Method for realizing accurate control of side lobe nulls of sensor array beam response

Abstract

The application discloses a kind of sensor array beam response sidelobe arbitrary nulling accurate control implementation method.This method is first according to sensor array relevant parameter and constructs array manifold and selects desired nulling area;Then in combination with the thought of sensor array beam response accurate control, iteration formula of beam pattern weighting vector is constructed;Finally, the iteration solution of beam pattern weighting vector is carried out, and beam pattern design is realized.The method of the application introduces the autocorrelation matrix formed by the array manifold corresponding to the desired nulling area in the objective function of CAPON beamformer, so as to realize the effective minimization of the beam output power in the area;At the same time, in combination with the design idea of sensor array beam response accurate control, beam response control and nulling area control are organically integrated, and the accuracy of nulling area control is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of sensor array signal processing technology, specifically to a method for precise control of arbitrary nulls in the sidelobes of a sensor array beam response. Background Technology

[0002] Beamforming is an important research direction in the field of sensor array signal processing. By applying appropriate weighting coefficients to the observation data of spatially distributed array elements and performing weighted superposition, an array output can be formed, thereby achieving coherent superposition of the desired signal while effectively suppressing noise and interference. The quality of a beamformer can be evaluated from aspects such as its sidelobe level, array gain, main lobe width, robustness, and main lobe response. The beamforming method commonly used in engineering practice is the conventional beamforming method, which uses the array manifold vector corresponding to the main lobe pointing angle as the weighting vector. This type of method is simple to implement, has low computational complexity, and has good stability and engineering practicality, but its sidelobe suppression capability is limited, often resulting in a high sidelobe level.

[0003] The received signal of a sensor array typically consists of the target signal, interference signal, and background noise. The generation mechanisms of background noise and interference signals are diverse, potentially originating from environmental disturbances, the equipment itself, external interference, and other radiation sources. In complex environments, the array's received signal often operates at a low signal-to-noise ratio (SNR); simultaneously, multipath propagation is prevalent due to the environment. Therefore, in sensor array signal processing, precise beam response control to create low sidelobes helps mitigate the impact of multipath effects; precise beammap null design can effectively suppress interference, thereby further improving the SNR.

[0004] Current methods for sensor array beammap design can be broadly categorized into three types: beammap design methods based on convex optimization algorithms, beammap design methods based on meta-learning methods, and beam response precision control methods based on virtual source placement. Convex optimization-based beammap design methods typically model sidelobe-level control and main lobe response control as convex optimization problems and employ interior-point methods for efficient solutions, offering high modeling flexibility and moderate computational complexity. Meta-learning-based beammap design methods, on the other hand, find the optimal solution by designing a suitable objective function and utilizing global optimization algorithms such as genetic algorithms and simulated annealing. However, these methods involve significant computational cost and the results exhibit a degree of randomness. Beam response precision control methods based on virtual source placement originate from the CAPON adaptive beamformer concept. By artificially adding virtual interference sources to the covariance matrix and inputting them into the beamformer to obtain corresponding weighting vectors, precise control of the beam response in a specific azimuth is achieved, thus enabling precise beammap design. These methods are characterized by low computational cost. X. Ai et al. proposed a multi-point fast beam pattern accurate response control method (X. Ai, L. Gan, MPARC: A fast beam pattern synthesis algorithm based on adaptive array theory, Signal Process. 189 (2021) 108259.), which realizes fast low sidelobe beam pattern design. However, due to its special beam response control point selection mechanism, it has certain limitations in the accuracy of beam pattern null design and cannot achieve null design at specific angles.

[0005] Therefore, in order to meet the practical need for precise control of beammap null regions under complex interference environments, this invention discloses a method for precise control of arbitrary beammap null regions to improve the control accuracy of null regions. Summary of the Invention

[0006] To address the issue of beam pattern null design accuracy, this invention proposes a method for precise control of arbitrary nulls in the sidelobes of a sensor array beam response. By introducing an autocorrelation matrix composed of the array manifolds corresponding to the desired null regions into the objective function of the CAPON adaptive beamformer, and combining it with the idea of ​​precise beam response control based on virtual source placement, the beam response control and precise null design of the sensor array are realized.

[0007] To solve the above-mentioned technical problems, embodiments of the present invention provide the following technical solution: a method for precise control of arbitrary nulls in the sidelobes of a sensor array beam response, comprising:

[0008] S1: Based on the relevant parameters of the sensor array, construct the array manifold vector, and then form the array manifold matrix;

[0009] S2: Based on the actual interference suppression requirements, select the desired null region within the beam sidelobe region, and arrange the array manifold vectors within this region in columns to form the null region array manifold matrix;

[0010] S3: Construct the beammap weighted vector iterative formula, and use the array manifold vector corresponding to the main lobe pointing angle as the initial weighted vector for iteration;

[0011] S4: Initialize the iteration parameters, determine the beam response control angle for each iteration through iterative calculation, select the desired normalized beam response modulus, solve for the complex factor, update the weighting vector, and repeat the iteration until the preset termination condition is met.

[0012] S5: Using the weighted vector obtained from the final iteration, calculate the normalized beam response magnitude for each observation angle and convert it to decibel form to complete the beam pattern design.

[0013] Furthermore, in step S1, the array manifold vectors are constructed, which in turn form the array manifold matrix, specifically as follows:

[0014] The sensor array is a uniform linear sensor array, with the number of array elements set to be... The spacing between array elements is Wave speed is The signal frequency is Observation azimuth The range is Then the pointing angle The array manifold vector is:

[0015] :

[0016] superscript This indicates the transpose operation. Indicates exponentiation. The imaginary unit, It is a mathematical constant;

[0017] For all angles within the observed azimuth range, an array manifold matrix is ​​constructed. Assuming the beammap weighting vector is From the perspective of observation The beam response is defined as The normalized beam response value is defined as , Main lobe pointing angle The corresponding array manifold vector, superscript This indicates the conjugate transpose operation.

[0018] Furthermore, the expression for the manifold matrix of the null region array in step S2 is:

[0019] ;

[0020] Let be the array manifold vector pointing to angle θ. , These represent the lower and upper limits of the desired null region angle in the beammap, respectively.

[0021] Furthermore, the beammap weighted vector iteration formula in step S3 is:

[0022] ;

[0023] in, For the zero-trap control matrix, , It is the identity matrix. As a weighting factor and ≥0, superscript The superscript indicates the conjugate transpose operation. This represents the matrix inversion operation; Let be the weighted vector to be solved in the k-th iteration. The weighted vector is obtained in the (k-1)th iteration. For complex factors, The beam response control angle in the k-th iteration The corresponding array manifold vector.

[0024] Furthermore, the specific process of step S4 is as follows:

[0025] Step 4.1: Assume the main lobe region of the desired beam response is... The expected normalized beam response modulus in the main lobe region is The desired sidelobe region of the beam response is ,and ,in Given a value, representing the maximum modulus of the desired sidelobe normalized beam response; assuming the maximum modulus of the desired sidelobe normalized beam response is in decibels. ,but , then the first The difference in the normalized beam response modulus at each iteration is defined as:

[0026] ;

[0027] Step 4.2: Initialize the number of iterations Weighted vector Maximum number of iterations Trade-off factors ,calculate ;

[0028] Step 4.3: Proceed to the next step In the next iteration, calculate For the main lobe region ,calculate , characterizing the The difference in normalized beam response modulus within the main lobe region during each iteration is solved. As a pre-selected control angle for the main lobe region, This indicates the parameter values ​​that maximize the objective function; for the sidelobe region... Solve ;if If so, there is no pre-selected control angle in the side lobe region; otherwise, it will... As a pre-selected control angle within the side lobe region, among which To select the desired null region for the beam pattern;

[0029] Calculate the difference in normalized beam response magnitudes for the preselected control angles:

[0030] ;

[0031] Solve ,Will As the first The observation angle for beam response control in the next iteration; if there is no pre-selected control angle in the sidelobe region, then... Construct array manifold vectors ;

[0032] Step 4.4: Select the desired normalized beam response modulus. ,if ,but ;if ,but ;

[0033] Step 4.5: Solve for complex factors ,Will and Substitute and solve. “ " indicates the operation of solving complex phases;

[0034] Step 4.6: Iteratively solve for the weighted vector ,Will , , Substitute and solve , ;

[0035] Step 4.7: Repeat steps 4.3 to 4.6 to solve for the weighted vector using the iterative formula. ,until until, For the current iteration round, This represents the maximum number of iterations.

[0036] Furthermore, the decibel form of the beam pattern in step S5 is expressed as follows:

[0037] ;

[0038] in, For observation angle The decibel value of the beam pattern. To observe the azimuth angle; For the k-th iteration, the observation angle Relative to the pointing angle of the main lobe The normalized beam response value; k is the iteration number; The pointing angle of the main lobe; This is the conjugate transpose of the beammap weighting vector obtained in the kth iteration, with the superscript H indicating the conjugate transpose operation; It is an array manifold matrix; Main lobe pointing angle The corresponding array manifold vector; |.| represents the modulo operation.

[0039] The beneficial effects of the above-described technical solution of the present invention are as follows:

[0040] (1) By introducing an autocorrelation matrix consisting of the array manifold corresponding to the desired null region into the objective function of the CAPON adaptive beamformer, the precise control of the sidelobe null position of the beam pattern is realized.

[0041] (2) The beam response precision control method based on virtual source placement enables the main and side lobe levels to be adjusted as expected, thereby enhancing the overall response control capability of the beam pattern.

[0042] (3) By introducing phase control factors, the disturbance of other azimuth beam response levels during the iteration process is reduced, making the weight vector update more efficient, thereby significantly improving the convergence speed of the algorithm. Attached Figure Description

[0043] Figure 1 A flowchart illustrating a rapid method for precise control of arbitrary nulls in the sidelobes of a sensor array beam response.

[0044] Figure 2 A comparison diagram of beam response control for the main lobe and side lobes.

[0045] Figure 3 This is a comparison chart of zero-depression areas. Detailed Implementation

[0046] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0047] This invention proposes a method for precise control of arbitrary nulls in the sidelobes of a sensor array beam response. By introducing an autocorrelation matrix composed of the array manifolds corresponding to the desired null regions into the objective function of the CAPON adaptive beamformer and combining it with the idea of ​​a precise beam response control method based on virtual source placement, the beam response control and precise null design of the sensor array are realized.

[0048] CAPON adaptive beamformers possess the ability to minimize an objective function. By introducing an autocorrelation matrix composed of the array manifolds corresponding to the desired null region into its objective function, the beam output power within that region can be minimized using the CAPON adaptive beamformer principle; this is known as beammap null design. The beam response precision control method based on virtual source placement inherits the fundamental idea of ​​CAPON adaptive beamforming in its derivation, and its iterative formula exhibits a similar mathematical form to that of the CAPON beamformer. Combining the two allows for the realization of sensor array beam response control and precise null design.

[0049] The method for precise control of arbitrary nulls in the sidelobes of the sensor array beam response of the present invention includes the following steps:

[0050] S1: Based on the relevant parameters of the sensor array, construct the array manifold vector, and then form the array manifold matrix;

[0051] S2: Based on the actual interference suppression requirements, select the desired null region within the beam sidelobe region, and arrange the array manifold vectors within this region in columns to form the null region array manifold matrix;

[0052] S3: Construct the beammap weighted vector iterative formula, and use the array manifold vector corresponding to the main lobe pointing angle as the initial weighted vector for iteration;

[0053] S4: Initialize the iteration parameters, determine the beam response control angle for each iteration through iterative calculation, select the desired normalized beam response modulus, solve for the complex factor, update the weighting vector, and repeat the iteration until the preset termination condition is met.

[0054] S5: Using the weighted vector obtained from the final iteration, calculate the normalized beam response magnitude for each observation angle and convert it to decibel form to complete the beam pattern design.

[0055] In this embodiment, step S1 involves constructing array manifold vectors and then forming an array manifold matrix, specifically as follows:

[0056] The sensor array is a uniform linear sensor array, with the number of array elements set to be... The spacing between array elements is Wave speed is The signal frequency is Observation azimuth The range is Then the pointing angle The array manifold vector is:

[0057] ;

[0058] superscript This indicates the transpose operation. Indicates exponentiation. The imaginary unit, It is a mathematical constant;

[0059] For all angles within the observed azimuth range, an array manifold matrix is ​​constructed. Assuming the beammap weighting vector is From the perspective of observation The beam response is defined as The normalized beam response value is defined as , Main lobe pointing angle The corresponding array manifold vector, superscript This represents the conjugate transpose operation. In practical processing, the phase information of the beam response is usually not of concern, so its magnitude is often taken, i.e. This is called a beammap; it is usually represented in decibels (dB). .

[0060] In this embodiment, the expression for the manifold matrix of the null region array in step S2 is:

[0061] ;

[0062] Let be the array manifold vector pointing to angle θ. , These represent the lower and upper limits of the desired null region angle in the beammap, respectively.

[0063] Select the desired null region of the beam pattern based on actual needs. To select the desired null region in the beam pattern, , These are the lower and upper limits of the desired null region angle, respectively; the desired null region must be located in the beam sidelobe region. The array manifold vectors of the desired null region are arranged column-wise to form the null region array manifold matrix.

[0064] In this embodiment, the beammap weighted vector iteration formula in step S3 is:

[0065] ;

[0066] in, For the zero-trap control matrix, , It is the identity matrix. As a trade-off factor used to control beam null depth and ≥0, superscript The superscript indicates the conjugate transpose operation. This represents the matrix inversion operation; Let be the weighted vector to be solved in the k-th iteration. The weighted vector is obtained in the (k-1)th iteration. A complex factor is used to control the beam response. The beam response control angle in the k-th iteration The corresponding array manifold vector.

[0067] In this embodiment, step S4 is specifically performed as follows:

[0068] Step 4.1: Assume the main lobe region of the desired beam response is... The expected normalized beam response modulus in the main lobe region is The desired sidelobe region of the beam response is ,and ,in Given a value, representing the maximum modulus of the desired sidelobe normalized beam response; assuming the maximum modulus of the desired sidelobe normalized beam response is in decibels. ,but , then the first The difference in the normalized beam response modulus at each iteration is defined as:

[0069] ;

[0070] Step 4.2: Initialize the number of iterations Weighted vector Maximum number of iterations Trade-off factors ,calculate ;

[0071] Step 4.3: Proceed to the next step In the next iteration, calculate For the main lobe region ,calculate , characterizing the The difference in normalized beam response modulus within the main lobe region during each iteration is solved. As a pre-selected control angle for the main lobe region, This indicates the parameter values ​​that maximize the objective function; for the sidelobe region... Solve ;if If so, there is no pre-selected control angle in the side lobe region; otherwise, it will... As a pre-selected control angle within the side lobe region, among which To select the desired null region for the beam pattern;

[0072] Calculate the difference in normalized beam response magnitudes for the preselected control angles:

[0073] ;

[0074] Solve ,Will As the first The observation angle for beam response control in the next iteration; if there is no pre-selected control angle in the sidelobe region, then... Construct array manifold vectors ;

[0075] Step 4.4: Select the desired normalized beam response modulus. ,if ,but ;if ,but ;

[0076] Step 4.5: Solve for complex factors ,Will and Substitute and solve. “ " indicates the operation of solving complex phases;

[0077] Step 4.6: Iteratively solve for the weighted vector ,Will , , Substitute and solve , ;

[0078] Step 4.7: Repeat steps 4.3 to 4.6 to solve for the weighted vector using the iterative formula. ,until until, For the current iteration round, This represents the maximum number of iterations.

[0079] In this embodiment, the decibel form of the beam pattern in step S5 is expressed as follows:

[0080] ;

[0081] in, For observation angle The decibel value of the beam pattern. To observe the azimuth angle; For the k-th iteration, the observation angle Relative to the pointing angle of the main lobe The normalized beam response value; k is the iteration number; The pointing angle of the main lobe; This is the conjugate transpose of the beammap weighting vector obtained in the kth iteration, with the superscript H indicating the conjugate transpose operation; It is an array manifold matrix; Main lobe pointing angle The corresponding array manifold vector; |.| represents the modulo operation.

[0082] The method for precise control of arbitrary nulls in the sidelobes of the sensor array beam response described above has at least the following advantages:

[0083] (1) By introducing an autocorrelation matrix consisting of the array manifold corresponding to the desired null region into the objective function of the CAPON adaptive beamformer, the precise control of the sidelobe null position of the beam pattern is realized.

[0084] (2) The beam response precision control method based on virtual source placement enables the main and side lobe levels to be adjusted as expected, enhancing the overall response control capability of the beammap; as shown in step 4.6 above, the beammap weighted vector iteration formula is: ,in .Will Substituting into the calculation expression for the normalized beam response magnitude, we can further obtain the result at the 1st... The normalized beam response modulus value corresponding to the observation angle selected for beam response control after each iteration.

[0085] The calculation results show that the normalized beam response amplitude at this angle meets the preset control requirements, thus realizing the control of the beam response at this angle. That is, each iteration update of the weighting vector corresponds to the adjustment of the beam response at a specific observation angle. By implementing iterative control sequentially for different observation angles, the response level of the beam pattern in the main lobe and side lobe regions can be gradually adjusted, thereby realizing the adjustment of the main and side lobe levels.

[0086] (3) By introducing phase control factors, the disturbance of other azimuth beam response levels during the iteration process is reduced, making the weight vector update more efficient, thereby significantly improving the convergence speed of the algorithm.

[0087] Further details: The iterative formula for the beammap weighted vector is as follows: ,in .

[0088] Definition of the first The perturbation of the beam pattern before and after the next iteration is ,in The value range is the range of the current controlled angle. The set of all observed azimuth angles.

[0089] Under the above definition, in the iterative formula phase factor For the The beam pattern perturbation before and after each iteration is adjusted. By selecting this phase factor, the changes in the beam pattern at uncontrolled azimuth angles before and after iteration can be kept within a small range, thereby effectively reducing the perturbation of the response level of other azimuth beams during the iteration process and improving the overall stability of the beam pattern.

[0090] The working principle of the present invention is explained below with reference to specific embodiments:

[0091] Based on the above method, this embodiment conducts simulation experiments to verify the performance advantages of the proposed method for rapid implementation of precise control of arbitrary nulls in the sidelobes of sensor array beam response compared to existing methods.

[0092] In the simulation experiment, a uniform sensor array was used, with 21 sensors and an element spacing of [missing information]. The signal frequency is The speed of sound is The main lobe pointing angle of the beam is The range of observation azimuth angles is Discrete angle interval is The desired zero-depression area is... The desired main lobe region of the beam response is... Within the desired main lobe region, the normalized beam response magnitude is consistent with the beam response magnitude formed by the −60dB Dolph–Chebyshev weighting method. The desired sidelobe region of the beam response is... The maximum modulus of the normalized beam response within the desired sidelobe region is selected as The maximum number of iterations is 1000, and the tradeoff factor is... The proposed method and the MPARC method were used to attempt to design the desired beam pattern, and the results were compared with beam patterns obtained using conventional beamforming methods.

[0093] Figure 2 , Figure 3 The performance comparison between the MPARC method and the method of this invention in beammap design is shown. Figure 2This indicates that both the MPARC method and the method of this invention can achieve good design results in beam response control in the main lobe region and the side lobe region, demonstrating that both methods have basic beam pattern shaping capabilities. Figure 3 This demonstrates that the method of the present invention exhibits a significant advantage over the MPARC method in terms of control accuracy in the zero-depression region. The method of the present invention precisely controls the zero-depression region to remain within the specified range. The MPARC method can only control the zero-depression region to remain within the specified range. It exists in relation to the expected zero-depression region. The deviation is shown. This result demonstrates the superiority of the method of the present invention in achieving precise control of arbitrary zero-depression regions.

[0094] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for precise control of arbitrary nulls in the beam response sidelobes of a sensor array, characterized in that, include: S1: Based on the relevant parameters of the sensor array, construct the array manifold vector, and then form the array manifold matrix; S2: Based on the actual interference suppression requirements, a desired null region is selected within the beam sidelobe region. The array manifold vectors within this region are arranged column-wise to form a null region array manifold matrix. The expression for the null region array manifold matrix is: ； Let be the array manifold vector pointing to angle θ. , These represent the lower and upper limits of the angle of the desired null region in the beam pattern, respectively. S3: Construct the beammap weighted vector iterative formula, and use the array manifold vector corresponding to the main lobe pointing angle as the initial weighted vector for iteration; the beammap weighted vector iterative formula is: ； in, For the zero-trap control matrix, , It is the identity matrix. As a weighting factor and ≥0, superscript The superscript indicates the conjugate transpose operation. This represents the matrix inversion operation; Let be the weighted vector to be solved in the k-th iteration. The weighted vector is obtained in the (k-1)th iteration. For complex factors, The beam response control angle in the k-th iteration The corresponding array manifold vector; S4: Initialize the iteration parameters, determine the beam response control angle for each iteration through iterative calculation, select the desired normalized beam response modulus, solve for the complex factor, update the weighting vector, and repeat the iteration until the preset termination condition is met; specifically: Step 4.1: Assume the main lobe region of the desired beam response is... The expected normalized beam response modulus in the main lobe region is The desired sidelobe region of the beam response is ,and ,in Given a value, representing the maximum modulus of the desired sidelobe normalized beam response; assuming the maximum modulus of the desired sidelobe normalized beam response is in decibels. ,but , then the first The difference in the normalized beam response modulus at each iteration is defined as: ； Step 4.2: Initialize the number of iterations Weighted vector Maximum number of iterations Trade-off factors ,calculate ; Step 4.3: Proceed to the next step In the next iteration, calculate For the main lobe region ,calculate , characterizing the The difference in normalized beam response modulus within the main lobe region during each iteration is solved. As a pre-selected control angle for the main lobe region, This indicates the parameter values ​​that maximize the objective function; for the sidelobe region... Solve ;if If so, there is no pre-selected control angle in the side lobe region; otherwise, it will... As a pre-selected control angle within the side lobe region, among which... To select the desired null region for the beam pattern; Calculate the difference in normalized beam response magnitudes for the preselected control angles: ； Solve ,Will As the first The observation angle for beam response control in the next iteration; if there is no pre-selected control angle in the sidelobe region, then... Construct array manifold vectors ; Step 4.4: Select the desired normalized beam response modulus. ,if ,but ;if ,but ; Step 4.5: Solve for complex factors ,Will and Substitute and solve. " " indicates the operation of solving complex phases; Step 4.6: Iteratively solve for the weighted vector ,Will , , Substitute and solve , ; Step 4.7: Repeat steps 4.3 to 4.6 to solve for the weighted vector using the iterative formula. ,until until, For the current iteration round, This represents the maximum number of iterations. S5: Using the weighted vector obtained from the final iteration, calculate the normalized beam response magnitude for each observation angle and convert it to decibel form to complete the beam pattern design.

2. The method for precise control of arbitrary nulls in the sidelobes of the sensor array beam response according to claim 1, characterized in that, In step S1, the array manifold vectors are constructed, which in turn form the array manifold matrix, specifically as follows: The sensor array is a uniform linear sensor array, with the number of array elements set to be... The spacing between array elements is Wave speed is The signal frequency is Observation azimuth The range is Then the pointing angle The array manifold vector is: ； superscript This indicates the transpose operation. Indicates exponentiation. The imaginary unit, It is a mathematical constant; For all angles within the observed azimuth range, an array manifold matrix is ​​constructed. Assuming the beammap weighting vector is From the perspective of observation The beam response is defined as The normalized beam response value is defined as , Main lobe pointing angle The corresponding array manifold vector, superscript This indicates the conjugate transpose operation.

3. The method for precise control of arbitrary nulls in the sidelobes of the sensor array beam response according to claim 1, characterized in that, The decibel form of the beam pattern in step S5 is expressed as follows: ； in, For observation angle The decibel value of the beam pattern. To observe the azimuth angle; For the k-th iteration, the observation angle Relative to the pointing angle of the main lobe The normalized beam response value; k is the iteration number; The pointing angle of the main lobe; This is the conjugate transpose of the beammap weighting vector obtained in the kth iteration, with the superscript H indicating the conjugate transpose operation; It is an array manifold matrix; Main lobe pointing angle The corresponding array manifold vector; |.| represents the modulo operation.

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