Joint information and interference beamforming method for active sensing and communication integrated system

Abstract

The application provides a joint information and interference beamforming method for an active listening and communication integrated system, and belongs to the technical field of wireless information monitoring. In view of the problem that the existing wireless information monitoring cannot improve the listening performance and guarantee the service quality of legal communication users at the same time, the application first constructs a multi-antenna beamforming joint optimization model for simultaneous transmission of information and interference, then equivalently converts the multi-antenna beamforming joint optimization model into a power distribution optimization problem, and obtains a closed-form expression of the global optimal solution of the problem. Compared with the traditional SDP method, the application can obtain the optimal solution in a Multiple-Input Multiple-Output (MIMO) system with significantly reduced calculation complexity.

Description

Technical Field

[0001] This application relates to the field of wireless information surveillance technology, and in particular to a method for joint information and interference beamforming for integrated active eavesdropping and communication systems. Background Technology

[0002] For successful wireless surveillance, the channel conditions of the listening link must be superior to those of suspicious communications. However, when monitors passively listen to suspicious users (SUs), these channel conditions are often difficult to meet because monitors typically stay away from suspicious users to avoid detection.

[0003] To improve the performance of wireless information surveillance, the concept of active eavesdropping was proposed. This involves using artificial interference to reduce the transmission rate of suspicious transmitters (SRs) in single-input single-output (SISO) Rayleigh fading channels. Subsequently, the idea of ​​interference-assisted active eavesdropping has been extended to various scenarios, including block fading channels with multiple sources (SUs), multiple-input multiple-output (MIMO) systems, STAR-RIS-assisted eavesdropping systems, UAV-assisted active eavesdropping systems, and mobile antenna-enabled systems, among others. Existing research shows that using artificial interference can effectively improve eavesdropping performance. However, applying jamming signals can degrade the quality of service (QoS) of legitimate communication users (CUs).

[0004] To simultaneously ensure effective eavesdropping and communication performance, existing technologies have proposed new scenarios that consider the QoS requirements of legitimate CUs and the eavesdropper's eavesdropping performance, assuming that all communication nodes are equipped with a single antenna in this scenario. Further existing technologies have investigated full-duplex (FD) MIMO systems, maximizing the probability of uninterrupted eavesdropping while satisfying the signal-to-interference-plus-noise ratio (SINR) constraints of legitimate CUs. However, these existing technologies assume that legitimate monitors only transmit information signals and do not utilize interference signals to improve eavesdropping performance. In fact, the idea of ​​joint information and interference beamforming has been widely applied to physical layer security in MIMO systems. However, existing technologies do not consider using interference signals to improve eavesdropping performance while ensuring the communication quality of legitimate users in active eavesdropping systems, resulting in limited performance of current integrated active eavesdropping and communication systems. Summary of the Invention

[0005] In view of the above problems, embodiments of this application provide a joint information and interference beamforming method for an integrated active eavesdropping and communication system, so as to overcome the above problems or at least partially solve the above problems.

[0006] The joint information and jamming beamforming method for an integrated active eavesdropping and communication system provided in this application includes: With the aim of simultaneous and same-frequency active interference eavesdropping and communication, a signal transmission model for an integrated active eavesdropping and communication system is constructed. During the signal transmission process, the full-duplex base station sends information to legitimate communication users through multiple antennas, while simultaneously sending interference signals to suspicious receivers. Based on the inter-user channel, a joint optimization model for multi-antenna beamforming that transmits information and interference simultaneously is established. The multi-antenna beamforming joint optimization model is equivalent to a power allocation optimization model. Solve for the optimal solution of the power allocation optimization model, and determine the optimal interference beamforming vector and the optimal communication beamforming vector based on the optimal solution; Power allocation of the transmit antenna of the full-duplex base station in the active eavesdropping and communication integrated system is performed based on the optimal interference beamforming vector and the optimal communication beamforming vector to achieve low-power information and interference signal transmission of the full-duplex base station.

[0007] Optionally, the signal transmission model for the integrated active eavesdropping and communication system includes a full-duplex base station, legitimate communication users, suspicious transmitters, and suspicious receivers, wherein: The communication channel from the full-duplex base station to the suspected receiver is the first baseband equivalent channel; The communication channel from a full-duplex base station to a legitimate communication user is the second baseband equivalent channel; The communication channel from the suspicious transmitter to the suspicious receiver is the first channel; The communication channel from the suspicious transmitter to the legitimate communication user is the second channel; The communication channel from the suspected transmitter to the full-duplex base station is the third channel.

[0008] Optionally, the establishment of a joint beamforming optimization model for simultaneous transmission of information and interference signals based on inter-user channels includes: Define the signal-to-interference-plus-noise ratio (SIR) for legitimate communication users; Define the signal-to-interference-plus-noise ratio (SIR) for full-duplex base stations and suspicious receivers; Based on the signal-to-interference-plus-noise ratio (SINR) of legitimate communication users, full-duplex base stations, and suspicious receivers, a joint optimization model for multi-antenna beamforming that simultaneously transmits information and interference signals is established as follows: in, For the first channel, For the second channel, For the third channel, This is the first baseband equivalent channel. This is the second baseband equivalent channel. yes The conjugate transpose of . yes The conjugate transpose of . and These are the communication beamforming vector and the interference beamforming vector to be designed, respectively. The transmission power of the suspected transmitter. The variance of receiver noise for legitimate users. For legitimate communication users, the signal-to-interference-plus-noise ratio (SIR) is... The receiving antenna noise variance of a full-duplex base station. This represents the variance of the receiving antenna noise of the suspected receiver. The modulus of a complex number, The Euclidean norm of a vector; For the signal-to-interference-plus-noise ratio of a full-duplex base station, The signal-to-interference-plus-noise ratio (SIR) of the suspected receiver; Indicates constraints. This represents a joint optimization model for multi-antenna beamforming.

[0009] Optionally, the power allocation optimization model is: in, , , These are the actual weighting coefficients to be designed; and They represent and The normalized vector; This is a power allocation optimization model.

[0010] Optionally, the process of finding the optimal solution to the power allocation optimization model and determining the optimal interference beamforming vector and the optimal communication beamforming vector based on the optimal solution includes: If the first baseband equivalent channel and the second baseband equivalent channel are orthogonal, then the optimal interference beamforming vector and the optimal communication beamforming vector are determined according to the first equivalent model. If the first baseband equivalent channel and the second baseband equivalent channel are not orthogonal, then the optimal interference beamforming vector and the optimal communication beamforming vector are determined according to the second equivalent model.

[0011] Optionally, determining the optimal interference beamforming vector and the optimal communication beamforming vector based on the first equivalent model includes: Transform the power allocation optimization model into the first equivalent model: The optimal solution for the real weight coefficients is determined by solving the first equivalent model; Based on the optimal solution of the real weight coefficients, the optimal interference beamforming vector and the optimal communication beamforming vector are obtained as follows:

[0012] in, For the optimal communication beamforming vector, The optimal interference beamforming vector. This represents the Euclidean norm of a vector.

[0013] Optionally, determining the optimal interference beamforming vector and the optimal communication beamforming vector according to the second equivalent model includes: Transform the power allocation optimization model into a second equivalent model: in, , , for conjugate, for Conjugate; and The unknown complex weight coefficients to be optimized. This is the first constraint. This is the second constraint condition; Solve for the optimal complex weight coefficients of the second equivalent model under different conditions; Based on the obtained optimal complex weight coefficient solution, the optimal beamforming vector and the interference beamforming vector are determined as follows: ;in, for exist Projection on null space, for The unit norm vector.

[0014] Optionally, the step of solving for the optimal complex weight coefficients of the second equivalent model under different conditions includes: 1) If The optimal complex weight coefficient solution is: in, For complex weights, , This is the solution for the optimal complex weight coefficients; 2) If and The optimal complex weight coefficient solution is: ; 3) If and The optimal complex weight coefficient solution is:

[0015] in, and For complex weights.

[0016] The specific beneficial effects are as follows: First, this invention constructs a joint optimization model for joint transmit beamforming that simultaneously supports active eavesdropping and legitimate communication, and uses semidefinite relaxation techniques to transform the non-convex joint optimization problem into a convex semidefinite programming problem, and proves that the convex semidefinite programming problem has a rank-one optimal solution. Second, in order to reduce computational complexity, this invention further transforms the convex semidefinite programming problem into a power allocation optimization problem, and finally proposes a closed-form expression for the global optimal solution of the joint optimization model, obtaining the optimal interference beamforming vector and the optimal communication beamforming vector. Thus, it designs interference beams and communication beams that simultaneously perform active eavesdropping and communication systems, ensuring effective eavesdropping on suspicious users while meeting the SINR requirements of legitimate users. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1A system model that simultaneously performs active listening and communication; Figure 2 For the simulation examples, the BS average transmit power and number of transmit antennas for Algorithm 1 and Algorithm 2 are given. Relationship diagram; Figure 3 The total CPU runtime and number of transmitting antennas for Algorithm 1 and Algorithm 2 in the simulation case. Relationship diagram; Figure 4 The average transmit power and number of transmit antennas for joint transmit beamforming, conventional MRC beamforming, and conventional ZF beamforming in the simulation case are given. Relationship diagram; Figure 5 The average transmit power of BS in the simulation case is calculated as follows: (The text abruptly ends here, so the translation stops as well.) Relationship diagram; Figure 6 The graph shows the relationship between the average transmit power of the BS and the transmit power of the ST in the simulation case of joint transmit beamforming, conventional MRC beamforming and conventional ZF beamforming. Detailed Implementation

[0019] Exemplary embodiments of this application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of this application are shown in the drawings, it should be understood that this application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of this application and to fully convey the scope of this application to those skilled in the art.

[0020] This invention provides a joint information and jamming beamforming method for an integrated active eavesdropping and communication system, which may include: Step 1: With the aim of simultaneous and same-frequency active interference eavesdropping and communication, a signal transmission model for an integrated active eavesdropping and communication system is constructed. During the signal transmission process, the full-duplex base station sends information to legitimate communication users through multiple antennas, while simultaneously sending interference signals to suspicious receivers. Reference Figure 1 , Figure 1 As shown in the figure, the system model is capable of both active eavesdropping and communication. It consists of a full-duplex base station (FD-BS), a legitimate communication user (CU), a suspicious transmitter (ST), and a suspicious receiver (SR).

[0021] FD-BS equipped root transmitting antenna and Root receiving antenna, and , The self-interference assumption between the transmitting and receiving antennas is eliminated by existing self-interference cancellation techniques, specifically the self-interference cancellation techniques in references [1], [2], [3], or [4]. Meanwhile, CU, ST, and SR are all equipped with a single antenna.

[0022] The baseband equivalent channels from FD-BS to SR and CU are respectively expressed as follows: and , This is the first baseband equivalent channel. This is the second baseband equivalent channel. The channels from ST to SR, CU, and FD-BS are respectively represented as follows: , and , For the first channel, For the second channel, Let this be the third channel. Assume that all channels are uncorrelated flat Rayleigh fading channels, where each element of the channel vector is a circularly symmetric complex Gaussian (CSCG) random variable with zero mean and unit variance.

[0023] ST's baseband signal It can be represented as: (1) in, Indicates the transmission power of the suspected transmitter ST; This indicates suspicious information transmitted from a suspicious transmitter (ST) to a suspicious receiver (SR).

[0024] While receiving suspicious information from the ST, the FD-BS simultaneously transmits legitimate information to the legitimate communication user CU. To achieve successful eavesdropping, interference signals will be transmitted from the FD-BS to the SR. Therefore, the FD-BS's baseband signal... It can be represented as: (2) in, It is the information signal sent from the FD-BS to the CU; It is an interference signal sent from the FD-BS to the SR; and These are the communication beamforming vector and the interference beamforming vector to be designed, respectively. The variance is expressed as The distribution of the random variable.

[0025] Step 2: Based on the inter-user channel, establish a joint optimization model for multi-antenna beamforming that enables simultaneous transmission of information and interference; Optionally, step 2 may include the following steps: Step 2.1: Define the signal-to-interference-plus-noise ratio (SIR) for legitimate communication users in the system model; A common metric for evaluating the performance of a legitimate communication user's control unit (CU) is the signal-to-interference-plus-noise ratio (SINR). Therefore, the signal received by the CU... It can be represented as: (3) in, yes The conjugate transpose of . It is the receiving noise of the CU.

[0026] Due to baseband signal , , and Since they are independent random variables, the received signal power of the CU can be expressed as: (4) in, This represents the variance of the receiver noise for legitimate users. Indicates statistical expectation. The modulus of a complex number; Subsequently, the SINR at the legitimate communication user can be expressed as: (5) Equation (5) can be used to determine the achievable rate of legitimate communication users under low-complexity decoding.

[0027] Step 2.2: Define the signal-to-interference-plus-noise ratio (SIR) of the full-duplex base station and the suspected receiver; In active surveillance, the full-duplex base station FD-BS sends artificial interference signals to the suspicious receiver SR and simultaneously receives suspicious signals from ST. FD-BS employs advanced self-interference cancellation technology, which can negate the self-interference effects between the transmitting and receiving antennas. The receiver beamforming vector to be designed is denoted as... The received signal at FD-BS It can be represented as: (6) in, This refers to the received noise of the FD-BS. For receiving beamforming vector The conjugate transpose of; SINR at FD-BS can be expressed as: (7) in, , The Euclidean norm of a vector; This represents the noise variance of the receiving antenna in the FD-BS. Analysis reveals that: when hour, This will reach its maximum value. Therefore, Maximum-Ratio Combining (MRC) is optimal for receiver beamforming, meaning the maximum SINR at FD-BS can be obtained as follows: (8) In addition, the received signal at the suspicious receiver SR It can be represented as: (9) in, for The conjugate transpose of . For the channel from ST to SR, This is the received noise of the SR.

[0028] The SINR at the suspicious receiver SR can be expressed as: (10) in, This represents the variance of the receiving antenna noise of the suspected receiver; It is important to note here that: if and only if Only when the instantaneous listening rate is not zero can FD-BS successfully decode suspicious information.

[0029] Step 2.3: Based on the signal-to-interference-plus-noise ratio (SIR) of legitimate communication users, full-duplex base stations, and suspicious receivers, establish a joint optimization model for multi-antenna beamforming.

[0030] As analyzed above, in order to minimize the power consumption of the FD-BS, provide a satisfactory SINR for the CU, and ensure successful eavesdropping, the joint optimization problem of information and interference transmission beamforming can be modeled as follows: (11) in, This represents the constraint conditions; the first constraint condition is actually... , represents the minimum received SINR requirement of the CU, and the second constraint is the constraint condition for successful listening; Represents the joint optimization model; Step 3: Convert the multi-antenna beamforming joint optimization model into an equivalent power allocation optimization model; First, based on semidefinite relaxation, the joint optimization model is transformed into a semidefinite relaxation joint optimization model; Using the semidefinite relaxation (SDR) technique, equation (11) can be relaxed into the following convex semidefinite programming problem: (12) in, , , , , This represents the communication beamforming vector matrix to be designed. This represents the receiving beamforming vector matrix to be designed. This represents the baseband equivalent channel matrix from FD-BS to CU. This represents the baseband equivalent channel matrix from FD-BS to SR. For matrix traces, express It is a positive semi-definite matrix. express It is a positive semi-definite matrix; This represents a semidefinite relaxation joint optimization model; Since SDR cannot guarantee a rank-one solution, solving P1-SDR usually only yields a suboptimal solution for P1. However, in the embodiment of the application, it is proven that P1-SDR has a rank-one optimal solution. and The optimality of SDR was verified.

[0031] The proof is as follows: Since P1-SDR is a convex problem, its Lagrangian function can be defined as: (13) in, and These are the dual variables corresponding to the two constraints in P1-SDR.

[0032] Assumption and If it is the optimal solution for P1-SDR, then it is the same as... and The directly relevant KKT conditions can be expressed as: (14) (15) (16) (17) (18) in, and For optimal dual variables; It is the identity matrix; From equation (18), we can see that the optimal solution is... and Must be located separately and In the null space. Therefore, the following lemma can be obtained: Lemma 1: A semidefinite relaxation joint optimization model always exists that satisfies and The optimal emission covariance matrix and .

[0033] in, for rank, for The rank of ; the specific proof of Lemma 1 is described in the appendix to the proof of Lemma 1.

[0034] Based on Lemma 1, it is evident that solving the semidefinite relaxation joint optimization model P1-SDR yields a rank-one optimal solution. Furthermore, P1-SDR is a standard SDP problem, which can be efficiently solved using the CVX toolbox. The method for obtaining the rank-one optimal solution using the semidefinite relaxation joint optimization model P1-SDR is presented as Algorithm 1. The following Algorithm 1 summarizes the calculation of the optimal communication beamforming vector. and optimal interference beamforming vector The process. Algorithm 1: Optimal Solution for Joint Transmission Beamforming Based on SDR ① Input: Instantaneous channels for all nodes: , , , , ; Received noise variance per antenna: , , ; ST's transmit power: ; SINR requirements for CU: . ②Steps: 1. Solve for P1-SDR to obtain and ; 2. If : calculate , calculate ; 3. Otherwise: calculate and ; 4. End 5. Calculate using singular value decomposition (SVD) respectively. and . ③ Output: Optimal Communication Beamforming Vector and optimal interference beamforming vector .

[0035] The main computational burden of Algorithm 1 comes from solving the SDP problem P1-SDR. Specifically, given the solution accuracy... The worst-case complexity of solving the SDP using the primal-dual interior-point method is O(n). ,in K For the number of users, N Let P1 be the number of antennas. Analysis reveals that the complexity of solving the P1-SDR problem increases with the number of antennas. N It grows exponentially. Especially in large-scale MIMO systems, when N As the value increases, the computational burden of solving P1-SDR will become unbearable.

[0036] Secondly, based on the above analysis, in order to reduce computational complexity, the semidefinite relaxation joint optimization model P1-SDR is equivalently represented as a power allocation optimization model. Specifically, to avoid the exponential growth of computational complexity that occurs when solving the semidefinite relaxation joint optimization model P1-SDR using convex optimization tools, we first define... and ,in, and express and For a normalized vector (unit vector), the following lemma can be obtained: Lemma 2: The optimal solution of a semidefinite relaxation joint optimization model can always be expressed as: (19) in, , , These are real weighting coefficients; As can be seen from Lemma 2, the optimal communication beamforming vector Must be located in and In the spanned space, the optimal interference beamforming vector Must be located in Zhang Cheng's space. The specific proof of Lemma 2 is described in the appendix to the proof of Lemma 2.

[0037] As analyzed above, the joint optimization model P1 is equivalent to the semidefinite relaxation joint optimization model P1-SDR. Since the semidefinite relaxation joint optimization model P1-SDR has a rank-one optimal solution, substituting (19) into the semidefinite relaxation joint optimization model P1-SDR, the original joint optimization model P1 can be equivalently expressed as the following power allocation optimization model: (20) in, , , For the actual weight coefficients to be designed, This is a power allocation optimization model.

[0038] As can be seen from equation (20), it is only necessary to obtain the optimal solution of P1-EQV. , , Then, the optimal communication beamforming vector and the optimal interference beamforming vector can be easily obtained by equation (19). The optimal solution will be obtained by calculation of the closing value below.

[0039] Step 4: Solve for the optimal solution of the power allocation optimization model, and determine the optimal interference beamforming vector and the optimal communication beamforming vector based on the optimal solution.

[0040] Optionally, step 4 may include the following sub-steps: Step 401: Determine the projection of the second baseband equivalent channel onto the null space of the first baseband equivalent channel; Specifically, define for exist Projection on null space: (twenty one) Its unit norm vector is defined as: (twenty two) From equation (21) - equation (22), we can obtain that Lemma 3: Let , , If the optimal solution is P1-EQV, then when There will always be a time for it. ;when There will always be a time for it. .

[0041] The specific proof of Lemma 3 is described in the appendix to the proof of Lemma 3.

[0042] Step 402: Determine the optimal interference beamforming vector and the optimal communication beamforming vector when the first baseband equivalent channel and the second baseband equivalent channel are orthogonal; From Lemma 3, we know that when There will always be a time when... At this point, the first baseband equivalent channel and the second baseband equivalent channel are orthogonal, so P1-EQV can be equivalently represented as the first case P1-EQV-CASE1: (twenty three) The optimal solution under P1-EQV-CASE1 can be obtained by solving equation (23). , , Substituting the obtained optimal solution into equation (19), the optimal communication beamforming vector can be directly obtained. and optimal interference beamforming vector They are respectively: (twenty four) (25).

[0043] Step 403: Determine the optimal interference beamforming vector and the optimal communication beamforming vector when the first baseband equivalent channel and the second baseband equivalent channel are not orthogonal; when There will always be a time when... At this point, the first baseband equivalent channel and the second baseband equivalent channel are not orthogonal. Based on equations (21) and (22). It can be represented as ,in , .

[0044] P1-EQV can be equivalently represented as the second case, P1-EQV-CASE2: (26) in, and The unknown complex weight coefficients to be optimized. and They are respectively and Conjugate; This is the first constraint. This is the second constraint.

[0045] Through geometric analysis, the optimal solution of P2-EQV-CASE2 can be divided into the following three cases: Scenario 1: When When, it indicates that the first constraint condition of equation (26) is satisfied. 'Relationship, and the second constraint takes' At this time, we have: (27) Scenario 2: When and When, it indicates that the first constraint condition of equation (26) is satisfied. 'Relationship and the second constraint takes' At this time, we have: (28) Scenario 3: When and When, it indicates that both the first and second constraints of equation (26) are satisfied. The relationship at this time is: (29) (30) When the optimal solution to P2-EQV-CASE2 is obtained and Then, the optimal beamforming vector of P1 can be obtained through equation (82). and interference beamforming vector : (31) Algorithm 2 uses the closed-form solution algorithm for joint transmit beamforming. The following section of Algorithm 2 summarizes the process of calculating optimal beamforming and interference beamforming, where the optimal communication beamforming vector... and interference beamforming vector It is always derived in a closed form as shown in equations (24), (25), and (31). Furthermore, it can be observed from equations (24) to (25) and (27) to (31) that the computational complexity of Algorithm 2 stems from... and The norm calculation can be completely omitted compared to Algorithm 1, greatly reducing computational redundancy. Algorithm 2: Closed-form solution for joint transmit beamforming ① Input: Instantaneous channels for all nodes: , , , , ; Received noise variance per antenna: , , ; ST's transmit power: ; SINR requirements for CU: . ②Steps: 1. Calculation ; 2. Calculation ; 3. Calculation , ; 4. If : Calculate using equations (24) and (25) respectively. and ; 5. Otherwise if and : Calculate using equation (27) respectively and And calculate using equation (31) and ; 6. Otherwise if and and : Calculate using equation (28) and And calculate using equation (31) and ; 7. Otherwise: Calculate using equations (29) and (30) and And calculate using equation (31) and ; 8. End. ③ Output: Optimal Communication Beamforming Vector and interference beamforming vector .

[0046] Simulation Case This simulation case evaluates the performance of the proposed method through simulation experiments. FD-BS is equipped with... Root receiving antenna. Channel vector. , , , and All terms are generated as independent CSCG random variables and obey the following rules. Distribution. The received noise of each antenna of all receivers is distributed. Generate ST transmit power from mW scan to mW, which is equivalent to to The simulation results were obtained by averaging 10,000 independent experiments.

[0047] For ease of comparison, traditional suboptimal beamforming algorithms, namely MRC beamforming and ZF beamforming, were selected as the benchmarks. For the MRC beamforming strategy, the communication beamforming vector and the interference beamforming vector can be expressed as follows: (32) in, and Assign weights to the actual power to be designed. This refers to the communication beamforming vector under the MRC beamforming strategy. This is the interference beamforming vector under the MRC beamforming strategy.

[0048] Substituting (32) into equation (12), we get: (33) The optimal power allocation weights can be derived as follows: (34) (35) For the ZF beamforming strategy, the communication beamforming vector and the interference beamforming vector can be expressed as follows: (36) in, and Assign weights to the actual power to be designed. This refers to the communication beamforming vector under the ZF beamforming strategy. This is the interference beamforming vector under the ZF beamforming strategy. At this point, Defined as exist Projected unit vector on null space: (37) Substituting (36) and (37) into equation (12), we get: (38) The optimal power allocation weight is: (39) (40).

[0049] Below, we first conduct a comparative experiment between the SDR-based joint transmit beamforming algorithm (Algorithm 1) and the closed-loop solution algorithm for joint transmit beamforming (Algorithm 2), and the results are as follows: Figure 2 As shown. From Figure 2 It can be seen that when , and At that time, the average transmit power of FD-BS With the number of transmitting antennas The relationship between the changes in power is clear. It can be seen that the optimal solution of the SDR-based joint transmission beamforming algorithm is completely consistent with the closed-loop solution algorithm for joint transmission beamforming. Meanwhile, the average transmit power of FD-BS varies with... N The increasing monotonically decreasing trend indicates that using more antennas in a large-scale MIMO system can reduce power consumption.

[0050] Secondly Figure 3 Comparison , and At that time, the total CPU running time of the two algorithms above is related to the number of transmit antennas. The relationship. From Figure 3 It can be seen that the total CPU runtime of the SDR-based joint transmit beamforming algorithm increases with the number of transmit antennas. It increases exponentially with the increase of [something]. It is particularly noteworthy that when [something] increases... At that time, the total CPU runtime of the SDR-based joint transmit beamforming algorithm exceeded 120 seconds, which would result in unacceptable latency for large-scale MIMO systems. In contrast, the total CPU runtime of the closed-loop solution algorithm for joint transmit beamforming is only about 0.04 seconds, which is negligible compared to the SDR-based algorithm. Furthermore, the total CPU runtime of the closed-loop solution algorithm for joint transmit beamforming is almost unaffected by the number of transmit antennas. The impact, this Very large-scale practical applications are very important.

[0051] Finally, the performance of the proposed closed-loop solution algorithm for joint transmission beamforming, the traditional MRC beamforming method, and the traditional ZF beamforming method are compared. The average transmit power of the FD-BS using the proposed joint transmission beamforming method is compared with that of the traditional algorithm. Relationship such as Figure 4 As shown, where , and Clearly, the proposed joint transmission beamforming method can provide minimal power consumption, from Figure 4 As can be observed, the power consumption of the present invention, conventional MRC beamforming, and conventional ZF beamforming schemes increases with... The power consumption decreases monotonically as the power increases. Furthermore, it can be observed that the power consumption of the proposed joint transmission beamforming scheme is lower than that of conventional MRC beamforming and conventional ZF beamforming schemes. When At that time, the average power consumption of the proposed joint transmission beamforming scheme was approximately Compared to traditional ZF beamforming schemes, it has lower costs. Compared to traditional MRC beamforming schemes, it has lower costs. .

[0052] It should be noted that the optimal solution of the optimization model shown in equation (12) is subject to... and The significant impact on channel gain. As shown in equation (11), when... When the signal strength is low, the transmit power of the BS needs to be increased. Assuming all channels satisfy free-space propagation characteristics, the channel gain can be modeled as: (41) in, For the signal wavelength, The distance between the transmitting and receiving ends; set up The distance between ST and SR. The distance between ST and BS. for Channel gain, for The channel gains of the two channels satisfy the following relationship: (42) Figure 5 This demonstrates the average transmit power of the FD-BS and The relationship, among which , , and As can be seen from the figure, the joint transmission beamforming scheme proposed in this invention achieves the lowest average transmit power consumption for FD-BS, which proves the efficiency of the proposed algorithm. Furthermore, Figure 5 The paper clearly demonstrates the difference in average transmit power consumption of FD-BS required by the proposed joint transmit beamforming scheme, conventional MRC beamforming, and conventional ZF beamforming scheme. It increases monotonically with the increase of . In fact, it can be seen from equation (42) that as The increase of channel gain ratio This will increase, forcing base stations to consume more power to weaken the link quality for suspicious users.

[0053] Figure 6 The average BS transmit power and The relationship, among which , , and As can be seen from the figure, the average transmit power consumption of the FD-BS required by the joint transmit beamforming scheme proposed in this invention, the conventional MRC beamforming, and the conventional ZF beamforming scheme increases with... The power consumption increases monotonically with increasing power. Furthermore, the joint transmission beamforming algorithm proposed in this invention maintains the lowest power consumption while ensuring the same system performance, further verifying the superiority of this invention.

[0054] References: Literature [1] BP Day, AR Margetts, DW Bliss, and P. Schniter, "Full-duplexMIMO relaying: Achievable rates under limited dynamic range," IEEE Journal of Areas Commun. , vol. 30, no. 8, pp. 1541–1553, Sep. 2012. Literature [2] SW Kim, YJ Chun, and S. Kim, “Co-channel interferencecancellation using single radio frequency and baseband chain,” IEEE Trans.Commun. , vol. 58, no. 7, pp. 2169–2175, Jul. 2010. Literature [3] T. Riihonen, S. Werner, and R. Wichman, “Mitigation of loopback selfinterference in full-duplex MIMO relays,” IEEE Trans. Signal Process. , vol. 59, no. 12, pp. 5983–5993, Dec. 2011. Literature[4]T. Snow, C. Fulton, and WJ Chappell, “Transmit-receiveduplexingusing digital beamforming system to cancel self-interference,” IEEETrans.Microw. Theory Tech., vol. 59, no. 12, pp. 3494–3503, Dec. 2011. Proof of Lemma 1 (Appendix): From equations (19) and (20), it can be seen that, and They can be equivalently expressed as follows: (43) (44) 1) Proof: Because and Therefore, it exists. and , N This indicates the number of antennas, which can then be obtained according to equation (44): (45) in, Describes the rank of a matrix; In addition, due to ,but Must be located The null space, therefore: (46) Therefore, it exists: (47) 2) Proof: Because and ,have , Combining , From equation (43), we can derive: (48) In addition, due to ,but Must be located The null space, therefore: (49) when At that time, obviously It should be true. At that time, obviously It should be true.

[0055] Assumption ,but Next, we will prove that there exists a condition that satisfies this condition. The optimal communication transmission covariance matrix.

[0056] First, under the above assumptions, prove and It must be true. If From equation (43), we can see that Therefore, there are This result contradicts the first assumption. Similarly, if From equation (43), we can see that This result also contradicts the first assumption. Therefore, when or equivalent There will always be a time when... and .

[0057] The next goal is to construct an equivalent expression for the optimal solution. Let... express The basis of the null space (easily proven) and (parallel), where, express N A complex matrix with 1 row and 1 column. Multiply both sides of equation (43) by... and : (50) in, express The conjugate transpose of; The reason why the last equation in equation (50) is true is Furthermore, due to The left side of equation (50) must be ;because , there must be ;because The right side of equation (50) must exist Based on the above analysis, there must be... as well as: (51) This holds true in equation (50), from which we can derive... yes A basis of the null space, let yes Another basis of the null space, and satisfying (because and (parallel), therefore we can conclude: (52) in, express The conjugate transpose of; Furthermore, multiplying both sides of equation (44) by... and We can obtain: (53) The reason why the last equation is true is... Substituting equation (52) into equation (53), we can obtain In other words, It is A basis of the null space, and also The basis of the null space. Furthermore, it can be seen from equation (18) that... Definitely In the null space, Definitely In the null space. Therefore, and "Always" can be represented as: (54) (55) in , , For real values, For complex values, for . conjugate.

[0058] Next, proof is needed. It is necessary to maintain the optimal point. Substituting equations (54) and (55) into the problem P1-SDR, we can obtain the objective function of equation (12) by analyzing it: (56) From the first constraint of equation (12), we can obtain: (57) Since equation (52) holds, the last equation also holds. Furthermore, from the second constraint of equation (12), we can obtain: (58) Since equation (51) holds, the last equation also holds. From the third constraint of equation (12), we can obtain: (59) (60) It can be directly observed from equation (59) that the optimal solution is at the term It must be zero because it does not change the three constraints of equation (12), but it will always increase the objective function value. Therefore, the optimal... and It can be restated as: (61) (62) Finally, prove the solution of the following newly constructed solution: (63) (64) Similarly, this is the optimal solution for P1-SDR. Substituting equations (61) to (64) into the problem P1-SDR, we obtain the objective function of equation (12): (65) From the first constraint of equation (12), we can obtain: (66) From the second constraint of equation (12), we can obtain: (67) From the third constraint of equation (12), we can obtain: (68) (69) From equation (65), we can see that and This will provide the same optimal objective value for problem P1-SDR. Furthermore, from equations (66) to (69), we can conclude that... and All constraints of P1-SDR are satisfied. Therefore, and It is also the optimal solution for P1-SDR.

[0059] From all the above analyses, it can be seen that the optimal point always exists. and optimal solution and .

[0060] Proof of Lemma 2 (Appendix): Lemma 1 shows that the optimal solutions to problems P1 and P1-SDR can be the same, meaning that synchronization information and interference beamforming can be considered the optimal transmission strategies. Furthermore, since the optimal dual variables satisfy... , Therefore, the optimal beamforming vector can be obtained from the following cases.

[0061] Case 1: Assumption , Based on the assumed definition, according to equations (43) and (44), it can be seen that... and It must be true. Furthermore, according to equation (18), we can obtain... , .

[0062] Therefore, we can finally conclude that: , .

[0063] Scenario 2: Assumption , Based on the assumed definition, according to equations (43) and (44), it can be seen that... and This must hold. Furthermore, according to equation (43), the following inequality holds: (70) like Then the optimal solution for P1 is the same as in case 1. If ,because Must with Parallel, that is, Therefore, it can be Represented as The basis of the null space. Then, through equation (18), the optimal beamforming vector can be expressed as follows: , ,in It is a power allocation factor used for communication beamforming.

[0064] Scenario 3: Assumption , Based on the assumed definition, according to equations (43) and (44), it can be seen that... This must be true. Therefore, it exists: (71) like Then the optimal solution for P1 is the same as in case 1. If ,because Must with Parallel, that is, Therefore, it can be Represented as The basis of the null space. Then, through equation (18), the optimal beamforming vector can be expressed as follows: , ,in It is a power allocation factor used to interfere with beamforming.

[0065] Case 4: Assumption , Based on the assumed definition, according to equations (43) and (44), it can be seen that... Established.

[0066] like Then there is According to equations (43) and (44), and It must be true. Because... Must with Parallel, that is, Therefore, it can be Represented as The basis of the null space. Then, multiply both sides of equation (43) by... and Therefore, equation (72) holds true: (72) The reason why the last equation in equation (72) is true is .because , Then there must be First, we can obtain yes The basis of the null space, and then according to equation (18), the optimal beamforming vectors can be expressed as follows: and .

[0067] like , combined Must with Parallel, that is, Therefore, it can be Represented as The basis of the null space. Then, multiply both sides of equation (43) by... and Therefore, equation (73) holds true: (73) The reason why the last equation in equation (73) is true is .because , Then there must be Therefore, there must be ,in yes The basis of the null space. Then, multiply both sides of equation (43) by... and Therefore, equation (74) holds true: (74) The reason why the last equation in equation (74) is true is .therefore, Too Basis of the null space. Further assumptions yes Another basis of the null space (at this time) (This is necessarily true). Then, multiply both sides of equation (43) by... and Therefore, equation (75) holds true: (75) The reason why the last equation in equation (75) is true is From the observation of equation (75), we can see that... Definitely in In the null space, therefore It must be true (because if) , It will be (The null space is the only basis), which means that there is Similar to the proof of Lemma 1, it can be further proved that... and They can be represented as follows: (76) (77) in, and It is a real number. For the sake of brevity, the proof is omitted here.

[0068] Based on the above analysis, it can be concluded that and It can always be expressed as and Q.E.D.

[0069] Proof of Lemma 3 (Appendix): when At that time, we can know that... and They are orthogonal. Therefore, the problem P1-EQV can be equivalently represented as: (78) in , , Let these be the real weights to be designed. Assume... , and This is the optimal power allocation for P1-EQV-1; therefore, the following new solution can always be constructed: (79) Subsequently, substituting equation (79) into problem P1-EQV-CASE1, we can obtain the new solution. , and It can provide the same optimal objective function value and satisfy the remaining two constraints. Therefore, in equation (79) , and This is also optimal for problem P1-EQV-1. Therefore, it is appropriate. Sometimes, .

[0070] when At that time, we can know that... and They are not orthogonal. Therefore, by defining (21) and (22), we know that... It can always be by and This means, that is: (80) in and For complex weights. Furthermore, because there are... Then it must exist: (81) By analyzing equation (81), it is certain that: (82) Where the definition and The weights are unknown. Substituting equations (81) and (82) into problem P1-EQV, we obtain the following equivalent optimization: (83) Assumption , and If it is the optimal solution for P1-EQV-CASE2, then the following new solution can always be constructed: (84) Substituting equation (84) into problem P1-EQV-CASE2, a new solution can be obtained. , and Both provide the same optimal objective value (and satisfy the second constraint), while the first constraint always provides more degrees of freedom. Therefore, at the optimal point, there must be... Q.E.D.

[0071] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0072] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0073] The above provides a detailed description of the joint information and interference beamforming method for an integrated active eavesdropping and communication system provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A joint information and jamming beamforming method for integrated active eavesdropping and communication systems, characterized in that, The method includes: With the aim of simultaneous and same-frequency active interference eavesdropping and communication, a signal transmission model for an integrated active eavesdropping and communication system is constructed. During the signal transmission process, the full-duplex base station sends information to legitimate communication users through multiple antennas, while simultaneously sending interference signals to suspicious receivers. Based on the inter-user channel, a joint optimization model for multi-antenna beamforming that transmits information and interference simultaneously is established. The multi-antenna beamforming joint optimization model is equivalent to a power allocation optimization model. Solve for the optimal solution of the power allocation optimization model, and determine the optimal interference beamforming vector and the optimal communication beamforming vector based on the optimal solution; Power allocation of the transmit antenna of the full-duplex base station in the active eavesdropping and communication integrated system is performed based on the optimal interference beamforming vector and the optimal communication beamforming vector to achieve low-power information and interference signal transmission of the full-duplex base station.

2. The method according to claim 1, characterized in that, The signal transmission model for the integrated active eavesdropping and communication system includes a full-duplex base station, legitimate communication users, suspicious transmitters, and suspicious receivers, wherein: The communication channel from the full-duplex base station to the suspected receiver is the first baseband equivalent channel; The communication channel from a full-duplex base station to a legitimate communication user is the second baseband equivalent channel; The communication channel from the suspicious transmitter to the suspicious receiver is the first channel; The communication channel from the suspicious transmitter to the legitimate communication user is the second channel; The communication channel from the suspected transmitter to the full-duplex base station is the third channel.

3. The method according to claim 2, characterized in that, The aforementioned joint beamforming optimization model for simultaneous transmission of information and interference signals based on inter-user channels includes: Define the signal-to-interference-plus-noise ratio (SIR) for legitimate communication users; Define the signal-to-interference-plus-noise ratio (SIR) for full-duplex base stations and suspicious receivers; Based on the signal-to-interference-plus-noise ratio (SINR) of legitimate communication users, full-duplex base stations, and suspicious receivers, a joint optimization model for multi-antenna beamforming that simultaneously transmits information and interference signals is established as follows: ； in, For the first channel, For the second channel, For the third channel, This is the first baseband equivalent channel. This is the second baseband equivalent channel. yes The conjugate transpose of . yes The conjugate transpose of . and These are the communication beamforming vector and the interference beamforming vector to be designed, respectively. The transmission power of the suspected transmitter. The variance of receiver noise for legitimate users. For legitimate communication users, the signal-to-interference-plus-noise ratio (SIR) is... The receiving antenna noise variance of a full-duplex base station. This represents the variance of the receiving antenna noise of the suspected receiver. The modulus of a complex number The Euclidean norm of a vector; For the signal-to-interference-plus-noise ratio of a full-duplex base station, The signal-to-interference-plus-noise ratio (SIR) of the suspected receiver; Indicates constraints. This represents a joint optimization model for multi-antenna beamforming.

4. The method according to claim 3, characterized in that, The power allocation optimization model is as follows: ； in, , , These are the actual weighting coefficients to be designed; and They represent and The normalized vector; This is a power allocation optimization model.

5. The method according to claim 4, characterized in that, The process of finding the optimal solution to the power allocation optimization model, and determining the optimal interference beamforming vector and the optimal communication beamforming vector based on the optimal solution, includes: If the first baseband equivalent channel and the second baseband equivalent channel are orthogonal, then the optimal interference beamforming vector and the optimal communication beamforming vector are determined according to the first equivalent model. If the first baseband equivalent channel and the second baseband equivalent channel are not orthogonal, then the optimal interference beamforming vector and the optimal communication beamforming vector are determined according to the second equivalent model.

6. The method according to claim 5, characterized in that, The step of determining the optimal interference beamforming vector and the optimal communication beamforming vector according to the first equivalent model includes: Transform the power allocation optimization model into the first equivalent model: ； The optimal solution for the real weight coefficients is determined by solving the first equivalent model; Based on the optimal solution of the real weight coefficients, the optimal interference beamforming vector and the optimal communication beamforming vector are obtained as follows: ； ； in, For the optimal communication beamforming vector, The optimal interference beamforming vector. This represents the Euclidean norm of a vector.

7. The method according to claim 6, characterized in that, The step of determining the optimal interference beamforming vector and the optimal communication beamforming vector according to the second equivalent model includes: Transform the power allocation optimization model into a second equivalent model: ； in, , , for conjugate, for Conjugate; and The unknown complex weight coefficients to be optimized. This is the first constraint. This is the second constraint condition; Solve for the optimal complex weight coefficients of the second equivalent model under different conditions; Based on the obtained optimal complex weighting coefficient solution, the optimal beamforming vector and the interference beamforming vector are determined as follows: ； in, for exist Projection on null space, for The unit norm vector.

8. The method according to claim 7, characterized in that, The process of solving the optimal complex weight coefficient solutions of the second equivalent model under different conditions includes: 1) If The optimal complex weight coefficient solution is: ； in, For complex weights, , This is the solution for the optimal complex weight coefficients; 2) If and The optimal complex weight coefficient solution is: ； 3) If and The optimal complex weight coefficient solution is: ； ； in, and For complex weights.

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