arrival angle of the desired signal estimated by the multiple signal classification algorithm as Denote the arrival angles of the respective interference signals estimated by the multiple signal classification algorithm as Step 5. Obtain the expected signal angle ambiguity region Θ based on the arrival angle estimation error empirical value Δ and the expected signal arrival angle estimated by the multiple signal classification algorithm s , and obtain the interference signal angle ambiguity region Θ based on the arrival angle estimation error empirical value Δ and the arrival angles of each interference signal estimated by the multiple signal classification algorithm j ; Step 6. Determine the number of processing channels M according to the number of interference signals M p = 2M + 1. The processing channels include 1 desired signal channel, M interference channels, and M auxiliary channels; Step 7: Initialize the dimension U for calculating the steering vector d = N, and set the maximum deviation factor f of the auxiliary channel p ; Step Eight: Initialize the deviation factor C of the current auxiliary channel p = 0; Step Nine: Initialize the processing angles θ of M auxiliary channels f1 , θ f2 , …, θ fM as follows: Step 10: Set the current interference channel and auxiliary channel index i = 1; Step 11: Modify the processing angle of the i-th auxiliary channel to: where ε represents the auxiliary channel angle step; Step Twelve: Divide the U-dimensional steering vector of the arrival angle of the i-th interference signal estimated by the multiple signal classification algorithm by U d and use the resulting quotient as the weight w of the i-th interference channel d . ji ; where the superscript "T" represents matrix transpose, e is the base of the natural logarithm, j in the e exponent is the imaginary unit, and π is the circumference ratio; Step Thirteen: Divide the U of the modified processing angle of the i-th auxiliary channel d dimensional steering vector by U d , and use the obtained quotient as the weight w of the i-th auxiliary channel fi ; Step Fourteen: Compare the relative magnitudes of U d and N; If U d = N, then execute Step 15; Otherwise, execute Step 16; Step 15: Store the weights of the i-th interference channel calculated in Step 12, and then execute Step 16; Step Sixteen: Calculate and store the output signal r of the current ith interference channel and the output signal r of the ith auxiliary channel according to the weight of the ith interference channel calculated in Step Twelve, the weight of the ith auxiliary channel calculated in Step Thirteen, and the received data unit matrix r ji and the output signal r of the ith auxiliary channel fi ; Step 17: Compare the magnitude of i with the number of interference signals M; If i = M, execute Step 18, otherwise let i = i + 1 and return to execute Step 11; Step Eighteen: Calculate the feasible solution of the initial value of the cancellation angle according to r ji and r fi ; If the number of feasible solutions is equal to M, directly use the feasible solutions as the initial values for the iteration of the M interference center angles to execute Step 23; If the number of feasible solutions is greater than M, then screen the feasible solutions, and the selected feasible solutions form an optional set Θ for the initial value of the cancellation angle, D and then execute Step 19; Step Nineteen: Determine whether the number of elements in the optional set Θ of the cancellation angle initial values D is equal to M; If the number of elements in the optional set Θ of the cancellation angle initial values D is equal to M, then output M interference center angles θ j1 , θ j2 , …, θ jM , and then execute step twenty-three; Otherwise, execute Step 20; Step Twenty: Let the current auxiliary channel deviation factor C p = C p + 1; Step twenty-one, determine the magnitude relationship between C p and f p – 1; If C p > f p – 1, then perform Step Twenty-Two; Otherwise, return to Step 10; Step 22. Let the dimension of the steering vector calculation be U d = U d – 1, and return to execute Step 8; Step twenty-three, set the angular velocities ω1, ω2, …, ω of each interference M to be all 0; Step 24: Based on each interference center angle output in Step 19 and the angular velocities of each interference set in Step 23, obtain the cancellation angle matrix of all interferences at L sampling moments: where: θ jm,l = θ jm + ω m l, m = 1, 2, …, M; l = 1, 2, …, L Step twenty-five, read the weights of the M interference channels stored and the arrival angle of the desired signal estimated by the multiple signal classification algorithm in Step four Calculate the refined arrival angle of the desired signal by using the received data unit matrix r in Step two and the cancellation angles at L sampling moments Step twenty-six: Divide the N-dimensional steering vector of the refined desired signal arrival angle by N, and use the obtained quotient as the desired signal channel weight w s ; Step 27: According to the cancellation angles at L sampling moments in Step 24, the desired signal channel weights in Step 26, and the interference channel weights stored in Step 15, calculate the cancellation factors of each interference at L sampling points; Step 28: According to the cancellation factors obtained in Step 27, the desired signal channel weights in Step 26, the interference channel weights stored in Step 15, and the received data unit matrix r in Step 2, output the interference-cancelled signal y.

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