A space-frequency multi-beam anti-interference method and system based on conjugate gradient algorithm

Abstract

The invention relates to the field of navigation signal processing, and discloses a space-frequency multi-beam anti-interference method and system based on a conjugate gradient algorithm. The method comprises: adopting a space-frequency adaptive processing method, constraining the direction of an expected signal at each independent frequency point of a space-frequency signal, performing minimum variance distortionless response (MVDR) beamforming, realizing distortionless response of the signal, and forming a null in the interference direction. MVDR beamforming of multiple signal directions is performed in parallel to realize space-frequency multi-beam anti-interference processing, and then a conjugate gradient (CG) algorithm is used to iteratively solve the inverse of the autocorrelation matrix in the MVDR beamforming, and a Krylov subspace is gradually constructed in the iterative process, which can converge within the number of iterations less than the data dimension, is more stable than direct matrix inversion, and the computational complexity is reduced by one order of magnitude compared with direct matrix inversion, thereby reducing the computational complexity of space-frequency multi-beam anti-interference and improving the stability of the algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of navigation signal processing, and more specifically to a space-frequency multi-beam anti-interference method and system based on a conjugate gradient algorithm. Background Art

[0002] The characteristics of navigation satellite signals determine that aviation or ground receiving equipment is extremely susceptible to ambient noise or even artificial suppression interference. In severe cases, the receiving equipment cannot receive satellite positioning normally. Adaptive array antenna is an important technical approach to suppress suppression interference. This technology uses the spatial characteristics of the array to form a spatial null in the direction of the interference wave to suppress high-power interference.

[0003] According to the signal constraints, the spatial filtering algorithm can be designed as unconstrained, single-direction constrained minimum variance distortionless response (MVDR) and multi-direction constrained linear minimum variance (LCMV). Under the premise that the array aperture and the number of array elements are determined, the LCMV beamforming method of the multi-constraint method consumes the array degrees of freedom, which reduces the algorithm's interference suppression ability. The unconstrained method selects an array element as a receiving reference and cannot provide array receiving gain. The MVDR beamforming method with single-direction constraints constrains the incoming direction, forms the maximum gain of the array in the signal direction, and suppresses interference in other directions. This method can maximize the array's signal receiving ability and interference suppression ability. However, navigation satellites are dispersed in space, so it is necessary to constrain the incoming direction of each satellite separately and process it in parallel, so that the satellite navigation receiver can capture and track the corresponding satellite signals in parallel. This is the core processing idea of ​​the navigation multi-beam anti-interference receiving system, which is characterized by parallel processing, stacking anti-interference processing algorithm resources, obtaining the maximum signal receiving gain, and providing the strongest interference suppression capability.

[0004] The disadvantage of spatial domain filtering is that it has limited ability to suppress broadband interference signals. In engineering applications, it is often combined with time domain or frequency domain to perform space-time adaptive processing (STAP) or space-frequency adaptive processing (SFAP). If the number of discrete Fourier transform (DFT) points in SFAP is the same as the number of delay taps in STAP, the mean of the time domain output after SFAP processing is the same as the STAP output, and the two processing architectures are equivalent. The wider the signal bandwidth, the more DFT points or tap delays there are, resulting in a higher computational complexity in the interference processing process.

[0005] The MVDR beamforming process requires the calculation of the inverse of the autocorrelation matrix. If the matrix dimension is M, the computational complexity of the direct inverse operation is The autocorrelation matrix required for broadband processing has a large dimension, which is not conducive to the real-time and high-speed processing of the MVDR algorithm in hardware platform practice. It consumes a lot of resources. At the same time, limited precision implementation may cause the autocorrelation matrix to be singular and the inverse operation to be unstable. Summary of the invention

[0006] In order to overcome the above-mentioned defects of the prior art, the present invention provides a space-frequency multi-beam anti-interference method and system based on a conjugate gradient algorithm to solve the problems existing in the above-mentioned background technology.

[0007] The present invention provides the following technical solution: a space-frequency multi-beam anti-interference method based on a conjugate gradient algorithm, comprising:

[0008] S1: Perform K-point discrete Fourier transform (DFT) on each data of the digital intermediate frequency signal received by the M-channel antenna array to obtain frequency domain data;

[0009] S2: Select the same frequency point of each antenna frequency domain data to form the spatial domain array signal of the current frequency point, accumulate L groups of data blocks after calibrating the array signal amplitude and phase, form a spatial frequency processing data matrix, and estimate the data autocorrelation matrix of each frequency point;

[0010] S3: Based on the desired signal steering vector, the minimum variance distortionless response (MVDR) beamforming algorithm is used at each independent frequency point to achieve narrowband spatial domain beamforming;

[0011] S4: The inverse of the autocorrelation matrix of each frequency point data in the MVDR beamformer is iteratively solved by the conjugate gradient (CG) algorithm to reduce the computational complexity of the MVDR algorithm;

[0012] S5: Perform inverse discrete Fourier transform (IDFT) on the frequency domain processed output signal to restore the time domain output;

[0013] S6: Execute space-frequency MVDR beamforming of P beams in parallel, and independently output P time-domain beam signals to achieve space-frequency multi-beam anti-interference.

[0014] Preferably, the antenna array of S1 receives a digital intermediate frequency signal obtained by low-noise amplification, filtering, down-conversion and AD analog-to-digital conversion of the array antenna receiving signal; the FPGA outputs a baseband complex signal through digital pre-filtering and IQ conversion of the M-channel digital intermediate frequency signals after AD conversion, and accumulates K points to obtain an array data matrix.

[0015] Preferably, S2 obtains a space-frequency processing data matrix based on the array data matrix through a K-point DFT transformation; selects the same frequency point of each antenna receiving frequency domain data to form a space-domain array signal of the current frequency point; calibrates the array signal amplitude and phase and accumulates L groups of data blocks to estimate the array autocorrelation matrix of the frequency point.

[0016] Preferably, S3 calculates the desired signal steering vector according to the direction of the desired signal and the array position vector; performs MVDR narrowband beamforming at the kth frequency point to point the maximum gain of the array in the desired direction and simultaneously forms a null in the interference direction.

[0017] Preferably, S4 iteratively solves the inverse of the autocorrelation matrix of each frequency point data in the MVDR beamformer based on the CG algorithm; the CG algorithm is based on the data matrix, and gradually constructs the Krylov subspace during the iteration process, and can converge within the number of iterations less than the data dimension. Its computational complexity is reduced by one order of magnitude compared with direct matrix inversion.

[0018] To achieve the above object, the present invention provides the following technical solution: a space-frequency multi-beam anti-interference system based on a conjugate gradient algorithm, implementing the above space-frequency multi-beam anti-interference method based on a conjugate gradient algorithm, comprising:

[0019] Antenna array module: a standard spacing antenna array with M array elements, including but not limited to a uniform circular array, a uniform rectangular array, and a hexagonal array;

[0020] RF channel module: used to receive array signals and perform low-noise amplification, filtering, down-conversion and AD analog-to-digital conversion to output M digital intermediate frequency signals to FPGA;

[0021] DFT transformation module: transforms the time domain array signal into the frequency domain by using fast Fourier transform (FFT);

[0022] Steering vector generation module: It is used to constrain the distortion-free response of the signal by generating the steering vector of the array in the direction of the desired signal;

[0023] MVDR beamforming module: used to execute the MVDR beamforming algorithm and use the CG algorithm to reduce the computational complexity of matrix inversion;

[0024] IDFT transformation module: By adopting the inverse fast Fourier transform (IFFT), the frequency domain processing output signal is transformed into the time domain and provided to the navigation receiving device.

[0025] Technical effects and advantages of the present invention:

[0026] The present invention adopts a space-frequency adaptive processing method to constrain the desired signal direction at each independent frequency point of the space-frequency signal, performs minimum variance distortionless response (MVDR) beamforming, realizes distortionless response of the signal, and forms a null in the interference direction. The MVDR beamforming of multiple signal directions is performed in parallel to realize space-frequency multi-beam anti-interference processing, and then the conjugate gradient (CG) algorithm is used to iteratively solve the inverse of the autocorrelation matrix in the MVDR beamforming. The Krylov subspace is gradually constructed during the iteration process, and it can converge within the number of iterations less than the data dimension. It is more stable than direct matrix inversion, and the computational complexity is reduced by one order of magnitude compared with direct matrix inversion.

[0027] By introducing the conjugate gradient (CG) algorithm into the MVDR beamforming process, the linear system equation subspace iteration method is used to equivalently solve the inverse of the autocorrelation matrix. The CG algorithm is based on the data matrix and the Krylov subspace is gradually constructed in the iterative process. It can converge within the number of iterations less than the data dimension and is more stable than direct matrix inversion. Compared with direct matrix inversion, its computational complexity is reduced by one order of magnitude to The computational complexity of broadband processing is reduced, thereby reducing the computational complexity of space-frequency multi-beam anti-interference and improving the stability of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of space-frequency multi-beam anti-interference processing based on conjugate gradient algorithm;

[0029] Figure 2 It is a uniform circular array structure;

[0030] Figure 3 This is a schematic diagram of the convergence speed of the conjugate gradient algorithm;

[0031] Figure 4 It is a space-frequency multi-beam anti-interference processing system based on the conjugate gradient algorithm. DETAILED DESCRIPTION

[0032] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention. In addition, the forms of the various structures recorded in the following embodiments are merely illustrative. The space-frequency multi-beam anti-interference method and system based on the conjugate gradient algorithm involved in the present invention is not limited to the various structures recorded in the following embodiments. All other implementations obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0033] like Figure 1 This embodiment provides a space-frequency multi-beam anti-interference method based on a conjugate gradient algorithm, including:

[0034] S1: Perform K-point discrete Fourier transform (DFT) on each data of the digital intermediate frequency signal received by the M-channel antenna array to obtain frequency domain data.

[0035] In this embodiment, the antenna array of S1 receives the digital intermediate frequency signal obtained by low-noise amplification, filtering, down-conversion and AD analog-to-digital conversion of the array antenna receiving signal; the FPGA outputs the baseband complex signal of the M-channel digital intermediate frequency signal after AD conversion through digital pre-filtering and IQ conversion, and accumulates K points to obtain the array data matrix.

[0036] It should be specifically explained that in a standard spacing antenna array with M antenna elements, each element receives navigation signals and interference signals from different directions; the array received signal is low-noise amplified, filtered, down-converted, and AD analog-to-digital converted, and the FPGA samples to obtain M digital intermediate frequency signals, and performs digital pre-filtering and IQ conversion to output baseband complex signals; the multi-beam anti-interference module accumulates K point data to obtain x m =[x m (n), x m (n-1), …x m (n-K+1)] T ,in(·) T represents transpose, m = 1, ..., M. Perform K-point DFT transformation on the data received by each antenna to obtain frequency domain data

[0037] S2: Select the same frequency point of each antenna frequency domain data to form the spatial domain array signal of the current frequency point, accumulate L groups of data blocks after calibrating the array signal amplitude and phase to form a spatial-frequency processing data matrix, and estimate the data autocorrelation matrix of each frequency point.

[0038] In this embodiment, S2 obtains a space-frequency processing data matrix based on the array data matrix through a K-point DFT transformation; selects the same frequency point of each antenna receiving frequency domain data to form a space-domain array signal of the current frequency point; calibrates the array signal amplitude and phase and accumulates L groups of data blocks to estimate the array autocorrelation matrix of the frequency point.

[0039] It should be specifically noted that the same frequency point of each antenna receiving frequency domain data is selected to form the spatial array signal of the current frequency point in It represents the kth frequency point after DFT transformation of the time domain data of the mth unit antenna, and its expression is as follows:

[0040]

[0041] where x mi =x m (n-i+1); after calibrating the array signal amplitude and phase, narrowband spatial filtering is performed at this frequency point:

[0042]

[0043] in(·) H represents the conjugate transpose, w(k)=[w1(k),…,w M (k)] T Represents the kth frequency weight vector. Narrowband filtering of all frequency points is equivalent to broadband array processing of the entire frequency band. If the number of DFT points in SFAP is the same as the number of delay taps in STAP, the mean of the time domain output after SFAP processing is completed is the same as the STAP output, and the two processing architectures are equivalent;

[0044] The K-point array received data blocks are accumulated into L groups of data blocks to form a space-frequency processing data matrix, and the M×M-dimensional array autocorrelation matrix of the k-th frequency point is calculated as

[0045]

[0046] in Represents the k-th frequency point array signal vector after the l-th input signal data block is transformed by DFT.

[0047] S3: Based on the desired signal steering vector, a minimum variance distortionless response (MVDR) beamforming algorithm is used at each independent frequency point to achieve narrowband spatial domain beamforming.

[0048] In this embodiment, S3 calculates the desired signal steering vector according to the direction of the desired signal and the array position vector; performs MVDR narrowband beamforming at the kth frequency point so that the maximum gain of the array points to the desired direction and forms a null in the interference direction.

[0049] It should be specifically explained that, according to the expected signal to (θ, φ), the k-th frequency point steering vector is calculated

[0050]

[0051] Among them, p m represents the position vector of the antenna array, u represents the direction vector of the incoming wave, and k represents the wave number in the incoming wave direction (θ, φ)

[0052]

[0053] Assume that the processing signal bandwidth is B s , the carrier frequency is f c , the kth frequency point in SFAP can be expressed as

[0054]

[0055] Where Δf = B s / K represents the SFAP frequency domain processing interval;

[0056] This embodiment uses a standard pitch uniform circular array (UCA) and establishes a Cartesian coordinate system with the center of the array as the origin. Figure 2 As shown in Figure 1, one antenna unit is arranged at the origin of the coordinate system, and six antenna units are evenly arranged on the ring. Substituting the position vector of the UCA array into the array steering vector, we get

[0057]

[0058] If you expect u s The maximum gain is formed in the direction, and narrowband beamforming is performed at the kth frequency point. The minimum variance distortionless response (MVDR) weight vector expression is:

[0059]

[0060] The MVDR algorithm needs to calculate the inverse of the autocorrelation matrix, and its calculation complexity is

[0061] S4: The conjugate gradient (CG) algorithm is used to iteratively solve the inverse of the autocorrelation matrix of each frequency point data in the MVDR beamformer to reduce the computational complexity of the MVDR algorithm.

[0062] In this embodiment, the S4 iteratively solves the inverse of the autocorrelation matrix of each frequency point data in the MVDR beamformer based on the CG algorithm; the CG algorithm is based on the data matrix, and gradually constructs the Krylov subspace during the iteration process. It can converge within the number of iterations less than the data dimension. Its computational complexity is reduced by one order of magnitude compared with direct matrix inversion.

[0063] It should be noted that by using the CG algorithm to iteratively calculate the MVDR algorithm Operation, reducing the computational complexity of the MVDR algorithm;

[0064] By using the CG subspace iteration method Since the sampling autocorrelation matrix is ​​a real symmetric non-singular matrix, the above process can be obtained by the linear system equation Equivalent solution; CG algorithm is a commonly used subspace iterative method for solving linear system equations; CG algorithm is an important improved form of the steepest descent algorithm, belongs to the Krylov subspace category, and is one of the important iterative techniques for solving sparse symmetric positive definite systems; Krylov subspace algorithm is a popular subspace processing algorithm based on the projection framework; CG algorithm is based on the data matrix, and gradually constructs the Krylov subspace during the iteration process, and can converge within the number of iterations less than the data dimension; its computational complexity is reduced by one order of magnitude to compared with direct matrix inversion. Reduced the computational complexity of SFAP;

[0065] Initialize the CG algorithm first w0 = 0 and define the initial residual Conjugate gradient search direction p1=r0, residual power The nth iteration process of the conjugate gradient algorithm is as follows:

[0066] (1) Calculate the intermediate variable s n and solution vector iteration step factor α n

[0067]

[0068] (2) Update the solution vector

[0069] w n =w n-1 +α n p n

[0070] (3) Update the residual (gradient) vector

[0071] r n =r n-1 =α n w n

[0072] (4) Calculate the residual power ρ n+1 and the search direction iteration step factor β n+1

[0073]

[0074] β n+1 =ρ n+1 / ρ n

[0075] (5) Update search direction

[0076] p n+1 =r n +β n+1 p n

[0077] The CG algorithm is based on the data matrix and gradually constructs the Krylov subspace in the iterative process. The convergence process is as follows: Figure 3 As shown in Figure 2, the convergence speed is better than the steepest descent algorithm and can converge within a number of iterations less than the data dimension. Its computational complexity is reduced by one order of magnitude to Reduced the computational complexity of SFAP;

[0078] The important properties satisfied in the CG algorithm include:

[0079] (1) Search direction vector relative to the matrix Conjugation of:

[0080] (2) Orthogonality of residual vector:

[0081] (3) The gradient vector obeys the extended subspace theorem: that is, the residual of the nth step is orthogonal to the direction vector of this step and the previous steps:

[0082] (4) Finite-step iterative convergence: Maximum number of iterations n max ≤M;

[0083] (5) Decline: This means that the search direction of the n+1th iteration is always the negative direction of the gradient;

[0084] The CG iteration stopping criterion can be selected to satisfy any of the following two points: (1) The residual power ρ n+1 Less than 2 times of the noise power; (2) The number of iterations is equal to the number of antenna array elements;

[0085] The CG algorithm iteration is a process of gradually constructing a Krylov subspace, where the conjugate direction vector group and the residual vector group The same Krylov subspace is:

[0086]

[0087] if has r different eigenvalues, the CG algorithm will terminate the iteration after at most r steps. Define the energy norm Then, at the nth iteration, the convergence performance of the CG algorithm can be derived through the Chebyshev polynomial:

[0088]

[0089] where w * is the optimal solution vector, k is a matrix The condition number is the ratio of the maximum eigenvalue to the minimum eigenvalue of the matrix; the above formula shows that the matrix The larger the condition number, the slower the CG algorithm converges, and the smaller the condition number, the faster the algorithm converges.

[0090] S5: Perform an inverse discrete Fourier transform (IDFT) on the frequency domain processed output signal to restore the time domain output.

[0091] S6: Execute space-frequency MVDR beamforming of P beams in parallel, and independently output P time-domain beam signals to achieve space-frequency multi-beam anti-interference.

[0092] It should be specifically noted that, assuming that P beams need to be formed, the steering vector is calculated based on the pth desired signal where p = 1, ..., P, u p Indicates the desired direction of the pth beam; performs MVDR beamforming of P beams in parallel, independently outputs P time-domain beam signals, and finally outputs the digital signals after multiple digital beamforming to the back-end receiving device to capture and track the navigation signals in the corresponding direction.

[0093] The present embodiment provides an implementation system corresponding to a space-frequency multi-beam anti-interference method based on a conjugate gradient algorithm, including an antenna array module, a radio frequency channel module, a DFT transformation module, a steering vector generation module, an MVDR beamforming module and an IDFT transformation module. The antenna array module is connected to the radio frequency channel module, the radio frequency channel module is connected to the DFT transformation module, the DFT transformation module is connected to the MVDR beamforming module, the steering vector generation module is connected to the MVDR beamforming module, and the MVDR beamforming module is connected to the IDFT transformation module.

[0094] The antenna array module is a standard spacing antenna array with M array elements, including but not limited to a uniform circular array, a uniform rectangular array, and a hexagonal array;

[0095] The radio frequency channel module is used to receive array signals and perform low-noise amplification, filtering, down-conversion, and AD analog-to-digital conversion of the signals to output M digital intermediate frequency signals to the FPGA;

[0096] The DFT transformation module transforms the time domain array signal into the frequency domain by using a fast Fourier transform (FFT);

[0097] The steering vector generation module generates a steering vector of the array in the direction of the desired signal to constrain the signal's distortion-free response;

[0098] The MVDR beamforming module is used to execute the MVDR beamforming algorithm and use the CG algorithm to reduce the computational complexity of matrix inversion;

[0099] The IDFT transformation module transforms the frequency domain processing output signal into the time domain by using the Inverse Fast Fourier Transform (IFFT) and provides it to the navigation receiving device.

[0100] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

[0101] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A space-frequency multi-beam anti-interference method based on conjugate gradient algorithm, characterized in that: include: S1: Perform K-point discrete Fourier transform (DFT) on each data of the digital intermediate frequency signal received by the M-channel antenna array to obtain frequency domain data; S2: Select the same frequency point of each antenna frequency domain data to form the spatial domain array signal of the current frequency point, accumulate L groups of data blocks after calibrating the array signal amplitude and phase, form a spatial frequency processing data matrix, and estimate the data autocorrelation matrix of each frequency point; S3: Based on the desired signal steering vector, the minimum variance distortionless response (MVDR) beamforming algorithm is used at each independent frequency point to achieve narrowband spatial domain beamforming; S4: The inverse of the autocorrelation matrix of each frequency point data in the MVDR beamformer is iteratively solved by the conjugate gradient (CG) algorithm to reduce the computational complexity of the MVDR algorithm; S5: Perform an inverse discrete Fourier transform (IDFT) on the frequency domain processed output signal to restore the time domain output; S6: Execute space-frequency MVDR beamforming of P beams in parallel, and independently output P time-domain beam signals to achieve space-frequency multi-beam anti-interference.

2. The space-frequency multi-beam anti-interference method based on the conjugate gradient algorithm according to claim 1 is characterized in that: The antenna array of S1 receives the digital intermediate frequency signal obtained by low-noise amplification, filtering, down-conversion and AD analog-to-digital conversion of the array antenna receiving signal; FPGA outputs the baseband complex signal of the M-channel digital intermediate frequency signal after AD conversion through digital pre-filtering and IQ conversion, and accumulates K points to obtain the array data matrix.

3. The space-frequency multi-beam anti-interference method based on the conjugate gradient algorithm according to claim 1 is characterized in that: The S2 obtains a space-frequency processing data matrix based on the array data matrix through K-point DFT transformation; Select the same frequency point of each antenna to receive frequency domain data to form a spatial array signal of the current frequency point; The array signal amplitude and phase are calibrated and L groups of data blocks are accumulated to estimate the array autocorrelation matrix of the frequency point.

4. The space-frequency multi-beam anti-interference method based on the conjugate gradient algorithm according to claim 1 is characterized in that: The S3 calculates the desired signal steering vector according to the direction of the desired signal and the array position vector; performs MVDR narrowband beamforming at the kth frequency point to point the maximum gain of the array to the desired direction and form a null in the interference direction.

5. The space-frequency multi-beam anti-interference method based on the conjugate gradient algorithm according to claim 1 is characterized in that: The S4 iteratively solves the inverse of the autocorrelation matrix of each frequency point data in the MVDR beamformer based on the CG algorithm; The CG algorithm is based on the data matrix and gradually constructs the Krylov subspace during the iteration process. It can converge within the number of iterations less than the data dimension. Its computational complexity is reduced by one order of magnitude compared with direct matrix inversion.

6. A space-frequency multi-beam anti-interference system based on a conjugate gradient algorithm, implementing a space-frequency multi-beam anti-interference method based on a conjugate gradient algorithm as described in any one of claims 1 to 5, characterized in that: include: Antenna array module: a standard spacing antenna array with M array elements, including but not limited to a uniform circular array, a uniform rectangular array, and a hexagonal array; RF channel module: used to receive array signals and perform low-noise amplification, filtering, down-conversion and AD analog-to-digital conversion to output M digital intermediate frequency signals to FPGA; DFT transformation module: transforms the time domain array signal into the frequency domain by using fast Fourier transform (FFT); Steering vector generation module: It is used to constrain the distortion-free response of the signal by generating the steering vector of the array in the direction of the desired signal; MVDR beamforming module: used to execute the MVDR beamforming algorithm and use the CG algorithm to reduce the computational complexity of matrix inversion; IDFT transformation module: By adopting the inverse fast Fourier transform (IFFT), the frequency domain processing output signal is transformed into the time domain and provided to the navigation receiving device.

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