Transmit waveform and reflected beamforming joint design method for intelligent reflecting surface assisted radar communication integrated system

Abstract

Dual-Function-Radar-Communication (DFRC) systems can alleviate the spectrum congestion problem by sharing hardware platforms, but the complex wireless environment will affect its performance. Reconfigurable Intelligent Surface (RIS) can effectively improve this problem. This paper studies a joint design method of DFRC transmit waveform and RIS reflection beamforming, which minimizes the Cramer-Rao bound of radar parameter estimation and takes the communication user signal-to-noise ratio requirement as a constraint under the symbol-level precoding system. The proposed joint design problem is formulated as a non-convex optimization problem, which is solved by using the alternating optimization and successive convex approximation (SCA) technique, and the penalty function is introduced to ensure feasibility. The transmit waveform sub-problem is transformed into a convex problem by Shur relaxation; the RIS reflection coefficient sub-problem is iteratively optimized by using the difference convex function processing and SCA. Numerical results show that the proposed algorithm can improve the radar parameter estimation and communication performance simultaneously.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, and specifically relates to a method for the joint design of transmitted waveform and reflected beamforming in an integrated intelligent reflector-assisted radar communication system. Background Technology

[0002] With the rapid growth in demand for wireless applications, the radio frequency spectrum is becoming increasingly congested, and spectrum sharing is considered a necessary solution. In practice, many radar and wireless communication systems have overlapping spectrums and similar RF front-end structures, allowing them to share spectrum and hardware platforms. This situation has spurred the development of Dual-Function Radar-Communication (DFRC) technology to fundamentally solve the mutual interference problem between the two. Currently, based on different focuses, DFRC waveform design can be divided into three categories: radar-centric, communication-centric, and joint optimization of radar and communication functions. Among them, DFRC with joint optimization of radar and communication functions adopts a shared waveform design approach, without imposing specific structural constraints on the waveform form. It can be flexibly adjusted directly according to radar and communication performance requirements, making it one of the current hot topics.

[0003] In radar, the Cramere-Rao bound (CRB) is a crucial performance indicator in target parameter estimation, providing a lower bound on the variance of unbiased parameter estimation as a fundamental performance limit. In communication, traditional linear block-level precoding schemes cannot guarantee communication performance for every user, only average performance. In contrast, Symbol-Level Precoding (SLP) can utilize known symbol information to transform destructive multi-user interference into constructive interference (CI), achieving more reliable multi-user communication. Furthermore, for radar functions, SLP allows for the design of instantaneous transmission waveforms in each snapshot, providing greater degrees of freedom.

[0004] In practical applications, the performance of DFRC systems largely depends on the wireless propagation environment. However, obstacles are unavoidable in real-world scenarios, affecting the normal operation of radar and communication functions. The emergence of Reconfigurable Intelligent Surfaces (RIS) offers a novel solution to this problem. RIS adjusts the phase shift of the incident signal by modifying the reflecting elements, enabling reconfiguration of the wireless propagation environment. In systems involving RIS, traditional algorithms based on semidefinite relaxation typically ignore the resulting rank-one constraint and reconstruct a rank-one solution through a randomization step, but this may be infeasible, thus requiring better processing methods.

[0005] Based on the above advantages, this invention designs a RIS-assisted DFRC system based on SLP and customizes a special method to solve the joint design problem of transmit waveform and beamforming. Summary of the Invention

[0006] The purpose of this invention is to propose a joint design method for transmit waveform and reflected beamforming in a smart reflector-assisted radar-communication integrated system. This invention proposes an algorithm based on Alternating Optimization (AO), Shure relaxation, Successive Convex Approximation (SCA), and penalty methods for the joint design of transmit waveform and reflected beamforming in a RIS-assisted DFRC system. Results show that the design of this invention outperforms traditional RIS-assisted DFRC systems. The specific steps of the joint design method for transmit waveform and reflected beamforming in a RIS-assisted DFRC system are as follows:

[0007] Step 1: Construct a joint design optimization problem for the transmit waveform and reflected beamforming of the RIS-assisted DFRC system. The radar optimization adopts the minimum CRB criterion, and the communication constraint adopts the minimum signal-to-interference-plus-noise ratio (SINR) requirement of the user under the CI precoding criterion.

[0008] Step 2: Use the AO framework to decouple the variables, resulting in the emission signal optimization subproblem and the reflection vector optimization subproblem.

[0009] Step 3: By introducing auxiliary variables and the Shure relaxation technique, the transmission signal optimization subproblem is transformed into a convex optimization problem, which is then effectively solved using existing convex optimization techniques.

[0010] Compared with existing systems, the RIS-assisted DFRC system of the present invention has the following advantages:

[0011] (1) Compared with the traditional RIS-assisted DFRC system based on block-level precoding, the present invention is based on symbol-level precoding system, which can improve the accuracy of radar target detection parameter estimation while ensuring the minimum SINR requirement of users.

[0012] (2) By introducing RIS, this invention realizes the radar target detection task in complex environments and greatly improves radar performance while ensuring user communication quality. Attached Figure Description

[0013] To more clearly illustrate the embodiments of this application or the existing technical solutions, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 Comparison of CRB performance for estimating target parameters in different systems;

[0015] Figure 2 The impact of the number of RIS array elements on the target parameter estimation CRB in different systems;

[0016] Figure 3 The impact of communication user SINR requirements on target parameter estimation CRB in the algorithm of this invention under different numbers of users;

[0017] Figure 4 The impact of the number of RIS array elements in the algorithm of this invention on the target parameter estimation CRB under different numbers of users. Detailed Implementation

[0018] The present invention, namely a method for the joint design of transmit waveform and reflected beamforming for a RIS-assisted DFRC system, is further described below with reference to the accompanying drawings and examples.

[0019] This invention presents a joint design method for transmit waveform and reflected beamforming in a RIS-assisted DFRC system. Employing an alternating optimization approach, and utilizing SCA and penalty methods, this invention proposes an efficient algorithm for the joint design of transmit waveform and reflected beamforming in a RIS-assisted DFRC system within an AO framework. The basic idea of ​​the algorithm is to alternately optimize the transmit signal matrix and the RIS reflection coefficient vector. The transmit signal matrix subproblem can be transformed into a convex problem and effectively solved by introducing auxiliary variables and using Shure relaxation techniques. The RIS reflection coefficient vector subproblem is solved iteratively using the SCA algorithm, and a solution approximating rank-one is constructed by combining it with the penalty method. The specific implementation steps of this method are as follows:

[0020] Step 1: For the joint design problem of transmit waveform and reflected beamforming in a RIS-assisted DFRC system, the criterion is to minimize the CRB of radar parameter estimation, and the SINR requirement of communication users under the CI precoding criterion is used as a constraint. Consider a RIS-assisted DFRC system with M base station antennas and N RIS reflector array elements, which are uniform linear arrays. The base station serves U single-antenna users and simultaneously detects point targets. The point targets are only located on non-line-of-sight paths, while the communication users are located on both line-of-sight and non-line-of-sight paths. Let the channel vectors from the base station and the RIS to the u-th user be respectively... and The Rayleigh fading channel from the base station to the RIS is represented as follows:

[0021]

[0022] Where κ is the Rayleigh factor, and the line-of-sight channel from the base station to the RIS is... The guide vectors are represented as follows:

[0023]

[0024] Where θ R With θ B These are the departure angle and arrival angle from the base station to the RIS, respectively. Let the reflection coefficient matrix of the RIS be Φ = diag(v), and the total channel from the base station to the user be expressed as:

[0025]

[0026] Define φ as half the angle of the CI region, and let s be the expected received symbol for the u-th user at time l. u,l Therefore, under the CI precoding criterion, the distance from the actual received noise-free signal of the u-th user to its decision boundary is expressed as:

[0027]

[0028] Define the minimum SINR required for the u-th user as Γ u The received noise power is The distance from the CI boundary to the decision boundary under the minimum received SINR requirement is expressed as:

[0029]

[0030] Define the radar received noise power as The estimated CRB at angle θ is expressed as:

[0031]

[0032] Where α is the complex channel coefficient, B = G T Φ T a(θ)aT (θ)ΦG is the channel matrix through which the echo signal passes. Defined as the partial derivative of B with respect to θ. Let d be the steering vector of RIS at angle θ. RIS λ represents the spacing between adjacent RIS array elements, and λ is the carrier wavelength.

[0033] Let the transmitted signal matrix to be optimized be . R X =XX H RIS reflection coefficient vector Define d as the distance from the actual received noise-free signal of user u to its decision boundary under the CI precoding criterion. u，l The distance from the CI boundary to the decision boundary under the minimum received SINR requirement is The total energy emitted is P T The overall optimization model is expressed as:

[0034]

[0035] Step 2: Using an AO framework-based method, problem (27) is transformed into two relatively easy-to-solve subproblems to alternately optimize the transmitted signal matrix and the RIS reflection coefficient vector.

[0036] Given the RIS reflection coefficient vector v, removing irrelevant constant terms from the objective function transforms the communication constraint into a compact form, expressed as follows: in:

[0037]

[0038] Question (27) concerning X and R X The subproblem can be represented as:

[0039]

[0040] Given X and R X In the objective function, CRB is explicitly represented by v, as follows:

[0041]

[0042] Where R1 = diag(a) H (θ))G * G T diag(a(θ)), R2=diag(a H (θ))G * R X * G Tdiag(a(θ)). Similarly, let v represent the communication constraint, expressed as in:

[0043]

[0044] After removing irrelevant constant terms from the objective function, the subproblem of problem (27) with respect to v can be expressed as:

[0045]

[0046] Step 3: By introducing an auxiliary variable and using the Schuler relaxation technique, problem (29) is transformed into a convex problem that is easier to solve. An auxiliary variable u is introduced, the Schuler complement theorem is applied to the objective function, and the non-convex constraint R is applied... X =XX H When performing Shure relaxation, question (29) is transformed into:

[0047]

[0048] Where e l I represents the L×L identity matrix L The problem is a convex problem, which can be solved efficiently using existing convex optimization algorithms.

[0049] Step 4: By introducing auxiliary variables and combining the SCA algorithm and penalty method, problem (32) can be transformed into a convex problem for iterative solution. The following matrix is ​​defined to handle the constant modulus constraint:

[0050]

[0051] Problem (32) is equivalent to:

[0052]

[0053] Introducing two auxiliary variables u1 and u2, and using the Schur complement theorem, we transform them into convex positive semidefinite constraints. Problem (35) is equivalently transformed into:

[0054]

[0055] The objective function of problem (36) can be transformed by algebraic transformation into the sum of convex and concave functions, defined as:

[0056]

[0057] in:

[0058]

[0059] Problem (36) is considered as an objective function that is a difference convex function, i.e. For problems with non-convex rank-one constraints, the SCA algorithm and penalty method are used to handle the problem and the rank-one constraint. The basic process is as follows:

[0060] 1) In the iteration, the convex function is found using a first-order Taylor expansion. A linear lower bound Let the current iteration number be r, which is defined as:

[0061]

[0062] 2) Replace with Ignoring the rank-one constraint, the subproblem under the SCA algorithm in the r-th iteration is constructed as follows:

[0063]

[0064] This problem is a convex problem and can be solved using existing convex optimization algorithms.

[0065] 3) When the SCA loop converges, a generally accepted result will be obtained. The suboptimal solution. (Constraints) Equivalent conversion in for The largest eigenvalue is determined and transformed into a differentiable form, which is then used as a penalty term in the objective function. Using the suboptimal solution obtained through SCA algorithm iterations as the initial value, the rank-one constraint is approximated iteratively. In the (p+1)th iteration of the penalty method, the optimization problem is expressed as:

[0066]

[0067] in for The eigenvector corresponding to the largest eigenvalue.

[0068] The specific process for solving problem (36) is as follows:

[0069] 1) Input parameters F i，l Convergence condition δ th

[0070] 2) Initialization settings: r = 0, v (0) ,

[0071] 3) Start the iteration:

[0072] i. Calculate using equation (39)

[0073] ii. Update via (40)

[0074] iii.r = r + 1

[0075] 4) Stop the loop if the objective function converges or reaches the upper limit of the number of iterations.

[0076] 5) Initialization settings: p = 1,

[0077] 6) Start iteration:

[0078] i. Update via (41)

[0079] ii. If Then ρ = 2ρ, otherwise p = p + 1.

[0080] 7) Stop the loop if the objective function converges or the maximum number of iterations is reached.

[0081] 8) Output And reconstruct it into vector v

[0082] In summary, the complete solution process for the joint design method of transmit waveform and reflected beamforming of the RIS-assisted DFRC system based on the AO framework is as follows:

[0083] 1) Input parameter B, γ i P T

[0084] 2) Initialization settings: r = 1, v (0)

[0085] 3) Start iteration

[0086] i. Calculate X through (33) (r+1)

[0087] ii. Update using formulas (35) to (41)

[0088] iii.r = r + 1

[0089] 4) Stop the loop if the objective function converges or reaches the upper limit of the number of iterations.

[0090] Example

[0091] The invention uses Matlab simulations to further illustrate the joint design method for transmit waveform and reflected beamforming in a RIS-assisted DFRC system.

[0092] 1) Simulation system parameter settings

[0093] Unless otherwise specified, the number of transmit antennas M=8, the number of RIS array elements N=32, the number of transmit signal snapshots L=50, and the total transmit power P in each simulation of the DFRC system. T =30dBm, noise σ R =σ u = -80dBm, u = 1, ..., U, all users have the same SINR requirement, i.e., Γ u Let Γ = , u = 1, ..., U. The base station, RIS, and point target are located at coordinates (0m, 0m), (4m, 5m), and (4m, 0m), respectively. The four users are located at coordinates (40m, 0m), (40m, -10m), (50m, -10m), and (50m, 10m), respectively. Consider a distance-dependent path fading model. K0 = -30dB, d0 = 1m, the fading indices on the base station-RIS, RIS-user, and base station-user links are 2.2, 2.2, and 3, respectively, and the Rice factor is set to 0.5.

[0094] 2) Compare system settings

[0095] To visually demonstrate the changes in CRB as the objective function under different scenarios, this embodiment uses the proposed method (SLP) to plot CRB variation graphs and compares them with several other typical RIS-assisted system design methods: a RIS-assisted DFRC system (BLP) using block-level precoding for communication constraints; a symbol-level DFRC system (max SNR) based on maximizing radar detection signal-to-noise ratio for radar optimization criteria; a symbol-level DFRC system (Random RIS) under random RIS reflection coefficients; and a RIS-assisted radar-only system (Raday only). The unit for CRB on the vertical axis of the image is dB.

[0096] 3) Simulation experiments and result analysis

[0097] The present invention conducted four simulation examples, covering different communication parameters, the number of RIS array elements, and the changes in CRB under different methods. Figure 1 For the case where the number of users U = 4, Figure 2 This is for the case where the number of users U = 2.

[0098] pass Figure 1It can be seen that the algorithm proposed in this invention outperforms other cases in terms of performance under different SINR requirements. Under low communication service quality requirements, the CRB value in the SLP case is about 0.02 dB higher than that in the BLP and Radar-only cases. This is because under low communication service quality requirements, the user's SINR requirement is easily met, and the radar function dominates the dual-function waveform optimization, thus closely resembling the radar-only case. Furthermore, due to the randomness of BLP, under low user SINR requirements, the CRB value of BLP is about 0.02 dB lower than that of SLP, which can be ignored. However, under high SINR requirements, the radar performance of SLP shows superiority. It can be seen that as the communication service quality requirement further increases, the CRB in the SLP case is lower than that in the BLP case. This is because the SLP design provides greater freedom for radar detection functions compared to BLP.

[0099] pass Figure 2 It can be seen that, under different numbers of RIS array elements, the SLP case still outperforms the max SNR, Random RIS, and BLP cases. The performance gap between the SLP and Random RIS cases increases with the increase of N, which reflects the importance of optimizing the reflection coefficient.

[0100] pass Figure 3 It can be seen that both the increase in the number of users and the increase in users' SINR requirement Γ lead to a decrease in radar performance, reflecting the trade-off between radar and communication performance in the DFRC system. This demonstrates the feasibility of the algorithm proposed in this invention.

[0101] pass Figure 4 It can be seen that as the number of RIS array elements N increases from 4 to 48, the CRB decreases by 28.71 dB, 28.42 dB, 28.33 dB, and 27.78 dB for U = 1, 2, 3, and 4, respectively. This demonstrates the significant improvement that RIS brings to radar functionality, and this improvement slightly decreases as the number of users increases; that is, the performance gap between different users also slightly increases with the increase of N.

[0102] In summary, the method described in this invention exhibits excellent overall performance. Compared to other representative methods, the proposed method achieves the lowest CRB value, indicating optimal parameter estimation performance. When applied to a DFRC system, this invention can simultaneously guarantee the SINR requirements of communication users under the CI precoding criterion and ensure solution feasibility, demonstrating high practical value.

Claims

1. A joint design method for transmitted waveform and reflected beamforming in a dual-function radar-communication (DFRC) system assisted by a reconfigurable intelligent surface (RIS). Its features are reflected in the following: Based on Alternating Optimization (AO), Successive Convex Approximation (SCA) algorithm and penalty method, a joint design method for DFRC transmitted signal and RIS beamforming under the AO framework is proposed; this method is applicable to the optimization method of DFRC transmitted signal and RIS reflection coefficients with the criterion of minimizing the Cramér-Rao Bound (CRB) of radar parameter estimation and the constraint of the signal-to-interference-plus-noise ratio (SINR) requirement of communication users under the constructive interference (CI) precoding criterion. Within the AO framework, this algorithm reconstructs the original problem into a fractional optimization problem with equality constraints and a fractional optimization problem with constant modulus constraints; and employs methods such as Schur relaxation, SCA algorithm, and penalty methods to effectively solve the subproblems; specifically, it includes the following steps: S1. For the joint design problem of transmit waveform and reflected beamforming in a RIS-assisted DFRC system, the criterion is to minimize the CRB of radar parameter estimation, and the SINR requirement of communication users under the CI precoding criterion is used as a constraint. The number of base station antennas in the RIS-assisted DFRC system is defined as M, the number of RIS reflector array elements as N, the number of snapshots as L, the number of users per antenna as U, and the CRB of radar parameter estimation at angle θ as CRB(θ). The transmit signal matrix to be optimized is... R X =XX H RIS reflection coefficient vector Under the CI precoding criterion, the distance from the actual received noise-free signal of user u to its decision boundary is d. u，l The distance from the CI boundary to the decision boundary under the minimum received SINR requirement is The total energy emitted is P T Its optimization model is: Where tr(·) represents the operation of taking the trace of a matrix. Represents matrix R X It is a positive semi-definite matrix; S2. An AO-based approach is adopted to transform problem (1) into two relatively easy-to-solve subproblems, which are used to alternately optimize the transmitted signal matrix and the RIS reflection coefficient vector. S3. The subproblem concerning the transmitted signal matrix can be expressed as: Where B is the total channel through which the radar echo signal passes. Given its partial derivative with respect to the target direction, this invention transforms subproblem (2) into a convex problem that is easy to solve by introducing auxiliary variables and Schul relaxation; S4. Transforming the CRB and communication constraints into a form concerning v, the subproblem of the RIS reflection coefficient can be expressed as: Where R1 = diag(a) H (θ))G * G T diag(a(θ)), R2=diag(a H (θ))G * R X * G T diag(a(θ)), D=diag(0,1,...,N-1), by introducing auxiliary variables and Schuler's complement theorem to deal with the fractions in the objective function of problem (3), the problem can be transformed into an optimization problem with a difference convex function as the objective function and a rank-one constraint; the present invention solves complex non-convex optimization problems by using the SCA algorithm and penalty method.

2. The method for jointly designing the transmitted waveform and reflected beamforming of an integrated intelligent reflector-assisted radar communication system according to claim 1, characterized in that, In step S1, it is considered that the point target is located only on the non-line-of-sight path, while the communication user is located on both the line-of-sight and non-line-of-sight paths; let the channel vectors from the base station and RIS to the u-th user be respectively... and Base station to RIS channel representation Let the reflection coefficient matrix of RIS be... The total channel from the base station to the user is represented as: Define φ as half the angle of the CI region, and let s be the expected received symbol for the u-th user at time l. u，l Therefore, under the CI precoding criterion, the distance from the actual received noise-free signal of the u-th user to its decision boundary is expressed as: Define the minimum SINR required for the u-th user as Γ u The received noise power is The distance from the CI boundary to the decision boundary under the minimum received SINR requirement is expressed as: Define the radar received noise power as The estimated CRB at angle θ is expressed as: Where α is the complex channel coefficient, B = G T Φ T a(θ)a T (θ)ΦG, Let B be the partial derivative with respect to θ. Let d be the steering vector of RIS at angle θ. RIS λ represents the spacing between adjacent RIS array elements, and λ is the carrier wavelength.

3. The method for jointly designing the transmitted waveform and reflected beamforming of an integrated intelligent reflector-assisted radar communication system according to claim 1, characterized in that, Given the RIS reflection coefficient vector v, removing irrelevant constant terms from the objective function transforms the communication constraint into a compact form, expressed as follows: in: e l I represents the L×L identity matrix L The lth column; Problem (1) concerning X and R X The subproblem can be represented as problem (2); given X and R X In the objective function, CRB is explicitly represented by v, as follows: Similarly, let v represent the communication constraint, expressed as in: By removing irrelevant constant terms from the objective function, the subproblem of problem (1) with respect to v can be expressed as problem (3).

4. The method for jointly designing the transmitted waveform and reflected beamforming of an integrated intelligent reflector-assisted radar communication system according to claim 1, characterized in that, In step S3, by introducing auxiliary variables and Schur complement, problem (2) is transformed into a convex problem that is easier to solve; by introducing auxiliary variable u, the objective function is processed using the Schur complement theorem, and the non-convex constraint R is applied. X =XX H When performing Shure relaxation, question (2) is transformed into: This problem is a convex problem, which can be solved efficiently using existing convex optimization algorithms.

5. The method for jointly designing the transmitted waveform and reflected beamforming of an integrated intelligent reflector-assisted radar communication system according to claim 1, characterized in that, In step S4, by introducing auxiliary variables and Schur complement, and combining the SCA algorithm and penalty method, problem (3) can be transformed into a convex problem for iterative solution; the following matrix is ​​defined to handle constant modulus constraints: Problem (3) is equivalent to: Introducing two auxiliary variables u1 and u2, and using the Schur complement theorem, we transform them into convex positive semidefinite constraints. Problem (13) is then equivalently transformed into: The objective function of problem (14) can be transformed by algebraic transformation into the sum of convex and concave functions, defined as: in: Problem (14) is considered as a problem with a difference convex function as the objective function and a non-convex rank-one constraint. The SCA algorithm and penalty method are used to handle the problem and the rank-one constraint.

6. The method for jointly designing the transmitted waveform and reflected beamforming of an integrated intelligent reflector-assisted radar communication system according to claim 5, characterized in that, The objective function in subproblem (14) can be expressed as a difference convex function. Then, the SCA algorithm and penalty method are used to solve the problem. The basic process is as follows: 1) In the iteration, the convex function is found using a first-order Taylor expansion. A linear lower bound Let the current iteration number be r, which is defined as: 2) Replace with Ignoring the rank-one constraint, the subproblem under the SCA algorithm in the r-th iteration is constructed as follows: This problem is a convex problem, which can be solved efficiently using existing convex optimization algorithms. 3) When the SCA loop converges, a generally accepted result will be obtained. The suboptimal solution; constrain Equivalent conversion in for The largest eigenvalue is obtained and transformed into a differentiable form, which is then used as a penalty term in the objective function. Using the suboptimal solution obtained through SCA algorithm iteration as the initial value, the rank-one constraint is approximated through an iterative method; in the (p+1)th iteration of the penalty method, the optimization problem is expressed as: in for The eigenvector corresponding to the largest eigenvalue.

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