Locating system middle section optimization design method based on RIS

Abstract

The invention discloses a profile optimization design method in a positioning system based on an RIS, and the method comprises the steps: building a system model, determining the system composition elements, namely an access point (AP), the RIS, UE and the position relation of the AP, the RIS and the UE, and building a signal model and a measurement model. Fisher information analysis is carried out, a correlation matrix and parameters are calculated, and a position error boundary expression is deduced. And then an optimal RIS profile design strategy is provided, an optimization problem is constructed, and an optimal covariance matrix and RIS profile design are obtained through matrix analysis and derivation. Meanwhile, hardware limitation is considered, constrained RIS profile design is proposed, an optimization problem with constraints is constructed, and an RIS profile meeting actual hardware constraints is obtained through solving by an alternating minimization technology. The present invention improves the positioning accuracy of user equipment (UE).

Description

Technical Field

[0001] The invention relates to a wireless positioning method, in particular to an optimization design method for a reconfigurable intelligent surface (RIS) profile in an orthogonal frequency division multiplexing (OFDM) system. Background Art

[0002] In the continuous evolution of modern wireless communication technology, reconfigurable smart surface (RIS) has gradually emerged as a promising emerging technology, showing unique advantages in meeting the growing demand for high-precision positioning in future communication systems.

[0003] The demand for high-precision positioning in next-generation wireless communication systems (such as 6G) has risen sharply. Although millimeter wave and terahertz communication technologies have the potential to significantly broaden bandwidth, the increase in carrier frequency causes the signal to suffer more severe path attenuation, which in turn significantly limits its coverage. In this context, RIS has attracted widespread attention due to its special working mechanism. It consists of a large number of programmable components and can flexibly control the propagation of electromagnetic waves by precisely adjusting parameters such as the phase of the components, opening up a new path to improve system performance and presenting broad application prospects in many key fields such as wireless communication networks, the Internet of Things, and autonomous driving.

[0004] In the field of positioning applications, RIS has significant advantages. When the line-of-sight (LoS) path in the traditional positioning system is blocked by various obstacles, RIS can effectively introduce new multipath components, making positioning possible in scenarios that were originally extremely difficult or even impossible. Even in the presence of LoS paths, RIS can make full use of the information carried by the newly generated virtual LoS paths to significantly improve positioning accuracy. The fundamental principle is to add additional reference points to the positioning process, thereby effectively enhancing the accuracy and reliability of positioning. Based on these outstanding characteristics, RIS has attracted much attention in the field of beyond-5G positioning technology and has become the focus of many studies. For example, Keykhosravi et al. studied the 3D downlink positioning and synchronization problems of single-input single-output (SISO) systems with the help of planar RIS; Dardari et al. explored the method of using large-size RIS for LoS / NLoS positioning under near-field conditions; Elzanaty et al. conducted an in-depth analysis of the position and direction error bounds in RIS-assisted positioning; Abu-Shaban et al. proposed an innovative architecture for near-field positioning using RIS as a lens; Alexandropoulos et al. studied the method of positioning through multiple RIS equipped with a single receiving radio frequency (RF) chain. These research results fully demonstrate the huge potential and broad application prospects of RIS in the field of positioning technology.

[0005] However, despite many research results, the current RIS profile design methods still face many challenges. On the one hand, the existing design strategies have obvious deficiencies in considering actual constraints (such as hardware limitations, total power constraints, etc.). For example, when Song et al. studied RIS-assisted non-line-of-sight wireless perception, although they jointly optimized the beamforming modes of AP and RIS to reduce the Cramer-Rao bound (CRB) of UE position-related parameters, they did not fully consider the RIS hardware limitations, such as the actual phase adjustment range and accuracy of RIS elements. This may make the designed RIS profile difficult to accurately implement in actual hardware, thereby affecting the positioning performance. Although the self-sensing RIS architecture proposed by Shao et al. is innovative, the total power constraint was not deeply considered during the design process, which may lead to excessive system energy consumption and is not conducive to long-term stable operation in practical applications. On the other hand, the performance of RIS profile design strategies in different scenarios varies. Rahal et al. used the near-field wavefront curvature to design the RIS profile, which can improve the positioning performance in specific scenarios, but when the scene parameters (such as distance, signal strength, etc.) change, the performance of this method may fluctuate greatly, and there is a lack of a general and efficient design method that can be widely applied to various complex scenarios. This makes it difficult to quickly adjust the RIS profile according to the needs of different scenarios in practical applications to balance various performance indicators, and it cannot fully meet the strict requirements of future communication systems for high-precision positioning.

[0006] In summary, in the RIS-assisted positioning system, in-depth research on profile optimization design methods, full consideration of various practical constraints, and improvement of positioning accuracy are of vital importance to promoting the development of wireless communication technology, which is also the core problem that the present invention is committed to solving. Summary of the invention

[0007] Purpose of the invention: The purpose of the present invention is to provide a profile optimization design method in a RIS-based positioning system for improving the positioning accuracy of a user equipment (UE).

[0008] The method of the present invention mainly comprises: constructing a signal model based on RIS, constructing a positioning reception model, designing an optimal profile design for RIS, considering the RIS profile optimization design under constraint conditions, and applying a specific algorithm to achieve high-precision user position estimation.

[0009] Technical solution: The profile optimization design method in the positioning system based on RIS of the present invention comprises the following steps:

[0010] Step (1), reconfigurable smart surface system model construction: determine the system composition, establish a positioning system including AP, RIS, and UE, and clarify the position relationship; set signal transmission parameters; determine the signal expression; derive the received signal expression; construct a measurement model, determine the discrete signal sampling method; decompose the propagation delay; simplify the discrete signal expression; obtain the frequency domain received measurement signal expression;

[0011] Step (2), perform Fisher information analysis and PEB analysis related calculations; design the optimal profile design for RIS: take PEB as the indicator, construct the RIS profile optimization problem under the total power constraint, and derive the optimal covariance matrix and RIS profile design;

[0012] Step (3), considering the RIS hardware limitations, defining the RIS profile constraints, constructing a constrained optimization problem, using the alternating minimization technique, updating the variable W and the RIS profile matrix respectively, and iteratively optimizing to obtain a RIS profile that satisfies the constraints and has good performance.

[0013] Furthermore, the method of step (1) is:

[0014] Specific steps for building a reconfigurable intelligent surface system model:

[0015] Step (11), determine the system composition. Consider a typical RIS-enabled non-line-of-sight NLoS positioning system, which consists of a single-antenna access point (AP), a RIS with L uniform linear reconfigurable elements, and a single-antenna user equipment UE located in the non-line-of-sight coverage area of ​​the AP. At this time, the line-of-sight LoS path between the AP and the UE is blocked by various obstacles. The RIS is used to establish a virtual LoS path from the AP to the UE to achieve positioning. The position is represented by a 2D Cartesian coordinate system, and is defined as is the AP position vector is the RIS reference point position vector, where is the position vector of the lth element, is the UE position vector, p UE In the Cartesian coordinate system, it can be expressed as [p x , p y ] T , which can be expressed in spherical coordinates as [r, θ] T , r is the distance from the origin to the UE, θ is the angle of the human-radiated signal relative to the positive x-axis;

[0016] Step (12), setting signal transmission parameters: Consider the downlink communication scenario where the RIS is enabled with a blocked LoS path. Assume that the AP transmits a series of OFDM symbols with a bandwidth of B, where B is divided into M subcarriers, i.e., B = MΔf, each subcarrier has a bandwidth of Δf, and the OFDM symbol duration is T = 1 / Δf. The cyclic prefix CP duration is defined as T cp , total symbol duration T s =T+T cp ;

[0017] Step (13), determine the signal expression: According to the above settings, the transmitted continuous-time OFDM signal is expressed as

[0018]

[0019] Where x[n,m] is the data sample transmitted on the mth carrier of the nth OFDM symbol, N is the number of OFDM symbols, and rect T (t) is a rectangular pulse, which is equal to 1 when t∈[0,T] and 0 otherwise.

[0020] Step (14), derive the received signal expression: Based on the transmission signal model and system structure, the passband received signal through the AP-RIS-UE link is expressed as

[0021]

[0022] Where α is the concatenated channel coefficient of the AP-RIS and RIS-UE paths, and f c is the carrier frequency, is the delay vector between AP and UE on different elements of RIS, and α = α br α ru , G T is the AP antenna gain, P T is the total transmitted power, λ c is the wavelength, φ 0 is the phase shift, is the UE side antenna gain,

[0023] Specific steps for constructing the measurement model:

[0024] Step (17), determine the discrete signal sampling method: Under the assumption that the UE and AP are synchronized, the discrete signal y[k, n] corresponding to the kth sample in the nth symbol is obtained by sampling at t=nT s +T cp +kT / M is obtained by sampling the continuous time signal y(t), and the expression is

[0025]

[0026] Step (18), decomposition of propagation delay: The total propagation delay through the lth RIS element [T(t)]l can be decomposed into [τ(t)] l =[τ br ] l +[τ r (t)] l +[τ ru ] l ,in is the propagation delay between the AP and the lth RIS element, is the propagation delay between the lth RIS element and the UE, [τ r (t)] t is the delay of the lth RIS element at time t, assuming that the RIS configuration [τ r，n ] l =[τ r (nT s +T cp )] l feasible, and [τ r，n ] l ∈[0,1 / f c ),

[0027] Step (19), simplify the discrete signal expression: To make the expression more compact, some approximate simplifications y[k, n] are adopted to be

[0028]

[0029] in τ r =τ br +τ ru , assuming x[n, m] = 1, arrange y[k, n] into a matrix Among them, F DFT is the discrete Fourier transform DFT matrix, y n =[y[0,n],...,y[M-1,n]] T , Γ r =[γ r，0 , ..., γ r，N-1 ],

[0030] Step (20) obtains the frequency domain received measurement signal expression: using the discrete Fourier transform property Y r Transformed to the frequency domain, considering the existence of noise, the frequency domain received measurement signal is finally expressed as:

[0031]

[0032] where Z is the frequency domain observation noise, whose columns are transformed from zero mean and covariance matrix into is drawn from a circularly symmetric complex Gaussian distribution.

[0033] Furthermore, the method of step (2) is:

[0034] Fisher information matrix design specific steps:

[0035] Step (21), measurement matrix conversion: First, the measurement matrix in step (20) is converted into a concise vector form, that is,

[0036]

[0037] where h r =vec(a(φ ru )b T (τ r )), and determine vec(Z T ) is

[0038] Step (22), calculate h r，aug Fisher information matrix (FIM): Let u = [(a(IMr)h)″, (a(IM8)h)″ and Calculate h according to the given formula r，aug The FIM, that is

[0039]

[0040] By substituting the relevant expressions, we get

[0041]

[0042] in

[0043] Step (23), define and calculate the FIM about θ: further define the channel parameter set to be estimated as By formula

[0044]

[0045] Computing the FIM about θ involves Calculation of h r =vec(a(φ ru )b T (τ r )). Here, each Indicates h rThe derivative of the corresponding element in with respect to the parameter vector θ. Specifically, H θ，i The rows are calculated as follows:

[0046] This term indicates h r The elements in r The derivative of . is a coefficient related to signal propagation, a T (φ ru ) is the angle φ ru The associated vector, is b(τ r ) About τ r The i-th element of the derivative vector of .

[0047] Here is h r The elements in ru The derivative of . is a(φ ru )About φ ru The derivative vector of [b(τ r )] i is b(τ r )The i-th element of the vector.

[0048] This formula represents h r The derivative of the real part of the elements in with respect to α, where a T (φ ru ) and [b(τ r )] i As defined above.

[0049] This is h r The derivative of the elements in with respect to the imaginary part of α, j is the imaginary unit, a T (φ ru ) and [b(τ r )] i The meaning remains unchanged.

[0050] Will Substituting into the above formula, we can get:

[0051]

[0052] Expanding this expression further, we get:

[0053]

[0054] Among them, each f ij The calculation of is as follows:

[0055] here is the coefficient The square of the modulus, yes The squared norm of a vector, Representation Matrix Trace of.

[0056] With f1 1 similar, is a combination of the correlation coefficient and the vector norm, is the trace of another matrix.

[0057] It also involves the calculation of vector norms and matrix traces.

[0058] Contains the conjugate transpose product of the vector and the matrix trace.

[0059] Here we have the conjugate of the coefficients and the conjugate transpose product of the vector and the matrix trace.

[0060] It is also an expression consisting of coefficients, vector norm, and matrix trace.

[0061] Finally, a more complex but clear FIM expression for θ is obtained, and it is pointed out that the expression can be simplified by choosing the center of the RIS as the reference point (e.g., using This simplification is of great significance in the subsequent optimization problem solving and system performance analysis. It can help us study and design RIS profiles more effectively and improve the system's positioning performance and other related indicators.

[0062] Specific steps for PEB expression design:

[0063] Step (24), define the relevant parameter vector: First, define the parameter vector related to the UE position as where p UE =[p x , p y ] T Indicates the position of the UE in the Cartesian coordinate system. This step lays the foundation for the subsequent calculation of the Jacobian matrix and the derivation of the PEB expression, and clarifies the key parameters related to the UE position and its representation in the vector.

[0064] Step (25), calculate the Jacobian matrix: calculate the Jacobian matrix with respect to θ and The Jacobian matrix T of

[0065]

[0066] The Jacobian matrix T describes the The relationship between the changes in the FIM about θ is converted to the FIM about plays a key role in the FIM process,

[0067] Step (26), get the FIM: By combining the FIM expression about θ obtained previously And the Jacobian matrix T, according to the formula Get about The FIM expression is:

[0068] Step (27), derive the PEB expression: using the previously obtained According to the relationship between PEB and FIM, the PEB expression is derived. It is known that PEB can be expressed as Further calculation of C p To get the specific PEB expression, calculate C p When and T are expressed as block matrices, namely and Then use the block matrix inversion formula Calculate each of them separately and get Therefore, there is It can also calculate Through these calculations, we finally get C p The closed form expression of

[0069] in C p Substitution The complete PEB expression is obtained, which provides the objective function for the subsequent optimization of RIS profile.

[0070] Specific steps for optimal RIS profile design:

[0071] Step (28), construct the RIS profile optimization problem: the positioning performance is evaluated using the position error bound (PEB) as an indicator, and the RIS profile optimization problem is constructed under the total power constraint, that is,

[0072]

[0073] Where P T Represents the total transmission power. Through a series of derivations, PEB is expressed as the covariance matrix R with the RIS profile r The relevant form, that is,

[0074]

[0075] Further expressed as

[0076]

[0077] in Step (29), construct the RIS profile optimization problem:

[0078]

[0079] Where P T Represents the total transmit power. Through a series of derivations, PEB is expressed as r Related forms:

[0080]

[0081] Further expressed as:

[0082]

[0083] Step (30), optimize R r Related items and reconstruction optimization problems: First, R r Related terms are simplified, that is, tr[R φ}、 and Available R r The structure is simplified, and then R is determined r The optimal form is R r =UΛU H ,here, is a Hermitian matrix (i.e., Λ=Λ H ), U represents the * (φ ru )and Zhang Cheng's normalized subspace is in For the convenience of derivation, Λ is further expressed as Further simplifying tr{R φ}、 and As follows: φ}=λ 11 ||a(φ ru )|| 2 , Next, reconstruct the optimization problem and substitute the simplified result into the result:

[0084]

[0085] Due to the inequality Always holds, so Therefore, there is tr{C p}≥φ(λ 11 ,λ 22 ),in And if and only if λ 12 = 0, the equation holds true.

[0086] Step (31), reformulate and solve the optimization problem: Based on the previous derivation, the RIS profile optimization problem is reformulated as an optimization problem with some newly defined parameters, namely

[0087]

[0088] in is an expression related to the previous derivation. Define auxiliary parameters and Solving the optimization problem yields:

[0089]

[0090] Step (32), determine the optimal covariance matrix and RIS profile design: According to the results obtained above, the optimal covariance matrix R r Re-expressed as

[0091]

[0092] in Then we discuss the design of RIS profile Γ r The optimal strategy is to reasonably allocate a * (φ ru )and The number of times to balance the PEB associated with the position coordinates, determine Make RIS profile And satisfy

[0093] Furthermore, the method of step (3) is:

[0094] Specific steps for constraining the RIS profile problem construction and design:

[0095] Step (31), define the RIS profile constraint: Considering the RIS hardware limitation, for the RIS configuration of the lth element during the nth OFDM symbol [γ r，n ] l , define the actual RIS profile matrix as Γ r =[γ r，0 , γ r，1 , ..., γr，N-1 ], whose effective constraint set For {[γ r，n ] l :[γ r，n ] l |=1,∠[γ r，n ] l ∈[0, 2π)},

[0096] Step (32), construct the optimization problem: let Γ u Indicates that the expected covariance R can be achieved r A set of unconstrained RIS profiles, where W is for WW H =I L Under this constraint, the RIS profile design problem is constructed as

[0097]

[0098] Due to the non-convexity of the constraints and WW H =I L , this problem is difficult to solve directly, so we use the alternating minimization technique to deal with this problem in the next step.

[0099] The specific steps of W's update plan are:

[0100] Step (33), the optimization problem is simplified: fix Γ r , the optimization problem in the original step (32) is simplified to

[0101]

[0102] Combined with WW H =I L ,right Expand:

[0103]

[0104] Ignore constant terms The cost function can be rewritten as

[0105]

[0106] Step (34), singular value decomposition solution: Perform singular value decomposition, that is in is a left unitary matrix, is a diagonal matrix containing nonzero real-valued eigenvalues, is a right semiunitary matrix and (Assuming N>L),

[0107] Substitution have to:

[0108]

[0109] By analyzing the inequality relationship when When taking the equal sign, the optimal solution is satisfy In order to maximize the objective function,

[0110] Γ r The update scheme steps are as follows:

[0111] Step (35), substitute W to simplify the objective function: Substitute the estimated value of W into the original objective function to obtain r Optimization problem

[0112]

[0113] Since each element of RIS can be designed independently, the problem can be further decomposed into

[0114]

[0115] in

[0116] Step (36), consider the unit module constraint solution: Consider the unit module constraint, assuming The optimization problem can be rewritten as

[0117]

[0118] Using trigonometric relationships The closed form solution is

[0119] Step (37), obtain the RIS profile design: using the phase estimate Considering the unit mode constraint, the final RIS profile design is obtained By alternating the above r and W, optimizing them in an iterative minimization manner until a specific termination criterion is met.

[0120] Compared with the prior art, the present invention has the following beneficial effects:

[0121] The method of the present invention focuses on an orthogonal frequency division multiplexing (OFDM) positioning system assisted by a reconfigurable smart surface (RIS). In view of the situation where the line-of-sight path between an access point (AP) and a user equipment (UE) is blocked, a system model including a single-antenna AP, a multi-element RIS and a single-antenna UE is constructed to clarify the position relationship of each component, set the AP to transmit an OFDM signal and derive the expression of the received signal, and sample and simplify the frequency domain measurement signal; then Fisher information analysis and position error bound (PEB) analysis are carried out, and on this basis, an optimal RIS profile design strategy is proposed under the total power constraint with PEB as an indicator, and the optimal covariance matrix and configuration method are obtained. At the same time, considering the RIS hardware limitation, the alternating minimization technique is used to construct and solve the constrained RIS profile design problem, and the iterative optimization obtains a RIS profile that satisfies the constraints and has good performance, which effectively improves the positioning performance. The proposed constraint method performs well in a variety of scenarios and is close to the performance of the optimal solution, which is of great significance for the integration of perception and communication functions in future 6G applications.

[0122] Through the above process, the RIS signal model and positioning reception model are constructed. In the system construction and analysis, the execution of each step should ensure accurate reflection of the communication characteristics and position relationship of the system, providing a reliable foundation for the subsequent profile design and optimization. In the profile design and optimization, the construction and solution of the optimization problem should ensure that the RIS profile design with the best positioning performance under the actual constraints can be obtained, thereby providing a strong guarantee for the positioning service in the wireless communication system. BRIEF DESCRIPTION OF THE DRAWINGS

[0123] Figure 1 Typical RIS-assisted SISO system downlink transmission scenario diagram,This figure shows the architecture of a typical RIS-assisted single-input single-output (SISO) system in a downlink transmission scenario, where the BS is the base station responsible for sending wireless signals;

[0124] Figure 2 The performance sharing factor λ of the achievable error bound under different RIS profile design strategies over time 1 Variation diagram, which shows the Cramer-Rao bound (CRB) for τ under different RIS profile design strategies, including the proposed optimal scheme, fixed time sharing factor (Fixed TF) scheme, random scheme and directional scheme. r and φ ru and the corresponding position error bound (PEB) performance over time sharing factor λ 1 The changes of τ r Cramer-Rao bound (CRB) performance diagram; (b) φ ru Cramer-Rao bound (CRB), (c) position error bound (PEB) performance;

[0125] Figure 3 The performance of the reachable error bound varies with the distance r under different RIS profile design strategies. This figure depicts the performance of the reachable error bound as the distance increases from to under different RIS profile design strategies. r CRB, φ ru The variation trend of the performance indicators of the reachable error bound, such as CRB and PEB, where (a) τ r Cramer-Rao Bound (CRB) performance, (b) φ ru Cramer-Rao bound (CRB) performance, (c) position error bound (PEB) performance;

[0126] Figure 4 The performance of the reachable error bound under different RIS profile design strategies varies with the number of RIS elements L. This figure shows that under different RIS profile design strategies, when the number of RIS elements L increases from to, τ r ,φ ru and p UE The change of error bound performance, where (a) τ r Cramer-Rao Bound (CRB) performance, (b) φ ru Cramer-Rao bound (CRB) performance, (c) position error bound (PEB) performance;

[0127] Figure 5 Different position uncertainty levels σ p The performance of PEB can be reached as a function of distance. This figure shows the uncertainty level σ at different locations. p Variation of the reachable PEB performance with distance for the proposed optimal and constrained RIS profile design strategies;

[0128] Figure 6 Variation of achievable PEB performance with distance for different numbers of OFDM symbols N: The figure depicts the variation of achievable PEB performance with distance for the proposed optimal and constrained RIS profile design algorithms for different numbers of OFDM symbols N (N=200, N=500 and N=1000). DETAILED DESCRIPTION

[0129] With the continuous development of modern wireless communication technology, the demand for high-precision positioning technology is becoming increasingly urgent. As an emerging technology, reconfigurable intelligent surface (RIS) has shown great potential in improving positioning accuracy. Based on the RIS-assisted orthogonal frequency division multiplexing (OFDM) positioning system, the present invention proposes a systematic and innovative RIS profile optimization design scheme to address many challenges faced by existing RIS profile design methods in practical applications, such as insufficient consideration of hardware limitations and power constraints, and limited adaptability to different scenarios.

[0130] The present invention first starts with the construction of the system model, accurately describes the relationship between the components in the system and the signal transmission characteristics, and lays a solid foundation for subsequent analysis. Then, Fisher information analysis and position error bound (PEB) analysis are carried out in depth, and the internal laws of the system are revealed through rigorous mathematical derivation, so as to clarify the optimization target. On this basis, the optimal RIS profile design strategy is elaborated in detail, and the total power constraint is fully considered to obtain the optimal covariance matrix and RIS profile configuration method with practical guiding significance. At the same time, in view of the RIS hardware limitations, the alternating minimization technology is innovatively used to solve the problem of constrained RIS profile design, and a RIS profile that meets the actual constraints and has excellent performance is obtained through iterative optimization. In the entire implementation process, each step is closely connected and interlocking, and together constitutes a complete and efficient RIS profile optimization design system, which aims to provide a practical solution for high-precision positioning in future wireless communication systems and promote the development and progress of related technologies in practical applications.

[0131] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0132] Example

[0133] Step 1. Establishment of reconfigurable intelligent surface (RIS) system model, signal model and measurement model. Specific steps for building the reconfigurable intelligent surface system model:

[0134] Step (11), determine the system composition. Figure 1 ,Consider a typical RIS-enabled non-line-of-sight (NLoS) positioning system, which consists of a single-antenna access point (AP), a RIS with L uniform linear reconfigurable elements, and a single-antenna user equipment (UE) located in the non-line-of-sight coverage area of ​​the AP. At this time, the line-of-sight (LoS) path between the AP and the UE is blocked by various obstacles. The RIS is used to establish a virtual LoS path from the AP to the UE to achieve positioning. The position is represented using a 2D Cartesian coordinate system, and the definitions are respectively is the AP position vector is the RIS reference point position vector (where is the position vector of the lth element), is the UE position vector, p UE In the Cartesian coordinate system, it can be expressed as [p x , p y ] T , which can be expressed in spherical coordinates as [r, θ] T , r is the distance from the origin to the UE, and θ is the angle of the RF signal relative to the positive x-axis.

[0135] Step (12), setting signal transmission parameters: Consider the downlink communication scenario where the LoS path is blocked and RIS is enabled. Assume that the AP transmits a series of orthogonal frequency division multiplexing (OFDM) symbols with a bandwidth of B, where B is divided into M subcarriers, i.e., B = MΔf, each subcarrier has a bandwidth of Δf, and the OFDM symbol duration is T = 1 / Δf. The cyclic prefix (CP) duration is defined as T cp , total symbol duration T s =T+T cp .

[0136] Step (13) Determine the signal expression: According to the above settings, the transmitted continuous-time OFDM signal is expressed as

[0137]

[0138] Where x[n,m] is the data sample transmitted on the mth carrier of the nth OFDM symbol, N is the number of OFDM symbols, and rect T (t) is a rectangular pulse (equal to 1 when t∈[0, T], otherwise equal to 0) Step (14), derive the received signal expression: Based on the transmission signal model and system structure, the passband received signal through the AP-RIS-UE link is expressed as

[0139]

[0140] Where α is the concatenated channel coefficient of the AP-RIS and RIS-UE paths, and f c is the carrier frequency, is the delay vector between AP and UE on different elements of RIS, and (G T is the AP antenna gain, P T is the total transmitted power, λ c is the wavelength, φ 0 is the phase shift), (G R is the UE side antenna gain).

[0141] Specific steps for constructing the measurement model:

[0142] Step (17), determine the discrete signal sampling method: Under the assumption that the UE and AP are synchronized, the discrete signal y[k, n] corresponding to the kth sample in the nth symbol is obtained by sampling at t=nT s +T cp +kT / M is obtained by sampling the continuous time signal y(t), and the expression is

[0143]

[0144] Step (18), decompose the propagation delay: the total propagation delay through the lth RIS element [τ(t)] l It can be decomposed into [τ(t)] l =[τ br ] l +[τ r (t)] l +[τ ru ] l ,in is the propagation delay between the AP and the lth RIS element, is the propagation delay between the lth RIS element and the UE, [τ r (t)] t is the delay of the lth RIS element at time t, assuming that the RIS configuration [τ r，n ] l =[τ r (nT s +T cp )] l feasible, and [τ r，n ] l ∈[0,1 / f c ).

[0145] Step (19), simplify the discrete signal expression: To make the expression more compact, some approximations (described in detail in Appendix A) are used to simplify y[k, n] to

[0146]

[0147] in τ r =τ br +τ ru , assuming x[n, m] = 1, arrange y[k, n] into a matrix Among them, F DFT is the discrete Fourier transform (DFT) matrix, Y r =[y 0 ,y 1 , ..., y N-1 ], y n =[y[0,n],...,y[M-1,n]] T , Γ r =[γ r，0 , ..., γ r，N-1 ].

[0148] Step (20) obtains the frequency domain received measurement signal expression: using the discrete Fourier transform property Y rTransformed to the frequency domain, considering the existence of noise, the frequency domain received measurement signal is finally expressed as

[0149]

[0150] where Z is the frequency domain observation noise, whose columns are transformed from zero mean and covariance matrix into is drawn from a circularly symmetric complex Gaussian distribution.

[0151] Step 2. Based on the assumption that the UE location information is known, the strategy for optimally designing the RIS profile Fisher information matrix design specific steps:

[0152] Step (21), measurement matrix conversion: First, the measurement matrix in step (20) is converted into a concise vector form, that is,

[0153]

[0154] where h r =vec(a(φ ru )b T (τ r )), and determine vec(Z T ) is

[0155] Step (22), calculate h r，aug Fisher information matrix (FIM): Let u = [(a(IMr)h)″, (a(IM8)h)″ and Calculate h according to the given formula r，aug The FIM, that is

[0156]

[0157] By substituting the relevant expressions, we get

[0158]

[0159] in

[0160] Step (23), define and calculate the FIM about θ: further define the channel parameter set to be estimated as By formula

[0161]

[0162] Computing the FIM about θ involves Calculation of h r =vec(a(φ ru )bT (τ r )). Here, each Indicates h r The derivative of the corresponding element in with respect to the parameter vector θ. Specifically, H θ，i The rows are calculated as follows:

[0163] This term indicates h r The elements in r The derivative of . is a coefficient related to signal propagation, a T (φ ru ) is the angle φ ru The associated vector, is b(τ r ) About τ r The i-th element of the derivative vector of .

[0164] Here is h r The elements in ru The derivative of . is a(φ ru )About φ ru The derivative vector of [b(τ r )] i is b(τ r )The i-th element of the vector.

[0165] This formula represents h r The derivative of the real part of the elements in with respect to α, where a T (φ ru ) and [b(τ r )] i As defined above.

[0166] This is h r The derivative of the elements in with respect to the imaginary part of α, j is the imaginary unit, a T (φ ru ) and [b(τ r )] i The meaning remains unchanged.

[0167] Will Substituting into the above formula, we can get:

[0168]

[0169] Expanding this expression further, we get:

[0170]

[0171] Among them, each f ij The calculation of is as follows:

[0172] here is the coefficient The square of the modulus, yes The squared norm of a vector, Representation Matrix Trace of.

[0173] With f 11 similar, is a combination of the correlation coefficient and the vector norm, is the trace of another matrix.

[0174] It also involves the calculation of vector norms and matrix traces.

[0175] Contains the conjugate transpose product of the vector and the matrix trace.

[0176] Here we have the conjugate of the coefficients and the conjugate transpose product of the vector and the matrix trace.

[0177] It is also an expression consisting of coefficients, vector norm, and matrix trace.

[0178] Finally, a more complex but clear FIM expression for θ is obtained, and it is pointed out that the expression can be simplified by choosing the center of the RIS as the reference point (e.g., using ), this simplification is of great significance in the subsequent optimization problem solving and system performance analysis, and can help us study and design RIS profiles more effectively and improve the system's positioning performance and other related indicators.

[0179] Specific steps for PEB expression design:

[0180] Step (24), define the relevant parameter vector: First, define the parameter vector related to the UE position as where p UE =[p x , p y ] T Indicates the position of the UE in the Cartesian coordinate system. This step lays the foundation for the subsequent calculation of the Jacobian matrix and the derivation of the PEB expression, and clarifies the key parameters related to the UE position and its representation in the vector.

[0181] Step (25), calculate the Jacobian matrix: calculate the Jacobian matrix with respect to θ and The Jacobian matrix T of

[0182]

[0183] The Jacobian matrix T describes the The relationship between the changes in the FIM about θ is converted to the FIM about plays a key role in the FIM process.

[0184] Step (26), get the FIM: By combining the FIM expression about θ obtained previously And the Jacobian matrix T, according to the formula Get about This step is to prepare for the subsequent calculation of PEB, because PEB is related to This transformation can focus the problem on the parameter vector directly related to the UE position. superior.

[0185] Step (27), derive the PEB expression: using the previously obtained According to the relationship between PEB and FIM, the PEB expression is derived. It is known that PEB can be expressed as Further calculation of C p To get the specific PEB expression, calculate C p When and T are expressed as block matrices, namely and Then use the block matrix inversion formula Calculate each of them separately and get Therefore, there is It can also calculate Through these calculations, we finally get C p The closed form expression of

[0186] in C p Substitution The complete PEB expression was obtained, which provided the objective function for the subsequent optimization of RIS profile.

[0187] Specific steps for optimal RIS profile design:

[0188] Step (28), construct the RIS profile optimization problem: the positioning performance is evaluated using the position error bound (PEB) as an indicator, and the RIS profile optimization problem is constructed under the total power constraint, that is,

[0189]

[0190] Where P T Represents the total transmission power. Through a series of derivations, PEB is expressed as the covariance matrix R with the RIS profile r The relevant form, namely

[0191]

[0192] Further expressed as

[0193]

[0194] in Step (29), construct the RIS profile optimization problem:

[0195]

[0196] Where P T Represents the total transmit power. Through a series of derivations, PEB is expressed as r Related forms:

[0197]

[0198] Further expressed as:

[0199]

[0200] Step (30), optimize R r Related terms and reconstruction optimization problem: First, simplify the Rr related terms, that is, tr{R φ}、 and Available R r Then determine R r The optimal form is R r =UΛU H .here, is a Hermitian matrix (i.e., Λ=Λ H ). U represents the * (φ ru )and Zhang Cheng's normalized subspace is in For the convenience of derivation, Λ is further expressed as Further simplification and As follows: φ}=λ 11 ||a(φ ru )|| 2 , Next, reconstruct the optimization problem and substitute the simplified result into the result:

[0201]

[0202] Due to the inequality Always holds, so Therefore, there is tr{C p}≥φ(λ 11 ,λ 22 ),in And if and only if λ 12 =0, the equation holds true.

[0203] Step (31), reformulate and solve the optimization problem: Based on the previous derivation, the RIS profile optimization problem is reformulated as an optimization problem with some newly defined parameters, namely

[0204]

[0205] in is an expression related to the previous derivation. Define auxiliary parameters and Solving the optimization problem yields:

[0206]

[0207] Step (32), determine the optimal covariance matrix and RIS profile design: According to the results obtained above, the optimal covariance matrix R r Re-expressed as

[0208]

[0209] in Then we discuss the design of RIS profile Γ r The optimal strategy is to reasonably allocate a * (φ ru )and The number of times to balance the PEB associated with the position coordinates, determine Make RIS profile And satisfy

[0210] Step 3. Considering the practical limitations of RIS hardware, a constrained RIS profile design method is proposed. The specific steps of constrained RIS profile problem construction design are:

[0211] Step (31), define the RIS profile constraint: Considering the RIS hardware limitation, for the RIS configuration of the lth element during the nth OFDM symbol [γ r，n ] l , define the actual RIS profile matrix as Γ r =[γ r，0 , γ r，1 , ..., γ r，N-1 ], whose effective constraint set For {[γ r，n ] l :|[γ r，n ] l |=1,∠[γ r，n ]l∈[0,2π)}.

[0212] Step (32), construct the optimization problem: let Γ u Indicates that the expected covariance R can be achieved r A set of unconstrained RIS profiles, where W is for WW H =I L Under this constraint, the RIS profile design problem is constructed as

[0213]

[0214] Due to the non-convexity of the constraints ( and WW H =I L ), this problem is difficult to solve directly, so we use the alternating minimization technique to deal with this problem in the next step.

[0215] The specific steps of W's update plan are:

[0216] Step (33), the optimization problem is simplified: fix Γ r , the original optimization problem (70) is simplified to

[0217]

[0218] Combined with WW H =I L ,right Expand:

[0219]

[0220] Ignore constant terms The cost function can be rewritten as

[0221]

[0222] Step (34), singular value decomposition solution: Perform singular value decomposition, that is in is a left unitary matrix, is a diagonal matrix containing nonzero real-valued eigenvalues, is a right semiunitary matrix and (Assume N>L).

[0223] Substitution have to:

[0224]

[0225] By analyzing the inequality relationship

[0226] when When taking the equal sign, the optimal solution is satisfy Thus maximizing the objective function.

[0227] Γ r The update scheme steps are as follows:

[0228] Step (35), substitute W to simplify the objective function: Substitute the estimated value of W into the original objective function to obtain r Optimization problem

[0229]

[0230] Since each element of RIS can be designed independently, the problem can be further decomposed into

[0231]

[0232] in Step (36), consider the unit module constraint solution: Consider the unit module constraint, assuming The optimization problem can be rewritten as

[0233]

[0234] Using trigonometric relationships The closed form solution is

[0235] Step (37), obtain the RIS profile design: using the phase estimate Considering the unit mode constraint, the final RIS profile design is obtained By alternating the above r and W, optimizing them in an iterative minimization manner until a specific termination criterion is met.

[0236] 1. Initialization phase: Samples are drawn from a complex Gaussian distribution with a mean of 0 and a variance of 1. r Initialize the elements of .

[0237] 2. Iteration loop stage repeats the following operations until the termination condition is met (for example, the maximum number of iterations I is reached). max Or the change of RIS profile between two iterations ΔΓ r is less than the set threshold ∈).

[0238] Step a: Decomposition operation uses singular value decomposition (SVD) technology to Decompose into in is the left-west matrix, is a diagonal matrix containing nonzero real-valued eigenvalues, is the right half-western matrix (satisfying Assume N>L).

[0239] Step b: Update W and calculate based on the decomposition result of step a Completed the update of W.

[0240] Step c: Update calculate

[0241] Step d: Update the RIS phase profile, for 1 = 1 to L and n = 0 to N-1, calculate Implement the update of RIS phase profile.

[0242] Step e: Construct Γ r Using the updated phase profile Constructing the RIS Profile Matrix 3. Termination and output stage When the termination conditions are met, the final constrained RIS profile is output

Claims

1. A profile optimization design method in a positioning system based on RIS, characterized in that: The steps include: Step (1), reconfigurable smart surface system model construction: determine the system composition, establish a positioning system including AP, RIS, and UE, and clarify the position relationship; set signal transmission parameters; determine the signal expression; derive the received signal expression; construct a measurement model and determine the discrete signal sampling method; Decompose the propagation delay; simplify the discrete signal expression; obtain the frequency domain received measurement signal expression; Step (2), perform Fisher information analysis and PEB analysis related calculations; Design the optimal profile design for RIS: Taking PEB as the indicator, construct the RIS profile optimization problem under the total power constraint, and derive the optimal covariance matrix and RIS profile design; Step (3), optimization design of RIS profile under constraints: Considering the RIS hardware limitations, define the RIS profile constraints, construct a constrained optimization problem, use the alternating minimization technique, update the variable W and the RIS profile matrix respectively, and iterate the optimization to obtain a RIS profile that satisfies the constraints and has good performance.

2. The profile optimization design method in the positioning system based on RIS according to claim 1, characterized in that: In the step (1): Specific steps for building a reconfigurable intelligent surface system model: Step (11), determine the system composition. Consider a typical RIS-enabled non-line-of-sight NLoS positioning system, which consists of a single-antenna access point (AP), a RIS with L uniform linear reconfigurable elements, and a single-antenna user equipment UE located in the non-line-of-sight coverage area of ​​the AP. At this time, the line-of-sight LoS path between the AP and the UE is blocked by various obstacles. The RIS is used to establish a virtual LoS path from the AP to the UE to achieve positioning. The position is represented by a 2D Cartesian coordinate system, and is defined as is the AP position vector is the RIS reference point position vector, where l=0,1,...,L-1 is the position vector of the lth element, is the UE position vector, p UE In the Cartesian coordinate system, it can be expressed as [p x , p y ] T , which can be expressed in spherical coordinates as [r, θ] T , r is the distance from the origin to the UE, θ is the angle of the human-radiated signal relative to the positive x-axis; Step (12), setting signal transmission parameters: Consider the downlink communication scenario where the RIS is enabled with a blocked LoS path. Assume that the AP transmits a series of OFDM symbols with a bandwidth of B, where B is divided into M subcarriers, i.e., B = MΔf, each subcarrier has a bandwidth of Δf, and the OFDM symbol duration is T = 1 / Δf. The cyclic prefix CP duration is defined as T cp , total symbol duration T s =T+T cp ; Step (13), determine the signal expression: According to the above settings, the transmitted continuous-time OFDM signal is expressed as Where x[n,m] is the data sample transmitted on the mth carrier of the nth OFDM symbol, N is the number of OFDM symbols, and rect T (t) is a rectangular pulse, which is equal to 1 when t∈[0,T] and 0 otherwise. Step (14), derive the received signal expression: Based on the transmission signal model and system structure, the passband received signal through the AP-RIS-UE link is expressed as Where α is the concatenated channel coefficient of the AP-RIS and RIS-UE paths, and f c is the carrier frequency, is the delay vector between AP and UE on different elements of RIS, and G T is the AP antenna gain, PT is the total transmit power, λ c is the wavelength, φ0 is the phase shift, G R is the UE side antenna gain, Specific steps for constructing the measurement model: Step (17), determine the discrete signal sampling method: Under the assumption that the UE and AP are synchronized, the discrete signal y[k, n] corresponding to the kth sample in the nth symbol is obtained by sampling at t=nT s +T cp +kT / M is obtained by sampling the continuous time signal y(t), and the expression is Step (18), decomposition of propagation delay: The total propagation delay through the lth RIS element [τ(t)]l can be decomposed into [τ(t)] l =[τ br ] l +[τ r (t)] l +[τ ru ] l ,in is the propagation delay between the AP and the lth RIS element, is the propagation delay between the lth RIS element and the UE, [τ r (t)] t is the delay of the lth RIS element at time t, assuming that the RIS configuration [τ r， n] l =[τ r (nT s +T cp )] l feasible, and [τ r，n ] l ∈[0,1 / f c ), Step (19), simplify the discrete signal expression: To make the expression more compact, some approximate simplifications y[k, n] are adopted to be in τ r =τ br +τ ru , assuming x[n, m] = 1, arrange y[k, n] into a matrix where F DFT is the discrete Fourier transform DFT matrix, Y r =[y0,y1,...,y N-1 ], y n =[y[0,n],...,y[M-1,n]] T , Γ r =[γ r，0 , ..., γ r,N-1 ], Step (20) obtains the frequency domain received measurement signal expression: using the discrete Fourier transform property Y r Transformed to the frequency domain, considering the existence of noise, the frequency domain received measurement signal is finally expressed as: where Z is the frequency domain observation noise, whose columns are transformed from zero mean and covariance matrix into The parameters are drawn from a circularly symmetric complex Gaussian distribution.

3. The profile optimization design method in the positioning system based on RIS according to claim 2 is characterized in that: The method of step (2): Fisher information matrix design specific steps: Step (21), measurement matrix conversion: First, the measurement matrix in step (20) is converted into a concise vector form, that is, where h r =vec(a(φ ru )b T (τ r )), and determine vec(Z T ) has a covariance matrix of Step (22), calculate h r，aug Fisher Information Matrix (FIM): Let u = [(a(IMr)h)″, (a(IM8)h)″ and Calculate h according to the given formula r，aug The FIM, that is By substituting the relevant expressions, we get in Step (23), define and calculate the FIM about θ: further define the channel parameter set to be estimated as By formula Computing the FIM about θ involves By substituting the relevant derivative expressions, we finally get a more complex but clear FIM expression about θ, and point out that the expression can be simplified by choosing the center of RIS as the reference point (such as using Specific steps for PEB expression design: Step (24), define the relevant parameter vector: First, define the parameter vector related to the UE position as where p UE =[p x , p y ] T Indicates the position of the UE in the Cartesian coordinate system. This step lays the foundation for the subsequent calculation of the Jacobian matrix and the derivation of the PEB expression, and clarifies the key parameters related to the UE position and its representation in the vector. Step (25), calculate the Jacobian matrix: calculate the Jacobian matrix with respect to θ and The Jacobian matrix T of The Jacobian matrix T describes the The relationship between the changes in the FIM about θ is converted to the FIM about plays a key role in the FIM process, Step (26), get the FIM: By combining the FIM expression about θ obtained previously And the Jacobian matrix T, according to the formula Get about The FIM expression is: Step (27), derive the PEB expression: using the previously obtained According to the relationship between PEB and FIM, the PEB expression is derived. It is known that PEB can be expressed as Further calculation of C p To get the specific PEB expression, calculate C p When and T are expressed as block matrices, namely and Then use the block matrix inversion formula Calculate each of them separately and get as well as Through these calculations, we finally get C p The closed form expression of in C p Substitution The complete PEB expression is obtained, which provides the objective function for the subsequent optimization of RIS profile. Specific steps for optimal RIS profile design: Step (28), construct the RIS profile optimization problem: the positioning performance is evaluated using the position error bound (PEB) as an indicator, and the RIS profile optimization problem is constructed under the total power constraint, that is, s.t.tr{R r }≤P T ,R r ≥0 Where P T Represents the total transmission power. Through a series of derivations, PEB is expressed as the covariance matrix R with the RIS profile r The relevant form, that is, Further expressed as in Step (29), construct the RIS profile optimization problem: s.t.tr{R r }≤P T ,R r ≥0 Where P T Represents the total transmit power. Through a series of derivations, PEB is expressed as r Related forms: Further expressed as: Step (30), optimize R r Related terms and reconstruction optimization problem: First, simplify the Rr related terms, that is, tr{R φ }、 and Available R r The structure is simplified, and then R is determined r The optimal form is R r =UΛU H ,here, is a Hermitian matrix (i.e., Λ=Λ H ), U represents the * (φ ru )and Zhang Cheng's normalized subspace is in For the convenience of derivation, Λ is further expressed as Further simplifying tr{R φ }、 and As follows: φ }=λ 11 ||a(φ ru )|| 2 , Next, reconstruct the optimization problem and substitute the simplified result into the result: Due to the inequality Always holds, so Therefore, there is tr{C p }≥φ(λ 11 ,λ 22 ),in And if and only if λ 12 = 0, the equation holds true. Step (31), reformulate and solve the optimization problem: Based on the previous derivation, the RIS profile optimization problem is reformulated as an optimization problem with some newly defined parameters, namely stλ 11 +λ 22 ≤P T ,l 11 >0,λ 22 >0 in is an expression related to the previous derivation. Define auxiliary parameters and Solving the optimization problem yields: Step (32), determine the optimal covariance matrix and RIS profile design: According to the results obtained above, the optimal covariance matrix R r Re-expressed as in Then we discuss the design of RIS profile Γ r The optimal strategy is to reasonably allocate a * (φ ru )and The number of times to balance the PEB associated with the position coordinates, determine Make RIS profile And satisfy 4. The profile optimization design method in the positioning system based on RIS according to claim 3 is characterized in that: The method of step (3): Specific steps for constraining the RIS profile problem construction and design: Step (31), define the RIS profile constraint: Considering the RIS hardware limitation, for the RIS configuration of the lth element during the nth OFDM symbol [γ r，n ] l , define the actual RIS profile matrix as Γ r =[γ r，0 , γ r，1 , ..., γ r,N-1 ], whose effective constraint set For {[γ r，n ] l :|[γ r，n ] l |=1,∠[γ r，n ] l ∈[0, 2π)}, Step (32), construct the optimization problem: let Γ u Indicates that the expected covariance R can be achieved r A set of unconstrained RIS profiles, where W is for WW H =I L Under this constraint, the RIS profile design problem is constructed as Due to the non-convexity of the constraints and WW H =I L , this problem is difficult to solve directly, so we use the alternating minimization technique to deal with this problem in the next step. The specific steps of W's update plan are as follows: Step (33), the optimization problem is simplified: fix Γ r , the original optimization problem (70) is simplified to stWW H =I L Combined with WW H =I L ,right Expand: Ignore constant terms The cost function can be rewritten as stWW H = I L Step (34), singular value decomposition solution: Perform singular value decomposition, that is in is a left unitary matrix, is a diagonal matrix containing nonzero real-valued eigenvalues, is a right semiunitary matrix and (Assuming N>L), Substitution have to: By analyzing the inequality relationship when When taking the equal sign, the optimal solution is satisfy In order to maximize the objective function, Γ r The update scheme steps are as follows: Step (35), substitute W to simplify the objective function: Substitute the estimated value of W into the original objective function to obtain r Optimization problem Since each element of RIS can be designed independently, the problem can be further decomposed into in Step (36), consider the unit module constraint solution: Consider the unit module constraint, assuming The optimization problem can be rewritten as Using trigonometric relationships The closed form solution is Step (37), obtain the RIS profile design: using the phase estimate Considering the unit mode constraint, the final RIS profile design is obtained By alternating the above r and W, optimizing them in an iterative minimization manner until a specific termination criterion is met.

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