Physical layer secure transmission method based on spatial Sigma-Delta modulation

Abstract

The invention relates to a physical layer communication technology, and provides a physical layer security transmission method based on space Sigma-Delta modulation, the physical layer security problem in downlink transmission is processed by using the space Sigma-Delta modulation, and the design of the Sigma-Delta modulator is processed into an optimization problem based on an L-order Sigma-Delta modulator: under the condition that the space Sigma-Delta modulator is not overloaded, the L-order Sigma-Delta modulator is not overloaded, the L-order Sigma-Delta modulator is not overloaded, the L-order Sigma-Delta modulator is not overloaded, the L-order Sigma-Delta modulator is not overloaded, and the L-order Sigma-Delta modulator is not overloaded. And when the ratio of the signal to the quantization noise of the legal user side is minimum, the maximum SQNR of the eavesdropper is less than 1 / eta. And a low-resolution DAC (Digital-to-Analog Converter) is utilized, and quantization noise is subjected to space shaping through Sigma-Delta modulation after optimization setting. According to the method, the hardware cost and the power consumption of large-scale MIMO implementation are reduced, serious quantization noise caused by rough quantization of a traditional low-resolution quantizer is naturally guided to potential eavesdroppers to protect legal users, and communication safety is achieved.

Description

Technical Field

[0001] The invention relates to a physical layer communication technology, and in particular to a physical layer security transmission technology based on space Sigma-Delta modulation. Background Art

[0002] In the current development of communication technology, the massive multiple-input multiple-output MIMO system can serve multiple users under the same time-frequency resource conditions due to its high data transmission rate and enhanced signal quality, thereby achieving significant improvements in spectrum efficiency, energy efficiency, reliability and coverage. On the other hand, due to the open nature of wireless communications, the risk of information leakage is becoming increasingly prominent. Through physical layer security technology combined with massive MIMO transmission technology, the data protection capability can be enhanced at the source, effectively resisting potential security threats and making communications more reliable, secure and efficient.

[0003] As the scale of the system expands, the hardware cost and power consumption of the RF front end become increasingly prominent, especially in the application of high-resolution digital-to-analog converters (DACs) and analog-to-digital converters (ADCs). In the downlink, the use of low-resolution DACs to achieve coarse quantization of massive MIMO at the physical layer or signal-level transceiver technology can significantly reduce costs and power consumption. However, the coarse quantization effect brought by the low-resolution DAC introduces severe quantization noise, which is particularly significant in massive MIMO systems. Nevertheless, quantization noise itself can be regarded as a potential security enhancement mechanism. Traditional physical layer security transmission technologies mainly focus on reducing the signal quality of eavesdropping channels through technical means such as collaborative interference or artificial noise to ensure the security of communications. These methods often require the consumption of additional resources, thereby reducing the resource utilization of the system. In an increasingly resource-intensive environment, communication technologies with higher resource utilization and high security are the key to future communications. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a physical layer security transmission method which can align quantization noise to an eavesdropper, thereby reducing the quality of the received signal of the eavesdropper.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technology is a physical layer security transmission method based on spatial Sigma-Delta modulation, comprising the steps of:

[0006] Parameter input steps: number of base station antennas N, number of legal users K, background noise variance The minimum SQNR threshold condition η that the eavesdropper needs to meet, the modulation order M, the user's angle range Θ, the eavesdropper's angle range Ξ, the number of user angle sample points I, the number of discrete sampling sample points J of the eavesdropper's angle range, the array antenna spacing d, the carrier wavelength λ, and the filter order L;

[0007] Optimization problem reconstruction steps: The design of the Sigma-Delta modulator is treated as an optimization problem: when the spatial Sigma-Delta modulator is not overloaded, the signal to quantization noise ratio of the legitimate user end is minimized, and the maximum SQNR of the eavesdropper is less than 1 / η; then the optimization problem is expressed by Charnes-Cooper transformation, and then converted using upper convex hull reconstruction to obtain the reconstructed optimization problem:

[0008]

[0009] ζ ≥ 0

[0010] Among them, β is the variable of the optimization problem using the upper convex hull reconstruction replacement, γ is the intermediate quantity determined by the noise shaping filter coefficient vector g, is the Charnes-Cooper transformation coefficient, ‖‖2 represents the L2 norm, and ‖‖1 represents the L1 norm;

[0011] Intermediate Intermediate [a; b; c] represents a column vector consisting of variables a, b, and c, variable i represents the angle sample point where the user is located, variable j represents the discrete sampling point in the angle range, α i is the user angle θ i The corresponding channel gain, α max is the maximum channel gain; the intermediate P is the peak power of each antenna in the real and imaginary parts;

[0012] Intermediate ω i is the angular frequency of the user’s angle range, ω j is the angular frequency of the eavesdropper’s angular range;

[0013] Optimization problem solving steps: The reconstructed optimization problem is solved iteratively through the principalization-minimization MM algorithm to obtain the final intermediate quantities β, γ, Thus according to and

[0014] Get the best noise shaping filter coefficient vector g to complete the optimization setting of Sigma-Delta modulator;

[0015] Transmission step: Use the optimized Sigma-Delta modulator to perform downlink transmission of user data.

[0016] The present invention proposes to use spatial Sigma-Delta modulation to deal with the physical layer security problem in downlink transmission. It adopts a physical layer security transmission method based on an L-order Sigma-Delta modulator, uses a low-resolution DAC, and performs spatial shaping of quantization noise through Sigma-Delta modulation, which not only improves the signal fidelity at the expected user, but also aligns the quantization noise to the eavesdropper, thereby reducing the quality of the eavesdropper's received signal.

[0017] The beneficial effect of the present invention is that it not only reduces the hardware cost and power consumption of large-scale MIMO implementation, but also naturally directs the severe quantization noise caused by the coarse quantization of the traditional low-resolution quantizer to potential eavesdroppers to protect legitimate users, thereby achieving communication security. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is the application scenario of the present invention;

[0019] Figure 2 It is a spatial Sigma-Delta architecture;

[0020] Figure 3 for the invention flow chart;

[0021] Figure 4 The noise shaping result of the embodiment;

[0022] Figure 5 is the bit error rate result of the embodiment;

[0023] Figure 6 Fixed angle sector results for the example. DETAILED DESCRIPTION

[0024] The application scenarios of the present invention are as follows Figure 1 The specific description is as follows:

[0025] A single-cell multi-user massive MIMO downlink transmission scenario is considered: a base station is equipped with N antennas, each of which is connected to a pair of low-resolution DACs, transmitting K data streams to the legitimate user CU, while a potential eavesdropper Eve eavesdrops on user messages within a certain angle range. The angle θ of the user belongs to the set The eavesdropper's angle is within a range In which The base station can use a uniform linear array ULA or a two-dimensional uniform planar array UPA. The following description takes the uniform linear array as an example. The channel vector h of the u-th user in the channel model is u The description is as follows:

[0026] h u =α u a(θ u )

[0027] In the formula is the complex channel gain, θ u ∈[-π / 2,-π / 2] represents the azimuth from the base station to the u-th user;

[0028]

[0029] a(θ) represents the array response vector at angle θ, where λ is the carrier wavelength, d is the antenna spacing, T represents the transpose. The baseband transmission process can be modeled as follows:

[0030]

[0031] in represents the complex baseband signal received by the uth legal user at time t; T′ is the transmission block length; x t is the transmitted signal at time t, v u,t is the additive complex Gaussian noise received by the u-th legitimate user at time t, with a mean of 0 and a variance of Complex Gaussian distribution represents the complex baseband transmission signal; ρ is a power normalization factor to ensure that each antenna and the imaginary part The peak power meets the following conditions:

[0032]

[0033] where P is the peak power of each antenna in the real and imaginary parts, ‖‖ ∞ represents the infinite norm. Therefore, the instantaneous total transmission power of the base station will not exceed To save energy and reduce implementation complexity, each transmit antenna in the base station is equipped with a pair of low-resolution DACs. This limits the transmitted signal x t must take the form of a discrete set:

[0034]

[0035] We use M to denote the number of quantization levels of DACs. Therefore, to satisfy the power constraint, the power normalization factor is given by ρ = P / (M-1) 2 Given.

[0036] Similarly, the eavesdropper model is the same, where the received signal received by the eavesdropper e at time t is y e,t :

[0037]

[0038] where h e =α e a(θ e ) represents the downlink channel from the base station to the eavesdropper, where the eavesdropping gain a(θ e ) represents the eavesdropping angle θ e The array response vector at is modeled similarly to the channel of the legitimate user.

[0039] make represents the symbol to be transmitted to the u-th user at symbol time t, where represents the symbol constellation set. In the current work, we will assume the use of QAM constellation, that is,

[0040]

[0041] s R represents the real part of the sign, s I represents the imaginary part of the symbol, and B is an arbitrary positive integer. The multi-user precoding task of physical layer security is to design x t The required symbol streams are formed on both the legitimate user and the eavesdropper side, satisfying the requirements from the discrete set. On the user side, the received symbol s u,t satisfy:

[0042]

[0043] Where c u >0 represents the scaling factor of user u. Each user obtains the detection symbol by

[0044]

[0045] Where dec is the decision function for the set {-2B+1,…,-1,1,…,2B-1}. At the same time, in order to reduce the probability of correct detection by the eavesdropper, we also have to force the symbols received by the eavesdropper to satisfy:

[0046]

[0047] where c e >0 is the scaling factor for the eavesdropper.

[0048] Next, the traditional time Sigma-Delta modulation technology is extended to space to adapt it to MIMO precoding. Figure 2 As shown, the application of spatial Sigma-Delta modulation in massive MIMO systems is demonstrated.

[0049] For the convenience of explanation, we omit the subscripts representing each antenna channel. Under spatial Sigma-Delta modulation, the received signal y can be equivalently expressed as:

[0050]

[0051] Where h = αa(θ) is the user's angle. Figure 2 , the original signal Applying the Sigma-Delta Modulator to the Original Signal To generate the transmission signal Specifically, we apply two Sigma-Delta modulators, one for the real part and the other for the imaginary part. The results are described below:

[0052]

[0053] Where w is the effective noise, which is composed of quantization noise and background noise, and is approximately Gaussian distributed with a mean of zero and a variance of As shown below:

[0054]

[0055] Where angular frequency ω=(2πd / λ)sin(θ), is a noise shaping filter, are the filter tap coefficients, the variables l = 1,…,L, and L is the filter order. These coefficients are chosen to fine-tune the quantization noise spectrum.

[0056] As a key note, in order to avoid infinite quantization noise due to the feedback loop, the system should not be overloaded. Overload can be prevented by limiting the amplitude of the input: Let A>0 be The maximum input amplitude, noise shaping filter coefficient vector g = (g1,...,g L ), the L1 norm of the in-phase and quadrature-phase components of the noise shaping filter coefficient vector is expressed as M represents the quantization level of DACs. For 0≤A≤M, and If ||g|| IQ-1 ≤MA, then for all n, we have and where q n is the quantization noise on the nth antenna.

[0057] Now we define the signal to quantization noise ratio SQNR, and it is reasonable to treat the design of the Sigma-Delta modulator as an optimization problem. The SQNR at the user end is given by:

[0058]

[0059] Signal Item With the original signal The amplitude A varies, This motivates us to consider the following alternatives to SQNR:

[0060]

[0061] The user's angle θ set Angle range of eavesdroppers In which Our approach optimizes the worst-case signal SQNR for the legitimate user without overloading the spatial sigma-delta modulator. At the same time, we want the best-case SQNR for the eavesdropper to be as bad as possible. This can be achieved by:

[0062]

[0063] ||g|| IQ-1 ≤MA

[0064] where 1 / η is the threshold of the eavesdropper’s SQNR. Note that in addition to the noise shaping filter coefficient vector g, we also jointly optimize the maximum signal amplitude A to achieve better performance.

[0065] Known user angle θ i and their channel gains α i , there are K user angles for a total of K users. And the range of the eavesdropper's angle and channel gain information α min ≤α eav ≤α max Since SQNR increases with the increase of α, we have the following statement:

[0066]

[0067] At the same time, the user's angle range Θ, the eavesdropper's angle range Ξ; the number of sample points of the user's angle range I, using variable i to represent the discrete sampling points of the user's angle range; the number of discrete sampling sample points of the eavesdropper's angle range J, using variable j to represent the discrete sampling points of the angle range, we evenly discretize Ξ in the following way:

[0068] min θ∈Ξ θ=θ1≤θ2≤…≤θ J =max θ∈Ξ θ

[0069] Transform the problem into the following form

[0070]

[0071] ||g|| IQ-1 ≤MA

[0072] Note the denominator of SQNR and transform it:

[0073]

[0074] Among them, the intermediate Intermediate [a; b; c] represents a column vector consisting of a, b, and c.

[0075]

[0076] Thus, the maxmin design can be transformed into a convex optimization problem and can be solved efficiently:

[0077]

[0078] ||γ||1≤MA,

[0079] ‖‖2 represents the L2 norm, ‖‖1 represents the L1 norm, and the intermediate quantity Intermediate

[0080] Now, we use Charnes-Cooper transformation to restate the above problem. Specifically, through variable transformation:

[0081]

[0082] By fixing The optimization problem is equivalent to

[0083]

[0084] The original problem is transformed into a more tractable form using the upper convex hull reconstruction, where the objective function is replaced by the variable β.

[0085]

[0086] ζ ≥ 0,

[0087] Due to the non-convex nature of the second constraint, this problem is inherently non-convex. To address this challenge, we adopt the Majorization-Minimization (MM) method to approximate this problem. In each iteration, we linearize the non-convex constraints using a first-order Taylor approximation, thereby converting the problem into a convex problem that can be solved efficiently. Specifically, we approximate the constraints as follows

[0088] in

[0089] is the solution at iteration l. By incorporating this approximation into the original problem, we obtain the following convex substitution problem at iteration l:

[0090]

[0091] After obtaining the target problem form, we now develop a proximal distance algorithm (PDA) for it. Let the number of iterations be k, and each iteration processes two main calculations: projection and proximal operator. First, we focus on the projection calculation. The specific projection of the constraint is calculated as follows:

[0092] 1) Projection of constraint 1

[0093] In the given problem, the formula projected onto the constraint set is defined by the following question:

[0094]

[0095] Here order The above problem can be rewritten as:

[0096]

[0097] in Such projections are computed in order to satisfy the linear constraints of the problem during the update step.

[0098] In the projection problem, the solution and They are given by:

[0099]

[0100] here, and Depend on The corresponding part is derived from represents the projection of constraint 1. Here, μ is used as the Lagrange multiplier, and μ can be iteratively determined by binary search to ensure that the constraint is fully satisfied. In this method, when the original point x k and β k When the constraints are satisfied, the projection is the origin; if not, the new projection point is calculated by adjustment so that it satisfies the constraints. This adjustment relies on the enhanced linear matrix equation, and by properly choosing μ, all conditions are still valid after the update.

[0101] 2) Projection of constraint 2

[0102] The problem projected onto this set of constraints can be stated as:

[0103]

[0104] Among them, the iteration of the MM algorithm is composed of γ l and represents, l represents the number of iterations of the MM algorithm. and As shown below:

[0105]

[0106] As above, λ is a Lagrange multiplier determined by binary search as it plays a key role in enforcing the constraints. Represents the projection of constraint two.

[0107] 3) Projection of Constraint Three

[0108] The projection problem onto a set of constraints is formulated as an optimization problem:

[0109]

[0110] γ ＊ The optimal solution is as follows:

[0111]

[0112] For the variable ζ ★ :

[0113]

[0114] Here τ is the Lagrange multiplier obtained by binary search, which is used to ensure that the above constraints are met and optimize the objective function, that is, minimize and The Euclidean distance between t and its previous iteration value. * represents the projection of constraint 3. By adjusting τ, a solution that satisfies both constraints and optimizes the distance can be found.

[0115] Next, the proximal operator Prox is used to update the variables. Its purpose is to find the best balance between the objective function and the constraints while maintaining the constraints of the original problem. The specific formula is as follows:

[0116]

[0117] Substituting the optimal solution of the projection into the proximal operator, the final solution to the problem is

[0118]

[0119] Regarding the signal precoding, we simulate the performance of spatial Sigma-Delta modulation at the signal level. The symbol stream for each user From the 64QAM constellation, the symbol stream length is T′=500. The precoding scheme used is the zero forcing (ZF) scheme. Definition

[0120]

[0121] It is|||| IQ-∞ The infinite norm applied to the in-phase and quadrature-phase components of the vector. Specifically, for a given spatial sigma-delta modulator, the ZF precoded signal is expressed as as follows:

[0122]

[0123] The normalization constant is the Moore-Penrose pseudo-inverse, the intermediate quantity D = Diag (σ w,1 ,…,σ w,K ), Diag represents the construction of a diagonal matrix, variance Each user's symbol stream comes from the QAM constellation. The normalization constant C is chosen to ensure that the Sigma-Delta modulator is not overloaded, that is,

[0124] Example steps Figure 3 As shown:

[0125] Step 1: Input parameters. Number of base station antennas N = 1024; Number of legal users K = 2; Transmission block length T = 500; Background noise variance The minimum SQNR threshold that the eavesdropper needs to meet is η = 2; the modulation order is M = 2, ..., 7; the channel from the base station to the user is h i and the eavesdropper's channel h e ; The user's angle is -2π / 18 and 2π / 18, the number of sample points I=K=2, the eavesdropper's angle range is (4π / 18, 5π / 18), the number of discrete sampling sample points J=24, and the sampling interval is 1°; the number of linear constraints is I+J+1=2+24+1; the array antenna spacing d=20; the antenna spacing ratio to the carrier wavelength d / λ=1 / 4; the filter order L=24; the initial value ρ0=2 and the maximum value ρ of the penalty variable ρ max =2 30 .

[0126] Step 2: Calculate the variables in the problem model constraints, specifically

[0127]

[0128] Step 3: Randomly initialize the iteration value β of the MM algorithm 0 , The maximum number of iterations L′ = 100, the termination threshold ∈, the iteration step l = 1; set the intermediate variable F = [Φ(ω i ),c i ]; Step 4: Linearize the non-convex constraints using the first-order Taylor expansion. Specifically,

[0129]

[0130] Step 5: Set the iteration step k = 1, set the maximum number of iterations K′ = 100, the termination threshold ∈, and the penalty variable ρ = ρ0;

[0131] Step 6: Update the projection of the constraint variables as well as Specifically,

[0132] For i=1,2,...,I ​​execute:

[0133] get as well as

[0134] Step 7: Update the projection of the variables under constraint 2 as well as Specifically,

[0135] For j=1,2,...,J execute:

[0136]

[0137] Step 8: Update the projection γ of the variables under constraint three ★ And ★ , specifically,

[0138] get

[0139]

[0140] Step 9: Use the I+J+1 projections obtained in the above steps as proximal update variables, that is,

[0141]

[0142] Step 10: Update PDA iteration step k=k+1.

[0143] Step 11: Update PDA variables¶ k =γnew , β k =β new ;

[0144] Step 12: Update the penalty variable ρ new =min(ρ*1.1,ρ max ), let ρ = ρ new ;

[0145] Step 13: Determine whether k is greater than K′. If so, set the output γ k , β k End the loop and go to step 15;

[0146] Step 14: Judgement | β k+1 -β k |≤∈ is true, if not, return to step 6, if yes, go to step 15;

[0147] Step 15: Update MM iteration step l=l+1.

[0148] Step 16: Update MM variables γ l =γ k , β=β k

[0149] Step 17: Determine whether l is greater than L′. If so, set the output γ l , β l End the loop and go to step 19;

[0150] Step 18: Judgement || γ l+1 -γ l ||≤∈, Is it true? If not, return to step 4. If true, go to step 19.

[0151] Step 19: Output variable γ l , β l .

[0152] The present invention designs the noise shaping filter g with the goal of optimizing the worst-case user's SQNR without overloading the Sigma-Delta modulator; in addition, we hope that the eavesdropper's best SQNR is as bad as possible.

[0153] (I) Noise shaping response

[0154] The system settings are as follows: the number of transmitting antennas N = 1024, the number of users K = 2, the filter order of Sigma-Delta is L = 24, the antenna spacing is d = λ / 4, and the gain of all channels is |α i |=1. From the user's perspective, there will be a trough in the noise response, and a peak will appear within the eavesdropper's angle range. The red vertical lines are located at -2π / 18 and 2π / 18, representing the angles of two users, and the green shaded angle range (4π / 18, 5π / 18) represents the angle range of an eavesdropper. The noise response function is expressed as follows:

[0155]

[0156] The noise shaping result is as follows Figure 4 As shown, there are obvious valleys at the fixed user angles -2π / 18 and 2π / 18, while peaks appear in the eavesdropper's angle range (4π / 18, 5π / 18). This shows that noise shaping effectively suppresses the quantization noise of the received signal at the user's angle, while the signal in the eavesdropper's range experiences a higher level of quantization noise. As the quantization level M increases, a more obvious noise shaping effect is indeed observed, indicating that the system is able to suppress quantization noise to varying degrees at different spatial angles. However, increasing the quantization level does not always lead to a linear enhancement of the noise shaping effect. As the quantization level continues to increase, the improvement brought by each increment may decrease because the quantization noise itself has been reduced to a lower level. This shows that in practical system design, it is crucial to choose an appropriate quantization level to balance performance and cost.

[0157] (II) Bit Error Rate

[0158] The bit error rate (BER) is selected as the performance indicator. The simulation parameters are as follows: the total number of transmitting antennas is set to N = 1024, and the uniform spacing between antennas is d = λ / 4. The system supports K = 2 legal users. The order of the Sigma-Delta modulator used in this setting is L = 24. Assume that due to real scenarios and actual deployment reasons, we cannot change the Sigma-Delta modulator during the experiment and can only design the Sigma-Delta modulator once.

[0159] The simulation results are as follows Figure 5As shown in the figure, the BER performance at different quantization levels M is evaluated and the BER of the user at a specific angle is compared with the BER of the eavesdropper within the defined angular sector. The results clearly show that the Sigma-Delta method performs significantly better than the quantized ZF scheme and is almost close to the unquantized method. This proves the superiority of the Sigma-Delta method in noise shaping and improving the quality of the user received signal. It is worth noting that the BER of the eavesdropper does not continue to decrease with the increase of the signal-to-noise ratio (SNR). This pattern shows that Sigma-Delta modulation can effectively improve the BER of the eavesdropper at different SNR levels, which is in line with the expected goal of secure communication. The enhancement of signal power does not significantly reduce the quantization noise at the eavesdropper's angle, thereby maintaining a high BER and strengthening the security measures against potential eavesdropping. Although the user enjoys a lower BER, the BER of the eavesdropper remains at a high level, especially at higher quantization levels, indicating that increasing the quantization level helps to improve the security against eavesdropping. However, this also leads to a slight increase in the user BER, presenting a consideration that needs to be weighed.

[0160] (III) Fixed angle sector design

[0161] The user's angle is fixed in the angle range Inside. User angle θ i Randomly from the preset angle interval [θ l ,θ u ], and the interval between them is not less than 1°. The system is set to N = 1024, the number of users K = 24, the modulator order L = 24, the antenna spacing d = λ / 4, and the channel gain of all users |α i |=1. The red vertical lines in the figure are located at -2π / 18 and 2π / 18, indicating the angular range of multiple users, and the green shaded angular range (4π / 18, 5π / 18) indicates the angular range of the eavesdropper.

[0162] Figure 6 (a) shows the noise shaping response of the Sigma-Delta modulator to multiple users under a -5dB signal-to-noise ratio (SNR) condition. Obviously, within the angular range of the user, the NSF response is significantly reduced, indicating that the noise is effectively suppressed, while within the angular range of the eavesdropper, the noise increases, enhancing security. Figure 6 (b) and Figure 6 (c) shows the bit error rate (BER) performance of the legitimate user and the BER of the eavesdropper. We see that our optimized fixed-user sector Sigma-Delta modulation scheme generally has better BER performance on the user side than the reference quantized ZF scheme, and is close to the unquantized ZF scheme. In addition, the BER of the eavesdropper does not change significantly, maintaining a high BER.

Claims

1. A physical layer secure transmission method based on spatial Sigma-Delta modulation, characterized in that: Includes steps: Parameter input steps: number of base station antennas N, number of legal users K, background noise variance The minimum SQNR threshold condition η that the eavesdropper needs to meet, the modulation order M, the user's angle range Θ, the eavesdropper's angle range Ξ, the number of user angle sample points I, the number of discrete sampling sample points J of the eavesdropper's angle range, the array antenna spacing d, the carrier wavelength λ, and the filter order L; Optimization problem reconstruction steps: The design of the Sigma-Delta modulator is treated as an optimization problem: when the spatial Sigma-Delta modulator is not overloaded, the signal to quantization noise ratio of the legitimate user end is minimized, and the maximum SQNR of the eavesdropper is less than 1 / η; then the optimization problem is expressed by Charnes-Cooper transformation, and then converted using upper convex hull reconstruction to obtain the reconstructed optimization problem: ζ ≥ 0, Among them, β is the variable of the optimization problem using the upper convex hull reconstruction replacement, γ is the intermediate quantity determined by the noise shaping filter coefficient vector g, is the Charnes-Cooper transformation coefficient, ‖‖2 represents the L2 norm, and ‖‖1 represents the L1 norm; Intermediate Intermediate [a; b; c] represents a column vector consisting of variables a, b, and c. Variable i represents the discrete sampling point of the angle range where the user is located. Variable j represents the discrete sampling point of the angle range. α i is the user angle θ i The corresponding channel gain, α max is the maximum channel gain; the intermediate P is the peak power of each antenna in the real and imaginary parts; Intermediate ω i is the angular frequency of the user’s angle range, ω j is the angular frequency of the eavesdropper’s angular range; Optimization problem solving steps: The reconstructed optimization problem is solved iteratively through the principalization-minimization MM algorithm to obtain the final intermediate quantities β, γ, Thus according to and Get the best noise shaping filter coefficient vector g to complete the optimization setting of Sigma-Delta modulator; Transmission step: Use the optimized Sigma-Delta modulator to perform downlink transmission of user data.

2. The method according to claim 1, characterized in that: The specific steps for solving the optimization problem are: Step 1: Randomly initialize the principal-minimize the MM iteration intermediate quantity β l ,γ l , The initial value of 0 , The total number of MM iterations is L′, the MM iteration termination threshold value ∈, and the MM iteration number variable l = 1; Set the initial value ρ0 and the maximum value ρ of the penalty variable ρ max , set the number of linear constraints to I+J+1, and set the intermediate variable F=[Φ(ω i ),c i ]; Step 2: Constraints Linearize using first-order Taylor expansion; Step 3: Set the proximal distance algorithm PDA iteration number variable k = 1, and randomly initialize the intermediate amount β of PDA iteration k , The initial value of 0 , Set variables for PDA iteration The initial value of T represents transposition, sets the maximum number of iterations K′, the PDA iteration termination threshold ∈, and the penalty variable ρ = ρ0; Step 4: Update the constraints on the intermediate quantities β, γ, Projection as well as Represents the projection of constraint one, and for i=1,2,…,I, execute: At the user angle θ i The projection of the variable χ under μ is the Lagrange multiplier; according to from get as well as Recalculate Step 5: Update the intermediate quantities β, γ, Projection as well as Represents the projection of constraint 2, and for j=1,2,...,J, execute: calculate calculate in, For constraints The result of linearization using first-order Taylor expansion; Step 6: Update the constraints for the three intermediate quantities γ, Projection of γ ＊ And ＊ , ＊ Represents the projection of constraint three: calculate get calculate τ is the Lagrange multiplier; Step 7: Use the I+J+1 projections obtained in steps 3-5 as the intermediate amount of the proximal update PDA iteration, that is, Step 8: Update the PDA iteration number variable k=k+1; Step 9: Update the intermediate quantity γ of the PDA iteration k =γ new , β k =β new ; Step 10: Update the penalty variable ρ new =min(ρ*1.1,ρ max ), let ρ = ρ new ; Step 11: Determine whether k is greater than K′. If so, set the output γ k , β k End the loop and go to step 13; if not, go to step 12; Step 12: Judgement | β k -β k-1 |≤∈ is true, if not, return to step 4; if yes, go to step 13; Step 13: Update MM iteration step l=l+1. Step 14: Update MM variables γ l =γ k , β l =β k Step 15: Determine whether l is greater than L′. If so, set the output γ l , β l End the loop and go to step 17; if not, go to step 16; Step 16: Judgement Is it true? If not, return to step 2; if yes, go to step 17; Step 17: Output variable γ l , β l .

3. The method according to claim 2, characterized in that: Constraints The result of linearization using first-order Taylor expansion is:

4. The method according to claim 2, characterized in that: The noise shaping filter coefficient vector g determines the intermediate quantity in, represents the real part, Represents the imaginary part.

5. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to claim 1 are implemented.

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