Design and optimization method of optical reflection ris assisted vlcp system under low snr

Abstract

The application discloses a method for designing and optimizing a VLCP system assisted by light reflection RIS under low signal-to-noise ratio, wherein the VLCP system comprises an intelligent wall adopting a smart surface RIS with mirror reflection, a transmitter and a user terminal equipped with a receiver with a liquid crystal smart surface, communication and positioning signals are integrated into the transmitter, the transmitter comprises an LED, and the method comprises the following steps: under low signal-to-noise ratio, taking asymptotic capacity as a communication metric constraint condition, taking a Cramer-Rao lower bound of positioning error as a positioning metric constraint condition, combining a positioning constraint satisfaction process based on a two-stage greedy algorithm and a communication performance maximization process based on a greedy strategy convex relaxation algorithm, optimizing elements of an RIS allocation matrix to maximize the asymptotic capacity, obtaining an optimal RIS allocation matrix, and completing the design and optimization of the VLCP system. In a low signal-to-noise ratio scene, the VLCP system of the application can significantly improve system performance by applying RIS.

Description

Technical Field

[0001] This invention relates to the field of integrated visible light communication and positioning technology, and in particular to a design and optimization method for a light reflection RIS-assisted VLCP system under low signal-to-noise ratio. Background Technology

[0002] With the increasing demand for high-speed communication and high-precision positioning in future smart home networks and Internet of Things (IoT) scenarios, Visible Light Communication and Positioning (VLCP) technology plays a crucial role in meeting the urgent needs of next-generation wireless systems. Combining the capabilities of Visible Light Communication (VLC) and Visible Light Positioning (VLP), VLCP technology aims to achieve the integration of communication, lighting, and positioning. This advanced technology fully utilizes the abundant bandwidth of the visible light spectrum to supplement the radio frequency (RF) systems expected to be strained by a large number of users in the upcoming sixth-generation (6G) communication networks. The use of light-emitting diodes (LEDs) to implement communication and positioning functions demonstrates the technology's resource efficiency and environmental friendliness. Compared to traditional RF wireless technologies, VLCP offers significant advantages such as no electromagnetic interference, high energy efficiency, high security, and low cost. Current research on VLCP primarily focuses on designing integrated signal transmission schemes to achieve the combination of communication and positioning functions. Furthermore, by studying parameter configuration and resource allocation issues in VLCP systems, key performance indicators such as positioning accuracy and communication rate have been jointly optimized. However, current research is mostly limited to traditional optimization aspects such as signal design and power allocation, failing to fully explore and utilize the spatial degrees of freedom of the physical layer to optimize system performance. Meanwhile, the nanometer-scale wavelength of visible light makes it highly susceptible to obstruction, shadows, and occlusion, resulting in significant sensitivity of VLCP signals to obstacles and substantial path loss during transmission.

[0003] VLCP is a novel technology that combines the advantages of VLC and VLP, and it is expected to be widely used in future indoor home networks. In current VLCP systems, data transmission is typically based on the Loss of Position (LoS) signal, using VLP positioning results to obtain Channel State Information (CSI) estimates, followed by data transmission. Because visible light is highly sensitive to line-of-sight transmission, line-of-sight obstruction exists in our daily lives, but the operation of VLCP systems under such conditions has not yet been considered. Currently, a relatively mature and effective method—Intelligent Metasurfaces (RIS)—exists to address this issue. RIS in the visible spectrum has been extensively studied in recent years; however, current research has not explored the application of RIS in cases of low received signal-to-noise ratio (SNR). Summary of the Invention

[0004] This invention addresses the lack of research on the application of Reflective RIS (Radio Reflection System) in low signal-to-noise ratio (SNR) scenarios by proposing a design and optimization method for a RIS-assisted VLCP system under low SNR conditions. The invention studies a RIS-assisted VLCP system with specular reflection under low SNR conditions to achieve simultaneous communication, positioning, and illumination, while simultaneously improving the quality of the received signal and mitigating the Loss-of-Spot (LoS) occlusion effect. Based on the proposed system model, Cramer-Rao lower bounds for asymptotic capacity and positioning error under low SNR conditions are derived. Furthermore, based on common terms in the low SNR capacity results, two optimization problems are formulated to maximize the asymptotic capacity, with the RIS allocation matrix used as an optimization variable under positioning accuracy constraints. To address the non-convex optimization problem, this invention utilizes convex relaxation, the monotonicity of functions, semidefinite relaxation, and a greedy algorithm. Based on these techniques, this invention proposes an integrated two-stage greedy algorithm and a convex relaxation algorithm based on a greedy strategy to determine the optimal RIS configuration. Specifically, the originally difficult problem is decomposed into two stages: a position constraint satisfaction stage and a communication performance maximization stage, and these two stages are optimized separately. To address the limitations of positioning accuracy, this invention uses simulations to verify the asymptotic capacity performance of a VLCP system with and without RIS under low signal-to-noise ratio conditions. Simulation results show that applying RIS to the VLCP system can significantly improve system performance in low signal-to-noise ratio scenarios, and also demonstrate the effectiveness of the proposed algorithm in solving the corresponding optimization problem.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A design and optimization method for a low signal-to-noise ratio light-reflective RIS-assisted VLCP system, wherein the VLCP system includes a smart wall employing a specularly reflective intelligent metasurface RIS, a transmitter, and a user terminal equipped with a liquid crystal intelligent metasurface. Communication and positioning signals are integrated into the transmitter, which includes LEDs. The method includes:

[0007] Under low signal-to-noise ratio, the asymptotic capacity is used as a communication metric constraint, and the Cramer-Rao lower bound of the positioning error is used as a positioning metric constraint. Combining the positioning constraint satisfaction process based on a two-stage greedy algorithm and the communication performance maximization process based on a convex relaxation algorithm with a greedy strategy, the elements of the RIS allocation matrix are optimized to maximize its asymptotic capacity, thus obtaining the optimal RIS allocation matrix and completing the VLCP system design and optimization.

[0008] Furthermore, the RIS allocation matrix satisfies the following constraints:

[0009]

[0010]

[0011] Where g n,i This represents an element in the RIS allocation matrix corresponding to the nth reflector and the i-th transmitter, where N is the number of reflectors. L Indicates the total number of transmitters. These represent the set of reflecting surfaces and the set of transmitters, respectively.

[0012] Furthermore, under low signal-to-noise ratio, the asymptotic capacity maximization problem P is expressed as:

[0013]

[0014] st

[0015] Tr(J -1 (u))≤D th ,

[0016]

[0017]

[0018] In the formula

[0019]

[0020] Where h represents the channel vector, h = h LoS +h NLoS h LoS h represents the Loss channel vector. NLoS D represents the NLoS channel vector constructed by RIS. th The threshold for positioning accuracy is represented by G, which is the RIS allocation matrix, and J(u) represents the Fisher information matrix. i and h j Let α represent the channel gain of the i-th and j-th channels, respectively, where α ∈ (0, N). L ), α i ∈[0,1];

[0021] For different optimization objectives, the optimization problem can be summarized into two subproblems P1 and P2:

[0022]

[0023] Furthermore, a two-stage greedy algorithm is used to solve the optimization problem P1:

[0024] Rewrite the optimization problem P1 as the optimization problem P1-a:

[0025]

[0026] Where 1 represents a matrix of all 1s. Represents the updated set of reflecting surfaces;

[0027]

[0028] In the formula, This represents the NLoS channel gain from the i-th LED to the user through the n-th reflector. To satisfy the number of remaining reflective surfaces after the positioning constraint stage;

[0029] When based on implementation When selecting the LED index based on the principle of maximization, the equation holds true, and the LED index is determined as follows:

[0030]

[0031] Then the selected RIS allocation matrix The nth row is determined by the following formula:

[0032]

[0033] Furthermore, a convex relaxation algorithm based on a greedy strategy is used to solve the optimization problem P2:

[0034] Optimization problem P2 can be rewritten as optimization problem P2-a:

[0035]

[0036] Where Q is a positive semi-definite matrix. α * For the optimal α, To optimize variables; M(α) is a symmetric matrix, and the elements of the matrix are determined by M. i,j =min{α i ,α j};

[0037] Based on relaxation, the optimization model is expressed as:

[0038] P2-b:max G,H Tr(QH)

[0039] stH≥0,

[0040]

[0041]

[0042] in

[0043] Combining the relaxed mapping relationship between G and H, the optimization problem P2-b is transformed into:

[0044] P2-c:max H,G Tr(QH)

[0045]

[0046] Tr(H)≤χ,

[0047]

[0048]

[0049]

[0050] in

[0051] For each row n, select a relaxation solution. The index i corresponding to the maximum value in the middle * Its form is expressed as:

[0052]

[0053] An alternating optimization algorithm is used to alternately optimize α and h until the convergence condition is met. Finally, the optimal RIS allocation matrix G is determined after multiple iterations. comm .

[0054] Furthermore, in the VLCP system, the channel gain of the i-th LED of the LoS channel is expressed as:

[0055]

[0056] Where m, A re d i These represent the Lambert index, PD area, and distance between the i-th LED and the receiver, respectively. and T represents the irradiance angle and incident angle of the i-th LED in the line-of-sight link, respectively. oc (·) represents the gain of the optical concentrator, T of (·) represents the filter gain.

[0057] Furthermore, in the VLCP system, the NLoS channel gain from the i-th LED to the user through the n-th reflector is expressed as:

[0058]

[0059] Where δ represents a factor that depends on the characteristics of the reflecting surface. This represents the irradiance angle of the i-th LED relative to the n-th reflective surface in a non-line-of-sight link. This represents the angle of incidence of the reflected light signal relative to the user at the nth reflector of the non-line-of-sight link.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] This invention proposes a RIS-assisted VLCP system for low signal-to-noise ratio (SNR) applications, considering the design and optimization of RIS parameters. Specifically, under a fixed positioning accuracy constraint, two optimization problems are formulated based on common terms in the low SNR capacity results. For these two optimization problems, an integrated two-stage greedy algorithm and a convex relaxation algorithm based on a greedy strategy are proposed, combining convex relaxation, function monotonicity, semidefinite relaxation, and greedy algorithms to solve the optimization problems. Finally, simulations verify the effectiveness of the proposed algorithms. Furthermore, the performance improvement brought about by applying RIS to the proposed VLCP system under low SNR conditions is also verified. Therefore, the proposed VLCP system, combined with specular reflection-based RIS, has significant advantages and will play a crucial role in future low SNR intelligent scenarios. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the architecture of a RIS-assisted VLCP system with low signal-to-noise ratio optical reflection constructed according to an embodiment of the present invention;

[0063] Figure 2 Case 1 provided for the embodiments of the present invention: When and At that time, the low signal-to-noise ratio asymptotic capacity results of the PSAI-constrained RIS-assisted VLCP system; among which D th =2m; D th =2m;

[0064] Figure 3 The following are the low signal-to-noise ratio capacity results for the RIS-assisted MISO VLCP system under three different scenarios provided in this embodiment of the invention; wherein (a) scenario 2: the PSAI-constrained RIS-assisted VLCP system in and Scenario 3: When and At that time, the capacity of the RIS-assisted VLCP system constrained by PIAI; Case 4: when and At that time, the capacity of the PIAI-constrained RIS-assisted VLCP system.

[0065] Figure 4 A comparison of the low signal-to-noise ratio capacity and the number of RIS elements in the RIS-assisted VLCP system provided in the embodiments of the present invention; wherein (a) the capacity and the number of RIS elements in cases 1 and 3; and (b) the capacity and the number of RIS elements in cases 2 and 4.

[0066] Figure 5The relationship between the low signal-to-noise ratio capacity and the number of RIS elements in different locations of the RIS-assisted VLCP system provided in this embodiment of the invention. r . Detailed Implementation

[0067] For ease of understanding, the following explanations are provided for some of the terms used in the specific embodiments of this invention:

[0068] Visible light communication (VLC) technology: Visible light communication technology is an emerging wireless communication technology that uses visible light for communication. With the widespread application of white LEDs, visible light communication technology has developed well.

[0069] LED: an abbreviation for Light Emitting Diode, is a type of semiconductor diode that can convert electrical energy into light energy. Like ordinary diodes, it consists of a PN junction and also has unidirectional conductivity.

[0070] PD: an abbreviation for Photodiode, is a semiconductor device that converts light signals into electrical signals, which can then be used to detect light. In optical communication, the device that receives the light signal at the terminal is the photodiode.

[0071] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments:

[0072] This invention proposes a design and optimization method for a light-reflective RIS-assisted VLCP system under low signal-to-noise ratio conditions. The VLCP system includes a smart wall employing a specularly reflective intelligent metasurface RIS, a transmitter, and a user terminal equipped with a liquid crystal intelligent metasurface. Communication and positioning signals are integrated into the transmitter, which includes LEDs. The method includes:

[0073] Under low signal-to-noise ratio, the asymptotic capacity is used as a communication metric constraint, and the Cramer-Rao lower bound of the positioning error is used as a positioning metric constraint. Combining the positioning constraint satisfaction process based on a two-stage greedy algorithm and the communication performance maximization process based on a convex relaxation algorithm with a greedy strategy, the elements of the RIS allocation matrix are optimized to maximize its asymptotic capacity, thus obtaining the optimal RIS allocation matrix and completing the VLCP system design and optimization.

[0074] The method specifically includes:

[0075] 1 System Model

[0076] like Figure 1As shown, this is an indoor RIS-assisted VLCP system with communication and positioning capabilities. In this system, communication and positioning signals are integrated into the transmitter, and the positioning power and communication power are correctly allocated to achieve simultaneous communication and positioning capabilities. The controller in the transmitter can adjust the direction of each reflector to change the transmission environment, providing a non-negligible non-line-of-sight link, thereby improving the corresponding system performance.

[0077] Figure 1 middle φ and ψ represent the irradiance and incident angles of the line-of-sight (LoS) link and the non-line-of-sight (NLoS) link, respectively, where φ represents the irradiance angle, ψ represents the incident angle, L indicates that the angle is related to LoS ​​transmission, and R indicates that the angle comes from NLoS transmission. and These represent the distance from the i-th LED to the n-th reflector, the distance from the user to the n-th reflector, and the LoS transmission distance from the i-th LED to the user, respectively. (This is mentioned in the system introduction.) These represent elements selected from the transmitter (LED) indicator set, respectively reflecting the RIS element indicators. The channel model can typically be represented as...

[0078] h = h LoS +h NLoS (1)

[0079] in h LoS h represents the Loss channel vector. NLoS Let represent the NLoS channel vector constructed by the RIS. We focus on the non-line-of-sight channel gain formed by the optical transmission links reflected by the reflective (mirror) array. In our study, the non-line-of-sight channel gain of diffuse reflection links is ignored because their impact on optical transmission is negligible. Specular reflection RIS are deployed on the wall because this type of RIS...

[0080] Compared to diffuse RIS, it exhibits significantly better performance. Specifically, the system model is described in detail below.

[0081] 1.1 Loss Channel Gain

[0082] In the proposed VLCP system, the LoS transport channel can be modeled as a Lambertian model. The channel gain of the i-th LED in the LoS channel can be expressed as...

[0083]

[0084] Where m, A re d i Let m be the Lambert index, PD area, and distance between the i-th LED and the receiver, respectively. Let m be the LED half-illuminance half-angle Θ. 1 / 2Related, characterized as m = -1 / log2(cos(Θ) 1 / 2 )).in and T represents the irradiance angle and incident angle of the i-th LED, respectively. oc (·) represents the gain of the optical concentrator, T of (·) represents the filter gain. T of (·) is usually set as a constant, while the optical focusing gain T oc (·) depends on the refractive index of the PD and the field of view (FoV). The relationship can be derived from...

[0085]

[0086] Where β is the refractive index of PD, Ψ FoV Let LoS be the field of view. Therefore, for the user, the LoS channel vector can be represented as...

[0087]

[0088] 1.2NLoS channel gain

[0089] The NLoS channel gain is comprised of the optical transmission links reflected from a smart wall equipped with a reflector array. The diffuse NLoS channel gain from ceilings, floors, and normal walls has minimal impact on optical transmission and is neglected in our work. Since this type of RIS offers significantly improved performance compared to diffuse RIS, a specular RIS is employed in the smart wall. The RIS-based specular reflection channel follows geometric optics principles and can be modeled as a spherical wave model. Therefore, an "additive" model is proposed to describe the approximate near-field propagation, and an allocation matrix is ​​defined to determine the matching relationship between the transmitter, the smart reflector, and the user equipped with an LC RIS-based receiver. Specifically, the NLoS channel gain based on the specular reflection RIS can be analyzed as follows.

[0090] The NLoS channel gain from the i-th LED to the user through the n-th reflector can be derived from...

[0091]

[0092] Where δ represents a factor that depends on the characteristics of the reflecting surface, and is usually assumed to be a constant. This represents the irradiance angle of the i-th LED relative to the n-th reflective surface in a non-line-of-sight link. This represents the angle of incidence of the reflected light relative to the user at the nth reflector of the non-line-of-sight link.

[0093] Based on the "crosstalk-free" characteristic of the optical RIS channel model, and assuming that each reflector can only serve one transmitter and one user at a time, an allocation matrix is ​​proposed. After determining the allocation matrix, the yaw and roll angles of the reflectors can be adjusted using a reverse lookup table to accurately reflect the transmitted signal from the transmitter. The service relationship between the transmitter and the reflector (i.e., the RIS allocation matrix) is typically represented as follows: in When service relationships are established, the corresponding elements in the allocation matrix are determined between the i-th transmitter, the n-th reflector, and the user (i.e., g). n,i =1). Meanwhile, according to the near-field model analysis, when the LED size is much smaller than the propagation distance, the narrow beamwidth causes the energy reflected by the RIS to concentrate within the narrow beam. Based on this, constraints on the RIS service relationship can be assumed. Given that each reflector can serve at most one transmitter and one user at any given time, the allocation matrix should satisfy the following constraints.

[0094]

[0095] According to the allocation matrix, the channel gain between the user and the i-th transmitter is expressed as:

[0096]

[0097] in Therefore, the user's NLoS channel vector can be represented as

[0098]

[0099] 2 Performance Indicators

[0100] In this section, we use asymptotic capacity as the communication metric and the Cramero lower bound (CRLB) of the positioning error as the positioning metric. The performance metrics can be derived as follows.

[0101] 1) Communication metric: Assuming the received signal vector The signal vector can be obtained from the input. and channel vector Therefore, its characteristics are

[0102]

[0103] in This indicates that the mean is zero and the covariance is... The Gaussian noise vector. Considering the peak intensity constraints and total or single average intensity constraints given by intensity modulation and direct detection (IM / DD) in the optical wireless channel (OWC), the asymptotic capacity at low signal-to-noise ratios can be characterized differently. Specifically, for peak and total average intensity (PSAI) constraints, the transmitted signal should satisfy the following constraints:

[0104]

[0105] in and α∈(0,N) L Meanwhile, for peak and single average intensity (PIAI) constraints, the transmitted signal should meet the following constraints:

[0106]

[0107] in and α ind ∈(0,1).

[0108] Table 1: Summary of asymptotic capacity of RIS-assisted VLCP systems under low signal-to-noise ratio conditions

[0109]

[0110] In our work, we considered two ways to define the asymptotic capacity under the above-mentioned constraint scenarios with different strengths. For the first method, let... Then the proportion, or Another method is through fixing let or

[0111] Based on the above discussion, the asymptotic capacity of a VLCP system under low signal-to-noise ratio (SNR) conditions can be described as follows. The asymptotic capacity of a PSAI-constrained VLCP system when the SNR is proportional can be expressed as:

[0112]

[0113] in And α i ∈[0,1]. Specifically, when asymptotic capacity can be expressed as

[0114]

[0115] For a fixed peak signal-to-noise ratio, let asymptotic capacity can be expressed as

[0116]

[0117] For a PIAI-constrained VLCP system, its asymptotic capacity can be expressed as follows.

[0118] When SNR is proportional, the asymptotic capacity can be expressed as:

[0119]

[0120] in, At the same time, for a fixed peak signal-to-noise ratio, let asymptotic capacity results representation

[0121]

[0122] The asymptotic capacity results are summarized in Table 1.

[0123] Therefore, the communication metric can be determined based on the asymptotic capacity results presented above. Since RIS only affects the channel vector, we separate the common term from all capacity results. Specifically, the asymptotic capacity optimization term determined by RIS is γ and

[0124] 2) Positioning Indicator: CRLB is chosen as the positioning error indicator. Specifically, we employ a positioning algorithm based on Received Signal Strength (RSS) information to obtain the receiver's location, given its low cost and high accuracy. Furthermore, based on the RSS positioning method, CRLB can be derived as follows.

[0125] Using the maximum likelihood estimator of the receiver position, the Fisher information matrix (FIM) can be expressed as:

[0126]

[0127] Among them, P p,i It is the positioning power of the i-th LED. This indicates the three-dimensional position of the receiver.

[0128] in

[0129]

[0130] at the same time,

[0131]

[0132] The partial derivatives of the LoS vector can be calculated directly, while the partial derivatives of the NLoS channel vector should satisfy...

[0133]

[0134] Where diag(·) and vec(·) represent diagonalization and vectorization operations, respectively. Assuming the LED is pointing downwards and the receiver is pointing upwards, the partial derivative can be calculated as follows:

[0135]

[0136]

[0137] in Indicates the position of the i-th LED. Indicates the position of the n-th reflecting surface. and Combining equations (17)-(22), it can be obtained through Tr(J) -1 (u)) Calculate and specify the CRLB for the positioning error.

[0138] Asymptotic capacity maximization under 3 location metric constraints

[0139] This section presents an asymptotic capacity maximization problem with CRLB as the location metric constraint. The elements of the allocation matrix are optimized to maximize its asymptotic capacity.

[0140] 3.1 Problem Statement

[0141] As shown in Table 1, our work considers asymptotic capacity results for four cases. It is worth noting that for three cases, the capacity expression is derived from shared common terms. Specifically, when the proportional signal-to-noise ratio approaches zero, the asymptotic capacity of the PSAI-constrained VLCP system is determined by γ. Therefore, the asymptotic capacity maximization problem can be simplified to...

[0142]

[0143] Where D th This represents the threshold for positioning accuracy. The asymptotic capacity maximization problem is a non-convex optimization problem and cannot be solved in polynomial time. For different optimization objectives, the optimization problem can be summarized into two subproblems. Represented as...

[0144]

[0145]

[0146] 3.2 Proposed Optimization Algorithm

[0147] For the two optimization problems proposed, we propose two algorithms to solve them, as detailed below.

[0148] 3.2.1 Solving P1 using a two-phase greedy algorithm:

[0149] We consider using a two-stage greedy algorithm to solve the optimization problem P1. For the communication performance metric ||h||1 chosen as the objective function, the variable G is adjusted to determine h. NLoS This affects the total channel gain h. By activating additional reflection paths, which is equivalent to increasing the number of non-zero elements in the allocation matrix G, the norm of the channel gain ||h||1 can be effectively improved. Meanwhile, based on the relationship between CRLB and G...

[0150]

[0151] Activate the reflection path with higher-order derivative gain (where g) i The corresponding element being 1) can enhance the positive definiteness of J(u), thereby reducing Tr(J -1 (u)). This is because activating multiple higher-order derivative reflection paths leads to an increase in the rank and eigenvalue of J(u), thereby enhancing positive definiteness and thus reducing J. -1 The magnitude of the eigenvalues ​​of (u).

[0152] However, maximizing ||h||1 typically requires activating a larger number of reflection paths. This approach may inadvertently introduce paths with low derivative gain, leading to insufficient information content in J(u), and consequently, a decrease in Tr(J). -1 The increase of (u)). Simultaneously, minimizing Tr(J). -1 (u) Prioritizing reflection paths with high derivative gain may compromise the ||h||1 value. For the proposed P1, local optimal selection of the reflector can lead to a global optimum satisfying the greedy selection property. Simultaneously, communication optimization under the localization constraint is independent of previous choices, exhibiting an optimal substructure. These properties meet the conditions required for the application of a greedy algorithm. Therefore, to alleviate the conflict between communication and localization, a two-stage greedy algorithm is employed in our work to solve the P1 problem.

[0153] Greedy algorithms are heuristic optimization methods that rely on making locally optimal decisions at each step, with the overall goal of converging to the global optimum. The application of greedy algorithms in this problem can be summarized in two stages: (i) satisfying the positioning constraint; and (ii) maximizing communication performance. In the first stage, the greedy strategy is to activate the minimum reflector to quickly satisfy the positioning accuracy constraint. In the second stage, we employ a greedy strategy to maximize the communication metric by optimizing the remaining reflectors.

[0154] First, initialize the allocation matrix. FIM Matrix Set of reflecting surfaces (mirrors) The sensitivity of each candidate (n,i) to the receiver position can be defined by the following formula:

[0155]

[0156] Where ||·||² represents the l²-norm of the vector. According to the greedy strategy, the pair with the highest sensitivity (n) is selected from all candidate pairs. * i * Accordingly, the allocation matrix can be updated according to the following principles:

[0157]

[0158] Assuming that in the t-th iteration, the FIM matrix... Based on the above update process, the FIM matrix in the (t+1)th iteration can be represented as:

[0159]

[0160] in This represents the channel gain at the t-th iteration. Specifically, Channel gain can be based on

[0161]

[0162] Based on equations (28) and (29), the allocation matrix can be updated while satisfying the RIS mirror constraint. The update process terminates until the positioning accuracy constraint or... Empty (even if all reflective surfaces are used, the positioning accuracy constraint cannot be met).

[0163] During the communication performance maximization phase, the remaining reflectors are used to maximize the l1-norm of the channel vector. Specifically, the updated reflector set is represented as...

[0164] From equation (24), we can observe that the objective function is linear with respect to G. Clearly, ||h||1 changes with g. n,i Monotonically increasing. The constraints in the RIS reflector can be rewritten as...

[0165]

[0166] The optimization problem P1 can be rewritten as follows:

[0167]

[0168] Where 1 represents a matrix consisting entirely of 1s, the objective function can be analyzed as follows:

[0169]

[0170] In the formula, To satisfy the requirement of having a certain number of remaining reflective surfaces after the positioning constraint stage, when based on the implementation... When choosing the LED index based on the principle of maximization, the equation holds true. That is, the LED index is determined as follows:

[0171]

[0172] Therefore, based on the selected type principle, the selected assignment matrix The nth row is determined by the following formula

[0173]

[0174] It can be seen that, Constrained by the RIS reflector. Simultaneously, the chosen allocation matrix maximizes the objective function of the problem.

[0175] Based on a two-stage greedy algorithm, under the constraint of positioning accuracy, the allocation matrix is ​​quickly determined to maximize the communication performance index ||h||1.

[0176] 3.2.2 Solving P2 using a convex relaxation algorithm based on a greedy strategy

[0177] For the optimization of P2, the optimization function can be rewritten as follows:

[0178]

[0179] Where M(α) is a symmetric matrix, and the elements of the matrix are determined by M. i,j =min{α i ,α j}, To optimize variables. Note that the Hessian matrix of the objective function is derived as follows: It is negative semi-definite. Therefore, the optimization process of α can be solved using standard convex optimization techniques such as those found in the CVX toolbox of MATLAB. Determining the optimal variable α * Then, the optimization objective in P2 can be restated as follows:

[0180]

[0181] in It can be considered a known symmetric matrix. To meet the positioning accuracy constraint, the principle of the G element is the same as in Section 4.3.2.1 for the first stage. Similarly, the optimal allocation of matrix elements in the communication process is based on the remaining reflective surface. Therefore, the P2 optimization problem of the communication process can be rewritten as follows:

[0182]

[0183] It can be seen that when When Q is a positive semi-definite matrix, matrix Q is a positive semi-definite matrix.

[0184] Based on the positive semi-determinism of Q, the binary constraint can be relaxed to g. n,i ∈[0,1]. Therefore, the objective problem P2-a can be solved using convex optimization methods such as semidefinite programming. Subsequently, integer solutions can be recovered through random rounding or branch and bound techniques. The details of the algorithm are summarized below.

[0185] First set objective function This can be rewritten as Tr(QH). Furthermore, a semi-deterministic constraint H≥0 is applied. Then, the binary variable g... n,i ∈{0,1} is relaxed to a continuous variable g n,i ∈[0,1], ignore the rank-1 constraint rank(H)=1, and retain the assignment constraint. Based on relaxation, the optimization model is represented as follows:

[0186]

[0187] Note that the relationship between h and G can be represented by the channel model. Constraints on the assignment matrix can be relaxed to constraints on H, and the relationship can be expressed as follows:

[0188]

[0189] Combining the relaxed mapping relationship between G and H, the optimization problem P2-b can be summarized as follows:

[0190]

[0191] Where χ=max‖h‖ 2 The allocation matrix can be calculated using constraints.

[0192] Since Q≥0, the optimization problem P2-c constitutes a convex semidefinite programming (SDP) problem, which can be solved efficiently in polynomial time using the interior-point method or a dedicated solver (such as CVX). Although the original objective in P2-c... This involves maximizing a convex function (which typically makes the problem non-convex), but the objective is reformulated as an auxiliary matrix variable. The linear function Tr(QH) on the quadratic form resolves this conflict. Specifically, the convexity of P2-c is maintained by ensuring a linear objective and convex constraints. This structural transformation decouples the quadratic dependency by introducing H, thus avoiding the inherent non-convexity of maximizing the quadratic form and guaranteeing convergence to the global optimum. Furthermore, Gaussian randomization is used to process the first-order constraint rank(H) = 1 to find a satisfying solution h. * Thus, the relaxation solution is derived.

[0193] Given a relaxation solution A greedy thresholding method is introduced to bridge the gap between binary constraints and relaxation operations. Although this method only yields an approximate optimal solution compared to branch and bound, its fast convergence makes it still suitable for our work. Specifically, for each row n, a relaxation solution is selected... The index i corresponding to the maximum value in the middle * Its form can be expressed as

[0194]

[0195] Therefore, the relaxation matrix It can be adjusted to G comm Note that the optimal value of α is dependent on h; therefore, given a fixed h in the t-th iteration... (t) The optimal variable α can be determined. * Meanwhile, according to the optimal variable α * The updated h is obtained in the (t+1)th iteration. (t+1) Therefore, an alternating optimization algorithm can be used to alternately optimize α and h until the convergence condition is met. Finally, after multiple iterations, the optimal G can be determined. comm .

[0196] By combining the greedy location constraint satisfaction process and the convex relaxation communication performance maximization process, the optimal allocation matrix of P2 is obtained through matrix fusion.

[0197] 3.2.3 Baseline Algorithm for the Proposed Optimization Problem

[0198] For comparison, an exhaustive search algorithm is chosen as the benchmark algorithm to demonstrate the efficiency of the proposed algorithm. For such complex and difficult optimization problems, the optimal solution can be obtained through exhaustive search. However, this solution technique is very intricate and impractical. In our work, we employ an exhaustive search method to ensure the optimal solution to the proposed problem. To reduce complexity, the process of satisfying the positioning accuracy constraint is the same as in Algorithm 1, and the optimization of the communication process uses an exhaustive search algorithm. By traversing all remaining reflective surfaces of the RIS, communication performance can be maximized under the positioning accuracy constraint.

[0199] 3.3 Computational Complexity Analysis

[0200] This section discusses the proposed optimization algorithm and the baseline algorithm, and the computational complexity of the two proposed optimization problems. For Algorithm 1, the computational complexity can be analyzed as follows: In the stage of satisfying the positioning constraints, G... loc The initialization of FIM requires Operations. For the main while loop, the worst-case number of iterations is... (Each reflecting surface can only be selected once). For the inner loop, calculating matrix S requires... Operations, optimal pair (n) * i * The selection process requires The operation, FIM and CRLB update process requires Operations. For communication processes, a single loop requires at most [number] operations. The operation is simpler because it only requires one pass through the matrix to determine the maximum element in each row. Therefore, the worst-case total computational complexity of Algorithm 1 is... Dominated by Phase 1.

[0201] For Algorithm 2, the details of its computational complexity can be analyzed. The method for the constraint satisfaction stage is the same as for Algorithm 1. Therefore, the complexity of this stage is... For the process of maximizing communication performance, considering the optimization of G comm The while loop of the alternating alpha optimization algorithm has a complexity primarily due to the iterative process. Assume the maximum number of iterations is T. max The complexity analysis is as follows: For each iteration, the complexity of solving the SDP problem P2-c is... This refers to the complexity of a typical SDP problem. It is used to generate candidate vectors h. * Gaussian randomization requires each iteration The operation is performed, where T represents the number of randomizations. Each iteration is analyzed using the interior-point method. The complexity of the matrix reconstruction process is Finally, adjust Get G comm The greedy strategy requires each iteration to This operation. Combining these two stages, the worst-case overall computational complexity of Algorithm 2 is... It is dominated by the solution process of the SDP problem.

[0202] The computational complexity analysis of a global optimization algorithm based on exhaustive search can be divided into two parts. The complexity of the localization optimization stage is... During communication, the worst-case computational complexity of the exhaustive search algorithm for the RIS allocation matrix optimization problem is... (Without RIS elements used in the location optimization process), its computational complexity is significantly higher due to its brute-force nature. Therefore, in the exhaustive search process for communication performance optimization, the worst-case total computational complexity of Algorithm 3 is... By comparing the complexity of Algorithm 3 and the algorithm proposed in this invention, we can see that Algorithms 1 and 2 achieve fast convergence due to their lower computational complexity. The comparison clearly demonstrates the effectiveness of the proposed low-complexity optimization algorithm for the given optimization problem. Furthermore, our proposed algorithm shows significant improvements in execution time and resource utilization. This is particularly important for real-time applications with limited computational resources and large-scale RIS deployments.

[0203] 4 Simulation Results

[0204] This section presents simulations highlighting the efficiency of our proposed algorithm in solving optimization problems in low signal-to-noise ratio (SNR) VLCP systems. Furthermore, these simulations reveal the potential of specular reflection RIS to improve the performance of VLCP systems. Assume a room with dimensions of 8m × 8m × 3m, with N... L =4 LEDs, one user, and one PD, then it has N r The deployment of the specular reflection RIS element is confined within a rectangular area, centered on the center point of the wall. This rectangular area is defined by two corners: (0.0m, 1.0m, 1.2m) and (0.0m, 7.0m, 2.9m). The RIS element area is set to 5×5m². 2 Ignoring the wall depth, the position of each RIS unit can be determined based on the number of mirrors, such as... Figure 1 As shown. Assuming the receiver's field of view is 80°, the incident angle of the LoS or NLoS link within the field of view is verified. Most parameters are referenced from relevant literature to ensure that our simulation environment is comparable to those used by other researchers. For ease of illustration, the LoS channel gain is normalized to... Meanwhile, the RIS reflection channel vector h NLoS The Gaussian noise vector z is also scaled by the same factor. Other simulation parameters are summarized in Table 2.

[0205] Table 2 Main Simulation Parameters

[0206]

[0207]

[0208] Figure 2 The results show the low signal-to-noise ratio (SNR) capacity and peak signal-to-noise ratio (PSNR) of the RIS-assisted VLCP system under PASI constraints. In comparison, the signal-to-noise ratio of this system approaches zero, and the positioning accuracy is constrained by D. th =2 and the number of RIS units N r =64 is fixed. As can be seen from the figure, "No RIS" means that the capacity is contributed solely by the Loss of Service (LoS) links. "Algorithm 1" and "Algorithm 2" represent the allocation matrices calculated by Algorithm 1 and Algorithm 2, respectively. "Exhaustive Search" indicates that the optimal allocation matrix is ​​determined by an exhaustive search algorithm. For this case, we consider the capacity results for two different α values.

[0209] Figure 2 'a' is The capacity result under the given conditions can be calculated using Algorithm 2 and the exhaustive search algorithm. The exhaustive search algorithm has extremely high complexity, but in practical applications, it can reduce infeasible implementations. However, for ease of comparison, we consider a simulation with N confined reflective surfaces. r=64 algorithm (more reflective surfaces will require unacceptable computation time). From Figure 2 As can be seen, the application of RIS can improve asymptotic capacity. Furthermore, the capacity result of the RIS allocation matrix based on the exhaustive search algorithm is slightly higher than that of Algorithm 2. This is due to the computational accuracy constraints of the SDP algorithm and the related approximations in Algorithm 2. Figure 2 As can be seen from Figure a, the efficiency of Algorithm 2 in this paper in solving optimization problems is high.

[0210] Figure 2 b is The capacity result under the given conditions can be calculated using Algorithm 2 and the exhaustive search algorithm. As can be seen from the figure, the capacity result calculated by Algorithm 2 is consistent with that calculated by the exhaustive search algorithm. This is because monotonicity was analyzed in P1. The efficiency of Algorithm 2 in solving P1 can be demonstrated by its low complexity and good solution.

[0211] Figure 3 The results for low signal-to-noise ratio capacity are shown in three cases. The positioning accuracy constraint is fixed at D. th =2m, the number of RIS elements is determined to be N r =64. The common terms in the three cases are represented by... This indicates that it can be calculated using Algorithm 1. From the figure, we can observe a fixed peak signal-to-noise ratio. Average signal-to-noise ratio disappears ( Figure 3 a) Peak signal-to-noise ratio Sum of signal-to-noise ratio ( Figure 3 (b) Fixed peak signal-to-noise ratio Individual average signal-to-noise ratio disappears ( Figure 3 The asymptotic capacity results of the PIAI-constrained system in (c) are shown. The capacity results demonstrate that the application of RIS can improve the system performance of the VLCP system. Furthermore, comparing the capacity results based on Algorithm 1 with those based on exhaustive search proves that Algorithm 1 is an effective method for solving the RIS configuration problem.

[0212] Figure 4 The simulation results show asymptotic capacity of a RIS-assisted VLCP system with different numbers of RIS elements. Specifically, the capacity results for the proportional signal-to-noise ratio are as follows: Figure 4 As shown in Figure a, the capacity results for fixed peak signal-to-noise ratio and vanishing average signal-to-noise ratio are as follows: Figure 4As shown in Figure b, increasing the number of RIS elements promotes the development of VLCP systems. Generally, the more RIS elements, the better the capacity result, and we can apply more reflective surfaces to achieve better performance in the future. However, the capacity increase in Case 1 differs from that in other cases. This is because the change in h alters the value of Q in P2-a, thus affecting the capacity result. Therefore, for special cases, we should carefully consider applying more reflective surfaces, taking into account the potential performance improvement and cost of RIS.

[0213] Figure 5 The figure shows the relationship between the low signal-to-noise ratio asymptotic capacity of a RIS-assisted VLCP system at different locations and the number of RIS elements. As can be seen from the figure, since the RIS deployment is based on one wall of the simulated room, the capacity at locations closer to the RIS is greater than that at locations farther from the RIS. This is obvious because the NLoS channel gain is better at short distances. Meanwhile, as the number of reflecting elements increases from N... r =Increase from 16 to N r =64, significantly enhancing the capacity of the RIS-assisted VLCP system. Simultaneously, the area affected by the RIS also expands. Therefore, VLCP systems based on mirror-reflective RIS possess significant advantages and will play a crucial role in future low signal-to-noise ratio intelligent scenarios (such as biological anechoic chambers or corridors).

[0214] This invention proposes a specular reflection-based RIS-assisted VLCP system for low signal-to-noise ratio (SNR) scenarios, considering the design and optimization of RIS parameters. Specifically, we analyze the low SNR asymptotic capacity and CRLB of the localization process under four conditions. Simultaneously, under a fixed localization accuracy constraint, we formulate two optimization problems based on the common terms of the low SNR capacity results. For these two optimization problems, combining convex relaxation, function monotonicity, SDR, and greedy algorithms, we propose an integrated two-stage greedy algorithm and a convex relaxation algorithm based on a greedy strategy, respectively. Finally, simulations verify the effectiveness of the proposed algorithms, and the performance improvement brought by applying RIS to the proposed VLCP system under low SNR conditions is also verified. Therefore, the proposed VLCP system, combined with specular reflection-based RIS, has significant advantages and will play a crucial role in future low SNR intelligent scenarios.

[0215] The key points and areas to be protected in this invention are:

[0216] 1) Based on a VLCP system operating under low SNR, a RIS-assisted communication-centric VLCP system model is constructed to realize the functions of VLC and VLP while reducing sensitivity to visible light Loss of Light (LoS) links. Simultaneously, the system's adjustability is improved. This invention utilizes the 6G candidate technology, Smart Metasurface (RIS), and incorporates it into the VLCP communication system to achieve the goal of simultaneously improving communication and positioning performance from an endogenous mechanism. The innovative aspects of this invention are the newly constructed RIS-assisted VLCP system channel model, the derivation of communication and positioning indicators under low SNR conditions, and the proposed system performance optimization scheme.

[0217] 2) Algorithm design. There are multiple solutions to the original optimization problem. The alternating optimization algorithm proposed in this invention has been verified and can be determined as an effective algorithm for finding the optimal solution, with strong convergence and high accuracy.

[0218] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A design and optimization method for a low signal-to-noise ratio light-reflective RIS-assisted VLCP system, the VLCP system comprising a smart wall using a specularly reflective intelligent metasurface RIS, a transmitter, and a user terminal equipped with a liquid crystal intelligent metasurface, wherein communication and positioning signals are integrated into the transmitter, the transmitter comprising LEDs, characterized in that, The method includes: Under low signal-to-noise ratio, the asymptotic capacity is used as a communication metric constraint, and the Cramer-Rao lower bound of the positioning error is used as a positioning metric constraint. Combining the positioning constraint satisfaction process based on a two-stage greedy algorithm and the communication performance maximization process based on a convex relaxation algorithm with a greedy strategy, the elements of the RIS allocation matrix are optimized to maximize its asymptotic capacity, thus obtaining the optimal RIS allocation matrix and completing the VLCP system design and optimization.

2. The design and optimization method for a low signal-to-noise ratio optical reflection RIS-assisted VLCP system according to claim 1, characterized in that, The RIS allocation matrix satisfies the following constraints: Where g n,i This represents an element in the RIS allocation matrix corresponding to the nth reflector and the i-th transmitter, where N is the number of reflectors. L Indicates the total number of transmitters. These represent the set of reflecting surfaces and the set of transmitters, respectively.

3. The design and optimization method for a low signal-to-noise ratio optical reflection RIS-assisted VLCP system according to claim 2, characterized in that, Under low signal-to-noise ratio, the asymptotic capacity maximization problem P is represented as: P: st Tr(J -1 (u))≤D th , In the formula Where h represents the channel vector, h = h LoS +h NLoS h LoS h represents the Loss channel vector. NLoS D represents the NLoS channel vector constructed by RIS. th The threshold for positioning accuracy is represented by G, which is the RIS allocation matrix, and J(u) represents the Fisher information matrix. i and h j Let α represent the channel gain of the i-th and j-th channels, respectively, where α ∈ (0, N). L ), α i ∈[0,1]; For different optimization objectives, the optimization problem can be summarized into two subproblems P1 and P2: P1: stTr(J -1 (u))≤D th , P2: stTr(J -1 (u))≤D th , 4. The design and optimization method for a low signal-to-noise ratio optical reflection RIS-assisted VLCP system according to claim 3, characterized in that, A two-stage greedy algorithm is used to solve the optimization problem P1: Rewrite the optimization problem P1 as the optimization problem P1-a: P1-a: s.t. Where 1 represents a matrix of all 1s. Represents the updated set of reflecting surfaces; In the formula, This represents the NLoS channel gain from the i-th LED to the user through the n-th reflector. To satisfy the number of remaining reflective surfaces after the positioning constraint stage; When based on implementation When selecting the LED index based on the principle of maximization, the equation holds true, and the LED index is determined as follows: Then the selected RIS allocation matrix The nth row is determined by the following formula:

5. The design and optimization method for a low signal-to-noise ratio optical reflection RIS-assisted VLCP system according to claim 3, characterized in that, Solving optimization problem P2 using a convex relaxation algorithm based on a greedy strategy: Optimization problem P2 can be rewritten as optimization problem P2-a: P2-a: s.t. Where Q is a positive semi-definite matrix. α * For the optimal α, To optimize variables; M(α) is a symmetric matrix, and the elements of the matrix are determined by M. i,j =min{α i ,α j }; Based on relaxation, the optimization model is expressed as: P2-b:max G,H Tr(QH) s.t. in Combining the relaxed mapping relationship between G and H, the optimization problem P2-b is transformed into: P2-c:max H,G Tr(QH) s.t. Tr(H)≤χ, in χ = max|h| 2 ; For each row n, select a relaxation solution. The index i corresponding to the maximum value in the middle * Its form is expressed as: An alternating optimization algorithm is used to alternately optimize α and h until the convergence condition is met. Finally, the optimal RIS allocation matrix G is determined after multiple iterations. comm .

6. The design and optimization method for a low signal-to-noise ratio optical reflection RIS-assisted VLCP system according to claim 3, characterized in that, In the VLCP system, the channel gain of the i-th LED in the LoS channel is expressed as: Where m, A re d i These represent the Lambert index, PD area, and distance between the i-th LED and the receiver, respectively. and T represents the irradiance angle and incident angle of the i-th LED in the line-of-sight link, respectively. oc (·) represents the gain of the optical concentrator, T of (·) represents the filter gain.

7. The design and optimization method for a low signal-to-noise ratio optical reflection RIS-assisted VLCP system according to claim 3, characterized in that, In the VLCP system, the NLoS channel gain from the i-th LED to the user through the n-th reflector is expressed as: Where δ represents a factor that depends on the characteristics of the reflecting surface. This represents the irradiance angle of the i-th LED relative to the n-th reflective surface in a non-line-of-sight link. This represents the angle of incidence of the reflected light signal relative to the user at the nth reflector of the non-line-of-sight link.

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