Multi-user downlink robust beam forming method based on differential privacy mechanism

Abstract

The invention belongs to the technical field of communication privacy protection, and particularly relates to a multi-user downlink robust beam forming method based on a differential privacy mechanism. The method comprises the following steps of: estimating a downlink channel vector by a user; the user adds differential privacy noise into the channel vector and feeds back the difference privacy noise to the base station; the base station enables the transmitting power to be minimized under the constraint of a signal to interference plus noise ratio according to the disturbed channel vector modeling optimization problem; using a positive semidefinite relaxation method to convert an optimization problem; using an S-process method to convert the non-convex constraint into a linear matrix inequality; solving a positive semidefinite programming problem by using a CVX optimizer; and restoring the rank-one constraint to obtain an optimal beam forming vector. According to the invention, the location privacy of the user can be effectively protected from being leaked; and on the premise that the requirement of the communication signal to interference plus noise ratio is met, the transmitting power is minimized, excellent system performance is kept, and good robustness and practical value are achieved.

Description

Technical Field

[0001] This invention belongs to the field of communication privacy protection technology, specifically relating to a multi-user downlink robust beamforming method based on differential privacy mechanism. Background Technology

[0002] During downlink communication between a base station and a user, the base station first transmits pilot signals. The user estimates downlink channel state information (CSI) based on the received signals and feeds it back to the base station to support transmission optimization operations such as precoding. However, channel state information is distance-dependent. If the raw channel state information is directly fed back, eavesdroppers may use this information to deduce the user's location, resulting in privacy breaches.

[0003] In the era of data-driven decision-making, privacy protection technologies face severe challenges. Traditional anonymization methods attempt to protect privacy by removing direct identifiers, but have proven to have fundamental flaws: attackers can re-identify individuals by linking to external data, and their protection lacks a rigorous mathematical foundation, making them vulnerable to attackers with background knowledge. While homomorphic encryption can perform computations in ciphertext, ensuring the confidentiality of data processing, its core limitation lies in the fact that the precise decrypted result still reveals individual information, and its enormous computational cost makes it unsuitable for large-scale data analysis scenarios. It is against this backdrop that differential privacy brings about a fundamental paradigm shift. By adding carefully calibrated random noise to query results, it provides provable and quantifiable privacy guarantees, ensuring that the impact of any single individual on the result is negligible; it achieves a precise trade-off between privacy protection and data utility through privacy budgeting (ε), making it particularly suitable for statistical data dissemination scenarios; its computational efficiency is far higher than homomorphic encryption, supporting large-scale interactive queries. These advantages make differential privacy the gold standard in the field of statistical data dissemination and sharing, and it is widely used in key areas such as population censuses and user behavior analysis, achieving a breakthrough in providing robust privacy guarantees while releasing the value of data. Summary of the Invention

[0004] To address the above problems, the present invention aims to provide a multi-user downlink robust beamforming method based on differential privacy mechanism.

[0005] The multi-user downlink robust beamforming method based on differential privacy mechanism provided by this invention includes the following specific steps:

[0006] Step 1: User estimates downlink channel vector;

[0007] Step 2: The user adds differential privacy noise to the downlink channel vector and feeds it back to the base station;

[0008] Step 3: The base station models the optimization problem based on the perturbed channel vector to minimize the transmit power under the signal-to-interference-plus-noise ratio constraint;

[0009] Step 4: Use the semi-positive definite relaxation method [1] to transform the optimization problem;

[0010] Step 5: Use the S-procedure method [2] to convert non-convex constraints into linear matrix inequalities;

[0011] Step 6: Solve the semidefinite programming problem using the CVX optimizer;

[0012] Step 7: Restore the rank-one constraint to obtain the optimal beamforming vector.

[0013] Furthermore:

[0014] In Step 2, the differential privacy noise is Laplace noise, and its probability density function is:

[0015] , (1)

[0016] in, , For sensitivity, For privacy budget. The true channel vector of user k is Add differential privacy noise The perturbated channel vector is obtained. It then uploads it to the base station.

[0017] In Step 3, the base station models an optimization problem based on the perturbed channel vector. Specifically, one base station is equipped with N antennas; there are K users, each equipped with one antenna. The signal transmitted by the base station to the k-th user is... Its average power is normalized to 1; the signal received by user k is:

[0018] , (2)

[0019] in, Let be the beamforming vector for user k. Let k be the channel vector. It is additive white Gaussian noise with a mean of 0 and a variance of . superscript Represents the conjugate transpose; considering differential privacy noise, the signal-to-interference-plus-noise ratio is expressed as:

[0020] , (3)

[0021] The interruption probability constraint is:

[0022] , (4)

[0023] in, For interruption probability, Given a lower bound for the signal-to-interference-plus-noise ratio (SINR), and with the objective function being the minimization of transmit power, we obtain the optimization problem:

[0024] , (5)

[0025] The semidefinite relaxation method described in Step 4 is used to transform the optimization problem. The specific operation process is as follows:

[0026] Step 4-1 Variable Substitution: Let The optimization problem (5) is transformed into:

[0027] , (6)

[0028] It needs to satisfy the rank-one constraint and the positive semi-definite constraint. The signal-to-interference-plus-noise ratio (SINR) (3) is converted to:

[0029] , (7)

[0030] Step 4-2 Rank-1 Relaxation: Since the rank-1 constraint is non-convex, it is relaxed, and the optimization problem is transformed into:

[0031] , (8)

[0032] Step 5 describes using the S-procedure method to transform non-convex constraints into linear matrix inequalities. Specifically, based on the interruption probability and the Laplace distribution, the noise distribution interval is calculated; let:

[0033] , (9)

[0034] get Therefore, the differential privacy noise range is:

[0035] , (10)

[0036] in, Transform the inequality into:

[0037] , (11)

[0038] Where I is the identity matrix. The signal-to-interference-plus-noise ratio (SINR) constraint is transformed into: (12)

[0039] Using the S-procedure method, based on the two inequalities above, we obtain the linear matrix inequality:

[0040] (13)

[0041] in, The optimization problem is transformed into a semidefinite programming problem:

[0042] (14)

[0043] Step 7 describes restoring the rank-one constraint to obtain the optimal beamforming vector. Specifically, the obtained solution... The rank may not be 1, therefore it is necessary to restore the rank-1 constraint. Perform eigenvalue decomposition and use the eigenvector corresponding to the largest eigenvalue. As an approximation, the optimal solution to the original problem is obtained.

[0044] The main features of this invention are:

[0045] In a system architecture consisting of multiple antenna base stations and multiple users, a differential privacy mechanism is introduced to perform privacy-preserving perturbation processing on downlink channel state information before uploading, effectively protecting user location privacy from leakage. Based on this, a robust beamforming method is adopted at the base station. By optimizing the beamforming matrix design, transmit power is minimized while ensuring that the signal-to-interference-plus-noise ratio (SINR) requirements are met. This scheme maintains excellent system performance even after the channel state information undergoes differential privacy perturbation, demonstrating good robustness and practical value. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the overall architecture of the communication system in this invention.

[0047] Figure 2 This is a flowchart illustrating the multi-user downlink robust beamforming method based on differential privacy mechanism in this invention.

[0048] Figure 3 This is a simulation illustration of a specific implementation of the present invention. Detailed Implementation

[0049] The present invention will be further described below with reference to the embodiments and accompanying drawings. However, the present invention is not limited to the specific embodiments, and those skilled in the art will recognize that various modifications are within the spirit and scope of the invention as defined and determined by the appended claims.

[0050] This invention introduces a privacy protection mechanism while taking into account the performance requirements of the communication system, achieving a balance between privacy and performance.

[0051] Example 1: First, the parameters used in this example are given in Table 1.

[0052] Table 1

[0053] .

[0054] Figure 1 This is the application scenario system model adopted by the present invention. This embodiment is based on a communication system that includes one base station and multiple mobile users. The base station is equipped with multiple antennas, and each user is equipped with one antenna, which has the ability to receive and transmit signals.

[0055] See Figure 2 This invention provides a multi-user downlink robust beamforming scheme based on differential privacy mechanism. Each step is described in detail below with reference to specific embodiments.

[0056] The user estimates the downlink channel vector and selects a randomly generated set of channel vectors for simulation testing.

[0057] The differential privacy budget ε is set to 100, and the differential privacy noise follows a Laplace distribution. Based on the Laplace probability density function... , Generate differential privacy noise and obtain the differential privacy noise vector. Add it to the real channel vector The perturbated channel vector is obtained. It then uploads it to the base station.

[0058] The base station has 3 antennas (N=3), and there are 3 users (K=3), each with 1 antenna. Therefore, the channel vector and beamforming vector are both 3-dimensional. The variance of the Gaussian white noise in the channel is set to 0.01. The base station models an optimization problem based on the channel vector, minimizing the transmit power under the signal-to-interference-plus-noise ratio (SINR) outage probability constraint. The outage probability is set to ρ=0.2, and the SINR constraint is... The target signal-to-interference-plus-noise ratio (SIR) γ was tested with different values: 0 dB, 2 dB, 4 dB...14 dB. The SIR is expressed as:

[0059]

[0060] Establish an optimization problem:

[0061]

[0062] We transform the optimization problem using a semidefinite relaxation method. Variable substitution: Let... Transform the optimization problem into , To satisfy the rank-one constraint and the positive semi-definite constraint, the signal-to-interference-plus-noise ratio (SINR) is converted to:

[0063]

[0064] Since the rank-one constraint is non-convex, we relax it, and the optimization problem is transformed into:

[0065]

[0066] Calculate the noise distribution interval based on the interruption probability and the Laplace distribution. Let... ,get Therefore, the differential privacy noise range is... ,in Transform the inequality into Where I is the identity matrix. The signal-to-interference-plus-noise ratio constraint is transformed into:

[0067] Using the S-procedure method, based on the two inequalities mentioned above, we obtain the linear matrix inequality:

[0068] ;

[0069] in, The optimization problem is transformed into a semidefinite programming problem:

[0070] ;

[0071] For semidefinite programming problems, the CVX optimizer can be used to solve them directly.

[0072] By restoring the rank-one constraint, the optimal beamforming vector is obtained. The solution is... The rank may not be 1, so the rank-1 constraint needs to be restored. Then, perform eigenvalue decomposition. ,in, Find the largest eigenvalue to obtain the optimal solution to the original problem. .

[0073] Based on the obtained optimal solution, the total transmit power P of the base station can be calculated, i.e. .

[0074] Table 2 shows the total transmit power P of the base station under different target signal-to-noise ratios γ.

[0075] Table 2

[0076] .

[0077] Figure 3 The paper demonstrates the variation of the total transmit power of the base station under different target signal-to-noise ratios (SNRs). It can be seen that as the target SNR increases, the information transmission rate increases accordingly, and the required transmit power of the base station also increases. However, even after introducing differential privacy perturbations, the system can still maintain a low transmit power level, which verifies the superior performance of the robust beamforming method employed in this invention.

[0078] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

[0079] References

[0080] [1] Luo ZQ, Ma WK, So MC, et al. Semidefinite Relaxation of Quadratic Optimization Problems[J]. IEEE Signal Processing Magazine, 2010, 27(3):20-34.

[0081] [2] Beck A, Eldar YC. Strong Duality in Nonconvex QuadraticOptimization with Two Quadratic Constraints[J]. Siam Journal on Optimization, 2006.

Claims

1. A multi-user downlink robust beamforming method based on differential privacy mechanism, characterized in that, The specific steps are as follows: Step 1: User estimates downlink channel vector; Step 2: The user adds differential privacy noise to the channel vector and feeds it back to the base station; Step 3: The base station models the optimization problem based on the perturbed channel vector to minimize the transmit power under the signal-to-interference-plus-noise ratio constraint; Step 4: Use the semidefinite relaxation method to transform the optimization problem; Step 5: Use the S-procedure method to convert non-convex constraints into linear matrix inequalities; Step 6: Solve the semidefinite programming problem using the CVX optimizer; Step 7: Restore the rank-one constraint to obtain the optimal beamforming vector.

2. The robust beamforming method according to claim 1, characterized in that, In Step 2, the differential privacy noise is Laplace noise, and its probability density function is: ， （1） in, , For sensitivity, For privacy budget; the true channel vector of user k is Add differential privacy noise The perturbated channel vector is obtained. It then uploads it to the base station.

3. The robust beamforming method according to claim 2, characterized in that, In Step 3, the base station modeling optimization problem based on the perturbed channel vector is as follows: Assume a base station with N antennas; K users, each with one antenna; the signal transmitted by the base station to the k-th user is... Its average power is normalized to 1; the signal received by user k is: ， （2） in, Let be the beamforming vector for user k. Let k be the channel vector. It is additive white Gaussian noise with a mean of 0 and a variance of . Considering differential privacy noise, the signal-to-interference-plus-noise ratio (SIR) is expressed as: ， （3） The interruption probability constraint is: ， （4） in, For interruption probability, Given a lower bound for the signal-to-interference-plus-noise ratio (SINR), and with the objective function being the minimization of transmit power, we obtain the optimization problem: ， （5）。 4. The robust beamforming method according to claim 3, characterized in that, The semidefinite relaxation method described in Step 4 transforms the optimization problem, and the specific process is as follows: Step 4-1 Variable Substitution: Let The optimization problem (5) is transformed into: ， （6） Satisfying the rank-one constraint and the positive semi-definite constraint; the signal-to-interference-plus-noise ratio (SINR) (3) is converted to: ， （7） Step 4-2 Rank-1 Relaxation: Since the rank-1 constraint is non-convex, we relax it, and the optimization problem is transformed into: ， （8）。 5. The robust beamforming method according to claim 4, characterized in that, Step 5 describes using the S-procedure method to convert non-convex constraints into linear matrix inequalities. Specifically, the noise distribution interval is calculated based on the interruption probability and the Laplace distribution. make: ， （9） get Therefore, the differential privacy noise range is: ， （10） in, Transform the inequality into: ， （11） Where I is the identity matrix; the signal-to-interference-plus-noise ratio constraint is transformed into: (12) Using the S-procedure method, based on the two inequalities above, we obtain the linear matrix inequality: （13） in, The optimization problem is transformed into a semidefinite programming problem: （14）。 6. The robust beamforming method according to claim 1, characterized in that, Step 7 describes restoring the rank-one constraint to obtain the optimal beamforming vector. Specifically, the obtained solution... The rank may not be 1, so it is necessary to restore the rank-1 constraint. Perform eigenvalue decomposition and use the eigenvector corresponding to the largest eigenvalue. As an approximation, the optimal solution to the original problem is obtained.

Images