A method for obtaining beamforming weight vectors in an integrated radar and communication system
By combining orthogonal polynomial fitting and Gauss-Legendal numerical integration with the Schmidt orthogonalization method, and using a dual-phase shifter architecture, the problems of high computational complexity and insufficient hardware performance of beamforming algorithms in radar-communication integrated systems are solved, achieving low-complexity and highly robust beamforming weight vector acquisition.
Patent Information
- Application Number
- CN202511930745.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-19
- Publication Date
- 2026-05-26
AI Technical Summary
In existing radar-communication integrated systems, beamforming algorithms suffer from the problem of suppressing desired signals under high signal-to-interference-plus-noise ratios (SINR), and matrix integral reconstruction algorithms have high computational complexity, making it difficult to meet real-time processing requirements. At the same time, quantization errors in hardware implementation devices lead to performance degradation.
An orthogonal polynomial is used to fit the interference subspace and combined with the Gauss-Legends numerical integration method for low-complexity solution. The projection operator is solved by Schmidt orthogonalization recursion. A dual phase shifter architecture is introduced to replace the traditional phase shifter and attenuator to realize the update of beamforming weight vector.
While reducing computational complexity, the algorithm's robustness and performance under low-quantization bit hardware are improved, achieving low-complexity, highly robust beamforming that is adaptable to high signal-to-interference-plus-noise ratio environments.
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Figure CN122092920A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of array signal processing technology, and in particular to a method for obtaining beamforming weight vectors in an integrated radar and communication system. Background Technology
[0002] Beamforming is a core technology in array signal processing. By controlling the amplitude and phase of each element in the array antenna, a beam with specific directionality can be formed, effectively suppressing interference and noise from other directions and significantly improving the signal-to-noise ratio of the array output. From the perspective of beamforming anti-interference, the core of radar-communication integration technology lies in constructing an independent and controllable transmit-receive link through shared aperture arrays and adaptive beamforming technology. This system utilizes the beamforming capability of a large-scale antenna array to form a high-gain directional beam in the main lobe direction to simultaneously achieve target azimuth perception and directional communication. At the same time, it constructs beam nulls in the azimuth of interference sources and effectively suppresses the energy of incoming interference waves through spatial filtering. By continuously sensing the electromagnetic environment through radar, the system can dynamically optimize the beamforming weight vector, forming a closed-loop control of "perception-decision-beam pointing update," ultimately achieving synergistic enhancement of perception and communication functions and efficient utilization of spectrum resources in adversarial environments.
[0003] However, the application of existing beamforming technologies in integrated communications still faces many challenges: First, in practical applications, factors such as mechanical platform jitter, interference source movement, and angle estimation errors can easily lead to array manifold mismatch, resulting in beam null shift and performance degradation. While traditional robust adaptive beamforming algorithms can improve robustness by widening nulls, they cannot completely eliminate the desired signal component in the sample covariance matrix, leading to the suppression of the desired signal at high signal-to-interference-plus-noise ratios. Second, while matrix integral reconstruction-based algorithms can avoid the suppression of the desired signal by reconstructing the interference plus noise covariance matrix, their high computational complexity makes them difficult to meet the requirements of real-time systems. Furthermore, at the hardware implementation level, quantization errors in digital phase shifters and attenuators can cause shallower beam nulls, making it difficult for traditional RF front-end architectures to achieve high performance with low quantization bits.
[0004] Taking all factors into consideration, existing methods for obtaining beamforming weight vectors based on integrated radar and communication systems have the following main shortcomings: 1. Traditional robust beamforming algorithms suffer from the problem of suppressing the desired signal under high signal-to-interference-plus-noise ratio (SINR), while matrix integral reconstruction algorithms have high computational complexity and are difficult to meet real-time processing requirements.
[0005] 2. At the hardware implementation level, device quantization errors will further degrade beamforming performance. Traditional RF front-end architectures based on phase shifters and attenuators have limited performance in scenarios with low quantization bits. Summary of the Invention
[0006] This application provides a method for obtaining beamforming weight vectors in an integrated radar and communication system, which solves the problems of high computational complexity and limited performance of traditional beamforming algorithms under low-quantization-bit hardware. It achieves a significant reduction in computational complexity while ensuring high performance, and has stronger robustness to low-quantization-bit hardware implementation scenarios.
[0007] This application provides a method for obtaining beamforming weight vectors in an integrated radar-communication system, including the following steps: S1: Establish a receiver signal model for a uniform linear array antenna in a radar-communication integrated system; S2: Introducing orthogonal polynomials and the Gauss-Legendal numerical integration method to perform low-complexity and fast fitting and solution of the disturbance subspace; S3: Introduce the Schmidt orthogonalization method to recursively solve the orthogonal complement space projection operator of the interference subspace and project it to obtain the beamforming weight vector; S4: Introduce the equivalent representation of the beamforming weight vector under the dual phase shifter architecture to obtain the updated value of the beam weight vector under the dual phase shifter architecture.
[0008] The beneficial effects of the above embodiments are as follows: This beamforming weight vector acquisition method, based on the projection-type beamforming weight vector of orthogonal polynomial fitting of the interference subspace, has performance similar to that of matrix integral reconstruction-type methods, but with significantly lower computational complexity. This beamforming weight vector acquisition method, combined with a dual-phase-shifter RF front-end hardware architecture, completes weight vector updates under low quantization bit widths. Replacing the traditional phase shifter and attenuator RF front-end architecture with a dual-phase-shifter architecture improves algorithm performance under low quantization bit widths and addresses the problem of insufficient algorithm robustness in low-quantization bit hardware implementation scenarios. This beamforming weight vector acquisition method solves the problems of high computational complexity, poor performance in low-quantization bit hardware scenarios, and desired signal suppression under high signal-to-interference-plus-noise ratios in existing methods, achieving low-complexity and highly robust beamforming.
[0009] Based on the above embodiments, this application can be further improved as follows: In one embodiment of this application, in step S1, it is assumed that the number of array elements is M and the element spacing is the wavelength of the incident signal. Half of, then The steering vector of the incoming wave is: ; The established receiver signal model is as follows: ; in, In order to receive signals, It is additive white Gaussian noise. For target signal, For the first There are 10 interfering signals, where K is the total number of interfering signals.
[0010] Assuming the interference signal, noise signal, and desired signal are uncorrelated, the covariance matrix of the received signal can be expressed as: ; in Represents the expected covariance matrix. The energy of the desired signal; The interference plus noise covariance matrix, Let the energy of the k-th interference signal be _____. This refers to noise energy.
[0011] Assume the interference broadening interval of the k-th interference signal is The total interference widening range is The interference plus noise covariance matrix obtained by the integral reconstruction method can be expressed as: ; right Perform eigenvalue decomposition. .in for Dimensional interference broadens the subspace. The energy components of the interference subspace in its dimension; for 3D noise subspace Let be the energy component of the noise subspace in its dimension.
[0012] The above analysis shows that the key to solving the interference plus noise covariance matrix using the sub-reconstruction method lies in obtaining the broadened interference signal subspace by integrating the steering vector. When the array structure information is precisely known, the subspace spanned by the steering vector within the interference broadening interval is the same as the broadened interference signal subspace. That is: .
[0013] In one embodiment of this application, in step S2, based on the theoretical foundation of the Weierstrass approximation theorem, the invention uses the best square approximation as the basis for actual calculation. For interval The set of all continuous functions on the set, Indicates the number of times not exceeding The subspace formed by polynomials. For a given To find the error Polynomial with the smallest norm This polynomial is what is called... The second-best square approximation polynomial satisfies the following equation: .
[0014] Based on orthogonal polynomial theory, it is possible to specifically construct .set up yes Regarding the weight function A sequence of orthogonal polynomials, then constitute A set of orthogonal bases. At this point, the best square approximation polynomial... can be exist The orthographic projection on is explicitly given: ; In the approximation scheme of this invention, Legendre polynomials are used as... An orthogonal basis of space, and its corresponding weight function The terms are equally weighted across the entire interval. Its general term formula is: ; Guided vector function In the interference-widened sub-interval The upper continuous, of which This represents the width of the expansion interval. (This is achieved through variable substitution.) ， Will From the interval Transform to And record it as ,Right now: ; As the best approximation in the sense of minimum mean square error yes exist The results of orthogonal projection calculations in space This indicates the inner product operation.
[0015] For high-order polynomials and large-scale arrays, the inner product can be calculated directly using the discrete summation method. The computational complexity is relatively high. To reduce computational complexity while maintaining accuracy, a 4-node Gauss-Legends numerical integral is used for approximation. ; The four integration nodes are as follows: and the corresponding weights .
[0016] therefore, The low-complexity approximate solution is as follows: .
[0017] By variable substitution Will From the interval Transform back You can get In the interval The best square approximation on: ; Based on the above analysis, the guide vector In subinterval The best square approximation on can be expressed in the following matrix form: ; in This represents the coefficient vector. The formula indicates that in... On the interval, can be Zhang Cheng's subspace representation, the corresponding coordinate vector is Right now: ; make Indicates the first The coefficient matrix corresponding to each broadened sub-interval. By examining all Orthogonal polynomial fitting is performed on each interference broadened sub-interval, and the resulting coefficient matrix is... Recorded as And the following subspace equivalence relation is obtained: ; This equivalence relation shows that, This is the fitting solution result of the interference subspace.
[0018] In one embodiment of this application, in step S3, the method for directly solving the orthogonal complement space projection operator is... To address the problem of excessively high computational complexity in matrix inversion, this invention employs a Schmitt orthogonalization recursive solution method, effectively avoiding matrix inversion operations and reducing computational complexity. The specific steps are as follows: First, construct the combination matrix, defining its dimension as... Combination matrix , where each column vector Corresponding to a basis vector, The number of array elements. The number of interference sub-intervals. Let be the order of the polynomial approximation.
[0019] Next, set the initial orthogonal basis matrix. This matrix will be updated gradually in subsequent steps through an iterative orthogonalization process.
[0020] Then index each column. Perform the following operations in sequence: 1) Calculate the normalized basis vectors ; 2) Remove orthographic projection components: ; Finally, based on the orthonormal basis matrix obtained recursively... ， The orthogonal complement space projection operator is calculated. .
[0021] Desired signal steering vector exist The projection on satisfies the relation Therefore, the optimal weighting vector for beamforming is... It can be represented as: .
[0022] In one embodiment of this application, in step S4, the dual-phase shifter RF front-end architecture achieves joint control of the amplitude and phase of the beamforming weights by configuring two independent phase shifters on each antenna element.
[0023] The solution obtained 3D optimal beamforming weight vector The complex coefficients corresponding to each array element ( All of these can be equivalently expressed in exponential form as The phase parameter and These correspond to two sets of phase shifts, respectively.
[0024] In actual hardware implementation, quantization is required to map continuous phase values to discrete phase states. A phase shifter with a bit width has a quantization step size of The set of discrete phase states that can be represented is Based on the nearest neighbor mapping principle, continuous phase is quantized into discrete values: ; Ultimately, the system uses two quantization phases. The synthesis achieves the target complex weight This results in the beamforming weight vector. This is represented as the superposition of two constant mode vectors, completing the update of the beamforming weight vector: . Attached Figure Description
[0025] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.
[0026] Figure 1 This is a schematic diagram of an integrated radar and communication scenario in an embodiment of this application.
[0027] Figure 2 This is a flowchart illustrating the steps of a method for obtaining beamforming weight vectors in a radar-communication integrated system according to an embodiment of this application.
[0028] Figure 3 This is a beamforming diagram comparing the method of this application with other algorithms in the embodiments of this application.
[0029] Figure 4 This is a comparison chart of the beamforming performance of this method and other algorithms under different signal-to-noise ratios in the embodiments of this application.
[0030] Figure 5 This is a comparison chart of the beamforming performance of the proposed method under different signal-to-noise ratios in the embodiments of this application, in the dual-phase shifter architecture and the traditional architecture. Detailed Implementation
[0031] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.
[0032] Example: like Figure 1 As shown, a method for obtaining beamforming weight vectors in an integrated radar-communication system includes the following steps: S1. Establish the receiver signal model of a uniform linear array antenna in a radar-communication integrated system. The number of array elements is M, and the element spacing is equal to the wavelength of the incident signal. Half of the receiver signal model: (1); in, In order to receive signals, It is additive white Gaussian noise. For target signal, The direction of the incoming wave to the target. For the first One interference signal, The direction of arrival of the k-th interference signal is given. express The steering vector of the incoming wave: (2).
[0033] This step accurately models the target, interference, and noise components in the received signal, providing a foundation for subsequent interference subspace fitting and weight vector solution.
[0034] S2 introduces orthogonal polynomials and the Gauss-Legendal numerical integration method to perform a low-complexity, fast fitting solution for the disturbance subspace. In the approximation scheme of this embodiment, Legendre polynomials are used as... An orthogonal basis of space, and its corresponding weight function The terms are equally weighted across the entire interval. Its general term formula is: (3); Guided vector function In the k-th interference broadening sub-interval The upper continuous, of which This represents the width of the expansion interval. (This is achieved through variable substitution.) ， Will From the interval Transform to And record it as ,Right now: (4); As the best approximation in the sense of minimum mean square error yes exist The results of orthogonal projection calculations in space. Among them, To represent the inner product operation, and in order to reduce computational complexity while ensuring accuracy, a 4-node Gauss-Legends numerical integral is used for approximation. (5); The four integration nodes are as follows: and the corresponding weights .
[0035] therefore, The low-complexity approximate solution is as follows: (6).
[0036] By variable substitution Will From the interval Transform back You can get In the interval The best square approximation on: (7).
[0037] Based on the above calculation process, the guiding vector In subinterval The best square approximation on can be expressed in the following matrix form: (8); in Represents the coefficient vector. Let Indicates the first The coefficient matrix corresponding to each broadened sub-interval is equivalent to the subspace corresponding to the k-th disturbance. By applying all The coefficient matrix obtained by orthogonal polynomial fitting of each interference broadening subinterval This represents the fitting result of the disturbance subspace. This step avoids directly calculating high-dimensional matrix integrals and, based on a polynomial fitting method, significantly reduces the computational complexity of disturbance subspace reconstruction while ensuring fitting accuracy.
[0038] S3 introduces the Schmidt orthogonalization method to recursively solve the orthogonal complement space projection operator of the interference subspace and project it to obtain the beamforming weight vector.
[0039] This embodiment uses the Schmitt orthogonalization method to recursively solve the orthogonal complement space projection operator. The specific steps are as follows: First, define the dimension as Combination matrix , where each column vector Corresponding to a basis vector, The number of array elements. The number of interference sub-intervals. Let be the order of the polynomial approximation.
[0040] Next, set the initial orthogonal basis matrix. This matrix will be updated gradually in subsequent steps through an iterative orthogonalization process.
[0041] Then index each column. Perform the following operations in sequence: 1) Calculate the normalized basis vectors ; 2) Remove orthographic projection components: .
[0042] Finally, based on the orthonormal basis matrix obtained recursively... ， The orthogonal complement space projection operator is calculated. .
[0043] Desired signal steering vector exist The projection on satisfies the relation Therefore, the optimal weighting vector for beamforming is... It can be represented as: (9).
[0044] This step solves the projection operator recursively, avoiding matrix inversion operations, further reducing computational complexity and meeting the requirements of real-time systems.
[0045] S4 introduces an equivalent representation of the beamforming weight vector under the dual phase shifter architecture to obtain the updated value of the beam weight vector under the dual phase shifter architecture.
[0046] The solution obtained 3D optimal beamforming weight vector The complex coefficients corresponding to each array element ( All of these can be equivalently expressed in exponential form as The phase parameter and These correspond to two sets of phase shifts, respectively.
[0047] for A phase shifter with a bit width has a quantization step size of The set of discrete phase states that can be represented is Based on the nearest neighbor mapping principle, continuous phase is quantized into discrete values: (10); Ultimately, the system uses two quantization phases. The synthesis achieves the target complex weight This results in the beamforming weight vector. This is represented as the superposition of two constant mode vectors, completing the update of the beamforming weight vector: (11).
[0048] This step replaces the traditional phase shifter + attenuator architecture, maintaining good beamforming performance even with low quantization bits, and improving the robustness of the hardware implementation.
[0049] The following is a verification example of the present invention applied to an integrated radar and communication system, which verifies that this embodiment can achieve performance similar to matrix reconstruction-type robust beamforming methods, and the computational complexity and computation time are much lower than those of matrix reconstruction-type algorithms.
[0050] The simulation parameters are shown in Table 1 below, and the root mean square error curve of the beamforming results is shown in Table 1 below. Figure 3 , Figure 4As shown, the curve represented by OPFS represents the method proposed in this invention, while the curve represented by RCM represents the matrix reconstruction-based beamforming method. It can be seen that the nulls in the beamforming patterns of the proposed algorithm and the matrix reconstruction-based method are close, and the method proposed in this invention has deeper interference nulls, making it more suitable for applications with strong interference resistance. Furthermore, as the signal-to-noise ratio (SNR) changes, the overall SNR performance of the two beamforming methods is comparable, but the method proposed in this invention has a greater advantage.
[0051]
[0052] The time required for a single parameter estimation by the proposed method and the joint estimation method based on orthogonal matching pursuit is shown in Table 2 below. The proposed method has a significant advantage in computation time.
[0053]
[0054] Figure 5 As shown, OPFS&ATT-SPS represents the signal-to-interference-plus-noise ratio (SIR) performance curve of this invention under the traditional phase shifter attenuator RF front-end architecture, while OPFS&DPS represents the SIR performance curve of this invention under the dual phase shifter RF front-end architecture. It can be seen that, furthermore, with changes in SIR, the dual phase shifter architecture introduced in this invention exhibits greater performance advantages.
[0055] The technical solutions provided in this application embodiment have at least the following technical effects or advantages: 1. Existing integral reconstruction-based robust beamforming methods have high computational complexity. This invention obtains the interference subspace by directly fitting an orthogonal polynomial and constructs its orthogonal complement space projection operator to solve for the optimal weight vector. At the same time, it introduces a fourth-order Gauss-Legend numerical integral and a Schmidt orthogonalization method to simplify the calculation, which greatly reduces the computational complexity.
[0056] 2. This invention combines the proposed algorithm with a dual phase shifter structure, achieving better performance than traditional RF front-end architectures at low phase shifter quantization bit widths.
[0057] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.
Claims
1. A method for obtaining beamforming weight vectors in an integrated radar-communication system, characterized in that, Includes the following steps: S1: Establish a receiver signal model for a uniform linear array antenna in a radar-communication integrated system; S2: Introducing orthogonal polynomials and the Gauss-Legendal numerical integration method to perform low-complexity and fast fitting and solution of the disturbance subspace; S3: Introduce the Schmidt orthogonalization method to recursively solve the orthogonal complement space projection operator of the interference subspace and project it to obtain the beamforming weight vector; S4: Introduce the equivalent representation of the beamforming weight vector under the dual phase shifter architecture to obtain the updated value of the beam weight vector under the dual phase shifter architecture.
2. The beamforming weight vector acquisition method according to claim 1, characterized in that: In step S1, the receiver signal model is as follows: ； Where the number of array elements is M, In order to receive signals, It is additive white Gaussian noise. For target signal, The direction of the incoming wave to the target. For the first One interference signal, Let be the direction of arrival of the k-th interference signal. express The guiding vector of the incoming wave.
3. The beamforming weight vector acquisition method according to claim 2, characterized in that: Guide vector: ； The element spacing is equal to the wavelength of the incident signal. Half of it.
4. The beamforming weight vector acquisition method according to claim 2, characterized in that: In step S2, the approximation scheme uses Legendre polynomials as... An orthogonal basis of a space, with corresponding weight functions The terms are equally weighted across the entire interval, and the general term formula is: ； Guided vector function In the interference-widened sub-interval The upper continuous, of which Indicates the width of the expansion interval; through variable substitution. ， Will From the interval Transform to And record it as ,Right now: ； As the best approximation in the sense of minimum mean square error yes exist The results of orthogonal projection calculations in space Indicates inner product operation; Approximate solution using 4-node Gauss-Legendal numerical integration: ； The four integration nodes are as follows: and the corresponding weights ; The low-complexity approximate solution is as follows: ； By variable substitution Will From the interval Transform back That is, to obtain In the interval The best square approximation on: ； Guide vector In subinterval The best square approximation on is represented in the following matrix form: ； in This expression represents the coefficient vector, and it shows that in On the interval, can be Zhang Cheng's subspace representation, the corresponding coordinate vector is ,Right now: ； make Indicates the first The coefficient matrix corresponding to each broadened subinterval is obtained by applying all... Orthogonal polynomial fitting is performed on each interference-widened sub-interval to obtain the coefficient matrix. The fitting solution for the interference subspace satisfies the following subspace equivalence relation: 。 5. The beamforming weight vector acquisition method according to claim 4, characterized in that: In step S3, the orthogonal complement space projection operator is solved recursively using the Schmidt orthogonalization method. The specific steps are as follows: First, define the dimension as Combination matrix , where each column vector Corresponding to a basis vector, The number of array elements. The number of interfering sub-intervals. The order of the polynomial approximation; Next, set the initial orthogonal basis matrix. ; Then index each column. Perform the following operations in sequence: 1) Calculate the normalized basis vectors ; 2) Remove orthographic projection components: ; Finally, based on the orthonormal basis matrix obtained recursively... ， The orthogonal complement space projection operator is calculated. ; Desired signal steering vector exist The projection onto the surface satisfies the following relation: ； Optimal weighting vector for beamforming Represented as: 。 6. The beamforming weight vector acquisition method according to claim 5, characterized in that: In step S4, the dual-phase shifter RF front-end architecture is used to achieve joint control of the amplitude and phase of the beamforming weight by configuring two independent phase shifters on each antenna element. in, 3D optimal beamforming weight vector Complex coefficients corresponding to each array element ( All of these are equivalently represented in exponential form as The phase parameter and These correspond to two sets of phase shifts, respectively.
7. The beamforming weight vector acquisition method according to claim 6, characterized in that: In step S4, in the hardware implementation, continuous phase values are mapped to discrete phase states through quantization processing; for A phase shifter with a bit width has a quantization step size of The set of discrete phase states that can be represented is ; Based on the nearest neighbor mapping principle, continuous phase is quantized into discrete values: ； Through two quantization phases The synthesis achieves the target complex weight This results in the beamforming weight vector. This is represented as the superposition of two constant mode vectors, completing the update of the beamforming weight vector: 。