A DOA estimation precision optimization-oriented active STAR-RIS assisted ISAC joint beamforming design method

Abstract

With the evolution of 6G towards integrated communication and sensing and deep coverage, the traditional cellular architecture faces the problem of limited communication and sensing capabilities in complex shadowing scenarios. Although reconfigurable intelligent surfaces can improve communication quality by reconfiguring the wireless propagation environment, passive RIS with only single-sided reflection capability still has problems such as limited coverage in the ISAC scenario. Active simultaneous transmission and reflection reconfigurable intelligent surfaces have full spatial coverage and active amplification capability, providing a new technical approach to performance improvement for ISAC systems. Based on this, the present application studies the active STAR-RIS assisted ISAC system, takes the Cramer-Rao bound of the angle of arrival parameter as the sensing index, studies the joint beamforming design problem under different echo receiving mechanisms, and compares the performance of passive RIS, active RIS, passive TAR-RIS and active STAR-RIS. The simulation results show that the active STAR-RIS has better performance than other types of RIS.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and intelligent sensing technology, and in particular to an active STAR-RIS-assisted ISAC joint beamforming design method for optimizing DOA estimation accuracy. Background Technology

[0002] With the rapid development of 6G technology, higher demands are being placed on the intelligence and environmental awareness capabilities of IoT devices. Future wireless networks will not only need to provide high-quality communication services but also possess precise environmental awareness capabilities to meet the needs of intelligent IoT device development. However, traditional communication and sensing systems operate independently, resulting in low resource utilization and increased hardware design complexity and implementation costs. Integrated Sensing and Communication (ISAC) technology has emerged as a key technology driving 6G networks towards high data rates and intelligence. ISAC achieves deep integration of communication and sensing functions by sharing hardware facilities and spectrum resources on a single platform, significantly improving spectrum efficiency and energy efficiency while substantially reducing hardware costs and system complexity. Although ISAC technology has certain advantages in system performance and resource utilization efficiency compared to traditional communication and sensing systems, it faces numerous challenges in complex propagation environments. As signal propagation distances increase, path loss significantly intensifies. In non-line-of-sight (NLOS) scenarios, signals become more dependent on favorable environmental conditions, and the propagation path becomes more sensitive. Numerous obstacles and multipath scattering effects along the propagation path can easily obstruct line-of-sight (LOS) signals, severely limiting the coverage of communication and sensing systems under adverse channel conditions. These issues significantly impact the performance of ISAC systems, necessitating effective solutions. In recent years, reconfigurable intelligent surfaces (RIS), as an emerging cutting-edge technology, have demonstrated great potential in addressing the complexity of signal propagation environments. RIS consists of numerous low-cost passive reflective elements that can intelligently reflect and guide wireless signals by dynamically adjusting the phase shift and amplitude of these elements, thus reconstructing the signal propagation environment and improving the coverage and channel quality of communication and sensing. The advantages of RIS in reducing power consumption and enhancing flexible deployment capabilities have made its application in 6G networks highly anticipated.

[0003] The intelligent reflective surface RIS is highly compatible with the integrated sensing and communication ISAC system. Compared with traditional communication methods, it can improve spectral efficiency and sensing and communication quality, while significantly reducing system power consumption. However, in traditional passive RIS-assisted ISAC systems, multiplicative fading occurs due to multipath effects, environmental instability, long-distance round-trip and multi-hop transmissions, resulting in low sensing accuracy.

[0004] Active STAR-RIS combines the signal amplification capability of active STAR-RIS with the full-space coverage capability of STAR-RIS (transmission / reflection). It can simultaneously enhance the transmission-side communication link and the reflection-side sensing link in scenarios where the direct link from the base station is blocked, thereby improving the applicability of the integrated sensing system in complex obstructed environments. In contrast, existing passive STAR-RIS solutions typically only consider transmission / reflection control and energy allocation, making it difficult to characterize the power consumption and noise amplification effects of active amplification. Furthermore, they are usually constructed only for a single-sided reflection link, failing to describe the dual-link coupling relationship of transmission communication and reflection sensing in STAR-RIS. Therefore, to address the technical problem that the objective function, power constraints, and optimization variables in existing passive or active STAR-RIS solutions are not directly applicable to active STAR-RIS-assisted integrated sensing systems, it is necessary to reconstruct a joint optimization model that simultaneously considers transmission / reflection control, active amplification, noise propagation, and the coupling relationship between communication and sensing. Summary of the Invention

[0005] This invention provides an active STAR-RIS-assisted ISAC joint beamforming method for optimizing DOA estimation accuracy. Based on an active STAR-RIS-assisted ISAC system, this invention utilizes a dual-function base station to simultaneously perform multi-user communication and radar sensing tasks. The system is equipped with N... t Root transmitting antenna and N r A dual-function base station BS with one receiving antenna communicates with K single-antenna users and uses an M-element active STAR-RIS to detect a potential target. The number of antennas is set to N. r =N t=N. When the potential target is located in the base station's blind zone, the direct link between the base station and the target is blocked by obstacles. Since the direct link between the base station and the target is blocked, the transmitted signal reaches the target via an auxiliary reflection link of the active STAR-RIS and returns along the same path. It is assumed that the sensing space is located on the reflection side and the communication space is located on the transmission side. There is a single sensing target of interest in the sensing space, and K single-antenna communication users in the communication space. It is assumed that the direct link between the BS and the target is blocked. To address the severe path loss, an active STAR-RIS-assisted ISAC structure is proposed, which installs a dedicated low-cost sensor with a uniform linear array of M elements on the base station. Specifically, the propagation loss includes at least: the first segment propagation loss of the link from the base station to the active STAR-RIS, the second segment propagation loss of the link from the active STAR-RIS to the communication user, and the third segment propagation loss of the link from the active STAR-RIS to the sensing target. Furthermore, this scenario considers a coherent time block of length L, during which the communication channel and sensing target parameters remain approximately constant.

[0006] Based on the above system settings, the method of the present invention includes the following steps:

[0007] S1. Construct an active STAR-RIS-assisted ISAC system model; the system includes a dual-function base station, an active STAR-RIS, multiple communication users, and sensing targets. The active STAR-RIS has transmission, reflection, and active amplification functions, used to assist communication users in receiving signals through a transmission link and to assist sensing target echo transmission through a reflection link when the direct link from the base station is blocked. The dual-function base station generates a transmission signal based on actual communication service data and sensing task requirements. The transmission signal includes communication signal components and sensing signal components, and is sent to the active STAR-RIS-assisted propagation environment after precoding.

[0008] S2. Based on the system model in step S1, construct the transmission-side communication receiving signal model and the reflection-side sensing echo signal model respectively. In the communication receiving signal model, the combined influence of the active STAR-RIS transmission coefficient on the communication signal, interference signal, and active amplification noise is considered. In the sensing echo signal model, the combined influence of the active STAR-RIS reflection coefficient on the target echo signal and sensing link noise is considered. The signal-to-interference-plus-noise ratio (SINR) of each communication user is used as the communication performance index, and the Cramer-Rao lower bound (CRB) of the target DOA estimation is used as the sensing performance index, resulting in the communication constraint expression and sensing index expression of the system model. Compared to the passive STAR-RIS-assisted ISAC system, the sensing index expression and communication constraint expression further introduce active amplification noise and its corresponding power consumption. Compared to the existing active RIS-assisted ISAC system, the sensing index expression and communication constraint expression simultaneously express the dual-link coupling relationship between the transmission-side communication link and the reflection-side sensing link. Based on this, a joint optimization problem is constructed with the objective of minimizing the target DOA estimate CRB, satisfying multi-user SINR constraints, base station power constraints, active STAR-RIS power constraints, and transmission / reflection coefficient constraints.

[0009] S3. Based on the joint optimization problem obtained in step S2, initialize the base station beamforming matrix, the active STAR-RIS transmission coefficient matrix, and the reflection coefficient matrix, and decompose the joint optimization problem into a base station beamforming sub-problem and an active STAR-RIS transmission coefficient and reflection coefficient optimization sub-problem;

[0010] S4. Under the condition of fixed active STAR-RIS transmission coefficient and reflection coefficient, the base station beamforming subproblem is equivalently transformed; the subproblem is transformed into an optimization problem about the transmit covariance matrix, and the optimal covariance matrix is ​​solved using the positive semidefinite relaxation method, thereby restoring the communication beamforming vector and the sensing beamforming vector.

[0011] S5. Under the condition of the beamforming matrix obtained in step S4, optimize the subproblems of transmission coefficient and reflection coefficient of active STAR-RIS; by introducing auxiliary variables and combining the MM method and SCA method to construct convex surrogate functions for the higher-order non-convex terms in the objective function and constraints, solve for the updated transmission coefficient matrix and reflection coefficient matrix of active STAR-RIS; among which, the transmission coefficient mainly affects the communication link, and the reflection coefficient mainly affects the sensing link. The two together affect the amplification noise, power consumption and communication sensing performance of active STAR-RIS. Therefore, the optimization process is different from the scheme of only optimizing the passive transmission / reflection phase shift or a single active reflection coefficient.

[0012] S6. Based on the current iteration results obtained in steps S4 and S5, determine whether the target value or CRB change in two adjacent outer iterations meets the preset convergence condition. If not, return to execute steps S4 and S5. If so, output the optimized base station beamforming matrix, active STAR-RIS transmission coefficient matrix, and reflection coefficient matrix to optimize the target DOA estimation accuracy under the condition of meeting communication performance constraints.

[0013] In step S1, the system includes a dual-function base station, an active STAR-RIS, K single-antenna communication users, and a sensing target. The direct link between the dual-function base station and the sensing target and communication users is blocked. The active STAR-RIS includes M units capable of simultaneous transmission and reflection modulation. Specifically, since the target is located in the base station's blind zone and the direct link between the base station and the target is blocked, the system's communication link will rely on the transmission side's "base station → active STAR-RIS → user" direct link. Simultaneously, since the sensing receiver is co-located with the base station, the scattered / echo signal generated by the target returns to the base station receiver after being reflected by the active STAR-RIS; that is, the echo propagates along a two-way closed-loop link of "base station → active STAR-RIS → target → active STAR-RIS → base station".

[0014] In step S2, the specific methods for constructing the communication received signal model, the sensing echo signal model, and the CRB are as follows:

[0015] S2.1 Define the active STAR-RIS transmission and reflection coefficient matrix;

[0016] ;

[0017] The reflection phase shift matrix and the transmission phase shift matrix are respectively represented as:

[0018] ;

[0019] The reflection amplitude matrix and the transmission amplitude matrix are respectively represented as:

[0020]

[0021] .

[0022] S2.2 Construct the transmission signal model of the t-th time slot of a dual-function base station;

[0023]

[0024] Among them, in the formula This represents the transmit beamforming precoding matrix used for communication signals. This represents the transmit beamforming matrix used for sensing signals, where the communication signal is... And satisfy Radar sensing signals and satisfy , For ease of subsequent representation, a beamforming joint matrix is ​​defined. and joint signals .

[0025] S2.3 Construct the received signal model of the Kth communication user and build the SINR expression for the Kth user;

[0026]

[0027] Among them This represents the baseband channel matrix between BS and user k. This indicates the channel between the BS and the active STAR-RIS. This represents the channel between the active STAR-RIS and user k, using advanced channel estimation techniques. It is assumed here that the channel state information has been fully acquired. This represents the white Gaussian noise (AWGN) between the BS and the active STAR-RIS. This represents the AWGN transmitted via active STAR-RIS to user k. Based on the received signal, the SINR expression for the k-th communication user is obtained as follows:

[0028]

[0029] Here, , represents the equivalent channel between the BS and the k-th user, and express The i-th column.

[0030] The SINR expression above reflects a re-characterization of communication metrics in active STAR-RIS scenarios: the communication user is located on the transmission side, and the transmission coefficient not only affects the desired communication signal and multi-user interference signals, but also the result of noise at the active STAR-RIS being amplified by the transmission link and propagated to the user end. Therefore, this SINR expression differs from the communication metrics in passive STAR-RIS scenarios that do not contain active amplification noise, and also differs from the communication metrics formed based on a single reflection link in ordinary active RIS scenarios.

[0031] S2.4 Construct a model of the echo signal of the sensing target;

[0032]

[0033] in It is the target's RCS. This represents the Loss of Target (LoS) channel from the active STAR-RIS to the target. , This represents the steering vector of the active STAR-RIS. This represents path loss, specifically The steering vector of the channel is represented by , where It is the DoA of the target relative to the active STAR-RIS. as well as These represent the AWGNs generated on the path from the active STAR-RIS to the target and the path from the active STAR-RIS back to the base station, respectively. The AWGNs generated on these paths undergo multiple attenuations along the link from the active STAR-RIS to the target, then reflected back to the active STAR-RIS, and finally transmitted back to the base station. Therefore, when the echo signal reaches the base station, its power is significantly lower than that of other signals and can be ignored. The echo signals are then stacked and vectorized to obtain the observed signal expression used for target parameter estimation.

[0034]

[0035] in The communication signal and the various noises generated in the path are simplified as follows: , , .

[0036] The aforementioned sensing echo signal model reflects a re-characterization of the sensing link in the active STAR-RIS scenario: the target is located on the reflecting side, and the reflection coefficient, while enhancing the target echo link, also alters the propagation and amplification characteristics of noise in the sensing link. Therefore, subsequent CRB derivation requires re-establishing the noise covariance and Fisher information matrix based on this reflecting side echo model to obtain a characterization of the sensing indicators under this model scenario.

[0037] S2.5 Construct the Fisher information matrix of the target parameters and derive the CRB expression;

[0038]

[0039] Based on this, the variable to be estimated can be obtained. CRB

[0040]

[0041] in , , .

[0042] As can be seen from the above CRB expression, the target perception accuracy index depends not only on the base station beamforming matrix and the reflection link gain, but also on the active STAR-RIS amplified noise and its power constraints. In other words, increasing the reflection coefficient amplitude may simultaneously enhance the target echo and noise terms. Therefore, the CRB index used in this invention is used to characterize the combined effect between signal enhancement, noise amplification, and power constraints, providing a basis for establishing subsequent joint optimization objectives.

[0043] S2.6, Construct a joint optimization problem;

[0044] Based on the reconstructed SINR and CRB expressions, the objective function, communication constraints, active STAR-RIS power constraints, and transmission / reflection coefficient constraints in the joint optimization problem are discussed. It can be observed that this optimization problem differs from the passive STAR-RIS optimization problem, which primarily revolves around transmission / reflection control, and also differs from the active RIS optimization problem, which revolves around a single reflection coefficient. The objective function and all constraints are coupled to varying degrees with the base station beamforming matrix, transmission coefficient matrix, and reflection coefficient matrix.

[0045]

[0046] Among the constraints , which represents the quality of service constraint for the kth communication user, used to ensure that the communication performance of each user is not lower than a preset threshold; This represents the power budget constraint of the active STAR-RIS, used to limit the sum of signal amplification power and noise amplification power in the transmission and reflection links; This represents the power budget constraint of the base station, used to limit the beamforming matrix; This indicates that the reflection phase and transmission phase of the nth element satisfy the unit mode constraint; This indicates that the active amplification of the nth unit on both the reflection and transmission sides is limited by the maximum amplification capability of the hardware. The objective function is derived from minimizing the CRB, since minimizing the CRB is equivalent to maximizing its denominator. Therefore, it is specifically expressed as:

[0047]

[0048] In step S4, the optimization method for the beamforming matrix is ​​as follows:

[0049] S4.1, Construct a beamforming optimization sub-problem;

[0050]

[0051] in

[0052]

[0053]

[0054]

[0055] S4.2 Introducing Auxiliary Variables And transform the objective function constraints;

[0056]

[0057] The above constraint can be further transformed into the following form using Schur complement.

[0058]

[0059] S4.3 Define the covariance matrix variables;

[0060]

[0061]

[0062] W i R is a rank-one Hermitian positive semi-definite matrix. w It is a Hermitian positive semi-definite matrix, i.e.

[0063]

[0064]

[0065] S4.4 Perform semidefinite relaxation treatment;

[0066]

[0067] S4.5, Restore the beamforming matrix;

[0068] The optimal solution to the semidefinite programming problem can be obtained using traditional convex optimization algorithms. Furthermore, once the optimal covariance matrix is ​​obtained from solving the SDP problem... The communication beam vector can then be recovered using the following closed-form expression. .

[0069]

[0070] The beamforming vector used for radar sensing can be calculated using Cholesky decomposition.

[0071]

[0072] in , and then combine and Thus, the optimization solution for the beamforming matrix is ​​completed.

[0073] In step S5, the optimization method for the active STAR-RIS transmission coefficient matrix and reflection coefficient matrix is ​​as follows:

[0074] S5.1 Construct the STAR-RIS coefficient optimization subproblem;

[0075] After obtaining the beamforming matrix in step S4, the original joint optimization problem is rewritten as a subproblem concerning the active STAR-RIS transmission coefficient matrix and the reflection coefficient matrix;

[0076]

[0077] in

[0078]

[0079]

[0080] S5.2 Reconstruct the STAR-RIS coefficient variables and transform the problem into an optimization problem;

[0081] definition At this point, the entire optimization problem can be reformulated as:

[0082]

[0083] in

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] Here Represents the set {1, 2} containing elements that are equal to or less than the set of elements that are equal to or less than Another different element, that is, if Then at this time, the corresponding ,if Then at this time .

[0095] S5.3 Introducing Auxiliary Variables and Then, the fractional objective function is reconstructed;

[0096]

[0097] The phase shift matrix is ​​fixed here. and At that time, auxiliary variables and The explicit optimal solution can be easily obtained, that is

[0098]

[0099] Received and After finding the optimal solution in the theory, the optimization problem of the phase shift matrix can then be reformulated as follows:

[0100]

[0101] S5.4 Construct a proxy function for the upper bound of the objective function in M / M;

[0102] For the first term of problem (0-36), based on the solution obtained in the nth iteration... It can be deduced that The upper bound is

[0103]

[0104] in , , However, the function It remains nonconvex, therefore, a tractor function for the optimization problem that is easy to handle is constructed through a second-order Taylor expansion. Here, we define...

[0105]

[0106]

[0107] Furthermore, through derivation, we can obtain

[0108]

[0109] in, Hessian matrix The largest eigenvalue, ,as well as Substituting these values ​​into the original problem, we can obtain the original function. proxy function

[0110]

[0111] in, .

[0112] S5.5 Constructing a proxy function for communication constraints;

[0113] Regarding the third term in problem (0-36), the term that clearly leads to non-convexity is... Therefore, a proxy function needs to be introduced here, as shown below.

[0114]

[0115] At this point, based on the aforementioned surrogate function, the constraints are transformed into...

[0116]

[0117] In the above formula, , .

[0118] S5.6 Define auxiliary variables and construct the upper bound surrogate function for the fourth term;

[0119] Regarding the fourth item of problem (0-36), the previously defined Here we will reuse this method, and define several new auxiliary variables as follows.

[0120]

[0121]

[0122]

[0123] Define an auxiliary function

[0124]

[0125] Its corresponding first and second derivatives can be expressed as follows:

[0126]

[0127]

[0128] At this time, the present invention will The upper bound surrogate function is represented as

[0129]

[0130] In the formula above, Represents the Hessian matrix The largest eigenvalue, , , , At the same time, because The inequality holds true, and This represents the Hessian matrix. The largest eigenvalue, and similar definitions exist, , .

[0131] Regarding the other part of this non-convex term Define the proxy function in the following way

[0132]

[0133] in, , In summary, the general surrogate function for this non-convex term is:

[0134]

[0135] in, , At this point, the optimization problem can be reformulated as follows:

[0136]

[0137] Update the auxiliary variables; use the iteratively optimized values ​​in the (S+1)th iteration. Then, auxiliary variables can be updated simultaneously. ;

[0138]

[0139] Finally, through alternating updates , , and The optimization problem is solved iteratively.

[0140] This invention also discloses an active STAR-RIS-assisted ISAC system for joint beamforming design. This system includes the following modules:

[0141] Parameter initialization module: used to obtain the system parameters of the active STAR-RIS assisted ISAC system, and initialize the base station beamforming matrix, the active STAR-RIS transmission coefficient matrix and reflection coefficient matrix, the number of iterations and the convergence threshold; the system parameters include at least the number of base station antennas, the number of STAR-RIS units, the number of communication users, target parameters, communication channel parameters, power budget parameters and communication quality constraint parameters.

[0142] CRB Calculation Module: This module is used to construct a communication received signal model and a sensed echo signal model based on the current base station beamforming matrix, active STAR-RIS transmission coefficient matrix, and reflection coefficient matrix. It also calculates the CRB value corresponding to the target DOA estimate based on the sensed echo signal model, and calculates the SINR value of each communication user based on the communication received signal model.

[0143] CRB Judgment Module: Used to determine whether the preset convergence condition is met based on the difference between the CRB value obtained in the current iteration and the CRB value in the previous iteration. When the preset convergence condition is met, the control algorithm ends the current iteration and enters the output module. When the preset convergence condition is not met, the control algorithm sequentially enters the beamforming optimization module and the STAR-RIS coefficient optimization module to continue updating the optimization variables.

[0144] Beamforming optimization module: Under the condition of fixed active STAR-RIS transmission coefficient matrix and reflection coefficient matrix, the joint optimization problem is transformed into a subproblem about the base station beamforming matrix; and the subproblem is subjected to equivalent transformation and semi-positive definite relaxation to solve for the updated base station communication beamforming vector and sensing beamforming vector, and then the updated base station beamforming matrix is ​​obtained.

[0145] The STAR-RIS coefficient optimization module is used to transform the joint optimization problem into a subproblem concerning the active STAR-RIS transmission coefficient matrix and reflection coefficient matrix under the condition of a fixed base station beamforming matrix. By introducing auxiliary variables and combining the MM method and SCA method, a convex surrogate function is constructed for the higher-order non-convex terms in the subproblem to obtain the updated active STAR-RIS transmission coefficient matrix and reflection coefficient matrix.

[0146] Output module: When the preset convergence condition is met, output the optimal value of the target DOA estimate CRB, as well as the base station beamforming matrix, active STAR-RIS transmission coefficient matrix and reflection coefficient matrix corresponding to the optimal value of the target DOA estimate CRB, as the joint optimization result of the active STAR-RIS assisted ISAC system.

[0147] Beneficial effects

[0148] This invention utilizes the simultaneous transmission, reflection, and signal amplification characteristics of an active STAR-RIS system. When direct links between the base station and communication users / sensing targets are obstructed, it can enhance the received signal of communication users through a transmission link and enhance the target echo signal through a reflection link, thereby expanding the coverage of the integrated sensing system and improving communication quality and target sensing capabilities in obstructed environments. Compared to traditional passive STAR-RIS solutions, this invention can further compensate for path loss in cascaded links, improving link gain in weak signal environments. Compared to traditional active RIS solutions, this invention can simultaneously serve communication users and sensing targets located on different spatial sides, improving the system's applicability in all-space sensing scenarios.

[0149] Meanwhile, since this invention targets the active STAR-RIS-assisted ISAC scenario, the active STAR-RIS simultaneously possesses transmission, reflection, and active amplification functions. This results in differences between the transmission-side communication link, the reflection-side sensing link, the active amplification noise propagation path, and the power consumption mode in the system compared to passive STAR-RIS or single-sided active RIS scenarios. Therefore, the performance characteristics described in existing passive STAR-RIS and active RIS scenarios are difficult to directly apply to the system model of this invention. Based on this, in the subsequent optimization model establishment, this invention reconstructs a communication SINR expression and a target DOA estimation CRB expression that match the active STAR-RIS link structure, and incorporates active amplification noise, transmission / reflection coefficients, noise propagation paths, and different power constraints into the objective function and constraint conditions. By constructing and solving the above-mentioned new joint optimization problem, it is possible to enhance the communication signal and target echo while suppressing the adverse effects of active noise amplification, making the optimization results more consistent with the actual working characteristics of active STAR-RIS, thereby improving the ability to meet communication performance constraints, reducing the target angle estimation CRB, and enhancing the joint optimization accuracy and overall performance of the integrated sensing system. Attached Figure Description

[0150] Figure 1 This is a system model diagram of the joint beamforming method for DOA estimation of the active STAR-RIS-ISAC system according to an embodiment of the present invention;

[0151] Figure 2 The flowchart illustrates the joint beamforming method for DOA estimation in an active STAR-RIS-ISAC system according to an embodiment of the present invention.

[0152] Figure 3 This is a schematic diagram illustrating the convergence of the algorithm of this invention.

[0153] in, Figure 3 The convergence performance of the proposed algorithm during the external iteration process is presented, where the horizontal axis represents the number of external iterations and the vertical axis represents the corresponding target DOA estimated CRB value. It can be seen that the CRB decreases rapidly in the first few iterations, indicating that the system's sensing performance is significantly improved after alternating optimization of the initial beamforming matrix and the STAR-RIS coefficient matrix. Subsequently, the CRB value fluctuates within a small range and gradually stabilizes, indicating that the algorithm converges to a stable solution within a finite number of iterations, demonstrating good convergence.

[0154] The fact that the curve does not exhibit a completely monotonically decreasing trend is likely due to several reasons. First, this patent employs an alternating optimization framework, where the beamforming matrix and STAR-RIS coefficient matrix are updated in blocks during each iteration of the outer layer. Since each optimization step is performed under the condition of a fixed set of variables, the overall objective value of the outer layer may not strictly maintain a successively monotonically decreasing trend. Second, the STAR-RIS coefficient optimization section introduces MM and SCA approximations, auxiliary variable updates, and convex surrogate functions. These processes ensure the solvability and local improvement of the current subproblem, but after mapping back to the original problem, the outer layer CRB value may exhibit a slight oscillation. Finally, the numerical solution process is also affected by CVX solution accuracy, stopping threshold settings, semi-definite relaxation, and beam recovery errors, resulting in small oscillations in the later stages of convergence.

[0155] Figures 4 to 7 This is a schematic diagram illustrating the specific experimental results of the present invention;

[0156] Specifically, considering the impact on base station transmission power, Figure 4 Reflecting on Increasing the base station transmit power from 25dBm to 50dBm resulted in an overall decrease in the CRB of all four schemes, indicating that increasing the base station transmit power effectively enhances target echo quality and improves DoA estimation accuracy. Among them, the active STAR-RIS-ISAC scheme consistently maintained the lowest CRB across the entire power range, with the most significant decrease; the active RIS-ISAC scheme was second; and the two passive schemes remained in the higher CRB range overall. This result firstly demonstrates that the introduction of active devices significantly enhances the system's ability to compensate for severe path loss; secondly, the STAR-RIS structure has a greater advantage in spatial reconstruction capability compared to the traditional RIS structure. Therefore, the combination of "active + STAR-RIS" exhibits the strongest improvement in sensing accuracy.

[0157] From the perspective of the impact of the number of RIS units Figure 5 The results show that as the number of RIS units increases from 8 to 16, the CRB of all schemes continues to decrease, indicating that increasing the number of reflective / transmittive units can improve the array control degrees of freedom, thereby enhancing the effective signal focusing capability and improving sensing performance. Consistent with the conclusions in the first figure, the active STAR-RIS-ISAC scheme remains the best and significantly outperforms the other three schemes across the entire range of unit numbers. This further illustrates that the improvement in system performance does not solely depend on higher transmit power, but is closely related to the spatial control capability of the RIS structure itself; as the number of units increases, the advantages of active STAR-RIS can be maintained, demonstrating its good scalability.

[0158] From the perspective of the impact of user SINR threshold Figure 6This reflects a divergence in the CRB trends of different schemes as communication QoS requirements increase. Overall, a higher SINR threshold compresses the degrees of freedom for sensing optimization, causing the CRB of some schemes to rise, indicating a resource competition relationship between communication and sensing. However, even under stricter communication constraints, the active STAR-RIS-ISAC scheme remains in the lowest CRB range, exhibiting only a relatively slow performance degradation; the active RIS-ISAC scheme is close to it, while the two passive schemes are significantly at higher CRB levels. This leads to the further conclusion that, with increased communication requirements, the active STAR-RIS architecture not only maintains high sensing accuracy but also demonstrates stronger robustness under the communication-sensing tradeoff.

[0159] From the perspective of the impact of RIS horizontal axis deployment position Figure 7 The results show that the CRB of all four schemes changes systematically with the lateral position of the RIS, indicating that the spatial deployment location of the RIS directly affects the cascade link loss and target echo intensity, thus impacting the final DoA estimation performance. Among them, the active STAR-RIS-ISAC scheme consistently achieves the lowest CRB across all locations, and its curve is the most stable overall, indicating its strongest adaptability to changes in deployment location; the active RIS-ISAC is second; while the passive STAR-RIS-ISAC and passive RIS-ISAC are in the higher CRB range. These results demonstrate that under varying actual deployment conditions, the active STAR-RIS scheme not only improves optimal performance but also enhances the system's tolerance to changes in scene geometry.

[0160] A unified conclusion can be drawn from the four figures: regardless of base station transmit power, number of RIS units, user SINR threshold, or RIS deployment location, the active STAR-RIS-ISAC scheme consistently exhibits the lowest CRB and the most stable performance advantages. This demonstrates a significant synergistic effect between active gain compensation capability and STAR-RIS's full-space control capability. The combination of these two technologies can more effectively suppress link attenuation, enhance target echo, and improve DoA estimation accuracy in complex propagation environments. Therefore, in RIS-assisted ISAC systems, active STAR-RIS is the optimal architecture that balances sensing accuracy, system robustness, and scenario adaptability. Detailed Implementation

[0161] Step 1: Initialize the outer iteration variables, including initializing the beamforming matrix. Active STAR-RIS reflectivity Active STAR-RIS transmission coefficient And set the outer iteration number n=0; wherein, the data types of the beamforming matrix, reflection coefficient and transmission coefficient are all complex numbers;

[0162] Step 2: Initially, based on the beamforming matrix obtained from the initialization... Active STAR-RIS reflectivity Calculate the Cramer-Rhodes boundary corresponding to the first iteration. And initialize the convergence judgment threshold ε;

[0163] Step 3: Enter the iteration

[0164] Step 4: Determine the result obtained in the current iteration Does it meet the convergence condition? ,in, This represents the CRB value calculated in the nth iteration; if it is not satisfied, proceed to step five and update the outer iteration number n = n + 1; if it is satisfied, proceed to step seven.

[0165] Step 5: Call the beamforming optimization module to solve the beamforming optimization subproblem Q1 and output the updated beamforming matrix. Wherein, all elements of the beamforming matrix are complex numbers;

[0166] Step 6: Apply the beamforming matrix obtained in Step 4 As input parameters, the STAR-RIS coefficient optimization module is invoked to solve the STAR-RIS coefficient optimization subproblem Q2, and the updated active STAR-RIS reflection coefficients are output. and transmission coefficient After completing the STAR-RIS coefficient optimization, update the auxiliary variables involved in the alternating optimization process, and then proceed to step four.

[0167] Step 7: Based on the judgment result of Step 4, output the optimal value of the target DOA estimate CRB when the preset convergence condition is met, and output the optimal beamforming matrix corresponding to the obtained CRB. Optimal Active STAR-RIS Reflectivity and the optimal active STAR-RIS transmittance .

Claims

1. A method for joint beamforming design of active STAR-RIS-assisted ISAC for optimizing DOA estimation accuracy, characterized in that, Includes the following steps: S1. Construct an active STAR-RIS-assisted ISAC system model; the system includes a dual-function base station, an active STAR-RIS, multiple communication users, and sensing targets; S2. Based on the system model, construct the transmission-side communication received signal model and the reflection-side sensing echo signal model respectively. In the model, consider the combined influence of the active STAR-RIS transmission coefficient on the communication signal, interference signal, and active amplification noise, as well as the combined influence of the active STAR-RIS reflection coefficient on the target echo signal and sensing link noise. Use the signal-to-interference-plus-noise ratio of each communication user as the communication performance index, and use the Cramer-Rao lower bound (CRB) of the target DOA estimation as the sensing performance index to obtain the communication constraint expression and sensing index expression of the system model. S3. Based on the joint optimization problem in step S2, initialize the base station beamforming matrix, the active STAR-RIS transmission coefficient matrix, and the reflection coefficient matrix, and decompose the joint optimization problem into a base station beamforming sub-problem and an active STAR-RIS transmission coefficient and reflection coefficient optimization sub-problem; S4. Under the condition of fixed active STAR-RIS transmission coefficient and reflection coefficient, the base station beamforming subproblem is equivalently transformed; the subproblem is transformed into an optimization problem about the transmission covariance matrix, and the optimal covariance matrix is ​​solved using the positive semidefinite relaxation method, thereby restoring the communication beamforming vector and the sensing beamforming vector.

2. A method as claimed in claim 1, characterized in that, The steps also include: S5. Under the condition of the beamforming matrix obtained in step S4, optimize the subproblems of active STAR-RIS transmission coefficient and reflection coefficient; by introducing auxiliary variables and combining the MM method and SCA method to construct convex surrogate functions for the higher-order non-convex terms in the objective function and constraints, and solve to obtain the updated active STAR-RIS transmission coefficient matrix and reflection coefficient matrix. S6. Based on the current iteration results obtained in steps S4 and S5, determine whether the target value or CRB change in two adjacent outer layer iterations meets the preset convergence condition. If not, return to execute steps S4 and S5. If so, output the optimized base station beamforming matrix, active STAR-RIS transmission coefficient matrix, and reflection coefficient matrix to optimize the target DOA estimation accuracy under the condition of meeting communication performance constraints.

3. A method as claimed in claim 1, characterized in that, In step S1, the system includes a dual-function base station, an active STAR-RIS, K single-antenna communication users, and a sensing target. The direct link between the dual-function base station and the sensing target and communication users is blocked. The active STAR-RIS includes M units capable of simultaneous transmission and reflection modulation. Since the target is located in the base station's blind zone, and the direct link between the base station and the target is blocked, the system's communication link will rely on the transmission side's "base station → active STAR-RIS → user" and its direct link. Because the sensing receiver is co-located with the base station, the scattered / echo signal generated by the target returns to the base station receiver after being reflected by the active STAR-RIS; that is, the echo propagates along a two-way closed-loop link of "base station → active STAR-RIS → target → active STAR-RIS → base station".

4. A method as claimed in claim 1, characterized in that, In step S2, the specific methods for constructing the communication received signal model, the sensing echo signal model, and the CRB are as follows: S2.1 Define the active STAR-RIS transmission and reflection coefficient matrix; ； The reflection phase shift matrix and the transmission phase shift matrix are respectively represented as: ； The reflection amplitude matrix and the transmission amplitude matrix are respectively represented as: ； S2.2 Construct the transmission signal model of the t-th time slot of a dual-function base station; Among them, in the formula This represents the transmit beamforming precoding matrix used for communication signals. This represents the transmit beamforming matrix used for sensing signals, where the communication signal is... And satisfy Radar sensing signals and satisfy , For ease of subsequent representation, a beamforming joint matrix is ​​defined. and joint signals ; S2.3 Construct the received signal model of the Kth communication user and build the SINR expression for the Kth user; Among them This represents the baseband channel matrix between BS and user k. This indicates the channel between the BS and the active STAR-RIS. This represents the channel between the active STAR-RIS and user k, using advanced channel estimation techniques. It is assumed here that the channel state information has been fully acquired. This represents the white Gaussian noise (AWGN) between the BS and the active STAR-RIS. This represents the AWGN transmitted via active STAR-RIS to user k. Based on the received signal, the SINR expression for the k-th communication user is obtained as follows: Here, , represents the equivalent channel between the BS and the k-th user, and express The i-th column. The above SINR expression reflects a re-characterization of communication metrics in the active STAR-RIS scenario: the communication user is located on the transmission side, and the transmission coefficient not only affects the desired communication signal and multi-user interference signal, but also affects the result of noise at the active STAR-RIS being amplified by the transmission link and propagated to the user end. S2.4 Construct a model of the echo signal of the sensing target; in It is the target's RCS. This represents the Loss of Target (LoS) channel from the active STAR-RIS to the target. , This represents the steering vector of the active STAR-RIS. Indicates path loss. The steering vector of the channel is represented by , where It is the DoA of the target relative to the active STAR-RIS. as well as These represent the AWGNs generated on the path from the active STAR-RIS to the target and the path from the active STAR-RIS back to the base station, respectively. The AWGNs generated on the path from the active STAR-RIS to the target and the path from the active STAR-RIS back to the base station undergo multiple attenuations along the link from the active STAR-RIS to the target, then reflected back to the active STAR-RIS, and finally transmitted back to the base station. Therefore, when the echo signal reaches the base station, its power is significantly less than that of other signals and can be ignored. The echo signals are then stacked and vectorized to obtain the observation signal expression used for target parameter estimation: in The communication signal and the various noises generated in the path are simplified as follows: , , . The above sensing echo signal model reflects the re-characterization of the sensing link in the active STAR-RIS scenario: the target is located on the reflecting side, and the reflection coefficient, while enhancing the target echo link, also changes the propagation and amplification characteristics of noise in the sensing link. S2.5 Construct the Fisher information matrix of the target parameters and derive the CRB expression; Based on this, the variable to be estimated can be obtained. CRB in , , . As can be seen from the above CRB expression, the target perception accuracy index depends not only on the base station beamforming matrix and reflection link gain, but also on the active STAR-RIS amplification noise and its power constraints. S2.6, Construct a joint optimization problem; Based on the aforementioned reconstructed SINR and CRB expressions, the objective function, communication constraints, active STAR-RIS power constraints, and transmission / reflection coefficient constraints in the joint optimization problem are considered. Among the constraints This represents the quality of service constraint for the kth communication user, used to ensure that the communication performance of each user is not lower than a preset threshold; This represents the power budget constraint of the active STAR-RIS, used to limit the sum of signal amplification power and noise amplification power in the transmission and reflection links; This represents the power budget constraint of the base station, used to limit the beamforming matrix; This indicates that the reflection phase and transmission phase of the nth element satisfy the unit mode constraint; This indicates that the active amplification of the nth unit on both the reflection and transmission sides is limited by the maximum amplification capability of the hardware. The objective function is derived from minimizing the CRB. Minimizing the CRB is equivalent to maximizing its denominator, specifically expressed as follows: 。 5. A method as claimed in claim 1, characterized in that, In step S4, the optimization method for the beamforming matrix is ​​as follows: S4.1, Construct a beamforming optimization sub-problem; in S4.2 Introducing Auxiliary Variables And transform the objective function constraints; The above constraint can be transformed into the following form using Schur complement. S4.3 Define the covariance matrix variables; W i R is a rank-one Hermitian positive semi-definite matrix. w It is a Hermitian positive semi-definite matrix, i.e. S4.4 Perform semidefinite relaxation treatment; S4.5, Restore the beamforming matrix; The optimal solution to the semidefinite programming problem can be obtained using traditional convex optimization algorithms. Furthermore, once the optimal covariance matrix is ​​obtained from solving the SDP problem... The communication beam vector can be recovered using the following closed-form expression. ; The beamforming vector used for radar sensing can be calculated using Cholesky decomposition. in , and then combine and This completes the optimization solution for the beamforming matrix.

6. A method as claimed in claim 1, characterized in that, In step S5, the optimization method for the active STAR-RIS transmission coefficient matrix and reflection coefficient matrix is ​​as follows: S5.1 Construct the STAR-RIS coefficient optimization subproblem; After obtaining the beamforming matrix in step S4, the original joint optimization problem is rewritten as a subproblem concerning the active STAR-RIS transmission coefficient matrix and the reflection coefficient matrix; in S5.2 Reconstruct the STAR-RIS coefficient variables and transform the problem into an optimization problem; definition At this point, the entire optimization problem can be reformulated as: in Here Represents the set {1, 2} containing elements that are equal to or less than the set of ... Another different element, that is, if Then at this time, the corresponding ,if Then at this time ; S5.3 Introducing Auxiliary Variables and Then, the fractional objective function is reconstructed; The phase shift matrix is ​​fixed here. and At that time, auxiliary variables and The explicit optimal solution can be easily obtained, that is Received and After finding the optimal solution in the theory, the optimization problem of the phase shift matrix can then be reformulated as follows: S5.4 Construct a proxy function for the upper bound of the objective function in M / M; Based on the solution obtained in the nth iteration It can be deduced that The upper bound is in , , ;function It remains nonconvex, therefore, a tractor function for the optimization problem that is easy to handle is constructed through a second-order Taylor expansion. Here, we define... Furthermore, through derivation, we can obtain in, Hessian matrix The largest eigenvalue, ,as well as Substituting these values ​​into the original problem, we can obtain the original function. proxy functions; in, ; S5.5 Constructing a proxy function for communication constraints; The term that causes non-convexity is We need to introduce a proxy function, as shown below: Based on the above proxy function, the constraints are transformed into... ， ； S5.6 Define auxiliary variables and construct the upper bound surrogate function for the fourth term; Define several new auxiliary variables as follows: Define an auxiliary function Its corresponding first and second derivatives can be expressed as follows: Will The upper bound surrogate function is represented as in, Represents the Hessian matrix The largest eigenvalue, , , , At the same time, because The inequality holds true, and This represents the Hessian matrix. The largest eigenvalue, and similar definitions exist, , . Regarding the other part of this non-convex term Define the proxy function in the following way in, , In summary, the general surrogate function for this non-convex term is: in, , At this point, the optimization problem can be reformulated as follows: 。

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