Beam design method of auxiliary dual-function radar communication system

Abstract

The present application discloses a beam design method for active reconfigurable smart reflector (active-RIS) assisted dual function radar and communication (DFRC), in which the radar serves a plurality of communication users while perceiving a target, while active RIS is used for communication enhancement. According to the method, on the premise of ensuring certain radar detection power, transmitting waveform with constant modulus and limited power budget, the WSR of a communication user is maximized by jointly designing transmitting beam forming of a radar and reflected beam forming of an active RIS (Radio Information System); and an efficient alternating optimization algorithm based on weighted minimum mean square error and fractional programming is provided to solve the proposed height non-convex optimization problem. A simulation result shows that compared with a passive RIS, the adding of the active RIS effectively improves the weighting sum rate of system communication.

Description

Technical Field

[0001] A beam design method for an assisted dual-functional radar communication system in the present application relates to the field of radar technology, specifically to the beam design technology of dual-functional radar communication. Background Art

[0002] With the advent of the fifth-generation mobile communication era, the number of connections of communication devices has increased sharply, and the required data transmission volume has become larger and larger. To solve this problem, various potential technologies have emerged, including massive MIMO technology, millimeter-wave communication, and ultra-dense networks. These technologies can significantly improve the data throughput and spectral efficiency of the system and can provide new services and applications. However, with the continuous increase in connected communication users and sensors, these technologies have also exacerbated the problem of spectrum scarcity.

[0003] Reconfigurable intelligent surfaces are widely used to reconstruct the signal propagation environment and can effectively solve the above problems. It consists of a large number of reflecting elements. By reasonably designing the phase shift of each reflecting unit, the phase of the incident signal can be changed, thereby controlling the direction of the signal. However, for passive RIS, since the path loss of the transmitter-RIS-receiver link is the product of the path losses of the transmitter-RIS and RIS-receiver paths, passive RIS cannot achieve significant performance improvement in many scenarios. Therefore, active RIS is introduced, which can simultaneously amplify the incident signal and change the phase shift of the incident signal.

[0004] For such systems, it is particularly important to design the transmitting beam of the radar and the reflecting beam of the active RIS under the conditions of ensuring the quality of service of communication users, the radar sensing performance, and limited power budget. Summary of the Invention

[0005] The purpose of the present application is to provide a beam design method for an assisted dual-functional radar communication system, especially a beam design method for an active reconfigurable intelligent surface (RIS)-assisted dual-functional radar communication system.

[0006] The present application solves the above technical problems through the following technical solutions:

[0007] A beam design method for an active reconfigurable intelligent surface (RIS)-aided dual-functional radar communication system, characterized in that the radar senses surrounding targets while providing communication services for multiple users, and the active RIS is used to enhance the communication performance of the system. Under the conditions of ensuring a certain radar detection power, a constant modulus transmit waveform, and a limited power budget, this design method maximizes the weighted sum rate of communication users by jointly designing the transmit beamforming of the radar and the reflection beamforming of the active RIS, and completes this design based on an efficient alternating optimization algorithm of weighted minimum mean square error (WMMSE) and fractional programming (FP), realizing the enhancement of the communication function of the radar system.

[0008] In order to better achieve the invention purpose of the application, the technical solution of the application is specifically improved through the following steps:

[0009] Furthermore, it is realized through the following process:

[0010] Step 1, input the corresponding channel information, including the channel h between the radar and the user d，k , the channel G between the radar and the active RIS, the channel h between the active RIS and the user r，k , the angle φ of the target relative to the radar, and the dynamic noise power of the active RIS and the channel Gaussian white noise power and set the total power budget p of the radar and the active RIS, the radar power allocation ratio ρ, and the power allocation ratio η for sensing on the radar;

[0011] Step 2, initialize the transmit beam T of the radar, the amplification factor matrix A and the phase shift matrix Θ of the active RIS, and the auxiliary variable ε through a randomization method;

[0012] Step 3, fix A and Θ, and solve for the linear estimate value s by minimizing the mean square error (MMSE) between the linear estimate symbol and the true communication symbol x k ; MMSE ;

[0013] Step 4, calculate the weighting coefficient ω according to the minimum mean square error e MMSE corresponding to s MMSE ;

[0014] Step 5, optimize the weighted minimum mean square error (WMMSE) problem corresponding to the weighting coefficient ω. Transform the original WMMSE problem into a semidefinite programming problem through convex quadratic transformation and homogenization methods. Use the semidefinite relaxation (SDR) method and the CVX toolbox to solve for W, and recover each column t of T through the Gaussian randomization or maximum eigenvalue approximation method k , as shown in Formulas 11 to 21;

[0015] Step 6: Fix \(T\), and use the Lagrangian dual transformation to equivalently transform the original weighted sum-rate maximization problem into an optimization problem regarding \(\varPsi\) (the product of \(A\) and \(\varTheta\)) and the auxiliary variable \(\alpha\). Based on the alternating optimization method, when \(\varPsi\) is fixed, solve for the optimal value of \(\alpha\) by taking the first-order partial derivative.

[0016] Step 7: After calculating the optimal \(\alpha\), optimize \(\varPsi\). By using the auxiliary variable \(\varepsilon\) initialized in Step 2, transform the fractional programming problem into an optimization problem regarding \(\varPsi\) and \(\varepsilon\) that only contains quadratic terms and linear terms. First, when \(\varPsi\) is given, solve for the optimal \(\varepsilon\) by taking the first-order partial derivative of the objective function. After obtaining the optimal \(\varepsilon\), separate \(\varPsi\) in the objective function and the constraints in the form of vector \(\boldsymbol{\psi}\) from other matrices through the matrix transformation in Theorem 5, forming a standard quadratic constraint quadratic programming problem, and use the CVX toolbox to solve for \(\varPsi\), and then solve for \(A\) and \(\varTheta\).

[0017] Step 8: Calculate the sum-rate \(R\) of the users according to \(T\), \(A\), and \(\varTheta\). If \(R\) does not reach the convergence condition, return to Step 3; if \(R\) reaches the convergence condition, output the optimal transmit beam \(T\), the amplification factor matrix \(A\) and phase shift matrix \(\varTheta\) of the active RIS, the user sum-rate \(R\), and the radar detection power \(P\). r 。

[0018] Furthermore, Steps 3 to 7 adopt the iterative alternating optimization method, and in each iteration, alternately optimize the transmit beamforming variable and the reflection beamforming variable, that is:

[0019] ... \(T\) k → \(\varPsi\) k → \(T\) k+1 → \(\varPsi\) k+1 ...

[0020] Each iteration can ensure the convergence of the alternating optimization algorithm.

[0021] Furthermore, the iterative alternating optimization method is as follows: First, fix \(A\) and \(\varTheta\), and optimize the transmit beamforming matrix \(T\) using the weighted minimum mean square error framework; then fix \(T\), and optimize \(A\) and \(\varTheta\) using fractional programming.

[0022] Furthermore, the implementation process of Step 3 is as follows:

[0023] Fix the amplification phase shift matrix \(\varPsi\) of the active RIS, that is, the product of \(A\) and \(\varTheta\), and introduce a linear estimation factor \(s\) at the communication user \(k\). k , use Equation 6 to calculate the linear estimation symbol and calculate the linear estimation symbol according to Equation 7 and the true symbol \(x\). kThe mean square error between is used to transform the weighted sum rate maximization problem into an equivalent weighted minimum mean square error (WMMSE) optimization problem. Since the WMMSE optimization problem is convex with respect to s k the optimal linear estimation factor can be derived according to Equation 8

[0024] Furthermore, the implementation process of step 4 is as follows:

[0025] Calculate the minimum mean square error and calculate the weighted MMSE coefficient to transform the weighted sum rate maximization problem of transmit beamforming into a weighted mean square error minimization (MMSE) problem.

[0026] Furthermore, the implementation process of step 6 is as follows:

[0027] After fixing the transmit precoding matrix W, by introducing an auxiliary variable α and using the alternating optimization method, when Φ is fixed, solve for the optimal α * .

[0028] The beneficial effects of this application are as follows: Using an active RIS in a DFRC system can improve the communication performance and sensing performance of the radar. The proposed joint optimization algorithm for the transmit beamforming matrix, active RIS amplification factor matrix, and phase shift matrix shows that under the conditions of ensuring a certain radar detection power, a constant modulus transmit waveform, and a limited power budget, the weighted sum rate of the system is significantly improved. The simulation results verify the effectiveness of the algorithm, indicating that the active RIS-assisted DFRC system is superior to the passive RIS-assisted DFRC system and the RIS-free DFRC system. Description of the Drawings

[0029] Figure 1 is the active RIS-assisted DFRC model;

[0030] Figure 2 is the active RIS-assisted DFRC scenario, which includes a DFRC-BS with M antennas, a RIS composed of N reflection elements, K single-antenna communication users, and a target.

[0031] Figure 3 is the convergence of the algorithm proposed in this application: the relationship between WSR and the number of iterations.

[0032] Figure 4 is the comparison of the DFRC transmission beam patterns under active RIS and passive RIS assistance.

[0033] Figure 5 is the relationship between WSR and the number of RIS reflection elements.

[0034] Figure 6It is the relationship between WSR and the total system power.

[0035] Figure 7 It is the relationship between the radar detection power and WSR when ρ = 0.8.

[0036] Figure 8 It is the relationship between WSR and the ratio of radar detection power when the detection power is 60 mW.

[0037] Figure 9 It is the relationship between WSR and the power splitting ratio when the detection power is 60 mW.

[0038] Figure 10 It is the flow chart of the beam design method for the assisted dual-functional radar communication system of this application; Detailed implementation manners

[0039] The technical solution to achieve the purpose of this application is: an alternating optimization algorithm for maximizing the weighted sum rate of a dual-functional radar communication system, including:

[0040] System model: A dual-functional radar equipped with M antennas provides communication services for K single-antenna communication users while sensing targets. An active RIS composed of N reflection units is installed near the communication users to assist radar communication to improve the service quality, as Figure 1 shown. In addition, a central controller is connected to the dual-functional radar and the active RIS to ensure that both can obtain all channel information. Assume that the target is far from the RIS, that is, the RIS only serves the communication users. Therefore, the signal received by the k-th communication user is

[0041]

[0042] where represents the transmit beamforming matrix, represents the linear precoding sent to the k-th communication user, and represent the channels between the dual-functional radar and the active RIS and between the dual-functional radar and the k-th communication user respectively, represents the channel between the active RIS and communication user k, A = diag([a1, a2,..., a N ) represents the amplification factor matrix of the active RIS, represents the phase shift matrix of the active RIS, represents the communication symbol, x k is the symbol sent to the k-th communication user, and it is assumed that the transmission symbols of each user are independent of each other, that is k ≠ j. represents the dynamic noise introduced by the active RIS, Denote the additive white Gaussian noise received by the \(k\)-th communication user.

[0043] Thus, the received signal-to-interference-plus-noise ratio (SINR) of the \(k\)-th communication user is

[0044]

[0045] where represents the equivalent end-to-end communication channel from the radar to the \(k\)-th communication user.

[0046] Assume \(\mu\) k is the weighting coefficient of the \(k\)-th communication user. Then, the weighted sum rate (WSR) of the system is

[0047]

[0048] Meanwhile, the radar also operates in the sensing mode to detect a target located in the \(\varphi\) direction. Then, the detection power in the target direction is

[0049]

[0050] where \(T_T\) H is the covariance matrix of the transmit beamforming matrix, is the steering vector in the direction \(\varphi\).

[0051] Optimization problem: Maximize the weighted sum rate of the system by designing the optimal transmit beamforming matrix \(R\), the RIS amplification factor matrix \(A\), and the RIS phase shift matrix \(\Theta\), i.e.,

[0052]

[0053] where \(P\) s is the power budget allocated to the dual-functional radar, and \(P\) a is the power budget allocated to the active RIS. The constraint represented by Equation (5b) ensures that the sensing power of the radar in the target direction \(\varphi\) is not lower than \(\eta P\) s , where \(0\leq\eta\leq1\) is the ratio of the transmit power used for radar sensing, which controls the trade-off between radar communication and sensing performance and ensures that sufficient power is allocated for radar sensing. The constraint represented by Equation (5c) is the constant modulus constraint imposed by the radar system to reduce radar signal distortion and thus reduce signal distortion caused by non-linear amplification of the transmitter. The constraint represented by Equation (5d) ensures that the power consumed by the active RIS does not exceed \(P\) a .

[0054] Optimization Algorithm: Since this optimization problem is highly non-convex, this application proposes a beam design method that decomposes the original problem into two sub-problems based on the alternating optimization method to solve for the optimal T, A, and Θ. First, fix A and Θ, and optimize the transmit beamforming matrix T based on the weighted minimum mean square error (WMMSE) framework. Then, fix T and optimize A and Θ using fractional programming (FP). Since A and Θ always maintain a product form, let for subsequent calculations.

[0055] a. Optimize the transmit beamforming matrix T based on the WMMSE framework:

[0056] Fix Ψ (i.e., fix A and Θ), and transform the weighted sum rate maximization problem into an equivalent WMMSE optimization problem. To achieve this transformation, the proposed algorithm introduces a linear estimate s at the k-th communication user k , then the received estimated symbol

[0057]

[0058] To obtain the optimal estimate, this method derives the mean square error between the linear estimate symbol and the true symbol x k according to the following theorem.

[0059] Theorem 1: Since the symbols and noises between communication users are independent of each other, the mean square error (MSE) is

[0060]

[0061] The proof refers to the derivation in Appendix A.

[0062] To minimize the symbol estimation error, the optimal linear estimate of the k-th communication user is derived according to the following theorem

[0063] Theorem 2: The mean square error (MSE) derived in Equation 7 is convex with respect to s k , and the unconstrained convex optimization problem can be solved by setting the first derivative to zero , that is:

[0064]

[0065] The corresponding minimum mean square error (MMSE) is

[0066]

[0067] The proof refers to the derivation in Appendix B.

[0068] To equivalently transform the non-convex problem with respect to T into a more tractable form, Theorem 3 is used for simplification.

[0069] Theorem 3: The problem of maximizing the weighted sum rate of the system can be equivalently transformed into the corresponding problem of minimizing the weighted mean square error (MMSE), where the weighted MMSE coefficient should be

[0070]

[0071] By selecting the above-mentioned weighted coefficients, the KKT conditions of both problems can be satisfied simultaneously. The WSR maximization problem in Equation (5) can be equivalently transformed into the weighted MSE minimization problem, that is

[0072]

[0073] For t k in Equation (11a), the objective function is a combination of quadratic and linear terms, and the constraints include quadratic equality constraints and quadratic inequality constraints, both of which make the optimization problem in Equation (11) non-convex. To handle the non-convex constraint represented by Equation (11b), this problem is equivalently transformed into a convex quadratic form according to Theorem 4.

[0074] Theorem 4: The left side of Equation (11b) can be transformed into

[0075]

[0076] Therefore, Equation (11b) can be rewritten as

[0077]

[0078] where is a positive semi-definite matrix. The proof refers to the derivation in Appendix C.

[0079] The constraint represented by Equation (11d) can be transformed into a standard quadratic constraint, that is

[0080]

[0081] where Obviously is a positive semi-definite matrix, which further makes the constraint represented by Equation (14) convex. At the same time, the constraint in Equation (11c) can also be transformed into

[0082]

[0083] Therefore, the non-convex problem in Equation (11) can be equivalently transformed into

[0084]

[0085] Since the objective function in Equation (16a) with respect to tk is quadratic. The constraints represented by Equation 16b and Equation 16d are standard quadratic inequality constraints. The existence of Equation 16c makes the optimization problem of Equation 16 a non - homogeneous quadratic - constrained quadratic programming (QCQP) problem, which can be homogenized into a semidefinite programming problem. Expanding the objective function in Equation 16a, the minimum mean - square error e k is expressed as

[0086]

[0087] Removing the terms unrelated to t k gives

[0088]

[0089] where and |z k | 2 = 1. Similarly, Equation 16b, Equation 16c, and Equation 16d can be transformed into the same form, that is

[0090]

[0091] where

[0092] The non - homogeneous QCQP problem in Equation 16 can be converted into an optimization problem for finding the optimal value, that is

[0093]

[0094] Let Using the properties of the matrix trace, the optimization problem in Equation 20 can be transformed into a semidefinite relaxation (SDR) problem, that is

[0095]

[0096] [W k M+1,M+1 = 1, Equation 21e

[0097]

[0098] rank(W k ) = 1, k = 1, ..., K, Equation 21g

[0099] Due to the non - convex constraint represented by Equation 21g, the optimization problem in Equation 21 is still a non - convex problem. By relaxing the rank - 1 constraint in Equation 21g, the above - mentioned optimization problem can be transformed into a standard semidefinite relaxation (SDR) problem and solved using the CVX toolbox in MATLAB software. However, the W solved by the CVX toolbox​k The rank-1 constraint may not be satisfied, and Gaussian randomization or maximum eigenvalue approximation may be needed to recover the columns t in T. k .

[0100] b. RIS reflection beamforming design based on fractional programming:

[0101] When the transmit precoding matrix W of the dual-function radar is given, the original maximization WSR problem in formula 5 can be simplified to

[0102]

[0103] Since the optimization problem in Formula 22 is a standard, non-convex maximization weighted sum rate (WSR) optimization problem, and the objective function in Formula 22a is in logarithmic and fractional form relative to the matrix Ψ, the optimization problem in Formula 22 is difficult to solve directly. This application introduces an auxiliary variable α based on the Lagrange dual transformation, and the above problem can be transformed into a more tractable form, that is,

[0104]

[0105] To solve the optimization problem in Formula 23, the alternating optimization method is used to decouple the optimization variables Ψ and α. Specifically, when Ψ is fixed, the optimization problem in Formula 23 is an unconstrained convex optimization problem. The optimal value α can be obtained * ,Right now

[0106]

[0107] When α is fixed, the optimization problem in Formula 23 can be transformed into a fractional programming problem, that is,

[0108]

[0109] The objective function in formula 25a can be equivalently transformed into

[0110]

[0111] Where ε is an auxiliary variable introduced, so the fractional programming problem in formula 25 is transformed into

[0112]

[0113] Given Ψ, the optimization problem in Formula 27 is an unconstrained convex problem with respect to ε. Let have

[0114]

[0115] Will Substituting (27a), by expanding the objective function in formula 27a and removing the terms independent of Ψ, two linear terms and two quadratic forms can be obtained, that is

[0116]

[0117] The presence of Ψ in other matrices makes its optimization difficult to solve. To make the objective function of formula 29 easier to solve, let Ψ = diag(ψ), and perform matrix transformation according to Theorem 5.

[0118] Theorem 5: Denote as a diagonal matrix, as an arbitrary vector in the N×1 dimensional space, as an arbitrary matrix in the N×N dimensional space, then there is

[0119] a H Θ H b = θ H A H b, formula 30a

[0120] a H Θ H DΘa = θ H A H DAθ, formula 30b

[0121] where is an N-dimensional vector, whose elements are the elements of matrix Θ on the main diagonal, that is, Θ = disg(θ). is a diagonal matrix, whose main diagonal elements are the elements of α, that is, A = diag(α). The proof is shown in Appendix D.

[0122] According to Theorem 5, the optimization variable Ψ in formula 29 can be separated from other matrices, that is

[0123]

[0124] To further simplify formula 31, terms of the same order are grouped together, and the linear term and quadratic term are represented by v and U respectively, that is

[0125]

[0126] Therefore, the objective function in formula 27a can be expressed as

[0127]

[0128] The constraint represented by formula 27b is also a quadratic term. According to Theorem 5, there is

[0129] ψ H Πψ ≤ P a , formula 34

[0130] where Π is a positive semi - definite matrix, that is

[0131]

[0132] Based on Equation (33) and Equation (34), the fractional programming optimization problem in Equation (27) can be rewritten as:

[0133]

[0134] s.t. ψ H Π ψ ≤ P a . Equation (36b)

[0135] The optimization problem in Equation (36) is a standard quadratic - constrained quadratic programming (QCQP) problem, which can be directly solved using the CVX toolbox. After obtaining the optimal ψ, we can get Ψ = diag(ψ), the amplification coefficient matrix A = |Ψ|, and the phase - shift matrix Θ = ∠Ψ. The following table summarizes the proposed joint beam design algorithm.

[0136]

[0137] c. Discussion on Convergence and Computational Complexity

[0138] Since this algorithm adopts an iterative alternating optimization method, and each iteration alternately optimizes the transmit beam - forming matrix and the reflection beam - forming matrix, that is

[0139] ...T k → Ψ k → T k+1 → Ψ k+1 ...

[0140] Since for each iteration, the optimization problems in Equation (21) and Equation (36) are convex problems, it can be guaranteed that the proposed alternating optimization algorithm will converge.

[0141] The computational complexity of this algorithm mainly depends on the updates of T and Ψ. When calculating T, the complexity mainly involves solving the SDR problem and eigenvalue decomposition, and their computational complexities are respectively:

[0142]

[0143] where ∈ represents the required solution accuracy. Similarly, when solving for Ψ, the complexity mainly depends on the QCQP problem, and its complexity is Generally speaking, the computational complexity of each iteration of the above - mentioned algorithm is

[0144]

[0145] Simulation Results

[0146] The dual-functional radar (DFRC) is equipped with M = 8 antennas whose coordinates are located at (0 m, 0 m), and the active RIS has N = 36 reflecting elements whose coordinates are located at (150 m, 0 m). The dual-functional radar (DFRC) transmits communication symbols to K = 4 mobile downlink communication users within a region centered at (150 m, 0 m) with a radius of 5 m. The total power budget of the system is P = 20 dBm, and the noise power is set to σ2 = -20 dBm. At the same time, the angle of the radar target is set to -45° of the radar, as Figure 2 shown.

[0147] The channel h between the DRFC and the communication users d，k is set to a Rayleigh fading channel, while the channels G and h related to the RIS r，k are set to Rician channels, that is

[0148]

[0149] where κ1 and κ2 are Rician factors and κ1 = κ2 = 10. and are the deterministic line-of-sight components of the channels. The vectors a(α1) and a(α2) are the transmit steering vector of the dual-functional radar and the receive steering vector of the active RIS respectively, and a(α 3，k ) is the reflection steering vector of the active RIS for the k-th communication user. G NLoS and are the non-line-of-sight (NLoS) Rayleigh fading components, which follow a circularly symmetric complex Gaussian distribution with zero mean and unit variance. β G and β r represent the path loss parameters respectively, which are related to the distances between the transmitter and the receiver.

[0150] In addition, based on the 3GPP propagation environment, a path loss model is defined, and 2.4 GHz is selected as the carrier frequency.

[0151] To illustrate the power allocation in the system, the relationship between the power-related symbols and the power allocation is described here. The total system power P is divided into the power budget P s of the dual-functional radar and the power budget P a of the active RIS. Denote ρ as the splitting ratio of the dual-functional radar in the total power, that is, P s = ρP, and P a = (1 - ρ)P. In addition, the power P s of the dual-functional radar can be further divided into the detection power P r and the communication power P c , and the power splitting ratio between the two is η, that is, Pr = ηP s Therefore, the power allocated to radar detection is P r = ηρP.

[0152] To evaluate the performance of the algorithm proposed in this application, three standard schemes are compared. The first is the passive RIS-assisted dual-functional radar communication scheme, the second is the dual-functional radar communication scheme without RIS assistance, and the last is the active RIS-assisted communication scheme only. To ensure a fair comparison, the simulation parameters of all schemes are the same.

[0153] Figure 3 The convergence of the alternating optimization scheme proposed in this application, as well as the convergence of the other three schemes, are given. In all schemes, it is assumed that the total power P of the system is 20 dBm. In the passive RIS-assisted DFRC and DFRC schemes without RIS, radar sensing requires 60% of the total power budget. In the two schemes of active RIS-assisted communication only and active RIS-assisted DFRC, the power splitting ratio between the active RIS and the transmitter is set to 0.8, and the power splitting ratio for radar sensing in active RIS-assisted DFRC is set to 0.75, so that the radar detection power is the same as that of passive RIS-assisted DFRC. From Figure 3 it can be seen that all schemes converge. Compared with active RIS-assisted communication only, the weighted sum rate (WSR) of active RIS-assisted DFRC is reduced by 4 bps / Hz because part of the power in DFRC is used to construct the beam pointing to the target, thereby reducing the power available for communication. At the same time, since the active RIS can effectively resist the multiplicative fading effect, the method proposed in this application has a WSR 3 bps / Hz higher than that of the passive RIS-assisted DFRC method.

[0154] Figure 4 The beam patterns of active RIS and passive RIS-assisted DFRC are given. In the above two schemes, the total system power is fixed at 20 dBm, the number of reflection units on the RIS is 36, the power budget for radar detection is 0.6 of the total power budget, and the total power splitting ratio ρ of the active RIS-assisted DFRC system is set to 0.8. It can be seen that the power allocated to radar sensing in both schemes meets the requirements of the constraints. In addition, the peak value in the RIS direction proves the effectiveness of communication. However, the communication peak value of the passive RIS-assisted DFRC scheme is higher than that of the active RIS scheme because a part of the total power of the system in the active RIS scheme is allocated to the active RIS, resulting in less available power in DFRC than in the passive RIS scheme, indicating that in the active RIS scheme, DFRC places more power on radar detection, and the communication performance can be compensated by the active RIS.

[0155] Figure 5The relationship between the number of RIS reflection units and the weighted sum rate (WSR) is given, where the total system power is still set to 20 dBm, the radar detection power ratio ηρ is 0.6, and the power splitting ratio parameter ρ of DFRC and the base station (BS) is set to 0.8. It can be seen that the WSR of all four schemes increases with the increase in the number of RIS reflection units. In addition, the schemes using RIS can achieve a higher WSR than those without RIS. When the number of RIS reflection units reaches 256, the performance of passive RIS-assisted DFRC is close to that of active RIS-assisted DFRC, which indicates that when the number of RIS reflection units is large, the power allocated to each reflection unit by the limited power of active RIS is very small, resulting in the performance of active RIS dropping to the same level as that of passive RIS.

[0156] Figure 6 The relationship between the weighted sum rate (WSR) and the total system power is given, where the number of RIS reflection units and the radar detection power ratio ηρ are set to 36 and 0.6 respectively, and the power splitting ratio of the total DFRC / BS system power is set to 0.8. It can be seen that the WSR of all four schemes increases with the increase in the total power. In addition, the schemes using RIS can significantly improve the WSR, while the WSR of the scheme without RIS only has a slight increase. This is because in the case without RIS, the channel between DFRC and communication users is relatively weak, and even with a large total power, the increase in WSR is limited. This is consistent with the above analysis, that is, the WSR of active RIS only assisting communication is better than the other two DFRC schemes, and the WSR of active RIS-assisted DFRC is higher than that of passive RIS.

[0157] Figure 7 The relationship between the required radar detection power and the weighted sum rate (WSR) is given, where the total system power and the number of RIS reflection units are Figure 6 set the same. In the scheme of active RIS, the power splitting ratio ρ of DFRC is 0.8, and the value range of the radar detection power ratio η is 0.1 - 0.9, and the corresponding radar detection power is determined by P r = ηρP. It can be seen that when the required radar detection power increases, the WSR of both active and passive RIS schemes decreases, which indicates that increasing the power allocated to radar detection in the DFRC system comes at the cost of reducing the available power for communication, resulting in a decrease in WSR. In addition, although the WSR of active RIS-assisted DFRC is higher than that of passive RIS, as the required radar detection power increases, the WSR of the scheme using active RIS drops faster than that of the scheme using passive RIS. This is because in the case of using active RIS, the power needs to be allocated to DFRC and active RIS. Therefore, as the radar detection power increases, the communication power drops faster when using active RIS than when using passive RIS, resulting in a faster decrease in WSR.

[0158] In addition, we study the impact of the radar detection power splitting ratio η on the WSR by limiting the detection power of DFRC. Set the total system power P t = 20 dBm and the detection power is P r = 60 mW. According to the formula P r = ηρP, when P t and P r are fixed, ηρ should be a constant, that is, 0 ≤ η, ρ ≤ 1. Set the range of η to be within 0.6 - 1. From Figure 8 it can be seen that as η increases, the WSR first increases and then decreases, and forms a peak (about 9 bps / Hz) at η = 0.7. The above downward trend is because the increase in radar detection power requires more power, thus reducing the available communication power and resulting in a decrease in WSR. In addition, in the upward trend, when η approaches 0.6, almost all the power is required for radar detection, which leads to a lower WSR. While meeting the radar detection performance, the available communication power increases with the increase of η, making the WSR also increase accordingly.

[0159] Figure 9 shows the relationship between the power splitting ratio ρ and the WSR, where the total system power and the radar detection power settings are the same as Figure 8 and ρ is limited between 0.6 - 1. It can be seen that, similar to Figure 8 , as ρ increases, the WSR of the system first increases and then decreases, and reaches a peak at ρ = 0.9. The decrease in WSR is because the power allocated to the active RIS decreases with the increase of ρ, making it difficult for the system to resist the multiplicative fading effect. In addition, when ρ is small, the power used for communication by DFRC is limited, resulting in a small WSR. However, as ρ increases, the power used for communication in DFRC also increases.

[0160] This application effectively proves that using an active RIS in a DFRC system can enhance the communication performance and sensing performance of the dual - function radar. The proposed joint optimization algorithm for the transmit beamforming matrix, active RIS amplification factor matrix, and phase - shift matrix shows that under the condition of ensuring a certain radar detection power, a constant - modulus transmit waveform, and a limited power budget, the weighted sum - rate at the communication user is significantly improved. The simulation results verify the effectiveness of the algorithm, indicating that the active - RIS - assisted DFRC system is superior to the passive - RIS - assisted DFRC system and the non - RIS - assisted DFRC system.

[0161] Explanation about the theorem:

[0162] A: Proof of Theorem 1

[0163] To derive a closed - form expression for the mean - square error (MSE), it is necessary to Substituting into the MSE, we have

[0164]

[0165] Since the communication symbol \(x\), the noise \(n_1\) at the RIS, and the noise \(n\) at the receiver of the communication user k are independent of each other,

[0166] Therefore

[0167]

[0168] In addition, assume that the communication symbols of different communication users are independent, that is

[0169]

[0170] Based on this characteristic above, we have

[0171]

[0172] Substituting Equation (39) and Equation (41) into Equation (38), we can get

[0173]

[0174] B: Proof of Theorem 2

[0175] Denote

[0176]

[0177] which does not contain the optimization variable \(s\) k . Therefore, the MSE can be rewritten as

[0178]

[0179] Obviously, Equation (44) is a quadratic form with respect to \(s\) k . Due to the non-negativity of the norm operation, always holds, making Equation (44) convex. Therefore, the optimal estimator can be determined by taking the derivative of \(e\) k , that is

[0180]

[0181] Due to the linear property of the derivative, the Wirtinger form partial derivative, and the independent assumption of the real and imaginary parts of the complex number, step (a) holds, that is

[0182]

[0183] Therefore, the optimal estimator of the minimum MSE is

[0184]

[0185] Substitute the optimal MMSE estimator into (44), and the corresponding MSE is

[0186]

[0187] C: Proof of Theorem III

[0188] To transform the constraint (11b) into a more tractable form, first process the left - hand side term as

[0189]

[0190] Therefore, the constraint (11b) can be rewritten as

[0191]

[0192] Let \(Z=(MI - aa^{\mathrm{H}})\), then we have H

[0193] Since \(a\) is a steering vector, \(aa^{\mathrm{H}}\) H is a matrix of rank 1, and it has only one eigenvalue, which is \(M\).

[0194] Therefore, \(Z=(MI - aa^{\mathrm{H}})\) has only one eigenvalue equal to 0, and the remaining eigenvalues are \(M\). Since all eigenvalues of \(Z\) are non - negative, \(Z\) is a positive semi - definite matrix, and the constraint (51) is convex. H

[0195] D: Proof of Theorem V Since \(\Theta\) is a diagonal matrix, and \(a\) and \(b\) are vectors, i.e.,

[0196]

[0197] Therefore, \(a^{\mathrm{H}}\Theta b\) can be expressed as H \(\Theta\) H

[0198]

[0199] where

[0200] In addition, \(a^{\mathrm{H}}\Theta D\Theta a\) can also be expressed as H \(\Theta\) H

[0201]

[0202] ​​​​The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A beam design method for assisting a dual-function radar communication system, characterized in that: The radar senses surrounding targets while providing communication services for multiple users. Active RIS is used to enhance the communication performance of the system. Under the conditions of ensuring a certain radar detection power, a constant modulus transmission waveform and a limited power budget, the weighted sum rate of communication users is maximized by jointly designing the radar's transmit beamforming and the active RIS's reflected beamforming. The communication function of the radar system is enhanced by an efficient alternating optimization algorithm based on weighted minimum mean square error and fractional programming.

2. The beam design method for the auxiliary dual-function radar communication system according to claim 1, characterized in that: This is achieved through the following process: Step 1: Input the corresponding channel information, including the channel h between the radar and the user. d，k , the channel G between the radar and the active RIS, the channel h between the active RIS and the user r，k , the angle φ of the target relative to the radar and the dynamic noise power of the active RIS and channel Gaussian white noise power And set the total power budget P of the radar and active RIS, the radar power allocation ratio ρ, and the power allocation ratio η for sensing on the radar; Step 2, initialize the radar's transmit beam T, the active RIS's amplification factor matrix A and phase shift matrix Θ, and the auxiliary variable ε by randomization; Step 3, fix A and Θ, and estimate the symbol by minimizing the linear With real communication symbol x k The MMSE between the two solves the linear estimate s MMSE ; Step 4: According to s MMSE The corresponding minimum mean square error e MMSE Calculate the weighting coefficient ω; Step 5, optimize the WMMSE problem corresponding to the weighted coefficient ω, transform the original WMMSE problem into a semi-positive definite programming problem through convex quadratic transformation and homogenization, use the SDR method and CVX toolbox to solve W, and restore the columns t of T through Gaussian randomization or maximum eigenvalue approximation method k ; Step 6: fix T, use Lagrange dual transformation to convert the original weighted sum rate maximization problem into an optimization problem about Ψ and auxiliary variable α, and solve the optimal value of α by taking the first-order partial derivative method under the condition of fixed Ψ based on the alternating optimization method; Step 7, after calculating the optimal α, optimize Ψ, and convert the fractional programming problem into an optimization problem about Ψ and ε that only contains quadratic terms and linear terms by using the auxiliary variable ε initialized in step 2; first, under the condition of given Ψ, the optimal ε is solved by taking the first-order partial derivative of the objective function, and after obtaining the optimal ε, the objective function and Ψ in the constraint are separated from other matrices in the form of vector ψ through matrix transformation to form a standard quadratic constrained quadratic programming problem, and Ψ is solved using the CVX toolbox, and then A and Θ are solved; Step 8: Calculate the user sum rate R based on T, A and θ. If R does not meet the convergence condition, return to step 3; if R meets the convergence condition, output the optimal transmit beam T, the amplification factor matrix A and phase shift matrix θ of the active RIS, the user sum rate R and the radar detection power P. r .

3. The beam design method for the auxiliary dual-function radar communication system according to claim 2, characterized in that: The steps 3 to 7 adopt an iterative alternating optimization method, and each iteration alternately optimizes the transmit beamforming variables and the reflective beamforming variables, that is: ...T k →Ψ k →T k+1 →Ψ k+1 ..., Each iteration can ensure the convergence of the alternating optimization algorithm.

4. The beam design method for the auxiliary dual-function radar communication system according to claim 3, characterized in that: The iterative alternating optimization method is as follows: first, A and Θ are fixed, and the transmit beamforming matrix T is optimized using a weighted minimum mean square error framework; then T is fixed, and A and Θ are optimized using fractional programming.

5. The beam design method for the auxiliary dual-function radar communication system according to claim 2, characterized in that: The implementation process of step 3 is as follows: The amplified phase shift matrix Ψ of the active RIS is fixed, which is the product of A and Θ, and a linear estimation factor s is introduced at the communication user k. k , calculate the linear estimate symbol And calculate the linear estimate symbol With the real symbol x k The mean square error between s and s is used to transform the weighted sum rate maximization problem into an equivalent WMMSE optimization problem. k is convex, and the optimal linear estimation factor is derived 6. The beam design method for the auxiliary dual-function radar communication system according to claim 2, characterized in that: The implementation process of step 4 is as follows: Calculate the minimum mean square error And by calculating the weighted MMSE coefficients, the weighted sum rate maximization problem of transmit beamforming is transformed into an MMSE problem.

7. The beam design method for the auxiliary dual-function radar communication system according to claim 2, characterized in that: The implementation process of step 6 is as follows: After fixing the transmit precoding matrix W, an auxiliary variable α is introduced and the alternating optimization method is used to solve the optimal α when Φ is fixed. * .

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