Robust self-interference suppression beam forming method based on multi-missile cooperative scene
By constructing a coupled channel model with circularly symmetric Gaussian distribution error and optimizing transmit beamforming, the problem of self-interference suppression performance degradation in multi-missile cooperative scenarios is solved, achieving robust self-interference suppression and normal reception of desired signals, and supporting simultaneous operation of multi-functional radar seekers at the same frequency.
Patent Information
- Application Number
- CN202511701464.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-19
- Publication Date
- 2026-02-10
AI Technical Summary
In multi-missile cooperative operation scenarios, existing self-interference suppression techniques fail to effectively consider the coupling channel estimation error between the receiving antenna and the transmitting antenna, resulting in performance degradation of in-band full-duplex function and making it difficult to achieve robust self-interference suppression.
A coupled channel model incorporating circularly symmetric Gaussian distribution errors is constructed. By optimizing transmit beamforming and setting constraints to maximize transmit beam gain and suppress self-interference signal power, the non-convex problem is transformed into a convex problem using semi-definite relaxation and Bernstein's inequality, thereby obtaining robust self-interference suppression capability.
In real-world environments, robust self-interference suppression is achieved, ensuring normal reception and demodulation of desired signals. Simultaneous transmission and reception at the same frequency is supported in multi-satellite cooperative operation, avoiding performance degradation under ideal channel design.
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Figure CN121508593A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of self-interference suppression technology, and specifically to a robust self-interference suppression beamforming method based on multi-launcher cooperative scenarios. Background Technology
[0002] In multi-missile collaborative operation scenarios, a single radar seeker needs to perform simultaneous, same-frequency transmission and reception when integrating multiple functions such as detection and inter-missile data links, requiring in-band full-duplex functionality. Achieving in-band full-duplex functionality hinges on self-interference suppression technology, preventing self-interference signals leaked from the transmitter to the receiver from affecting the normal reception and demodulation of the desired signal. As the scale of transceiver antenna arrays continues to increase, the coupling between transceiver antennas becomes increasingly complex, posing a significant challenge to traditional self-interference suppression technologies based on single or dual antennas.
[0003] For multi-antenna co-located transmit and receive antenna array systems, beamforming technology, especially transmit beamforming, is the preferred method for achieving self-interference suppression and preventing receive link blockage. By calculating the amplitude and phase of array element weights, signal transmission in the desired direction is achieved while reducing the power of self-interference signals and ensuring effective reception and demodulation of the desired signal. Furthermore, this method does not require additional components, thus offering advantages in cost and power consumption. Existing self-interference suppression methods lack consideration for the estimation error of the coupling channel between the receive and transmit antennas. Therefore, self-interference suppression beamforming algorithms based on accurate model coupling channel designs may experience significant performance degradation in practice, severely limiting the realization of in-band full-duplex functionality. Summary of the Invention
[0004] The purpose of this invention is to provide a robust self-interference suppression beamforming method based on multi-launch cooperative scenarios, avoiding the performance degradation problem of self-interference suppression beamforming designs using ideal channel designs in practical applications.
[0005] To achieve the above objectives, this invention provides a robust self-interference suppression beamforming method based on multi-launch cooperative scenarios, comprising: Step 1: Considering the non-ideal case, construct a coupled channel model that includes circularly symmetric Gaussian distribution error, and construct expressions for the baseband signal weighted by the transmit beamformer to form the transmit signal and the power of the self-interference signal received by the receiving array element. Step 2: Based on the expression for the self-interference signal power on the receiving array element, construct an optimization problem for self-interference suppression transmit beamforming that is robust to the estimation error, and maximize the transmit beam gain while constraining the upper limit of the self-interference signal power coupled on the receiving subarray. The optimization objective is set to maximize the transmit beam gain; the constraints are set as follows: ensuring that the power of the self-interference signal coupled on each receiver element in the receiver subarray is less than the set upper limit threshold; and the upper limit constraint of the full feed power of the transmit link. Step 3: Based on the optimization problem in Step 2, the original non-convex opportunity constraint problem is transformed into a convex problem by using the semi-positive definite relaxation and Bernstein's inequality approximation method. Finally, the transmit beam weight vector solution is obtained by singular value decomposition or Gaussian random vector method, so as to achieve robust self-interference suppression capability under non-ideal coupled channel and ensure normal reception of the desired signal.
[0006] Optionally, the coupled channel model includes: a transmitting subarray and a receiving subarray; the transmitting subarray consists of a transmitting beamformer and M transmitting links; the transmitting beamformer generates digital baseband signals and generates M digital baseband signals through a weighted algorithm, which are then transmitted to the M transmitting links respectively; each transmitting link includes M transmitting elements, which radiate signals into space; the M transmitting elements of the transmitting subarray transmit the transmitted signals to the receiving subarray through the coupling channel; The receiving subarray consists of a receiving beamformer and N receiving links; the receiving beamformer performs spatial weighting processing on the signals in the N receiving links; each receiving link includes a receiving subarray, which is used to receive the transmitted signal. In this process, the transmitted signal of each transmitting element reaches each receiving element through a dedicated path.
[0007] Optionally, the transmission link further includes: a transmission beamformer, a digital-to-analog converter, and a radio frequency transmitting device; The digital-to-analog converter transmits signals with the transmit beamformer, converting the digital baseband signal generated by the transmit beamformer into an analog baseband signal; the radio frequency transmitter transmits signals with the digital-to-analog converter, modulating the analog baseband signal into a radio frequency power signal, and sending it to the transmit array element with which it transmits signals.
[0008] Optionally, the receiving link further includes: a radio frequency receiving device and an analog-to-digital converter that transmit signals sequentially with the receiving array element; The receiving array element converts the transmitted signal into an radio frequency (RF) electrical signal, and the RF receiving device converts the RF electrical signal received by the receiving array element into a low-frequency, high signal-to-noise ratio (SNR) analog baseband signal; the analog-to-digital converter converts the analog baseband signal into a digital signal.
[0009] Optionally, in step 1, the process of generating the transmitted signal is represented as follows:
[0010] in, For baseband transmission signals, ,and ,in, Represents the mathematical expectation; For the emission weight, and , Represents an M-dimensional vector space over the complex field; For transmit link noise, and ; The transmit signal is the final feed for the transmit subarray, and , k represents the kth snapshot, and M is the number of transmitter elements in the co-located transmitter subarray.
[0011] Optionally, in step 1, the method for constructing the expression for the self-interference signal power includes: When transmitting signal After passing through the coupling channel, the transmitted signal The self-interference signal incident on the receiving subarray of N receiving elements is represented as:
[0012] in, Let be the non-ideal coupling channel matrix representing the coupling between each transmit and receive antenna pair, and , for A complex matrix of order 1; To receive link noise; the non-ideal coupled channel matrix is represented as:
[0013] in, For the estimation of the non-ideal coupled channel matrix H, and ; Let be the estimation error matrix of the coupled channel. , for Complex matrix of order; error matrix Each element for:
[0014] in, The estimation error matrix of the coupled channel The variance of all elements in the dataset; Self-interference signal power incident on the nth receiving element Represented as:
[0015]
[0016]
[0017] in, The nth row of the non-ideal coupled channel matrix H This indicates the conjugate transpose, and ; for The covariance matrix, and ; The estimation error matrix for the coupled channel The vector of estimation errors in the nth row is represented as:
[0018] in, It is a diagonal matrix, and the diagonal elements of the matrix are the variances. .
[0019] Optionally, in step 2, the optimization objective is expressed as:
[0020] in, The desired direction of the emission steering vector, and ; Construct optimization problem Optimization problem The medium gain expression G is based on the transmit full feed power. Adjustments were made; the optimization problem Represented as:
[0021] in, The desired self-interference signal power threshold, This represents the transmit power when the transmit link is fully fed. Let represent the weight on the m-th transmitting element.
[0022] Optionally, in step 3, the method of transforming the originally non-convex chance-constant problem into a convex problem through the approximation method of semi-positive definite relaxation and Bernstein's inequality includes: Step 3.1, Transformation and Optimization Problem The cost function is used to transform the self-interference signal power constraint into an interruption probability constraint.
[0023]
[0024] in, It is a semi-positive definite matrix, and ;Prob{} is the probability operation. The corresponding probability; Step 3.2, optimize the problem The problem is transformed into a semidefinite programming problem and computed using a semidefinite relaxation algorithm.
[0025]
[0026] in, It is a rank-1 positive semi-definite matrix, and tr() is the trace operation. To perform the real part operation; Step 3.3, rewrite the optimization problem in step 3.2. The opportunity constraint form in the problem further transforms the optimization problem into:
[0027]
[0028]
[0029]
[0030] in, , , , All are intermediate parameters, and ; for Unit array; Let m be the diagonal element of a rank-1 positive semi-definite matrix F. Step 3.4: The problem is finally transformed into a convex problem using the approximation method of Bernstein's inequality.
[0031]
[0032] in, b and w The slack variable introduced is vec(), which is a vectorized operation.
[0033] Compared with the prior art, the technical solution of the present invention has at least the following beneficial effects: The method described in this invention enables co-located antenna arrays to achieve excellent simultaneous and same-frequency transmission and reception performance under the influence of various interference factors in the actual environment; and even when there are estimation errors in the coupling channel, it can still achieve robust self-interference suppression effect on each co-located receiving element, maximize beam gain, ensure normal reception of the desired signal, support multi-missile coordination, and realize the multi-functional integration of radar seeker.
[0034] For scenarios where multiple missiles work together, requiring self-interference suppression for simultaneous multi-function transmission and reception such as radar seeker detection and inter-missile data link, the method described in this invention takes into account the coupling channel estimation error in the co-located antenna array system and makes a robust design, which can avoid the performance degradation problem of self-interference suppression beamforming design with ideal channel design in practical applications.
[0035] In the method described in this invention, step 1 considers an unbounded circularly symmetric Gaussian distributed coupled channel error model to closely approximate the actual situation and avoid the potential performance degradation problem that may occur when using a bounded coupled channel error model in practical applications.
[0036] In the method described in this invention, step 2 considers the suppression of self-interference signals on each receiving array element, which can ensure the normal operation of each receiving link, thereby avoiding the situation in practical applications where the self-interference suppression performance after receiving beamforming is strong but the RF front end of the receiving link is already blocked.
[0037] In the method described in this invention, step 3 utilizes the Berstein-type inequality method to approximate the originally non-convex chance-constrained problem as a convex problem, thereby avoiding the use of methods such as nonlinear solvers with high complexity. Attached Figure Description
[0038] Figure 1 This is a flowchart of the robust self-interference suppression beamforming method based on multi-missile cooperative scenarios described in this invention.
[0039] Figure 2 This is a schematic diagram of the coupled channel model in the robust self-interference suppression beamforming method based on multi-missile cooperative scenarios. Detailed Implementation
[0040] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0041] In the description of this invention, it should be noted that the terms "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.
[0042] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.
[0043] This invention provides a robust self-interference suppression beamforming method based on multi-missile cooperative scenarios. It robustly designs the coupling channel estimation error in a co-located transmit / receive antenna array system, avoiding the performance degradation problem inherent in self-interference suppression beamforming designs using ideal channel designs in practical applications. Figure 1 As shown, it specifically includes: Step 1: Considering the non-ideal case, construct a coupled channel model that includes circularly symmetric Gaussian distribution error, and construct expressions for the power of the baseband signal after weighted processing by the transmit beamformer to form the transmit signal and the power of the self-interference signal received by the receiving array element.
[0044] Construct a coupled channel model for the co-located transmit and receive antenna array, the coupled channel model including: a transmit subarray and a receive subarray.
[0045] Specifically, such as Figure 2 As shown, the transmitting subarray consists of a transmitting beamformer and M transmitting links. The transmitting beamformer generates digital baseband signals and, through a weighted algorithm, generates M digital baseband signals, which are then transmitted to the M transmitting links respectively. Each transmitting link includes: a digital-to-analog converter (DAC), a radio frequency (RF) transmitter, and a transmitting element, which are transmitted sequentially. The DAC transmits signals with the transmitting beamformer, converting the digital baseband signal generated by the beamformer into an analog baseband signal. The RF transmitter transmits signals with the DAC, modulating the analog baseband signal into an RF power signal. The transmitting element transmits signals with the RF transmitter, using the RF power signal as the transmission signal and radiating it into space to form a transmitting beam. The transmitting beamformer, DAC, RF transmitter, and transmitting element sequentially constitute the transmitting links of the transmitting subarray.
[0046] The M transmitting elements of the transmitting subarray transmit the transmitted signal to the receiving subarray through a coupling channel. The receiving subarray consists of a receiving beamformer and N receiving links. Each receiving link includes: a receiving element that transmits the signal sequentially, a radio frequency (RF) receiver, and an analog-to-digital converter (ADC). The receiving element receives the transmitted signal and converts it into an RF electrical signal. The RF receiver converts the RF electrical signal received by the receiving element into a low-frequency, high-signal-to-noise ratio analog baseband signal. The receiving elements and transmitting elements are fully connected, meaning that the transmitted signal from each transmitting element can reach each receiving element through a dedicated path. The ADC converts the analog baseband signal into a digital signal. The receiving beamformer performs spatial weighting processing on the digital signals in the N receiving links to achieve selective reception of signals from a specific direction and suppress interference signals and noise from other directions. This process is spatially equivalent to "forming a receiving beam pointing towards the target." The receiving elements, RF receiver, ADC, and receiving beamformer sequentially constitute the receiving links of the receiving subarray.
[0047] In this embodiment, the construction of the coupled channel model mainly considers beamforming design. Therefore, the frequency conversion, filtering and other processes of each stage of the radio frequency transmitting device are not modeled in detail. Instead, the main considerations are the transmission noise (i.e., transmission link noise) generated by the radio frequency transmitting device and the reception noise (i.e., reception link noise) generated by the radio frequency receiving device in the coupled channel model.
[0048] The process of generating the transmitted signal can be represented as: (Equation 1) (Equation 2) In the formula, For baseband transmission signals, ,and ,in, Represents the mathematical expectation; For transmit weights (i.e., transmit beamformer weights), and , Represents an M-dimensional vector space over the complex field; For transmit link noise, and ; The transmit signal is the final feed for the transmit subarray, and , k represents the kth snapshot (i.e. the kth sampling time window in the instantaneous sampling set), and M is the number of transmitting elements in the co-located transmitting subarray.
[0049] Assume the transmit power at full feed for each transmit link is Theoretically, the maximum transmission power of the entire launch array is .
[0050] When transmitting signal After passing through the coupling channel, the transmitted signal The self-interference signal incident on a receiving subarray with N receiving elements can be expressed as: (Equation 3) In the formula, Let be the non-ideal coupling channel matrix representing the coupling between each transmit and receive antenna pair, and , for A complex matrix of order 1; To account for the noise in the receiving link, and considering the estimation errors caused by the actual working environment and interference factors, the non-ideal coupled channel matrix can be further expressed as: (Equation 4) In the formula, For the estimation of the non-ideal coupled channel matrix H, and ; Let be the estimation error matrix of the coupled channel. Since the coupled channel estimation error generally follows a circularly symmetric Gaussian distribution, the error matrix... Each element They are all considered as complex numbers with a circularly symmetric Gaussian distribution: (Equation 5) In the formula, The estimation error matrix of the coupled channel The variance of all elements in the dataset; It is an abbreviation for Complex Normal Distribution.
[0051] Since the power of the self-interference signal caused by transmitted noise is much smaller than the power of the self-interference signal caused by the transmitted signal, the self-interference signal caused by transmitted noise is not considered. The power of the self-interference signal incident on the nth receiving element can be considered... It can be represented as: (Equation 6) (Equation 7) (Equation 8) In the formula, The nth row of the non-ideal coupled channel matrix H represents the coupling between all transmitting elements and the nth receiving element. This indicates the conjugate transpose. This is the estimate for the nth row of the corresponding coupled channel, and ; for The covariance matrix, and , for A complex matrix of order 1; The estimation error matrix for the coupled channel The vector of estimation errors in the nth row can be represented as: (Equation 9) In the formula, Let represent the covariance of the complex Gaussian distribution, which is a diagonal matrix whose diagonal elements are the variances. (i.e., the estimation error matrix of the coupled channel) (The variance of all elements in the dataset).
[0052] Step 2: Based on the expression for the self-interference signal power on the receiving array element, construct an optimization problem for self-interference suppression transmit beamforming that is robust to the estimation error, maximizing the transmit beam gain while constraining the upper limit of the self-interference signal power coupled on the receiving subarray.
[0053] The optimization objective is set to maximize the transmit beam gain; To minimize the impact of self-interference signals on each receiving link, the power of the self-interference signal received on each receiving element must be constrained to be as low as possible. Since the actual transmitting link has a power limit, the constraints are set as follows: 1) Ensure that the power of the self-interference signal coupled on each receiving element in the receiving subarray is less than the set upper limit threshold; 2) Upper limit constraint on the full feed power of the transmitting link.
[0054] The optimization objective is expressed as Equation 10, which serves as the transmit beam gain expression G (i.e., the cost function of the optimization problem): (Equation 10) In the formula, The desired direction of the emission steering vector, and .
[0055] Based on Equation 6, an optimization problem is constructed. Optimization problem The medium gain expression G is based on the transmit full feed power. Adjustments were made; the optimization problem Represented as: (Equation 11) In the formula, The desired self-interference signal power threshold; Let represent the weight on the m-th transmitting element.
[0056] Step 3, optimize the problem from Step 2. By employing semidefinite relaxation and approximation methods based on Bernstein-type inequalities, the originally non-convex chance-constrained problem is transformed into a convex problem for solution. Finally, the transmit beam weight vector is obtained through Singular Value Decomposition (SVD) or the Gaussian random vector method, achieving robust self-interference suppression capability under non-ideal coupled channels while ensuring the desired signal X. s Normal reception.
[0057] Step 3.1, Transformation and Optimization Problem The cost function is derived, and the self-interference signal power constraint is transformed into an interruption probability constraint.
[0058] (Equation 12) (Equation 13) In the formula, It is a semi-positive definite matrix, and ;Prob{} is the probability operation. The corresponding probability.
[0059] Step 3.2, optimize the problem The problem is transformed into a semidefinite programming problem and then computed using a semidefinite relaxation algorithm.
[0060] Original optimization problem This can be further expressed as: (Equation 14) (Equation 15) In the formula, It is a rank-1 positive semi-definite matrix, and tr() is the trace operation. This is an operation to extract the real part.
[0061] Step 3.3, rewrite the optimization problem in step 3.2. The opportunity constraint form in the problem further transforms the optimization problem into: (Equation 16) (Equation 17) (Equation 18) (Equation 19) In the formula, , , , All are intermediate parameters (see Equations 15-17), and ; for Unit array; Let m be the diagonal element of a rank-1 positive semi-definite matrix F.
[0062] Step 3.4: The problem is finally transformed into a convex problem by using the approximation method of Bernstein-type inequalities.
[0063] (Equation 20) (Equation 21) In the formula, b and w The slack variable introduced is vec(), which is a vectorized operation.
[0064] Based on Equation 18, the optimal positive semidefinite matrix solution of the rank-one positive semidefinite matrix F is obtained. According to the optimal positive semidefinite matrix solution In the middle-rank case, the final transmit beam weight vector solution is obtained using Singular Value Decomposition (SVD) or the Gaussian random vector method. .
[0065] In one embodiment, the CVX solver in MATLAB is used to obtain the final optimal solution. .
[0066] In summary, the robust self-interference suppression beamforming method based on multi-missile cooperative scenarios described in this invention adopts an unbounded circularly symmetric Gaussian distributed coupled channel error model, which avoids the performance degradation problem that may occur when using a bounded coupled channel error model in practical applications. When constructing the optimization problem, the suppression of self-interference signals on each receiving array element is taken into account, avoiding the situation where the self-interference suppression performance is strong after receiving beamforming but the RF front-end of the receiving link is already blocked.
[0067] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.
Claims
1. A robust self-interference suppression beamforming method based on multi-missile cooperative scenarios, characterized in that, include: Step 1: Considering the non-ideal case, construct a coupled channel model that includes circularly symmetric Gaussian distribution error, and construct expressions for the baseband signal weighted by the transmit beamformer to form the transmit signal and the power of the self-interference signal received by the receiving array element. Step 2: Based on the expression for the self-interference signal power on the receiving array element, construct an optimization problem for self-interference suppression transmit beamforming that is robust to the estimation error, and maximize the transmit beam gain while constraining the upper limit of the self-interference signal power coupled on the receiving subarray. The optimization objective is set to maximize the transmit beam gain; the constraints are set as follows: ensuring that the power of the self-interference signal coupled on each receiver element in the receiver subarray is less than the set upper limit threshold; and the upper limit constraint of the full feed power of the transmit link. Step 3: Based on the optimization problem in Step 2, the original non-convex opportunity constraint problem is transformed into a convex problem by using the semi-positive definite relaxation and Bernstein's inequality approximation method. Finally, the transmit beam weight vector solution is obtained by singular value decomposition or Gaussian random vector method, so as to achieve robust self-interference suppression capability under non-ideal coupled channel and ensure normal reception of the desired signal.
2. The robust self-interference suppression beamforming method based on multi-missile cooperative scenarios according to claim 1, characterized in that, The coupled channel model includes a transmitter subarray and a receiver subarray. The transmitter subarray consists of a transmitter beamformer and M transmitter links. The transmitter beamformer generates digital baseband signals and generates M digital baseband signals through a weighted algorithm, which are then transmitted to the M transmitter links respectively. Each transmitter link includes M transmitter elements, which radiate signals into space. The M transmitter elements of the transmitter subarray transmit the transmitted signals to the receiver subarray through the coupled channel. The receiving subarray consists of a receiving beamformer and N receiving links; the receiving beamformer performs spatial weighting processing on the signals in the N receiving links; each receiving link includes a receiving subarray, which is used to receive the transmitted signal. In this process, the transmitted signal of each transmitting element reaches each receiving element through a dedicated path.
3. The robust self-interference suppression beamforming method based on multi-missile cooperative scenarios according to claim 2, characterized in that, The transmission link also includes: a transmission beamformer, a digital-to-analog converter, and radio frequency transmission devices; The digital-to-analog converter transmits signals with the transmit beamformer, converting the digital baseband signal generated by the transmit beamformer into an analog baseband signal; the radio frequency transmitter transmits signals with the digital-to-analog converter, modulating the analog baseband signal into a radio frequency power signal, and sending it to the transmit array element with which it transmits signals.
4. The robust self-interference suppression beamforming method based on multi-missile cooperative scenarios according to claim 2, characterized in that, The receiving link further includes: a radio frequency receiving device and an analog-to-digital converter that transmit signals sequentially with the receiving array elements; The receiving array element converts the transmitted signal into an radio frequency (RF) electrical signal, and the RF receiving device converts the RF electrical signal received by the receiving array element into a low-frequency, high signal-to-noise ratio (SNR) analog baseband signal; the analog-to-digital converter converts the analog baseband signal into a digital signal.
5. The robust self-interference suppression beamforming method based on multi-missile cooperative scenarios according to claim 2, characterized in that, In step 1, the process of generating the transmitted signal is represented as follows: ； in, For baseband transmission signals, ,and ,in, Represents the mathematical expectation; For the emission weight, and , Represents an M-dimensional vector space over the complex field; For transmit link noise, and ; The transmit signal is the final feed for the transmit subarray, and , k represents the kth snapshot, and M is the number of transmitter elements in the co-located transmitter subarray.
6. The robust self-interference suppression beamforming method based on multi-missile cooperative scenarios according to claim 5, characterized in that, In step 1, the method for constructing the expression for the self-interference signal power includes: When transmitting signal After passing through the coupling channel, the transmitted signal The self-interference signal incident on the receiving subarray of N receiving elements is represented as: ； in, Let be the non-ideal coupling channel matrix representing the coupling between each transmit and receive antenna pair, and , for A complex matrix of order 1; To receive link noise; the non-ideal coupled channel matrix is represented as: ； in, For the estimation of the non-ideal coupled channel matrix H, and ; Let be the estimation error matrix of the coupled channel. , for Complex matrix of order; error matrix Each element for: ； in, The estimation error matrix of the coupled channel The variance of all elements in the dataset; Self-interference signal power incident on the nth receiving element Represented as: ； ； ； in, The nth row of the non-ideal coupled channel matrix H This indicates the conjugate transpose, and ; for The covariance matrix, and ; The estimation error matrix for the coupled channel The vector of estimation errors in the nth row is represented as: ； in, It is a diagonal matrix, and the diagonal elements of the matrix are the variances. .
7. The robust self-interference suppression beamforming method based on multi-missile cooperative scenarios according to claim 6, characterized in that, In step 2, the optimization objective is expressed as: ； in, The desired direction of the emission steering vector, and ; Construct optimization problem Optimization problem The medium gain expression G is based on the transmit full feed power. Adjustments were made; the optimization problem Represented as: ； in, The desired self-interference signal power threshold, This represents the transmit power when the transmit link is fully fed. Let represent the weight on the m-th transmitting element.
8. The robust self-interference suppression beamforming method based on multi-missile cooperative scenarios according to claim 3, characterized in that, In step 3, the method of transforming the originally non-convex chance-constant problem into a convex problem through semi-definite relaxation and Bernstein's inequality approximation includes: Step 3.1, Transformation and Optimization Problem The cost function is used to transform the self-interference signal power constraint into an interruption probability constraint. ； ； in, It is a semi-positive definite matrix, and ;Prob{} is the probability operation. The corresponding probability; Step 3.2, optimize the problem The problem is transformed into a semidefinite programming problem and computed using a semidefinite relaxation algorithm. ； ； in, It is a rank-1 positive semi-definite matrix, and tr() is the trace operation. To perform the real part operation; Step 3.3, rewrite the optimization problem in step 3.
2. The opportunity constraint form in the problem further transforms the optimization problem into: ； ； ； ； in, , , , All are intermediate parameters, and ; for Unit array; Let m be the diagonal element of a rank-1 positive semi-definite matrix F. Step 3.4: The problem is finally transformed into a convex problem using the approximation method of Bernstein's inequality. ； ； in, b and w The slack variable introduced is vec(), which is a vectorized operation.