RIS-assisted non-line-of-sight MU-ISAC system effective perception power maximization method and system

Abstract

The invention relates to an RIS-assisted non-line-of-sight MU-ISAC system effective perception power maximization method and system. The method comprises the following steps: S1, coding a binary bit sequence of a base station to obtain a signal x; s2, x is transmitted to a sensing target through the RIS, and effective sensing power ESP (j) is calculated; s3, judging whether the ESP (j) meets the condition that ESP (j)-ESP (j-1) is less than or equal to epsilon, and if so, skipping to S6; otherwise, taking the ESP (j) as an output parameter, skipping and executing S4, and enabling j to be equal to j + 1; s4, taking the effective sensing power ESP (j) obtained in the step S3 as an input parameter, executing a beam forming vector optimization method, and outputting the parameter ESP (j) from the step S3 and an M * 1 dimensional vector wk with complex elements; s5, taking the beam forming vector wk obtained in the step S4 and the ESP (j) as input parameters, executing an RIS phase shift matrix optimization method, and outputting the beam forming vector wk from the step S4 and an N * N-dimensional RIS phase shift matrix theta with complex elements; returning the obtained RIS phase shift matrix theta and the beam forming vector wk to S2, and calculating the ESP (j) of the jth iteration through an effective sensing power ESP calculation method; and S6, obtaining an effective sensing power optimal value as an output result.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital communication, and particularly relates to a method and system for maximizing the effective sensing power of an intelligent surface (RIS)-assisted multi-user integrated sensing and communication (MU-ISAC) system. Background Art

[0002] The intelligent surface RIS is highly compatible with the integrated sensing and communication (ISAC) system, which can improve the channel capacity and spectral efficiency, and at the same time significantly reduce the system power consumption, thereby enhancing the overall transmission performance. In a passive RIS-assisted ISAC system, due to reasons such as multipath effects, environmental instability, and non-ideality of RIS adjustment, the problem of multiplicative fading will occur, resulting in a decrease in the effective signal power (ESP) of the received signal at the receiving end. The signal transmission quality is used to measure the reduction effect of multiplicative fading in the integrated sensing and communication system, that is, the magnitude of the ESP of the received signal at the receiving end. When optimizing parameters such as the beam covariance matrix and the RIS phase shift matrix, the non-convex problem of rank 1 will inevitably occur.

[0003] After inquiry, the Chinese patent publication number CN118869014A is similar to the scenario and optimization objective of this article; the Chinese patent publication number CN118869014A discloses a method for optimizing the rate of an intelligent reflecting surface-assisted integrated sensing and communication system, which significantly improves the communication performance and sensing performance of the system. However, its defects are: it has too high requirements for channel state information (CSI), does not consider the energy consumption of RIS, and does not discuss in detail the optimization of sensing tasks. Summary of the Invention

[0004] Aiming at the defects existing in the prior art, the present invention provides a method and system for maximizing the effective sensing power (ESP) of an active intelligent surface (RIS)-assisted non-line-of-sight MU-ISAC system.

[0005] The present invention adopts the following technical solutions:

[0006] A method for maximizing the ESP of an RIS-assisted non-line-of-sight MU-ISAC system, comprising the following steps:

[0007] S1. The binary bit sequence of the base station, after bipolar coding, baseband shaping, and precoding, obtains a signal that can propagate in the wireless channel, and this signal can be equivalently expressed as: where, w k is an M×1-dimensional complex vector, representing the beam vector of the kth signal, s k is a complex number representing the symbol of the kth signal and satisfies E(·) is the expectation calculation, Denote \(s\) k as the conjugate complex number; both \(k\) and \(K\) are integers and satisfy \(1\leq k\leq K\);

[0008] S2. After the signal \(x\) in step S1 is transmitted by the RIS to the sensing target, the effective sensing power ESP at the active RIS is used as the sensing signal index; the ESP for the \(j\)-th iteration is calculated by the calculation method of the effective sensing power ESP (j) for calculation;

[0009] S3. Determine whether the result ESP obtained in step S2 (j) satisfies the inequality \(|ESP\) (j) \(- ESP\) (j-1) \(|\leq\varepsilon\). If it is satisfied, jump to and execute step S6; otherwise, use ESP (j) as the output parameter, jump to and execute step S4, and let \(j = j + 1\);

[0010] S4. Use the effective sensing power ESP obtained in step S3 (j) as the input parameter, execute the beamforming vector optimization method, and output the parameter ESP from step S3 (j) and the \(M\times1\)-dimensional vector \(w\) with all elements being complex numbers k ; where \(M\) is a natural number representing the number of rows of the vector, and the subscript \(k\) represents the \(k\)-th user;

[0011] S5. Use the beamforming vector \(w\) obtained in step S4 k and ESP (j) as the input parameters, execute the RIS phase shift matrix optimization method, and output the beamforming vector \(w\) from step S4 k and the \(N\times N\)-dimensional RIS phase shift matrix \(\varTheta\) with all elements being complex numbers; where \(N\) is a natural number representing the number of rows and columns of the matrix as the output function; return the obtained RIS phase shift matrix \(\varTheta\) and the beamforming vector \(w\) k to step S2, and calculate the ESP for the \(j\)-th iteration by the calculation method of the effective sensing power ESP (j) for calculation;

[0012] S6. Obtain the optimal value of the effective sensing power according to step S3 as the output result;

[0013] Preferably, in step S2, the calculation method of ESP is specifically as follows:

[0014] At the first calculation, the signal transmitted from step S1 and the initial RIS reflection phase shift matrix are required. Subsequently, the results \(w\) k and \(\varTheta\) output from step S5 can be used;

[0015] The system includes a base station, an active RIS, K single-antenna users, and T sensing targets; the set of communication users is κ = {1, 2, …, K}, and the set of sensing targets is τ = {1, 2, …, T}, where K and T are both positive integers; among them, the number of base station antennas is a positive integer M, and the number of reflection units of the active RIS is a positive integer N; κ is a 1×K-dimensional vector, and its elements are all natural numbers; k is denoted as the k-th user, then there is:

[0016]

[0017] Among them, y k represents the signal transmitted by the base station received at the user end, represents the channel from the RIS to the k-th user; β i is the phase shift matrix and amplification factor of the active RIS; represents the channel coefficient matrix from the base station to the RIS; x k = w k s k represents the k-th signal; and are the noise introduced by the active RIS and additive white Gaussian noise respectively; then the rate at which the signal reaches the user end after being reflected by the RIS is:

[0018]

[0019] In the non-line-of-sight scenario, the beam vector of the user is used to complete the sensing task and the ESP of the RIS is used as the sensing performance index. The RIS reflected signal is expressed as:

[0020]

[0021] Then, the covariance matrix corresponding to the RIS reflected signal is expressed as:

[0022]

[0023] Therefore, the RIS beam gain corresponding to the t-th target is expressed as:

[0024]

[0025] Among them, is the steering vector, θ t is the azimuth angle of the t-th sensing target, λ represents the wavelength, and d represents the antenna spacing;

[0026] Therefore, the effective sensing power ESP at the active RIS is:

[0027] P(w k , Θ) = ∑ t∈τ P r (wk , Θ, θ t )(8)

[0028] The function of this claim is to obtain the ESP through calculation, providing a basis for judging whether the optimization goal is achieved in the subsequent process.

[0029] Preferably, in step S4, the optimization method of the beamforming vector w is as follows:

[0030] S4.1. Initialization Let the convergence judgment constants ε1 and ε2 be real numbers approaching 0, the penalty factor η, and the coefficient α. Define and set the initial value F W (0) = 0, ESP (j) and V, and input the initial signal value;

[0031] S4.2. For the first time, use the data passed in by S4.1 to judge Whether it holds, and use the data from S4.6 subsequently; if it holds, jump to and execute step S4.7, otherwise jump to and execute step S4.3;

[0032] S4.3. Initialize the iteration count n = 0;

[0033] S4.4. Model the effective sensing power ESP problem at the system's active RIS as:

[0034]

[0035] where R min represents the minimum communication rate of each user, represents the phase shift vector of the RIS; θ t ∈[0, 2π] represents the azimuth angle of the t-th sensing target, P BS and P I are the transmit power of the base station and the maximum power limited by the active RIS respectively. C1 ensures the minimum communication rate R min of the communication users; C2 ensures the limitation of the base station transmit power; C3 ensures the active RIS power limitation; C4 ensures the limitation of the ESP difference of each target RIS; C5 is the limitation on the RIS phase shift matrix;

[0036] Define and V = vv H ; where, and rank(W k ) = 1 and and rank(V) = 1; W k and V are both positive semi-definite matrices, and v = diag(Θ) is the phase shift vector of the active RIS; thus, the effective sensing power P(wk , Θ) is expressed as:

[0037]

[0038] where, χ t = diag(a H (θ t ))G, for C1, we have:

[0039]

[0040] where, Define Tr(·) as the trace operation of the matrix; thus, the constraint C1 is re-expressed as:

[0041]

[0042] The constraints C2, C3, C4, and C5 are respectively changed to:

[0043] diag(Σ i∈κ W i ) ≤ (P BS / M)I M (12)

[0044]

[0045] where, diag(diag(·)) means first extracting the diagonal elements of the matrix and then generating a new diagonal matrix; is the ESP of the t-th sensing target, and P d is a constant;

[0046] The effective sensing power ESP problem at the active RIS of the system is rewritten as:

[0047]

[0048] Using the penalty term method to handle the objective function of Equation (16), the matrix rank-1 constraint is converted into an objective function penalty term; for the non-convex problem of rank(W k ) = 1, the following equivalent expression to the matrix rank-1 constraint is introduced:

[0049] ||W k || * - ||W k ||2 = 0 (17)

[0050] where, ||·|| * is the nuclear norm, and ||·||2 is the spectral norm; when rank(W k ) = 1, Equation (17) holds, since needs to satisfy ||Wk || * -||W k ||2 > 0; Introduce a penalty term to the objective function ||W k || * -||W k ||2. Introduce a penalty factor η, then equation (16) is rewritten as:

[0051]

[0052] Using the successive convex approximation method, perform a first-order Taylor expansion on -||W k ||2 to obtain its upper bound as:

[0053]

[0054] where is the eigenvector corresponding to the maximum eigenvalue;

[0055] Adopt the semi-definite relaxation algorithm to relax the non-convex rank-one constraint C5 to obtain a new problem:

[0056]

[0057] Through and equation (20) to obtain Denoted as and through calculate F W (n + 1), update the iteration number n = n + 1; Jump and execute step S3.5;

[0058] S4.5. According to the data passed in from step S4.4, judge whether F W (n + 1) - F W (n) ≤ ε2 holds; if it holds, jump and execute step S4.6, otherwise jump and execute step S4.4;

[0059] S4.6. Update the variable η = αη, Jump and execute step S4.2;

[0060] S4.7. According to the data passed in from S4.2, obtain Obtain the optimal beamforming vector w through eigenvalue decomposition * .

[0061] Preferably, in step S5, the optimization method of the RIS phase shift matrix Θ is as follows:

[0062] S5.1. Initialize, V 0 , and the convergence judgment constants ε3, ε4 are real numbers approaching 0, as well as the penalty factor η and the coefficient β; Define FV f(m) = ESP (j) -η(||V m || * -||V m ||²) and let the initial value F W (0) = 0, input the beamforming vector w k and ESP (j) ;

[0063] S5.2. At the first calculation, judge whether ||V 0 || * -||V 0 ||² ≤ ε3 holds. If it holds, jump to and execute step S5.7; otherwise, jump to and execute step S5.3, and subsequently use the data from step S5.6;

[0064] S5.3. Initialize the iteration number m = 0;

[0065] S5.4. Use eigenvalue decomposition to obtain the transmit signal beamforming vector w k , Equation (7) can be re - described as:

[0066]

[0067] Use the penalty - term method to process the objective function of Equation (21), convert the rank - 1 constraint of the matrix into a penalty term in the objective function; for the non - convex problem of rank(V)=1, introduce an expression equivalent to the rank - 1 constraint of the matrix as follows:

[0068] ||V k || * -||V k ||² = 0 (22)

[0069] When rank(V)=1, Equation (22) holds. Since it is necessary to satisfy ||V|| * -||V||² > 0; to obtain the matrix rank - 1 constraint, introduce a penalty term into the objective function, introduce a penalty factor η, then Equation (21) is re - described as:

[0070]

[0071] Use the continuous convex approximation method to perform the first - order Taylor expansion of -||V||² and obtain its upper bound as:

[0072]

[0073] where is the eigenvector corresponding to the largest eigenvalue of V n , then Equation (23) is written as:

[0074]

[0075] Through V m and Equation (25), V is obtained m+1 , and through F V (m) = ESP (j) -η(||V m || * -||V m ||²) to calculate F V (m + 1), and update the variable m = m + 1;

[0076] S5.5. According to the calculation result of S5.4, judge whether F V (m + 1)-F V (m) ≤ ε4 holds; if it holds, jump to and execute step S5.6, otherwise jump to and execute step S5.4;

[0077] S5.6. Update the variables η = βη, V 0 = V m Jump to and execute step S5.2;

[0078] S5.7. Obtain the result V according to the data passed in by S5.2 opt If rank(V opt ) ≤ 1, then use the eigenvalue decomposition method to recover the optimal RIS reflection phase shift vector v; if rank(V opt ) > 1, then use the Gaussian randomization method to obtain the optimal approximate solution of v; according to Θ = diag(v), obtain the RIS reflection phase shift matrix Θ;

[0079] The present invention also discloses a system for maximizing the effective sensing power of a RIS-assisted non-line-of-sight MU-ISAC system, which is used to execute the above method. The system includes the following modules:

[0080] Signal transmission module: The base station transmits a signal, digitally modulates the transmitted signal, and transmits it to the intelligent reflecting surface RIS and the user through free space; among them, the data type of the signal is complex;

[0081] Effective sensing power calculation module: Receive the transmitted signal of the signal transmission module as an input parameter, and calculate the effective sensing power ESP (j) ; where the subscript represents the result obtained in the jth iteration;

[0082] Effective sensing power judgment module: Judge whether the effective sensing power ESP (j) obtained by the effective sensing power calculation module satisfies |ESP (j) -ESP (j-1)|< ε, where the initial value of the effective sensing power is 0 and ε is a constant; if not satisfied, it is executed by the beamforming vector optimization module; if satisfied, it is executed by the output module;

[0083] Beamforming vector optimization module: takes the effective sensing power ESP obtained by the judgment module (j) as an input parameter, executes the beamforming vector optimization method, and outputs an M×1-dimensional vector w with all elements being complex numbers k ; where M is a natural number representing the number of rows of the vector; the subscript k represents the k-th user;

[0084] RIS phase shift matrix optimization module (takes the beamforming vector w obtained by the beamforming vector optimization module k as an input parameter, executes the RIS phase shift matrix optimization module, and outputs an N×N-dimensional matrix Θ with all elements being complex numbers; where N is a natural number representing the number of rows and columns of the matrix;

[0085] Output module: takes the optimal value of the effective sensing power obtained by the judgment module as the output result.

[0086] The technical introduction related to the present invention is as follows:

[0087] 1. Bipolar coding

[0088] As a line coding method in digital communication systems, bipolar coding exhibits more significant advantages compared to unipolar and non-return-to-zero (NRZ) coding. It alternately uses positive and negative levels to represent "1" in the data, while representing "0" as zero level, thus having better performance in anti-interference, anti-DC bias, and clock synchronization. Bipolar coding eliminates the DC component of the signal, which is beneficial for long-distance transmission, and at the same time improves the spectral utilization efficiency and bit error rate performance of the signal. For detailed content, reference can be made to "H.M.R. Al-Khafaji, S.A. Aljunid and H.A. Fadhil, "Spectral efficiency comparison of SAC-OCDMA systems using unipolar and bipolar encoding techniques," 2011 2nd International Conference on Photonics, Kota Kinabalu, Malaysia, 2011, pp. 1-5".

[0089] 2. Penalty term method

[0090] The penalty term is a commonly used method in optimization problems, mainly used to handle constraints or guide the model to achieve specific goals. In optimization problems, the penalty term is usually added to the objective function to impose penalties on solutions that do not meet certain conditions, thereby guiding the optimization process to gradually approach the feasible solution or the solution that conforms to specific constraints. The mathematical model is as follows:

[0091]

[0092] Its core idea is to transform the original constrained problem into an unconstrained problem by introducing a penalty function. By adjusting the form and parameters of the penalty function, the optimal solution of the original problem can be obtained without considering the constraint conditions. The new objective function is defined as;

[0093]

[0094] where P(x) is the penalty function, used to measure the degree to which the solution does not satisfy the constraints; λ > 0 is the penalty parameter, controlling the intensity of the penalty. The two equations have the same optimal solution. For details, see "X. Li, H. Xiao and J. Tian, "H. Tang and X.-F. Chen, "A Power Method to Convex-Concave Minmax Optimization Problems with Nonlinear Constraints," 2023 International Conference on New Trends in Computational Intelligence (NTCI), Qingdao, China, 2023, pp. 370-374.”

[0095] 3. Successive Convex Approximation Method

[0096] The Successive Convex Approximation (SCA) method is a commonly used means to solve non-convex mathematical optimization problems. Its core idea is to perform an equivalent transformation on the objective function or constraints in a local region, reformulate the original problem into a convex optimization form, and thus obtain an approximate solution to the original problem. For details, see "T. Wang, F. Fang and Z. Ding, An SCA and Relaxation Based Energy Efficiency Optimization for Multi-User RIS-Assisted NOMA Networks, IEEE Transactions on Vehicular Technology, vol. 71, no. 6, pp. 6843-6847, June 2022”.

[0097] 4. Semi - Definite Relaxation Method

[0098] In traditional optimization problems, it is often necessary to transform the objective function and constraint conditions into a linear programming problem for solution. However, in some cases, there are semi - definite constraints in the problem's constraint conditions, that is, the matrix is required to be semi - definite. And linear programming problems cannot directly handle such constraint conditions. The Semi - Definite Relaxation (SDR) method transforms the original semi - definite constraint into a linear constraint condition by introducing relaxation variables, so that the problem can be solved by linear programming methods. Specifically, this method transforms the semi - definite constraint into the form of the difference between a semi - definite matrix and a symmetric matrix, and transforms the problem into a linear programming problem of minimizing this difference. See specifically "M.J. Underhill, "Theory of Random Spurs and Spectrum - Collapse from SDR Phase - Noise and Carrier - Phase Measurements," 2018 IEEE International Frequency Control Symposium (IFCS), Olympic Valley, CA, USA, 2018, pp.1 - 4".

[0099] 5. Gaussian Randomization Method

[0100] Gaussian randomization is a commonly used randomization method for reducing the impact of random errors in experimental design and statistical inference. This method is based on the normal distribution (also known as the Gaussian distribution) and generates random numbers through given means and standard deviations. It can reduce the influence of individual differences or other interference factors on experimental results. See specifically "X.Yu, J.-C.Shen, J.Zhang and K.B.Letaief, "Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems," in IEEE Journal of Selected Topics in Signal Processing, vol.10, no.3, pp.485 - 500, April 2016".

[0101] When optimizing parameters such as the beam covariance matrix and the RIS phase shift matrix, the non-convex problem of rank-1 inevitably occurs. The present invention proposes a double-penalty method to solve this problem. First, the RIS reflection phase shift matrix is fixed, and the penalty term method is used to solve the optimal transmit beamforming vector. Secondly, the beamforming vector is fixed, and the penalty term method is used again to solve the RIS reflection phase shift matrix. Finally, the closed-form optimal solutions of the transmit beamforming vector and the RIS reflection phase shift matrix are obtained by using the alternating optimization and semi-definite relaxation method. Description of the Drawings

[0102] Figure 1 It is a model diagram of an active RIS-assisted MU-ISAC system according to a preferred embodiment of the present invention;

[0103] Figure 2 It is a flowchart of a method for maximizing the ESP of an active RIS-assisted MU-ISAC system according to a preferred embodiment of the present invention;

[0104] Figure 3 It is a flowchart of the steps for optimizing the transmit signal beamforming vector according to a preferred embodiment of the present invention;

[0105] Figure 4 It is a flowchart of the steps for optimizing the active RIS reflection phase shift matrix according to a preferred embodiment of the present invention;

[0106] Figure 5 It is a graph of the effective sensing power varying with the angle under different schemes;

[0107] Figure 6 It is a graph of the effective sensing power as the number of RIS reflection units increases under different schemes;

[0108] Figure 7 It is a system block diagram of a system for maximizing the effective sensing power of an active RIS-assisted MU-ISAC system according to a preferred embodiment of the present invention. Detailed Embodiments

[0109] The present invention will be further described below in conjunction with specific embodiments. The specific implementation manners of the present invention can be detailedly illustrated through the following embodiment diagrams.

[0110] Figure 1 It is a model diagram of an active RIS-assisted MU-ISAC system according to an embodiment of the present invention. The system includes a base station with a positive integer M number of antennas, a RIS with a positive integer N number of reflection units, K single-antenna users, and a sensing target, where K is a positive integer. The sets of RIS reflection units and users are respectively represented as: Among them, is a 1×N-dimensional vector, and all its elements are natural numbers, is a 1×K-dimensional vector, and all its elements are natural numbers.

[0111] Figure 2 This is the flowchart of the method for maximizing the effective sensing power of a RIS-assisted MU-ISAC system according to an embodiment of the present invention. Refer to Figure 2 , and this technical solution is mainly completed through the following steps:

[0112] Step 1: The base station sends a signal, digitally modulates it, and sends it to the active RIS and the user through free space; among them, the data type of the signal is complex, and the initial iteration number n is initialized;

[0113] Step 2: Initialize the convergence judgment value ε = 0.01 and calculate the effective sensing power ESP (n) ;

[0114] Step 3: Determine whether the effective sensing power ESP obtained by the effective sensing power calculation module satisfies |ESP (n) - ESP (n-1) | < ε, where the initial value of the effective sensing power is 0 and ε is a constant; if not satisfied, execute Step 4 and update the iteration number n = n + 1; if satisfied, execute Step 6;

[0115] Step 4: Execute the beamforming vector optimization method and output an M×1-dimensional vector w with all elements being complex numbers k ; where M is a natural number representing the number of rows of the vector; the subscript k represents the kth user;

[0116] Step 5: Take the beamforming vector w k obtained by the beamforming vector optimization module as the input parameter, execute the RIS phase shift matrix optimization method, and output an N×N-dimensional matrix Θ with all elements being complex numbers; where N is a natural number representing the number of rows and columns of the matrix, jump and execute Step 2;

[0117] Step 6: According to the result of Step 3, output the optimal value of the effective sensing power ESP opt .

[0118] Figure 3 This is the flowchart of the steps for optimizing the transmit beamforming vector according to an embodiment of the present invention, which is mainly completed through the following steps:

[0119] Step 1: Initialize, and the convergence judgment constants ε1, ε2 are real numbers approaching 0, the penalty factor η and the coefficient α are defined and let the initial value F W (0) = 0, ESP (j) and V and input the initial signal value;

[0120] Step 2: Judge Whether it holds. If it holds, execute Step Seven; otherwise, jump and execute Step Three;

[0121] Step Three: Initialize the iteration count n = 0;

[0122] Step Four: Obtain through Equation (22) and calculate F and update the iteration count n = n + 1 through calculating F W (n + 1);

[0123] Step Five: Determine whether F W (n + 1) - F W (n) ≤ ε2 holds. If it holds, jump and execute Step Six; otherwise, jump and execute Step Four;

[0124] Step Six: Update the variable η = αη, jump and execute Step Two.

[0125] Step Seven: Obtain the optimal beamforming vector w through eigenvalue decomposition * ;

[0126] Figure 4 This is the flow chart of the steps for optimizing the RIS reflection phase shift matrix in the embodiments of the present invention, which is mainly completed through the following steps:

[0127] Step One: Initialize V 0 and the convergence judgment constants ε3, ε4 as real numbers approaching 0, as well as the penalty factor η and the coefficient β; define F V (m) = ESP (j) - η(||V m || * - ||V m ||2) and set the initial value F W (0) = 0, input the beamforming vector w k and ESP (j) ;

[0128] Step Two: Determine whether ||V 0 || * - ||V 0 ||2 ≤ ε3 holds. If it holds, jump and execute Step Seven; otherwise, jump and execute Step Three;

[0129] Step Three: Initialize the iteration count m = 0;

[0130] Step Four: Obtain V m through V m+1 and Equation (27), and calculate F V (m) = ESP (j)-η(||V m || * -||V m ||2) Calculate F V (m + 1), update the variable m = m + 1;

[0131] Step Five: Judge F V (m + 1) - F V (m) ≤ ε4 holds; if it holds, jump to and execute Step Six, otherwise jump to and execute Step Four;

[0132] Step Six: Update the variable η = βη, V 0 = V m Jump to and execute Step Two;

[0133] Step Seven: Obtain the result V opt If rank(V opt ) ≤ 1, then use the eigenvalue decomposition method to recover the optimal RIS reflection phase shift vector v; if rank(V opt ) > 1, then adopt the Gaussian randomization method to obtain the optimal approximate solution of v; obtain the RIS reflection phase shift matrix Θ according to Θ = diag(v);

[0134] Figure 5 is the comparison diagram of the effective sensing power under different schemes. Among them, the number of users is 4, the number of base station antennas is 8, and the corresponding beam pattern of the target RIS when the number of reflection units is set to 48. According to the figure, whether it is the passive RIS-assisted ISAC system or the active RIS-assisted ISAC system (A-RIS-ISAC) proposed in the present invention, its ESP can reach the peak at (-60°, 0°, 60°), because the azimuth angle between the set RIS and the sensing target is (-60°, 0°, 60°); moreover, through comparison, it is found that: the scheme proposed in the present invention (i.e., A-RIS-ISAC) is higher than the passive RIS-assisted ISAC system (blue line) at the peak, indicating that the proposed scheme of active RIS-assisted MI-ISAC has significant advantages in filling blind spots and reducing multiplicative fading.

[0135] Figure 6 is the relationship diagram of the ESP at the RIS varying with the number N of RIS reflection units (i.e., A-RIS-ISAC). Among them, for the active RIS-assisted ISAC system and the passive RIS-assisted ISAC system, the ESP increases with the increase of N, because as N increases, its degrees of freedom also increase, thus achieving the goal of increasing the ESP. At the same time, at P BSWhen it is determined, the effective spectral efficiency (ESP) of the active RIS-assisted integrated sensing and communication (ISAC) system is higher than that of the passive RIS-assisted ISAC system. This is because under the C3 constraint in Equation (7), increasing β makes the amplification effect of the active RIS stronger, thus resulting in an increase in ESP. Moreover, for both the active RIS-assisted ISAC system and the passive RIS-assisted ISAC system, their ESP will increase with the increase of P BS because under the C2 constraint in Equation (7), increasing P BS can improve the transmitted signal power, thereby increasing ESP.

[0136] As Figure 7 shown, this embodiment discloses an active RIS-assisted multi-user integrated sensing and communication (MU-ISAC) system for maximizing the effective sensing power, which is used to execute the above method embodiment and includes the following modules:

[0137] Signal transmission module: The base station transmits a signal, digitally modulates it, and sends it to the active RIS and users through free space; among them, the data type of the signal is complex, and it jumps to and executes the effective sensing power calculation module;

[0138] Effective sensing power calculation module: At the sensing target receiving end, the signal sent by the signal transmission module is received as the input signal, and then reaches the active RIS after reflection; according to the calculation process of the effective sensing power, the effective sensing power ESP of the system is obtained (j) ;

[0139] Effective sensing power judgment module: Judge whether the effective sensing power ESP obtained by the effective sensing power calculation module (j) satisfies |ESP (j) -ESP (j-1) | < ε, where the initial value of the effective sensing power is 0 and ε is a constant; if not satisfied, it is executed by the beamforming vector optimization module; if satisfied, it is executed by the output module;

[0140] Beamforming vector optimization module: Take the effective sensing power ESP obtained by the judgment module (j) as the input parameter, execute the beamforming vector optimization method, and output an M×1-dimensional vector w with all elements being complex numbers k ; where M is a natural number representing the number of rows of the vector; the subscript k represents the k-th user;

[0141] RIS phase shift matrix optimization module: Take the beamforming vector w obtained by the beamforming vector optimization module k as the input parameter, execute the RIS phase shift matrix optimization module, and output an N×N-dimensional matrix Θ with all elements being complex numbers; where N is a natural number representing the number of rows and columns of the matrix;

[0142] Output module: Based on the optimal value of the effective sensing power obtained by the judgment module, it is used as the output result.

[0143] For other contents of this embodiment, reference may be made to the above method embodiment.

[0144] Although the embodiments of the present invention have been clearly described. However, for those skilled in the art, without departing from the principle and spirit of the method of the present invention, various changes, modifications, substitutions, and variations can be made to these embodiments. The scope of the present invention is defined by the appended claims and their equivalents, and still belongs to the scope of the method of the present invention and is still regarded as the protection scope of the present invention.

Claims

1. A method for maximizing effective perceived power of a non-line-of-sight MU-ISAC system assisted by RIS, characterized in that: The following steps are involved: S1, the base station's binary bit sequence, after bipolar coding, baseband shaping and precoding, obtains a signal that can be propagated in the wireless channel. The signal is equivalently expressed as: Among them, w k is an M×1 dimensional complex vector, representing the beam vector of the kth signal, s k is a complex number representing the sign of the kth signal and satisfies E(·) is the expected calculation, Indicates k The conjugate complex number of ; k and K are both integers and satisfy 1≤k≤K; S2, after the signal x in step S1 is transmitted to the sensing target through RIS, the effective sensing power ESP at the active RIS is used as the sensing signal indicator; the ESP of the jth iteration is calculated by the calculation method of the effective sensing power ESP. (j) Perform calculations; S3, judging the result ESP obtained in step S2 (j) Does it satisfy the inequality|ESP (j) -ESP (j-1) |≤ε, if satisfied, jump to step S6; otherwise, ESP (j) Jump to step S4 as an output parameter and set j=j+1; S4: The effective perceived power ESP obtained in step S3 is (j) As input parameter, a beamforming vector optimization method is performed, outputting the parameter ESP from step S3 (j) and an M×1-dimensional vector w whose elements are all complex numbers k ; Where M is a natural number, indicating the number of rows in the vector, and the subscript k indicates the kth user; S5. The beamforming vector w obtained in step S4 is k ESP (j) As input parameters, the RIS phase shift matrix optimization method is performed, and the output beamforming vector w from step S4 is k And the N×N dimensional RIS phase shift matrix Θ whose elements are all complex numbers; where N is a natural number, representing the number of rows and columns of the matrix as the output function; the obtained RIS phase shift matrix Θ and beamforming vector w k Return to step S2, and calculate the ESP of the jth iteration by the calculation method of the effective perceived power ESP. (j) Perform calculations; S6. Obtain the optimal value of effective sensing power as an output result.

2. The RIS-assisted non-line-of-sight MU-ISAC system effective perception power maximization method as claimed in claim 1, characterized in that: In step S2, the calculation method of ESP is as follows: During the first calculation, the signal passed in from step S1 is required and the initial RIS reflection phase shift matrix θ i ∈[0,2π],i=1,aN; The system includes a base station, an active RIS, K single-antenna users and T sensing targets; the set of communication users is κ = {1, 2, ... K}, the set of sensing targets is τ = {1, 2, ..., T}, K and T are both positive integers; the number of base station antennas is a positive integer M, the number of reflection units of the active RIS is a positive integer N; κ is a 1 × K dimensional vector, whose elements are all natural numbers; k is denoted as the kth user, then: Among them, y k Indicates the base station transmission signal received by the user end. represents the channel from RIS to the kth user; θ i ∈[0,2π],i=1,…N,β i is the phase shift matrix and amplification factor of active RIS; represents the channel coefficient matrix from the base station to the RIS; x k =w k s k represents the kth signal; and are the noise introduced by active RIS and additive white Gaussian noise respectively; then the rate at which the signal reaches the user end after being reflected by RIS is: In non-line-of-sight scenarios, the user's beam vector is used to complete the perception task and the ESP of the RIS is used as the perception performance indicator. The RIS reflection signal is expressed as: Then, the covariance matrix corresponding to the RIS reflection signal is expressed as: Therefore, the RIS beam gain corresponding to the t-th target is expressed as: in, is the steering vector, θ t is the azimuth of the tth perceived target, λ represents the wavelength, and d represents the antenna spacing; Therefore, the effective perceived power ESP at the active RIS is: P(w k ,Θ)=S t∈τ P r (w k ,Θ,Θ t ) (6).

3. The RIS-assisted non-line-of-sight MU-ISAC system effective perception power maximization method as claimed in claim 2, characterized in that: In step S2, when calculating for the first time, the ESP of the jth iteration is calculated by using the x from step S1 through the calculation method of the effective perceived power ESP. (j) Perform calculations.

4. The RIS-assisted non-line-of-sight MU-ISAC system effective perception power maximization method as claimed in claim 2 or 3, characterized in that: In step S4, the beamforming vector w k The optimization method is implemented in the following steps: S4.1, initialization, The convergence judgment constants ε1, ε2 are real numbers, the penalty factor η and the coefficient α are defined. And let the initial value F W (0) = 0, ESP (j) and V and enter the initial signal value; S4.2, first use the data passed in step S4.1 to determine If it is true, the data from step S4.6 will be used in the subsequent step; if it is true, jump to step S4.7, otherwise jump to step S4.3; S4.3, initialize the number of iterations n = 0; S4.

4. Model the effective perceived power ESP problem at the system active RIS as: Among them, R min represents the minimum communication rate of each user, represents the phase shift vector of RIS; θ t ∈[0,2π] represents the azimuth of the t-th perceived target, P BS and P I are the transmission power of the base station and the maximum power limited by the active RIS, respectively. C1 guarantees the minimum communication rate R of the communication user. min ; C2 ensures the limit of base station transmission power; C3 ensures the limit of active RIS power; C4 ensures the limit of ESP difference of each target RIS; C5 is the limit of RIS phase shift matrix; definition and V = vv H ;in, And rank(W k )=1 and And rank(V)=1;W k and V are both semi-positive matrices, and v = diag (Θ) is the phase shift vector of the active RIS; therefore, the effective sensing power P (w k ,Θ) is expressed as: Among them, χ t =diag(a H (θ t ))G, for C1: in, definition Tr(·) is the trace operation of the matrix; so the constraint C1 is re-expressed as: Constraints C2, C3, C4, and C5 are changed to: diag(Σ i∈κ W i )≤(P BS / M)I M (12) Where diag(diag(·)) means extracting the diagonal elements of the matrix first and then generating a new diagonal matrix; is the ESP of the t-th perceived target, P d is a constant; The effective perceived power ESP problem at the active RIS of the system is rewritten as: The penalty term method is used to process the objective function of formula (16), and the matrix rank 1 constraint is converted into the objective function penalty term; for rank (W k )=1, this non-convex problem introduces an equivalent expression to the matrix rank 1 constraint as follows: ||In k || * -||In k ||2=0 (17) Among them, ||·|| * is the nuclear norm, ||·||2 is the spectral norm; when rank(W k )=1, equation (17) holds true, because Need to meet ||W k || * -||W k ||2>0; introduce a penalty term ||W into the objective function k || * -||W k ||2, introducing the penalty factor η, then formula (16) is rewritten as: Using the continuous convex approximation method, for -||W k ||2First-order Taylor expansion, the upper bound is: in, for The eigenvector corresponding to the largest eigenvalue; Using the semi-positive definite relaxation algorithm, we relax the non-convex rank-one constraint C5 and obtain the new problem: pass And formula (20) to get and through Calculate F W (n+1), update the number of iterations n=n+1; jump and execute step S4.5; S4.

5. According to the data passed in step S4.4, determine F W (n+1)-F W (n)≤ε2; if so, jump to step S4.6; otherwise, jump to step S4.4; S4.6, update variable η=αη, Jump and execute step S4.2; S4.7, according to the data passed in step S4.2, obtain The optimal beamforming vector w is obtained by eigenvalue decomposition * .

5. The RIS-assisted non-line-of-sight MU-ISAC system effective perception power maximization method as claimed in claim 4 is characterized in that: In step S5, the optimization method of the RIS phase shift matrix θ is as follows: S5.

1. Input beamforming vector w k and ESP (j) , initialize V 0 And the convergence judgment constants ε3, ε4 are real numbers tending to 0, as well as the penalty factor η and the coefficient β; define F V (m) = ESP (j) -η(||V m || * -||V m ||2) and let the initial value F W (0) = 0; S5.2, in the first calculation, determine || V according to the data passed in step S5.1 0 || * -||V 0 ||2≤ε3 is true, if so, jump to and execute step S5.7, otherwise jump to and execute step S5.3, and then use the data from step S5.6; S5.3, initialize the number of iterations m = 0; S5.

4. Using eigenvalue decomposition, we can obtain the transmit signal beamforming vector w k , Formula (7) is re-described as: The penalty term method is used to process the objective function of formula (21), and the rank 1 constraint of the matrix is ​​converted into the penalty term in the objective function. For the non-convex problem of rank(V)=1, an expression equivalent to the rank 1 constraint of the matrix is ​​introduced as follows: ||V k || * -||V k ||2=0 (22) When rank(V)=1, equation (22) holds true, because Need to satisfy ||V|| * -||V||2>0; To obtain the matrix rank 1 constraint, a penalty term is introduced into the objective function, and a penalty factor η is introduced, then equation (21) is re-described as: Using the continuous convex approximation method, the first-order Taylor expansion of -||V||2 is obtained, and its upper bound is: in, V n The eigenvector corresponding to the maximum eigenvalue, then equation (23) is written as: By V m And formula (25) to obtain V m+1 , and through F V (m) = ESP (j) -η(||V m || * -||V m ||2) Calculate F V (m+1), update variable m=m+1; S5.

5. According to the calculation results of S5.4, determine F V (m+1)-F V (m)≤ε4; if so, jump to step S5.6; otherwise, jump to step S4.4; S5.

6. Update variable η=βη,V 0 =V m Jump and execute step S5.2; S5.

7. Get the result V based on the data passed in S5.2 opt If rank(V opt )≤1, the optimal RIS reflection phase shift vector v is recovered by eigenvalue decomposition; if rank(V opt )>1, the Gaussian randomization method is used to obtain the optimal approximate solution of v; and the RIS reflection phase shift matrix Θ is obtained according to Θ=diag(v).

6. A RIS-assisted non-line-of-sight MU-ISAC system effective perception power maximization system, used to execute the method according to any one of claims 1 to 5, characterized in that: Includes the following modules: Signal transmission module: The base station sends a signal, performs digital modulation on the signal, and sends it to the intelligent reflection surface RIS and the user through free space; wherein the data type of the signal is complex number; Effective perceived power calculation module: receives the signal sent by the signal sending module as an input parameter and calculates the effective perceived power ESP of the system (j) ; The subscript represents the result obtained in the jth iteration; Effective perceived power judgment module: judges the effective perceived power ESP obtained by the effective perceived power calculation module (j) Satisfied |ESP (j) -ESP (j-1) |<ε, where the initial value of effective sensed power is 0 and ε is a constant; if not satisfied, ESP (j) As output parameters, it is executed by the beamforming vector optimization module; if satisfied, it is executed by the output module; Beamforming vector optimization module: The effective perceived power ESP obtained by the judgment module (j) As input parameter, the beamforming vector optimization method is executed, and the output elements are all complex M×1 dimensional vector w k ; Where M is a natural number, indicating the number of rows in the vector; subscript k indicates the kth user; RIS phase shift matrix optimization module: The beamforming vector w obtained by the beamforming vector optimization module is k As input parameters, the RIS phase shift matrix optimization module is executed, and the output elements are all complex N×N dimensional matrices Θ; Where N is a natural number, indicating the number of rows and columns of the matrix; Output module: obtains the optimal value of the effective sensing power according to the judgment module as the output result.

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