Semi-active IRS system channel estimation method and system based on random and fixed sampling

Abstract

The invention discloses a semi-active IRS system channel estimation method and system based on random and fixed sampling, and belongs to the technical field of wireless communication. The method comprises the following steps: sampling a first channel model between a user and a reflecting surface and a second channel model between the reflecting surface and a base station based on a received signal, and carrying out preliminary estimation on the first channel model and the second channel model to obtain a first estimation result and a second estimation result; obtaining a first angle estimation value between the user and the reflecting surface and a second angle estimation value between the reflecting surface and the base station based on the first estimation result and the second estimation result; obtaining a first full-dimensional channel between the user and a reflecting surface channel based on the first angle estimation value, and obtaining a second full-dimensional channel between the reflecting surface and a base station channel based on the second angle estimation value; and constructing a cascade channel based on the first full-dimensional channel and the second full-dimensional channel. According to the method, the channel state can be accurately estimated, and channel reconstruction is completed.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a semi-active IRS system channel estimation method and system based on random and fixed sampling. Background Art

[0002] The communications industry has experienced rapid growth in recent years, with significant increases in cellular traffic and data rates. Due to their abundant spectrum resources, millimeter wave (mmWave) and terahertz (THz) frequency bands have attracted widespread attention in sixth-generation (6G) wireless networks and their subsequent technologies. Channel estimation is a key research area in wireless communication systems, crucial for achieving high-quality signal transmission. Therefore, accurately acquiring channel state information ensures the performance of wireless communication systems.

[0003] However, in practice, channel estimation for a single millimeter-wave system is already a significant challenge, and the addition of intelligent reflecting surfaces (IRSs) further complicates channel estimation. Existing channel state estimation methods typically involve estimating separate IRS-BS and MS-IRS channels, passive channels, or related channel parameters. Some researchers have exploited the redundancy in multi-user passive channels to design a three-phase estimator based on least squares and linear minimum mean square error (LMMEE) estimation. However, this approach is extremely expensive and complex for obtaining channel state information. Summary of the Invention

[0004] The present invention aims to address the deficiencies of the existing technology and proposes a channel estimation method and system for a semi-active IRS system based on random and fixed sampling. Unlike passive intelligent reflecting surfaces, this method utilizes active elements on the reflecting surface to accurately estimate channel state information while greatly reducing the channel estimation overhead and system computational complexity, ultimately completing channel reconstruction.

[0005] To achieve the above object, the present invention provides the following solution: a semi-active IRS system channel estimation method based on random and fixed sampling, comprising the following steps:

[0006] S1. Sampling a first channel model between a user and a reflecting surface and a second channel model between the reflecting surface and a base station based on a received signal, and performing a preliminary estimation on the first channel model and the second channel model to obtain a first estimation result and a second estimation result;

[0007] S2. Obtain a first angle estimation value between the user and the reflecting surface and a second angle estimation value between the reflecting surface and the base station based on the first estimation result and the second estimation result respectively;

[0008] S3. Obtain a first full-dimensional channel between the user and the reflecting surface channel based on the first angle estimation value, and obtain a second full-dimensional channel between the reflecting surface and the base station channel based on the second angle estimation value;

[0009] S4. Construct a cascade channel based on the first omni-dimensional channel and the second omni-dimensional channel.

[0010] Further preferably, the first channel model is:

[0011]

[0012] Where K represents the number of user antennas; N represents the reflector array elements; L F represents the total number of paths between the user and the reflecting surface; B I (θ I ), and P F denote the reflector array response matrix, user array response matrix and diagonal path gain matrix respectively; θ I,l 、φ T,l and ρ F，l are the arrival angle of the reflecting surface, the departure angle of the user and the gain of the lth path respectively; b I (θ I，l )and All are steering vectors;

[0013] The second channel model is:

[0014]

[0015] Where M represents the number of base station antennas; L G represents the total number of paths between the reflection surface and the base station; φ I，l ,θ R，l and ρ G，l represent the departure angle at the reflection surface, the arrival angle at the base station, and the gain of the lth path in the lth path respectively; B R (θ R ), and P G are the base station array response matrix, the reflector array response matrix, and the diagonal path gain matrix, respectively; b R (θ R，l )and are steering vectors.

[0016] Further preferably, the sampling method includes:

[0017] Sampling the first channel module and the second channel model using a sparse matrix to obtain a submatrix;

[0018] Performing a second-layer random sampling on the submatrix to obtain unit transmission symbols and noise observations;

[0019] The method of sampling the first channel model to obtain the submatrix C0 includes:

[0020]

[0021] Where, represents the first row selection matrix; and Represent the sparse matrices used by the reflection surface and the user respectively; N n,s and N t,s They represent the number of elements sampled at the reflection surface end in the F channel and the number of user antennas sampled.

[0022] The method of sampling the second channel model to obtain the submatrix C1 includes:

[0023]

[0024] Where, represents the second row selection matrix; and Represent the sparse matrices of the reflection surface and base station sampling respectively;

[0025] Perform the second layer of random sampling on the sub-matrix C0 to obtain the noise observation Y F The methods include:

[0026]

[0027] Where Ω represents the uniform sampling spatial pattern, P Ω represents the first sampling operator; N represents additive white Gaussian noise;

[0028] Perform the second layer of random sampling on the submatrix C1 to obtain the noise observation Y G The methods include:

[0029]

[0030] Where, E Ω Represents the second sampling operator.

[0031] Further preferably, the method for obtaining the first estimation result includes:

[0032] The low-rank matrix recovery method is used to estimate the submatrix C0 and the estimated result is:

[0033]

[0034] In the formula, ||.|| F represents the Frobenius norm; δ 2 Indicates tolerance;

[0035] The estimation results are re-expressed using the nuclear norm regularization method:

[0036]

[0037] Where μ>0 represents the regularization parameter; ||.|| * represents the nuclear norm;

[0038] Recovering the re-expressed estimation result according to the Frobenius norm representation of the nuclear norm;

[0039]

[0040] Where U represents the left factor matrix of low-rank matrix decomposition; V represents the right factor matrix of low-rank matrix decomposition;

[0041] Get the estimated result after recovery and rank

[0042] Further preferably, the method for obtaining the first angle estimation value includes:

[0043] Based on the sub-matrix Get the covariance matrix T1 and covariance matrix T2;

[0044] Based on the covariance matrix T1 and covariance matrix T2, the eigenvalue decomposition of root-MUSIC is used to obtain the arrival angle on the reflecting surface and the user's departure angle

[0045] Further preferably, the method for obtaining the first full-dimensional channel includes:

[0046] Based on the angle of arrival and the departure angle Get the steering vector of the reflecting surface and the user;

[0047] obtaining a path gain based on the steering vector;

[0048] Based on the angle of arrival The departure angle and path gain The first full-dimensional channel is obtained.

[0049] Further preferably, the method for obtaining the cascade channel includes:

[0050]

[0051] Where, represents the first full-dimensional channel; represents the second full-dimensional channel; the superscript T represents transpose.

[0052] The present invention also provides a semi-active IRS system channel estimation system based on random and fixed sampling, comprising: a sampling module, an estimation module, a calculation module and a construction module;

[0053] The sampling module is used to sample a first channel model between the user and the reflecting surface and a second channel model between the reflecting surface and the base station based on the received signal, and perform preliminary estimation on the first channel model and the second channel model to obtain a first estimation result and a second estimation result;

[0054] The estimation module obtains a first angle estimation value between the user and the reflecting surface and a second angle estimation value between the reflecting surface and the base station based on the first estimation result and the second estimation result respectively;

[0055] The calculation module obtains a first full-dimensional channel between the user and the reflection surface channel based on the first angle estimation value, and obtains a second full-dimensional channel between the reflection surface and the base station channel based on the second angle estimation value;

[0056] The building module builds a cascade channel based on the first full-dimensional channel and the second full-dimensional channel.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] The present invention is based on a semi-active IRS channel estimation method based on fixed and random sampling, combined with low-rank matrix completion (LRMC) technology, which significantly reduces the overhead and complexity of channel estimation. F and ρ G follow At the same time, all departure angles and arrival angles are evenly distributed within [30°, 150°]. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0060] Figure 11 is a flow chart of a channel estimation method for a semi-active IRS system based on random and fixed sampling according to an embodiment of the present invention;

[0061] Figure 2 A model diagram of a channel estimation system for a semi-active IRS system based on random and fixed sampling provided by an embodiment of the present invention;

[0062] Figure 3 This is a simulation diagram of the NMSE performance of semi-active channel estimation under different signal-to-noise ratio conditions in an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0064] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] Example 1:

[0066] like Figure 1 As shown, this embodiment provides a semi-active IRS system channel estimation method based on random and fixed sampling, which specifically includes the following steps:

[0067] S1. Based on the received signal, a first channel model between the user and the reflecting surface and a second channel model between the reflecting surface and the base station are sampled, and a preliminary estimation is performed on the sampled first channel model and the second channel model to obtain a first estimation result and a second estimation result.

[0068] Assume that the distance from user to reflecting surface (IRS) and from IRS to base station are respectively L F and L G paths, the first channel model between the user and the IRS is:

[0069]

[0070] Where K represents the number of user antennas; N represents the reflector array elements; L F represents the total number of paths between the user and the reflecting surface; B I (θ I ), and P F denote the reflector array response matrix, user array response matrix and diagonal path gain matrix respectively; θ I，l 、φT，l and ρ F，l denote the arrival angle of the reflecting surface, the departure angle of the user, and the gain of the lth path, respectively; where the arrival angle and departure angle are uniformly distributed in [0, π]; b I (θ I，l )and are steering vectors.

[0071] in,

[0072]

[0073] Where k represents the carrier wavelength; Indicates the antenna spacing.

[0074] According to the above method, the second channel model between the reflection surface and the base station can be obtained:

[0075]

[0076] Where M represents the number of base station antennas; L G represents the total number of paths between the reflection surface and the base station; φ I，l ,θ R，l and ρ G，l represent the departure angle at the reflection surface, the arrival angle at the base station, and the gain of the lth path in the lth path respectively; B R (θ R ), and P G are the base station array response matrix, the reflector array response matrix, and the diagonal path gain matrix, respectively; b R (θ R，l )and are steering vectors.

[0077] Thus, the channel model between the user and the base station is obtained:

[0078]

[0079] Where Ω = diag(ω), ω contains the phase shift information of the IRS element and is expressed as follows:

[0080]

[0081] Where, γ i and α i Represent the reflection coefficient and phase shift of the i-th reflection surface element respectively. i =1 means the i-th element is open, γ i =0 means that the i-th element is closed.

[0082] Based on the formula The channel model H can be expressed as:

[0083]

[0084] Where, It is a cascade channel; It represents Khatri-Rao product.

[0085] Because H S The high dimensionality of and the limited observations on the mixed receiver make it difficult to estimate H S Challenging.

[0086] Different from the passive intelligent reflector, after the base station receives and processes the first observation signal, it uses the base station as a transmitter and the second channel model between the base station and the IRS is:

[0087]

[0088] Where b I (φ I,l ) represents the array response vector at the reflection surface in the lth path; represents the array response vector at the base station in the lth path; B I (φ I ) represents the response matrix of the reflector array; represents the base station array response matrix.

[0089] In this embodiment, G is the channel model from the reflection surface to the base station, G1 is the channel model from the base station to the reflection surface, and the reflection surface beamforming matrix B in G1 and G is I (φ I ), base station beamforming matrix B R (θ R ) and the diagonal matrix P of the path gain G same.

[0090] In this embodiment, the sampling method includes: sampling the channel using a sparse matrix to obtain a sub-matrix; and performing second-layer random sampling on the sub-matrix to obtain unit transmission symbols and noise observations.

[0091] Specifically, different from the passive smart reflector, the sparse matrix only samples a single F channel to obtain the submatrix C0:

[0092]

[0093] Where, represents the first row selection matrix; and Represent the sparse matrices used by the reflection surface and the user respectively; N n,s and N t,sThey represent the number of elements sampled at the reflector end in the F channel and the number of antennas sampled for the user. Assume that the indicators of the user and the antenna selected on the reflector are recorded in W t and W n group. Then there is |W t |=N r,s and |W n |=N n,s , now define the user end antenna The same method is used to define the antenna N at the reflector surface n,u .

[0094] When using UBS, the subarray antennas are arranged from the first antenna to the Nth antenna of the original array of size N. s The antennas are uniformly selected. The sparse matrix of fixed sampling is constructed as follows:

[0095]

[0096] Among them, N s ≤N, it can be clearly seen that the aperture of the subarray is reduced and restricted according to the number of selected antennas.

[0097] When using GNS, a GNS sampler and The fixed sparse matrix is constructed as follows:

[0098]

[0099] in, Γ(N)=1+N-Θ 2 (N), the total number of antennas selected is N s =Γ(N)+Θ(N)-1.

[0100] Then perform the second layer sampling on the submatrix C0 to obtain the noise observation:

[0101]

[0102] Where, P Ω represents the uniformly sampled spatial pattern, P Ω represents the first sampling operator corresponding to Ω; N represents additive white Gaussian noise.

[0103] make is the noise pattern of C0, that is in So the noise observation Y F yes A subset of , namely:

[0104]

[0105] Where, [·] i,j Represents the (i,j)th entity of the matrix.

[0106] The vectorized representation of non-zero observations is:

[0107] y F =P Ω vec(C0),

[0108] In the formula, the very sparse matrix and Corresponding to the sampling mode Ω, while ρ Ω,F Represents the sampling ratio of LRMC, that is:

[0109]

[0110] Where, is the l0 norm, which is used to calculate the number of non-zero entries in a vector.

[0111] The training cost is determined by the overall sampling ratio, which is defined as the ratio of the number of samples to the number of entries in F, that is:

[0112]

[0113] By using the above method, the second channel model between the reflecting surface and the base station is sampled to obtain the sub-matrix C1:

[0114]

[0115] Where, represents the second row selection matrix; and Represent the sparse matrices of the reflection surface and base station sampling respectively;

[0116] Perform the second layer of random sampling on the submatrix C1 to obtain the noise observation Y G The methods include:

[0117]

[0118] Where, E Ω Represents the second sampling operator.

[0119] make represents the noise pattern of C1, that is in Get a vectorized representation of the nonzero observations:

[0120] y G =E Ω vec(C1),

[0121] In the formula, the very sparse matrix and

[0122] In this embodiment, the method for obtaining the first estimation result includes:

[0123] Using IMC from Medium estimate because Since it is low rank, the low rank matrix recovery method is first used to estimate the submatrix C0 and obtain the estimated result;

[0124]

[0125] In the formula, ||.|| F represents the Frobenius norm; δ 2 Indicates tolerance.

[0126] The estimation results are re-expressed using the nuclear norm regularization method;

[0127]

[0128] Where μ>0 is the regularization parameter; ||·|| * represents the nuclear norm.

[0129] According to the Frobenius norm representation of the nuclear norm, let C0 = UV H , restore the re-expressed estimation result;

[0130]

[0131] Where U represents the left factor matrix of low-rank matrix decomposition; V represents the right factor matrix of low-rank matrix decomposition.

[0132] Get the estimated results after recovery and rank

[0133] Similarly, the above method is used to obtain the second estimation result:

[0134] C1 is estimated by solving the low-rank matrix recovery problem:

[0135]

[0136] The above NP-hard problem can be reformulated using the nuclear norm regularization method as follows:

[0137]

[0138] According to the Frobenius norm representation of the nuclear norm, let C1 = UVH And solve to recover C1:

[0139]

[0140] After recovery and rank

[0141] S2. Obtain a first angle estimation value between the user and the reflecting surface and a second angle estimation value between the reflecting surface and the base station based on the first estimation result and the second estimation result respectively.

[0142] The method of obtaining the first angle estimate includes:

[0143] Based on submatrix Get the covariance matrix T1; specifically, the steps are as follows:

[0144] For virtual channels When using UBS sampling, X = C0, the singular value decomposition (SVD) can be used to easily obtain The subspace spanned by the steering vectors of the user and the uniform linear array on the reflective surface is obtained. When using GNS sampling, antennas are not selected continuously. In this case, C0 is a submatrix of X. Since part of the ULA antenna is not sampled, it cannot be directly processed using SVD decomposition. This embodiment solves this problem by first modeling the nth column of the matrix X:

[0145]

[0146] Where x n represents the nth column of channel X; Indicates that N n,u Array response of the antenna's ULA.

[0147] in, ρ l represents the gain of the lth path; Indicates that N t,u ULA array response of antennas; φ l represents the angle of the lth path; [·] n It means taking the nth item of a vector.

[0148] ρ l,n Modeled as an uncorrelated random source signal, we get x n The covariance matrix T1 of ; where T1 is a Toeplitz matrix. Let in, For a containing N n,u A vector of constants.

[0149] Specifically, T1 consists of Estimation methods include:

[0150]

[0151] Where, [·] i,: Represents the i-th row of the matrix; I d represents the sum of the added terms; and the base k i ∈W n Indicates that it corresponds to The index of the reflector antenna in the i-th row, based on k j ∈W n Indicates that it corresponds to The index of the reflector antenna in the jth row of . When there are a large number of columns, the above formula can accurately reconstruct T1, thereby producing accurate angle estimates.

[0152] Based on the eigenvalue decomposition of the covariance matrix T1 and root-MUSIC, the arrival angle on the reflecting surface is obtained Based on the covariance matrix T2, the user's departure angle can be obtained

[0153] Specifically, T2 is composed of The estimation method is:

[0154]

[0155] Similarly, based on the above steps, we get the Toeplitz matrices T3 and T4 with the angle information of the reflecting surface and the base station, and use the root-MUSIC algorithm to estimate the arrival angle based on T3 and T4. and departure angle

[0156] S3. Obtain a first full-dimensional channel between the user and the reflecting surface channel based on the first angle estimation value, and obtain a second full-dimensional channel between the reflecting surface and the base station channel based on the second angle estimation value.

[0157] The method of obtaining the first full-dimensional channel includes:

[0158] Based on angle of arrival and departure angle Get the steering vector of the reflecting surface and the user; and based on the steering vector, get the path gain

[0159]

[0160] Where, is the l0 norm, which is used to calculate the number of non-zero items in a vector.

[0161] The OMP algorithm can solve the above problems.

[0162] Based on angle of arrival Departure angle and path gain Get the first full-dimensional channel:

[0163]

[0164] Where Mat(·) represents mapping the parameters in the brackets to a matrix with a predefined dimension.

[0165] Similarly, based on the angle of arrival and departure angle Obtain the steering vectors of the base station and the reflecting surface, and estimate the path gain based on the steering vectors

[0166]

[0167] Then we get the second full-dimensional channel:

[0168]

[0169] S4. Construct a cascade channel based on the first omni-dimensional channel and the second omni-dimensional channel.

[0170] The cascade channel expression is as follows:

[0171]

[0172] Example 2:

[0173] This embodiment illustrates the method of the present invention through specific examples. The present invention improves the shortcomings of the semi-active intelligent reflection surface channel estimation method.

[0174] like Figure 2 As shown in Figure 1, the channel estimation system consists of a user with K, N, and M antennas, an IRS, and a base station. Assume that the direct path between the user and the base station is blocked, so the IRS is needed to assist in the transmission from the user to the base station. At the same time, there is a backhaul link between the IRS and the base station to complete the transmission of the signal. Specifically, with the number of paths L MR =L RB =2, the number of user antennas and the number of base station antennas are both 64 antennas, and the reflector array elements N = 128. Table 1 shows the general parameter settings, and channel estimation is performed based on the parameters in Table 1.

[0175] Table 1

[0176]

[0177] There are two paths from the user to the IRS and from the IRS to the base station. Therefore, the channel model between the user and the reflection surface is:

[0178]

[0179] in:

[0180]

[0181] According to the above method, the channel model between the reflection surface and the base station is obtained:

[0182]

[0183] After the base station receives and processes the first observation signal, the base station is used as a transmitter and the channel between the base station and the IRS is modeled as:

[0184]

[0185] Thus, the channel model between the user and the base station is obtained:

[0186]

[0187] Where Ω = diag(ω), which is expressed as:

[0188]

[0189] At the same time, according to the formula Channel H becomes:

[0190]

[0191] in, It is a cascade channel.

[0192] The sparse matrix is used to sample the F channel to obtain the submatrix C0:

[0193]

[0194] in, and

[0195] When using UBS, the subarray antennas are uniformly selected from the first antenna to the 22nd antenna of the original array of size 64. The fixed sampling matrix is constructed as follows, where it can be clearly seen that the aperture of the subarray is reduced and restricted according to the number of selected antennas:

[0196]

[0197] When using GNS, a GNS sampler Easily available:

[0198]

[0199] Among them, Θ(64)=7, Γ(N)=16, and the total number of antennas selected is 22.

[0200] Perform the second layer of random sampling on the submatrix C0 to obtain the noise observation:

[0201]

[0202] Where Ω represents the uniformly sampled spatial pattern, P Ω represents the first sampling operator corresponding to Ω; N represents additive white Gaussian noise.

[0203] make is the noise pattern of C0, that is in So the noisy observation result YF is A subset of , namely:

[0204]

[0205] Where, [·] i,j Represents the (i,j)th entity of the matrix.

[0206] The vectorized representation of non-zero observations is:

[0207] y F =P Ω vec(C0),

[0208] In the formula, the very sparse matrix and Corresponding to the sampling mode Ω, while ρ Ω,F Represents the sampling ratio of LRMC, that is:

[0209]

[0210] Where, is the l0 norm, which is used to calculate the number of non-zero entries in a vector.

[0211] The training cost is determined by the overall sampling ratio, which is defined as the ratio of the number of samples to the number of entries in F, that is:

[0212]

[0213] By using the above method, the channel model between the reflection surface and the base station is sampled to obtain the sub-matrix C1:

[0214]

[0215] Where, express The second row selects the matrix; and Represent the sparse matrices of the reflection surface and base station sampling respectively;

[0216] Perform the second layer of random sampling on the submatrix C1 to obtain the noise observation Y G The methods include:

[0217]

[0218] Where, E Ω Represents the second sampling operator.

[0219] make represents the noise pattern of C1, that is in Get a vectorized representation of the nonzero observations:

[0220] y G =E Ω vec(C1),

[0221] In the formula, the very sparse matrix and

[0222] In this embodiment, the method for obtaining the first estimation result includes:

[0223] Using IMC from Medium estimate because Since it is low rank, the low rank matrix recovery method is first used to estimate the submatrix C0 and obtain the estimated result;

[0224]

[0225] In the formula, ||.|| F represents the Frobenius norm; δ 2 Indicates tolerance;

[0226] The estimation results are re-expressed using the nuclear norm regularization method;

[0227]

[0228] Where μ>0 is the regularization parameter; ||·|| * represents the nuclear norm.

[0229] According to the Frobenius norm representation of the nuclear norm, let C0 = UV H , restore the re-expressed estimation result;

[0230]

[0231] Get the estimated results after recovery and rank

[0232] Similarly, the above method is used to obtain the second estimation result:

[0233] C1 is estimated by solving the low-rank matrix recovery problem:

[0234]

[0235] The above NP-hard problem can be reformulated using the nuclear norm regularization method as follows:

[0236]

[0237] According to the Frobenius norm representation of the nuclear norm, let And solve to recover C1:

[0238]

[0239] After recovery and rank

[0240] from Obtain the subspace spanned by the steering vectors of the uniform linear arrays on the user and the base station, and obtain the covariance matrix T1 based on the submatrix C0; the specific steps are as follows:

[0241] For virtual channels When using UBS sampling, X = C0, the singular value decomposition (SVD) can be used to easily obtain The subspace spanned by the steering vectors of the user and the uniform linear array on the reflective surface is obtained. When using GNS sampling, antennas are not selected continuously. In this case, C0 is a submatrix of X. Since part of the ULA antenna is not sampled, it cannot be directly processed using SVD decomposition. This embodiment solves this problem by first modeling the nth column of the matrix X:

[0242]

[0243] Where x n represents the nth column of channel X; Indicates that N n,u Array response of the antenna's ULA.

[0244] in, ρ l represents the gain of the lth path; Indicates that Nt,u ULA array response of antennas; φ l represents the angle of the lth path; [·] n It means taking the nth item of a vector.

[0245] ρ l,n Modeled as an uncorrelated random source signal, we get x n The covariance matrix T1 of ; where T1 is a Toeplitz matrix. Let in, is a vector containing 128 numbers.

[0246] Specifically, T1 consists of Estimation methods include:

[0247]

[0248] Where, [·] i,: Represents the i-th row of the matrix; I d Represents the sum of the added terms; base k i ∈W n Indicates that it corresponds to The index of the reflector antenna in the i-th row; j ∈W n Indicates that it corresponds to The index of the reflector antenna in the jth row. When there are a large number of columns, the above formula can accurately reconstruct T1, thereby producing accurate angle estimates.

[0249] Based on the eigenvalue decomposition of the covariance matrix T1 and root-MUSIC, the arrival angle on the reflecting surface is obtained Based on T2, the user's departure angle can be obtained

[0250] Specifically, T2 is composed of The estimation method is:

[0251]

[0252] Similarly, based on the above steps, we get the Toeplitz matrices T3 and T4 with the angle information of the reflecting surface and the base station, and use the root-MUSIC algorithm to estimate the arrival angle based on T3 and T4. and departure angle

[0253] According to the arrival angle and departure angle Construct the steering vectors of the base station and the user.

[0254] And based on the steering vector, the path gain is obtained

[0255]

[0256] Where, is the l0 norm, which is used to calculate the number of non-zero items in a vector.

[0257] The OMP algorithm can solve the above problems.

[0258] Based on angle of arrival Departure angle and path gain Get the first full-dimensional channel:

[0259]

[0260] Where Mat(·) represents mapping the parameters in the brackets to a matrix with a predefined dimension.

[0261] Similarly, based on the angle of arrival and departure angle Obtain the steering vectors of the base station and the reflecting surface, and estimate the path gain based on the steering vectors

[0262]

[0263] Then we get the second full-dimensional channel:

[0264]

[0265] The cascade channel expression obtained by the first full-dimensional channel and the second full-dimensional channel is as follows:

[0266]

[0267] like Figure 3 As shown in the figure, simulations compare the normalized mean square error performance of semi-active channel estimation using different sampling methods under different signal-to-noise ratio (PNR) conditions. Five sampling methods are used, including uniform block sampling (UBS), generalized nested sampling (GNS), GNS combined with low-rank matrix completion (GNS+LRMC), UBS combined with low-rank matrix completion (UBS+LRMC), and no sampling. Simulation results show that the channel estimation accuracy is the highest under the no-sampling condition, showing the best performance across all PNR ranges. In addition, the channel estimation accuracy using generalized nested sampling (GNS) is significantly higher than that of fixed sampling (UBS). When a second layer of sampling (i.e., GNS+LRMC) is combined with GNS, its performance is still better than UBS+LRMC, indicating that the GNS sampling mode has significant advantages in channel recovery.

[0268] Example 3:

[0269] This embodiment provides a semi-active IRS system channel estimation system based on random and fixed sampling, including: a sampling module, an estimation module, a calculation module, and a construction module.

[0270] The sampling module is used to sample the first channel model between the user and the reflecting surface and the second channel model between the reflecting surface and the base station based on the received signal, and to perform preliminary estimation on the sampled first channel model and the second channel model to obtain a first estimation result and a second estimation result.

[0271] The estimation module obtains a first angle estimation value between the user and the reflecting surface and a second angle estimation value between the reflecting surface and the base station based on the first estimation result and the second estimation result respectively.

[0272] The calculation module obtains a first full-dimensional channel between the user and the reflection surface channel based on the first angle estimation value, and obtains a second full-dimensional channel between the reflection surface and the base station channel based on the second angle estimation value.

[0273] The building module builds a cascade channel based on the first full-dimensional channel and the second full-dimensional channel.

[0274] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A channel estimation method for a semi-active IRS system based on random and fixed sampling, characterized in that: The following steps are involved: S1. Sampling a first channel model between a user and a reflecting surface and a second channel model between the reflecting surface and a base station based on a received signal, and performing a preliminary estimation on the first channel model and the second channel model to obtain a first estimation result and a second estimation result; S2. Obtain a first angle estimation value between the user and the reflecting surface and a second angle estimation value between the reflecting surface and the base station based on the first estimation result and the second estimation result respectively; S3. Obtain a first full-dimensional channel between the user and the reflecting surface channel based on the first angle estimation value, and obtain a second full-dimensional channel between the reflecting surface and the base station channel based on the second angle estimation value; S4. Construct a cascade channel based on the first omni-dimensional channel and the second omni-dimensional channel.

2. The channel estimation method for a semi-active IRS system based on random and fixed sampling according to claim 1, characterized in that: The first channel model is: Where K represents the number of user antennas; N represents the reflector array elements; L F represents the total number of paths between the user and the reflecting surface; B I (θ I ), and P F denote the reflector array response matrix, user array response matrix and diagonal path gain matrix respectively; θ I,l 、φ T,l and ρ F,l are the arrival angle of the reflecting surface, the departure angle of the user and the gain of the lth path respectively; b I (θ I,l )and All are steering vectors; The second channel model is: Where M represents the number of base station antennas; L G represents the total number of paths between the reflection surface and the base station; φ I,l ,θ R,l and ρ G，l represent the departure angle at the reflection surface, the arrival angle at the base station, and the gain of the lth path in the lth path respectively; B R (θ R ), and P G are the base station array response matrix, the reflector array response matrix, and the diagonal path gain matrix, respectively; b R (θ R，l )and are steering vectors.

3. The semi-active IRS system channel estimation method based on random and fixed sampling according to claim 2, characterized in that: The sampling method includes: Sampling the first channel module and the second channel model using a sparse matrix to obtain a submatrix; Performing a second-layer random sampling on the submatrix to obtain unit transmission symbols and noise observations; The method of sampling the first channel model to obtain the submatrix C0 includes: Where, represents the first row selection matrix; and Represent the sparse matrices used by the reflection surface and the user respectively; N n,s and N t,s They represent the number of elements sampled at the reflection surface end and the number of user antennas sampled in the F channel respectively; The method of sampling the second channel model to obtain the submatrix C1 includes: Where, represents the second row selection matrix; and Represent the sparse matrices of the reflection surface and base station sampling respectively; Perform the second layer of random sampling on the sub-matrix C0 to obtain the noise observation Y F The methods include: Where Ω represents the uniform sampling spatial pattern, P Ω represents the first sampling operator; N represents additive white Gaussian noise; Perform the second layer of random sampling on the submatrix C1 to obtain the noise observation Y G The methods include: Where, E Ω Represents the second sampling operator.

4. The semi-active IRS system channel estimation method based on random and fixed sampling according to claim 3, characterized in that: The method for obtaining the first estimation result includes: The low-rank matrix recovery method is used to estimate the submatrix C0 and the estimated result is: In the formula, ||.|| F represents the Frobenius norm; δ 2 Indicates tolerance; The estimation results are re-expressed using the nuclear norm regularization method: Where μ>0 represents the regularization parameter; ||.|| * represents the nuclear norm; Recovering the re-expressed estimation result according to the Frobenius norm representation of the nuclear norm; Where U represents the left factor matrix of low-rank matrix decomposition; V represents the right factor matrix of low-rank matrix decomposition; Get the estimated result after recovery and rank 5. The semi-active IRS system channel estimation method based on random and fixed sampling according to claim 4, characterized in that: The method for obtaining the first angle estimate includes: Based on the sub-matrix Get the covariance matrix T1 and covariance matrix T2; Based on the covariance matrix T1 and covariance matrix T2, the eigenvalue decomposition of root-MUSIC is used to obtain the arrival angle on the reflecting surface and the user's departure angle 6. The channel estimation method for a semi-active IRS system based on random and fixed sampling according to claim 5, characterized in that: The method for obtaining the first full-dimensional channel includes: Based on the angle of arrival and the departure angle Get the steering vector of the reflecting surface and the user; obtaining a path gain based on the steering vector; Based on the angle of arrival The departure angle and path gain The first full-dimensional channel is obtained.

7. The semi-active IRS system channel estimation method based on random and fixed sampling according to claim 1, characterized in that: The method for obtaining the cascade channel includes: Where, represents the first full-dimensional channel; represents the second full-dimensional channel; the superscript T represents transpose.

8. A semi-active IRS system channel estimation system based on random and fixed sampling, the system being used to implement the method according to any one of claims 1 to 7, characterized in that: include: Sampling module, estimation module, calculation module and construction module; The sampling module is used to sample a first channel model between the user and the reflecting surface and a second channel model between the reflecting surface and the base station based on the received signal, and perform preliminary estimation on the first channel model and the second channel model to obtain a first estimation result and a second estimation result; The estimation module obtains a first angle estimation value between the user and the reflecting surface and a second angle estimation value between the reflecting surface and the base station based on the first estimation result and the second estimation result respectively; The calculation module obtains a first full-dimensional channel between the user and the reflection surface channel based on the first angle estimation value, and obtains a second full-dimensional channel between the reflection surface and the base station channel based on the second angle estimation value; The building module builds a cascade channel based on the first full-dimensional channel and the second full-dimensional channel.

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