Intelligent reflecting surface system channel estimation method based on adaptive parallel factorization

Abstract

The application provides an intelligent reflecting surface system channel estimation method based on adaptive parallel factor decomposition, and the steps are as follows: firstly, an intelligent reflecting surface assisted multi-user multiple-input multiple-output uplink communication system is constructed; a pilot transmission mechanism is designed to construct a multi-user receiving signal tensor model, and the tensor model is converted into a third-order tensor model by using PARAFAC decomposition; secondly, the common channels of a user subset are estimated based on the third-order tensor model; and based on the common channels of the user subset, the common channels of the remaining users are estimated by using an adaptive tensor updating idea; finally, the independent channels of the remaining users are estimated by using a recursive least square tracking algorithm based on PARAFAC decomposition, so that the channel estimation of the multi-user cascade communication system is realized. The application effectively reduces the complexity of the PARAFAC decomposition process and improves the channel estimation performance.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and in particular to a channel estimation method for intelligent reflector systems based on adaptive parallel factor decomposition. Background Technology

[0002] Reconfigurable intelligent surfaces (RIS) are an emerging and promising technology in the upcoming 6th Generation (6G) communication systems. They possess the ability to modulate wireless channels, facilitating information transmission between base stations (BS) and user terminals (UTs). In RIS-assisted wireless communication systems, key design aspects such as beamforming, interference suppression, link adaptation, and resource optimization largely rely on the Channel State Information (CSI) of the two sub-links within the RIS system. Since the base station requires CSI to configure the passive RIS phase shift matrix to adjust the beam direction for beam gain and noise suppression, effectively acquiring CSI is a major challenge for this system, making high-precision channel estimation essential. However, due to the passive nature of RIS and its lack of signal processing capabilities, obtaining accurate channel state information is widely considered a significant challenge. Meanwhile, in multi-user multiple-input multiple-output (MIMO) systems, due to the large number of RIS reflector units and users, the channel matrix has a high dimension, requiring high pilot overhead for channel estimation and exhibiting very high computational complexity in multi-dimensional operations. Effectively reducing pilot overhead and the complexity of channel estimation algorithms is also a significant challenge.

[0003] In RIS-assisted MIMO communication systems, individual channel estimation between the user and the RIS, and between the RIS and the base station, is not feasible. It is necessary to obtain the Channel Indicators (CSIs) of two sub-channels to optimize the RIS phase shift matrix. We are more concerned with obtaining the CSI of the cascaded channel, which consists of a combination of the CSIs of two sub-channels. Existing CSI acquisition methods mainly include basic algorithms such as least squares and the traditional PARAFAC algorithm based on tensor decomposition. Benefiting from the strong uniqueness of tensor decomposition, tensor modeling has been successfully applied to solve the channel estimation problem of RIS systems, demonstrating superior estimation performance compared to basic algorithms such as least squares. However, the Bilinear Alternating Least Squares (BALS) algorithm based on Parallel Factor (PARAFAC) decomposition requires multiple iterations to reach convergence. We note that as the number of BS antennas, users, and RIS elements increases, the dimension of the cascaded channel increases. Due to the complexity of PARAFAC and the iteration, it introduces high algorithm complexity and parameter constraints. Summary of the Invention

[0004] To address the shortcomings of the aforementioned background technologies, this invention proposes a channel estimation method for intelligent reflector systems based on adaptive parallel factor decomposition. This method effectively reduces the complexity of the typical PARAFAC decomposition process and achieves estimation performance comparable to the BALS algorithm, making it better suited for channel estimation in multi-user RIS-assisted communication systems.

[0005] The technical solution of this invention is implemented as follows:

[0006] A channel estimation method for a smart reflector system based on adaptive parallel factorization, comprising the following steps:

[0007] S1: Construct a multi-user, multiple-input, multiple-output uplink communication system assisted by an intelligent reflector surface;

[0008] S2: Design a pilot transmission mechanism to construct a multi-user received signal tensor model, and use PARAFAC decomposition to convert the multi-user received signal tensor model into a third-order tensor model.

[0009] S3: Estimating the common channel of a subset of users based on a third-order tensor model of the received signal;

[0010] S4: Based on the estimated common channel of the user subset, estimate the common channel of the remaining users using the adaptive tensor update approach;

[0011] S5: Channel estimation for a multi-user cascaded communication system is achieved by using a recursive least squares tracking algorithm based on PARAFAC decomposition to estimate the independent channels of the remaining users.

[0012] The multi-user multiple-input multiple-output uplink communication system includes a base station, a RIS, and U single-antenna users; the U single-antenna users transmit signals, and the transmitted signals are reflected by the N passive reflective elements of the RIS to obtain reflected signals, which eventually reach the base station equipped with an M antenna array.

[0013] In step S2, the specific implementation method includes:

[0014] During channel estimation, U users simultaneously transmit orthogonal pilot signals. First, the phase shift mode of the RIS is divided into K blocks, k = 1…K. The s[k] of each block changes with the block k. The RIS phase shift mode for the k-th block is:

[0015]

[0016] Among them, s n,k ∈(0,1) represents the reflection amplitude of the nth passive reflective element on the kth block, φ n ∈(0,2π) represents the phase shift of the nth passive reflective element, n=1,...,N; the reflection phase shift matrix of RIS is Furthermore, within each block, U users simultaneously transmit orthogonal pilot sequences. These sequences repeat repeatedly in K blocks, satisfying XX H =I U The sequence X is divided into T time slots, X = [x[1]…x[T], and T≥U. Represents a column vector with N rows, [·] T Represents the transpose of a matrix;

[0017] After determining the phase shift of RIS, the received signal model of the U single-antenna user transmit signals is modeled using the tensor method as follows:

[0018] Y U [k]=Hdiag(s[k])G U X+B[k] (2);

[0019] in, In order to receive signals, It is a common channel from RIS to BS. It is the common channel set from U single-antenna users to RIS. It is additive white Gaussian noise;

[0020] Using an independent, identically distributed Rayleigh fading channel model as the benchmark for the common channel H and the independent channel G, the model is as follows:

[0021]

[0022] Among them, L α and Represent the path gain of the two channels, which follows large-scale fading; A and b u Represents small-scale fading channel parameters that follow a Rayleigh distribution;

[0023] Based on XX H =I U Simplify formula (2) and take get:

[0024]

[0025] Using the signal structure of tensors, the noise term was removed from the following development, and formula (4) was rewritten as:

[0026]

[0027] Among them, D k (S) = diag(s[k]) represents the diagonal matrix that maintains the k-th row of the RIS phase shift matrix S on its main diagonal; It can be viewed as a ternary tensor The k-th matrix slice, following the PARAFAC decomposition, is stacked along the dimensions of the k blocks. Generate a tensor model of the received signals from the 1st single-antenna user to the Uth single-antenna user, whose mode n product is expressed as:

[0028]

[0029] Among them, H,G U S is the three factor matrix of the tensor; This represents a third-order unit tensor with dimensions N×N×N. H represents the tensor. The product of the pattern n' of matrix H, where n'∈{1,2,3};

[0030] Using the trilinear decomposition of PARAFAC, the received signal tensor It can be represented in the following three forms:

[0031]

[0032]

[0033]

[0034] Here, ⊙ represents the Khatri-Rao product operation.

[0035] In step S3, the method for estimating the common channel of the user subset is as follows:

[0036] The BALS algorithm is used to estimate the channel state link information of a subset of users; the iterative solution is derived using an algorithm based on bilinear alternating least squares, where S is known and does not change during the iteration process, and the cost functions of H and g1 are expressed as follows:

[0037]

[0038]

[0039] in, Y1 is the estimated value of the common channel H. (1) The tensor pattern representing the received signal is expanded. Y1 is an estimate of g1. (2) The tensor mode 2 expansion representing the received signal, ||·|| F It is the F-norm;

[0040] The solution to the cost function in the above equation is:

[0041]

[0042]

[0043] in, Represents the pseudo-inverse operation of a matrix;

[0044] right Reconstruction is performed, and the iteration ends when the iteration error is less than the reconstruction error threshold ε, thus obtaining the estimated values ​​of g1 and H.

[0045] In step S4, the method for estimating the common channel for the remaining users is as follows:

[0046] For tensor models Part of it, when the number of users is u, u = 1, ..., U-1, utilizes two incomplete tensor models before and after the update. and Depend on The second dimension is sliced ​​to obtain the M×1×K slices; the PARAFAC model's bipartite structure is tracked by a third-order tensor with one-dimensional user count. The loading matrix G is updated for each added user, and all users are estimated after multiple updates. The specific implementation method is as follows:

[0047] Consider adding two tensor models before and after slicing. and The parallel factorization pattern has the following update rules:

[0048] Y u (2)=(S⊙H)G u , (14);

[0049] Y u+1 (2) =(S⊙H)G u+1 , (15);

[0050] In this multi-user RIS system, S and H are shared by multiple users. During the recursive update to estimate more users, channel H is considered invariant. In channel G, a weighting process is introduced. When estimating the components of the added slice PARAFAC decomposition, this can be achieved by minimizing the following exponential window least squares criterion:

[0051]

[0052]

[0053]

[0054] Where y(τ) represents the vector part of the tensor slice added each time. This indicates the pattern 2 expansion result of the tensor after each slice is added;

[0055] In formula (18), a windowing function is defined, where W u+1 =diag([λ u / 2 ,λ u-1 / 2 ,…,λ 1 / 2 [1]) is a weighted matrix, where λ is the forgetting factor exponent, and for Y u+1 (2) Applying exponential windowing means that each time a new user is added, all previously observed slices are assigned different weights, resulting in the following:

[0056]

[0057] in, This represents the pattern 2 expansion result of the tensor before each slice is added, y u+1 Vectorization of the received signal for adding new user slice portions;

[0058] Given the windowing weights and sliced ​​update data, for the recursive update of S⊙H in equations (14) to (15), the partial derivative of S⊙H is minimized by introducing a gradient function.

[0059]

[0060] When gradient function At that time, the derivation yielded:

[0061]

[0062] definition Then S⊙H can be represented as:

[0063]

[0064] Equations (14) and (15) can be rewritten as:

[0065]

[0066]

[0067] By Y u (2) To Y u+1 (2) The process is regarded as a tensor update. After the initial user estimation, tensor slices are continuously added to update other users. By using the above idea of ​​tensor recursive update, the received signal tensor model is continuously improved. After U-1 recursive updates, all users can be updated, and the estimation of the cascaded channel of the multi-user communication system is completed.

[0068] In step S5, the method for estimating the independent channels of the remaining users using the recursive least squares tracking algorithm based on PARAFAC decomposition is as follows:

[0069] During the recursive update process, S⊙H is continuously updated to achieve the desired result. and Recursive update, g u+1 To initialize the channels of the new slice portion, y u+1 To add a new user slice portion of the received signal vectorization form, where y u+1 =(Y U (2) ) :,u+1 First, the known H-channel state information before each update is used to track the slice update, and a preliminary g is obtained by substituting it into the input. u+1 The estimation results are as follows:

[0070]

[0071] at this time right and Two functions recursively update:

[0072]

[0073]

[0074] In the and The two functions are recursively updated to obtain the new result. Estimate:

[0075]

[0076] Utilize the newly obtained Re-estimation Its least squares solution is:

[0077]

[0078] because Not a square formation, but involves The pseudo-inverse operation needs to find The recursive update, whose rank-one update structure is obtained by the following formula:

[0079]

[0080] After updating, G is obtained using the following formula. u+1 Estimate:

[0081]

[0082] After U-1 recursive updates and exiting the loop, the final estimate G is achieved. U ; Based on the pattern tensor decomposition results The final result can be obtained Estimate:

[0083]

[0084] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0085] 1) This invention develops a tensor update algorithm, which updates the tensor model by continuously recursively updating the user-intelligent reflector matrix, and estimates the channel state information of the remaining users-intelligent reflectors. Based on the different channel path losses of different users and intelligent reflectors, a windowing function is introduced to improve the performance of channel estimation.

[0086] 2) Based on the developed tensor update idea, a recursive least squares tracking algorithm based on PARAFAC decomposition is derived to solve the channel estimation problem for the remaining users. The estimation performance and algorithm complexity of the overall algorithm are analyzed and compared with the traditional PARAFAC decomposition algorithm. The performance is close to that of the traditional PARAFAC decomposition algorithm and the algorithm complexity is improved by an order of magnitude.

[0087] 3) This invention effectively reduces the complexity of the typical PARAFAC decomposition process and achieves estimation performance comparable to the BALS algorithm. Attached Figure Description

[0088] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0089] Figure 1 This is a RIS-assisted multi-user MIMO wireless communication uplink scenario;

[0090] Figure 2 This is the time-domain pilot frame structure used in the channel estimation process of this invention;

[0091] Figure 3 This is a schematic diagram of the recursive update process of the received signal tensor model;

[0092] Figure 4 The normalized mean square error curve of the algorithm provided in this invention is compared with the traditional PARAFAC decomposition algorithm when the number of blocks K is 16 and the link signal-to-noise ratio varies.

[0093] Figure 5 This invention provides a graph showing the estimated performance variation of the algorithm scheme at different K values ​​as the link signal-to-noise ratio changes.

[0094] Figure 6 This is a graph showing the change in estimation performance of the present invention under different initial estimates as the link signal-to-noise ratio changes;

[0095] Figure 7 This is a flowchart of the present invention. Detailed Implementation

[0096] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0097] like Figure 7 As shown in the figure, this invention provides a channel estimation method for an intelligent reflector system based on adaptive parallel factorization. The specific steps are as follows:

[0098] S1: Construct a smart reflector-assisted multi-user multiple-input multiple-output (MIMO) uplink communication system. Smart reflector technology can independently control the amplitude and phase of the reflected signal through its metasurface reflective elements, thereby adjusting the beam direction to provide beam gain and suppress noise. Based on MIMO communication, a smart reflector-assisted system model is constructed to solve the system's channel estimation problem. Establish a system model as follows: Figure 1 The diagram illustrates a RIS-assisted multi-user MIMO wireless communication uplink scenario, considering the RIS path. In this scenario, the RIS path is taken into account, while the direct path is considered to be hindered due to unfavorable propagation conditions. U single-antenna users transmit signals, which arrive at a base station equipped with an M-antenna array. The RIS consists of N passive reflective elements, each capable of individually adjusting the phase shift of the reflected signal.

[0099] S2: Design a pilot transmission mechanism to construct a multi-user received signal tensor model, and use PARAFAC decomposition to convert the multi-user received signal tensor model into a third-order tensor model; construct a time-domain pilot transmission mode, divide the phase shift matrix of the intelligent reflector into blocks, and mathematically model the received signal at the base station of the multi-user system based on the mathematical model of the tensor. Under the constraint of unique decomposition, the received signal tensor model is sliced ​​and expanded in three forms.

[0100] In step S2, the specific implementation method includes:

[0101] During the entire channel estimation process, U users simultaneously transmit orthogonal pilot signals. First, the phase shift mode of the RIS is divided into K blocks, k = 1…K; as follows… Figure 2 As shown, s[k] of each block changes with block k. The RIS phase shift mode for the k-th block is:

[0102]

[0103] s[k] is a known phase-shifting mode, where s n,k ∈(0,1) represents the reflection amplitude of the nth passive reflective element on the kth block, φ n ∈(0,2π) represents the phase shift of the nth passive reflective element, where n = 1,...,N. The reflection phase shift matrix of RIS is... Furthermore, within each block, U users simultaneously transmit orthogonal pilot sequences. These sequences repeat repeatedly in K blocks, satisfying XX H =I U To ensure its orthogonality, the sequence X is divided into T time slots, X = [x[1]...x[T]], which requires X rows to be full rank, which means T≥U. Represents a column vector with N rows; [·] TThis represents the transpose. In the time domain, the pilot signal is divided into KT time slots, and U users transmit signals simultaneously. Therefore, the pilot overhead for channel estimation is UKT, which facilitates the application of tensor mathematical models to multi-user signal structures.

[0104] After determining the phase shift of RIS, the received signal model of the U single-antenna user transmit signals is modeled using the tensor method as follows:

[0105] Y U [k]=Hdiag(s[k])G U X+B[k] (2);

[0106] in, In order to receive signals, It is a common channel from RIS to BS. It is the common channel set from U single-antenna users to RIS. It is additive white Gaussian noise. For all channel models in this invention, an independent, identically distributed Rayleigh fading channel model is used as the benchmark for the common channel H and the independent channel G, and the following formula is used for modeling:

[0107]

[0108] Among them, L α and The path gain of two channels, A and B, follows a large-scale fading distribution, indicating different path losses between the channels and can be used to distinguish the communication quality of users. u This represents the small-scale fading channel parameters that follow a Rayleigh distribution.

[0109] Based on XX H =I U The signal structure of formula (2) is simplified by taking... get:

[0110]

[0111] To simplify the explanation of the signal model, a tensor signal structure is used, and the noise term is removed from the following development. The noise term will be considered later. Equation (4) can be rewritten as:

[0112]

[0113] Among them, D k (S) = diag(s[k]) represents the diagonal matrix that maintains the k-th row of the RIS phase shift matrix S on its main diagonal; It can be viewed as a ternary tensor The k-th matrix slice, following the PARAFAC decomposition, is stacked along the dimensions of the k blocks. Generate a tensor model of the received signals from the 1st single-antenna user to the Uth single-antenna user, whose mode n product is expressed as:

[0114]

[0115] Among them, H,G U S is the three factor matrix of the tensor; This represents a third-order unit tensor with dimensions N×N×N.

[0116] Tensor The product of the mode n' of matrix H, where n'∈{1,2,3}. Using the trilinear decomposition of PARAFAC, the received signal tensor... It can be represented in the following three forms:

[0117]

[0118]

[0119]

[0120] Here, ⊙ represents the Khatri-Rao product operation.

[0121] In this invention, a multi-user channel estimation method is formulated using the mode-two decomposition structure of the PARAFAC model, which is widely used due to the uniqueness of its factor decomposition.

[0122] S3: Estimate the common channel of user subsets based on the third-order tensor model of the received signal; for the multi-user received signal model, estimate the channel state information of single user-intelligent reflector and intelligent reflector-base station using the parallel factorization algorithm based on its subset.

[0123] Traditional channel estimation algorithms ignore the Khatri-Rao product structure of cascaded channels, which can reduce training overhead. The BALS algorithm uses tensor decomposition to estimate multiple users in batches, leading to higher algorithm complexity due to high-dimensional data processing. However, observations show that in an established uplink system, each user's composite channel shares the same RIS-BS channel H. This shared channel state information can be used to divide channel estimation into two parts without sacrificing generality. First, initial users are selected for channel estimation, and the shared H channel is obtained. In step S2, the obtained H channel information is used to estimate other users, which reduces training overhead and algorithm complexity.

[0124] The BALS algorithm is used to estimate the channel state link information of a subset of users; the iterative solution is derived using an algorithm based on bilinear alternating least squares, where S is known and does not change during the iteration process, and the cost functions of H and g1 are expressed as follows:

[0125]

[0126]

[0127] in, Y1 is the estimated value of the common channel H. (1) The mode indicating the received signal is expanded. Y1 is an estimate of g1. (2) This represents the mode 2 expansion of the received signal, ||·|| F It is the F-norm.

[0128] The solution to the cost function in the above equation is:

[0129]

[0130]

[0131] in, This represents the pseudo-inverse operation of a matrix.

[0132] right Reconstruction is performed, and the iteration stops when the iteration error is less than the reconstruction error threshold ε, yielding estimates of g1 and H. The reconstruction error threshold is set to ε = 10. -5 .

[0133] S4: Based on the estimated common channel of the user subset, the common channel of the remaining users is estimated using the adaptive tensor update idea; based on the special characteristics of the multi-user channel attributes of the system, all users share the same intelligent reflector - base station channel, a tensor update algorithm developed in this invention is adopted to update the tensor model by continuously recursively updating the user - intelligent reflector matrix, and to estimate the channel state information of the remaining users - intelligent reflector. Furthermore, based on the different channel path losses of different users and intelligent reflectors, a windowing function is introduced to improve the performance of channel estimation.

[0134] Based on the tensor signal modeling described above, a third-order tensor model of the received signals from multiple users was obtained. definition in It is an additive noise tensor. The goal of this invention is to estimate the multi-user channel matrices H and G. First, estimates of g1 and H are obtained. Based on the third-order tensor model of the multi-user received signals, the idea of ​​tracking PARAFAC decomposition is proposed.

[0135] Figure 3 For tensor recursive update models, for tensor models Part of it, when the number of users is u, u = 1, ..., U-1, utilizes two incomplete tensor models before and after the update. and Depend on The second dimension is sliced ​​to obtain the M×1×K slices. The PARAFAC model's bipartite structure is tracked using a third-order tensor with one-dimensional user counts. Each time a user is added, the loading matrix G is updated. After multiple updates, all users are estimated. The main recursive update idea is as follows:

[0136] Consider adding two tensor models before and after slicing. and The parallel factorization pattern has the following update rules:

[0137] Y u (2) =(S⊙H)G u , (14);

[0138] Y u+1 (2) =(S⊙H)G u+1 , (15);

[0139] In this system, due to the characteristics of a multi-user RIS system, S and H are shared by multiple users. During the recursive update process to estimate the data for more users, channel H is considered constant; in channel G, The distribution of PARAFAC decomposition results in varying communication quality for different users. To accommodate this distribution, a weighted process is introduced. When estimating the components of the PARAFAC decomposition with added slices, this can be achieved by minimizing the following exponential window least squares criterion:

[0140]

[0141]

[0142]

[0143] Where y(τ) represents the vector portion of the tensor slice added each time. This indicates the pattern 2 expansion result of the tensor obtained after each slice is added.

[0144] In formula (18), a windowing function is defined, where W u+1 =diag([λ u / 2 ,λ u-1 / 2 ,…,λ 1 / 2 [1]) is a weighted matrix, where λ is the forgetting factor exponent, and for Y u+1(2) By applying exponential windowing, where each new user is added, all previously observed slices are assigned different weights, resulting in the following:

[0145]

[0146] in, This represents the pattern 2 expansion result of the tensor before each slice is added, y u+1 Vectorized form of the received signal for adding new user slice portions.

[0147] Given the windowing weights and sliced ​​update data, for the recursive update of S⊙H in equations (14) to (15), the partial derivative of S⊙H is minimized by introducing a gradient function.

[0148]

[0149] When gradient function At that time, the derivation yielded:

[0150]

[0151] definition A simplified version can be obtained to recursively update S⊙H, namely:

[0152]

[0153] Equations (14) and (15) can be rewritten as:

[0154]

[0155]

[0156] By Y u (2) To Y u+1 (2) The process is regarded as a tensor update. After the initial user estimation, tensor slices are continuously added to update other users. By using the above idea of ​​tensor recursive update, the received signal tensor model is continuously improved. After U-1 recursive updates, all users can be updated, and the estimation of the multi-user cascaded communication system is completed.

[0157] S5: Channel estimation for a multi-user cascaded communication system is achieved by estimating the independent channels of remaining users using a recursive least squares tracking algorithm based on PARAFAC decomposition. Based on the tensor update concept developed in this invention, a recursive least squares tracking algorithm based on PARAFAC decomposition is derived to solve the channel estimation problem for remaining users. The overall estimation performance and algorithm complexity are analyzed, and compared with the traditional PARAFAC decomposition algorithm. The performance is close to that of the traditional PARAFAC decomposition algorithm, while achieving an order-of-magnitude improvement in algorithm complexity.

[0158] Based on the above analysis, a recursive least squares tracking algorithm based on PARAFAC decomposition is derived:

[0159] During the recursive update process, S⊙H is continuously updated to achieve the desired result. and Recursive update, g u+1 To initialize the channels of the new slice portion, y u+1 To add a new user slice portion of the received signal vectorization form, where y u+1 =(Y U (2) ) :,u+1 First, the known H-channel state information before each update is used to track the slice update, and a preliminary g is obtained by substituting it into the input. u+1 The estimation results are as follows:

[0160]

[0161] at this time right and Two functions recursively update:

[0162]

[0163]

[0164] In the and The two functions are recursively updated to obtain the new result. Estimate:

[0165]

[0166] Utilize the newly obtained Re-estimation Its least squares solution is:

[0167]

[0168] because Not a square formation, but involves The pseudo-inverse operation needs to find The recursive update, whose rank-one update structure is obtained by the following formula:

[0169]

[0170] After updating, G is obtained using the following formula. u+1 Estimate:

[0171]

[0172] After U-1 recursive updates and exiting the loop, the final estimate G is achieved. U ; Based on the pattern tensor decomposition results The final result can be obtained Estimate:

[0173]

[0174] In this invention, numerical results are provided to evaluate the performance of the proposed channel estimation method. The accuracy of the channel estimation is evaluated based on the normalized mean square error (NMSE), which is defined as follows:

[0175]

[0176] Among them, H c It is the cascade channel for the entire RIS system, H c =H*G U Note that the channel estimates H and G U Affected by scaling factor, Where △ G and △ H It is a diagonal matrix that includes column scaling ambiguity, such that △ H △ G =I N When the two are multiplied, scaling ambiguities are eliminated. These scaling ambiguities are irrelevant in this invention because they compensate for each other when constructing the estimate of the cascaded UT-RIS-BS channel. Therefore, the normalized mean square error of the cascaded channel is used to evaluate the performance of the proposed algorithm. The pilot signal matrix X and the RIS phase shift matrix S can be designed to satisfy XX respectively. H =I U and SS H =I K For a semi-unitary matrix, a feasible solution is to design X and S as truncated Discrete Fourier Transform (DFT) matrices, where R is the number of Monte Carlo simulations, and the signal-to-noise ratio (SNR) (dB) is defined as...

[0177]

[0178] In this invention, for the multi-user received signal tensor model Each subset of received signals needs to satisfy the Kruskal uniqueness condition in the PARAFAC decomposition. According to the uniqueness of the PARAFAC tensor decomposition, the tensor decomposition is unique when the k-rank of the three sub-factor matrices in the PARAFAC decomposition model satisfies the following formula, and its sufficient condition is:

[0179]

[0180] For the tensor tracking algorithm of this invention, since as well as The rank-one update structure needs to satisfy as well as The update process always maintains a full rank to ensure reversibility. During the update, the column rank is full, at which point K≥N, and there are certain restrictions on the number of blocks K.

[0181] According to the present invention, a performance comparison between the proposed algorithm and the traditional PARAFAC decomposition algorithm can be obtained, such as... Figure 4 As shown, the simulation parameter configuration of the present invention is detailed in Table 1.

[0182] Table 1 Simulation parameter configuration

[0183]

[0184] Figure 4 The normalized mean square error (MSE) curves of the proposed scheme are presented for signal-to-noise ratios (SNRs) of 0-30 dB, and compared with the traditional PARAFAC decomposition algorithm. Furthermore, the Cramero lower bound is used as a benchmark for the lower bound of estimation performance. Specifically, three schemes with different weighting coefficients λ = 0.5, λ = 1, and λ = 2 are studied. First, users with higher large-scale fading factors are selected for estimation, and then the results are continuously updated towards users with lower weighting coefficients. The results show that as the SNR increases, the MSE of the proposed scheme continuously decreases. When λ = 1, the proposed scheme exhibits performance comparable to the BALS scheme in the SNR range. The value of λ has a certain impact on the proposed scheme; certain errors can be observed when λ = 0.5 and λ = 2. Figure 5 In the previous section, the number of parameter blocks K was varied and its impact on estimation performance was discussed. It can be seen that a higher K leads to improved estimation performance, but this improvement comes at the cost of increased pilot overhead. Here, the trade-off between training overhead and performance is clearly evident. In the proposed scheme, a subset of users needs to be selected for initial CSI estimation. Therefore, in Figure 6Furthermore, the impact of the initial user subset on the NMSE of the proposed scheme was investigated. Three scenarios were considered: the channel estimation update algorithm was executed sequentially based on the users' large-scale fading coefficients from high to low (Scenario 1), random order (Scenario 2), and low to high (Scenario 3). Simulation results show that the algorithm performs best in the first case, especially in the low signal-to-noise ratio region. This is mainly because the first solution has better user channel quality and higher reliability, which helps to improve the initial estimation accuracy of the common estimate and reduce error propagation.

[0185] The overall algorithm framework and its complexity are shown in Table 2. The complexity is primarily measured by the number of multiplications performed on the matrix. and Its product complexity is For the operation of the Khatri-Rao product, the matrix but The complexity is Based on the algorithm complexity summary in Table 2, the total algorithm complexity is: The traditional PARAFAC decomposition BALS algorithm involves iterative operations, with a time complexity of O(n log n) for a single iteration. The number of iterations is I, and since S is known, the number of iterations generally does not exceed 10. The total ALS complexity is O(I). Under the experimental dimensions adopted in this invention, M=16, K=16, N=8, U=8, I=10, the results show that the complexity of the algorithm proposed in this invention is much lower than that of the BALS algorithm. The complexity comparison is shown in Table 3, and the complexity is reduced by 80%.

[0186] Table 2 Overall Algorithm Framework

[0187]

[0188]

[0189] Table 3. Complexity Comparison

[0190]

[0191] This invention develops an adaptive algorithm for the PARAFAC decomposition of the third-order tensor model of received signals in a multi-user RIS system. This invention effectively reduces the complexity of the traditional PARAFAC decomposition process by avoiding multiple iterations. Verification shows that the algorithm's performance is close to that of the BALS algorithm, with an order-of-magnitude reduction in complexity.

[0192] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A channel estimation method for an intelligent reflector system based on adaptive parallel factorization, characterized in that, The steps are as follows: S1: Construct a multi-user, multiple-input, multiple-output uplink communication system assisted by an intelligent reflector surface; S2: Design a pilot transmission mechanism to construct a multi-user received signal tensor model, and use PARAFAC decomposition to convert the multi-user received signal tensor model into a third-order tensor model. S3: Estimating the common channel of a subset of users based on a third-order tensor model of the received signal; S4: Based on the estimated common channel of the user subset, estimate the common channel of the remaining users using the adaptive tensor update approach; For tensor models Part of it, when the number of users is At that time, the two incomplete tensor models before and after the update are used. and The PARAFAC model's bipartite structure is tracked by a third-order tensor with one-dimensional user counts; the loading matrix is ​​updated with each added user. After multiple updates, the estimate was made for all users; among them, U represents the number of users per antenna. Depend on The added portion is obtained by adding slices in the second dimension. The slice, M is the number of antenna arrays equipped in the base station, and K is the number of phase shift mode divisions of the RIS; The specific implementation method is as follows: Consider adding two tensor models before and after slicing. and The parallel factorization pattern has the following update rules: （1）； （2）； in, Here is the reflection phase shift matrix of RIS. It is the common channel from RIS to BS; due to the characteristics of multi-user RIS systems, and Shared by multiple users, the channel is recursively updated to estimate the number of users. It is considered immutable; load matrix In this paper, a weighted process is introduced to estimate the components of the PARAFAC decomposition with added slices by minimizing the following exponential window least squares criterion: （3）； （4）； （5）； in, This represents the vector portion of each added tensor slice. This indicates the pattern 2 expansion result of the tensor after each slice is added; In formula (5), a windowing function is defined, where For weighted matrices, It is the forgetting factor index, for Applying exponential windowing means that each time a new user is added, all previously observed slices are assigned different weights, resulting in the following: （6）； in, This represents the result of the tensor's pattern 2 expansion before each slice is added. Vectorization of the received signal for adding new user slice portions; Given the windowing weights and the sliced ​​data update, for equations (1) to (2) The recursive update is achieved by introducing a gradient function. Find the partial derivative to minimize : （7）； When gradient function At that time, the derivation yielded: （8）； definition , ,but Represented as: （9）； Equations (1) and (2) are rewritten as: （10）； （11）； Depend on arrive The process is viewed as a tensor update. After the initial user estimation, tensor slices are continuously added to update other users; the received signal tensor model is continuously improved by using the above idea of ​​tensor recursive update; after... This recursive update updates all users, completing the estimation of the cascaded channel for the multi-user communication system. S5: Channel estimation for a multi-user cascaded communication system is achieved by using a recursive least squares tracking algorithm based on PARAFAC decomposition to estimate the independent channels of the remaining users. During the recursive update process, continuously update In turn, to achieve the goal of and Recursive update, To initialize the channels of the new slice, To add a new user slice portion of the received signal vectorization form, where First, the known H-channel state information before each update is used to track the slice update, and a preliminary result is obtained. The estimation results are as follows: （12）； at this time ,right and Two functions recursively update: （13）； （14）； In the and The two functions are recursively updated to obtain the new result. Estimate: （15）； Utilize the newly obtained Re-estimation Its least squares solution is: （16）； because Not a square formation, but involves The pseudo-inverse operation needs to find The recursive update, whose rank-one update structure is obtained by the following formula: （17）； After updating, we obtain the following formula: Estimate: （18）； exist After each recursive update and loop exit, the final estimate is achieved. Based on the pattern tensor decomposition results Get the final Estimate: （19）。 2. The channel estimation method for intelligent reflector systems based on adaptive parallel factorization according to claim 1, characterized in that, The multi-user multiple-input multiple-output uplink communication system includes a base station, a RIS, and U single-antenna users; the U single-antenna users transmit signals, and the transmitted signals are reflected by the N passive reflective elements of the RIS to obtain reflected signals, which eventually reach the base station equipped with M antennas.

3. The channel estimation method for intelligent reflector systems based on adaptive parallel factorization according to claim 2, characterized in that, In step S2, the specific implementation method includes: During channel estimation, U users simultaneously transmit orthogonal pilot signals; firstly, the phase shift mode of RIS is divided into K blocks. Each piece With block The RIS phase shift mode changes with the change, and for the k-th block, it is: （20）； in, This represents the reflection amplitude of the nth passive reflective element on the kth block. This represents the phase shift of the nth passive reflective element. The reflection phase shift matrix of RIS is: Furthermore, within each block, U users simultaneously transmit orthogonal pilot sequences. These sequences are repeated repeatedly in K blocks, satisfying , convert the sequence Divided into Each time slot ,and , Represents a column vector with N rows. Represents the transpose of a matrix; After determining the phase shift of RIS, the received signal model of the U single-antenna user transmit signals is modeled using the tensor method as follows: （21）； in, In order to receive signals, It is a common channel from RIS to BS. It is the channel set from U single-antenna users to the RIS. It is additive white Gaussian noise; Using an independent, identically distributed Rayleigh fading channel model as the common channel and channel set The benchmark, its model is: （22）； in, and This represents the path gain of the two channels, which follows large-scale fading. and Represents small-scale fading channel parameters that follow a Rayleigh distribution; based on Simplify formula (21) and take get: （23）； Using the signal structure of tensors, the noise term was removed from the following development, and formula (23) was rewritten as: （24）； in, This represents the diagonal matrix that maintains the k-th row of the RIS phase shift matrix S along its main diagonal; the matrix... It can be viewed as a ternary tensor The k-th matrix slice, following the PARAFAC decomposition, is stacked along the dimensions of the k blocks. Generate a tensor model of the received signal from the 1st single-antenna user to the Uth single-antenna user, whose mode n product is expressed as: （25）； in, The dimension is The third-order unit tensor, Tensor With matrix pattern product, ; Using the trilinear decomposition of PARAFAC, the received signal tensor It can be represented in the following three forms: （26）； （27）； （28）； in, This represents the Khatri-Rao product operation.

4. The channel estimation method for intelligent reflector systems based on adaptive parallel factorization according to claim 3, characterized in that, In step S3, the method for estimating the common channel of the user subset is as follows: The BALS algorithm is used to estimate the channel state link information of a subset of users; the iterative solution is derived using an algorithm based on bilinear alternating least squares, where S is known and does not change during the iteration process. and The cost functions are expressed as follows: （29）； （30）； in, For public channels The estimated value, The tensor pattern representing the received signal is expanded. for The estimated value, The tensor mode 2 expansion representing the received signal, It is the F-norm; The solution to the cost function in the above equation is: （31）； （32）； in, Represents the pseudo-inverse operation of a matrix; right Reconstruction is performed when the iteration error is less than the reconstruction error threshold. When the iteration ends, we get and The estimated value.

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