Channel estimation method and system for passive IRS system based on random and fixed sampling

Abstract

The application discloses a passive 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: two-layer sampling is performed on a cascaded channel to be estimated, and preliminary estimation is performed on the sampled cascaded channel to obtain a noise observation estimation result; a first angle estimation value of two-end antennas is obtained based on the noise observation estimation result; a precoder and a combiner are constructed based on the first angle estimation value, and a second angle estimation value of a reflecting surface is obtained based on the precoder and the combiner; a dictionary matrix is constructed based on the first angle estimation value and the second angle estimation value, and overall gain of a channel is obtained based on the dictionary matrix; and an estimation value of a cascaded channel matrix is obtained based on the first angle estimation value, the second angle estimation value and the overall gain, and channel recovery is completed. The application can reduce the complexity and cost of channel estimation under the condition of accurately estimating channel state information.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a channel estimation method and system for passive IRS systems based on random and fixed sampling. Background Technology

[0002] Intelligent reflectors (IRS), as a key technology for improving the spectral efficiency and coverage of wireless communication systems, face challenges in channel estimation due to its time-varying nature, high dimensionality, and complex propagation environments. Significant differences exist between millimeter-wave and terahertz (THz) channels: millimeter-wave channels typically exhibit sparse multipath structures, while terahertz channels require separate modeling due to path loss and molecular absorption effects. Combining traditional signal processing techniques with modern optimization methods has become a trend.

[0003] In practice, channel estimation for large-scale MIMO systems remains a significant challenge due to noise and multipath fading, prompting numerous researchers to propose various solutions. These include using low-rank matrix completion and the Root-MUSIC algorithm for parameterized estimation of hybrid MIMO systems, or extracting super-resolution angle parameters and path gains in stages through atomic norm minimization. To address the high-dimensionality problem of large-scale IRS deployments, a staged processing framework distinguishes between quasi-static BS-IRS channels and dynamic IRS-UE channels, updating estimates on differentiated time scales. However, all of these methods suffer from high estimation complexity and excessive overhead in acquiring channel state information. Summary of the Invention

[0004] This invention aims to address the shortcomings of existing technologies by proposing a channel estimation method for passive IRS systems based on random and fixed sampling. The method comprises the following steps:

[0005] S1. Perform two-layer sampling on the cascaded channel to be estimated, and make a preliminary estimate on the sampled cascaded channel to obtain the noise observation estimation result;

[0006] S2. Based on the noise observation estimation results, obtain the first angle estimate of the antennas at both ends;

[0007] S3. Construct a pre-encoder and a combiner based on the first angle estimate, and obtain a second angle estimate of the reflecting surface based on the pre-encoder and the combiner;

[0008] S4. Construct a dictionary matrix based on the first angle estimate and the second angle estimate, and obtain the overall channel gain based on the dictionary matrix;

[0009] S5. Based on the first angle estimate, the second angle estimate, and the overall gain, obtain the estimated value of the cascaded channel matrix to complete channel recovery.

[0010] More preferably, S1 includes the following steps:

[0011] S1.1 Model the cascaded channel to be estimated to obtain the cascaded channel model;

[0012] S1.2 Perform two-layer sampling on the cascaded channel model to obtain the noise observation estimation results.

[0013] More preferably, the method for obtaining the cascaded channel model includes:

[0014] Modeling the channel between the transmitter and the reflector, we obtain H. MR Channel model:

[0015]

[0016] In the formula, N t and N I These represent the number of transmitting antennas and the reflector array elements, respectively; L MR θ represents the total number of paths from the transmitter to the reflector. MR,l φ MR,l and γ MR,l Let a represent the angle of arrival at the reflector of the l-th path, the angle of departure at the transmitter, and the gain of the l-th path, respectively; I (θ MR,l )and All are steering vectors; A I (θ MR ), and Γ MR These represent the reflector array response matrix, the transmitter array response matrix, and the diagonal path gain matrix, respectively.

[0017] Modeling the channel between the reflector and the receiver yields H. RB Channel model:

[0018]

[0019] In the formula, N r Indicates the number of antennas at the receiving end; L RB φ represents the total number of paths between the reflector and the receiver. RB,l θ RB,l and γ RB,l Let a represent the departure angle at the reflector of the l-th path, the arrival angle at the receiver, and the gain of the l-th path, respectively; RB (θ RB,l )and All are steering vectors; A RB (θ RB ), and Γ RB These represent the receiver array response matrix, the reflector array response matrix, and the diagonal path gain matrix, respectively.

[0020] Based on the H MR Channel model and H RB The channel model yields the cascaded channel model H:

[0021]

[0022] In the formula, the superscript T indicates transpose; the superscript * indicates conjugate; The ◇ symbol represents the Kronecker product; the ◇ symbol represents the Khatri-Rao product. H represents MR Channel and H RB The composite of channel path gains; Γ represents the diagonal path gain matrix; ψ I Indicates the composite angle of the reflecting surface; A TR Represents the combined array response matrix;

[0023] in,

[0024] More preferably, the method for obtaining the noise observation estimation result by performing two-layer sampling on the cascaded channel model includes:

[0025] The cascaded channel is sampled using a sparse matrix to obtain the first layer of submatrix U0:

[0026]

[0027] In the formula, and These represent the sparse matrix of the reflector sampling and the sparse matrix of the transmitter sampling, respectively.

[0028] The submatrix U0 is sampled in a second layer to obtain the noise observation estimation result:

[0029]

[0030] In the formula, Ω represents the uniform sampling spatial sampling mode, and A Ω Indicates the corresponding sampling operator; N represents additive white Gaussian noise.

[0031] More preferably,

[0032] The submatrix U0 is estimated using the low-rank matrix recovery method, and the estimation result is obtained as follows:

[0033]

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

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

[0036]

[0037] In the formula, μ>0 represents the regularization parameter; ||.|| * Represents the nuclear norm;

[0038] The estimated result is recovered by using the Frobenius norm representation of the nuclear norm:

[0039]

[0040] In the formula, U represents the left factor matrix of the low-rank matrix decomposition; V represents the right factor matrix of the low-rank matrix decomposition.

[0041] Where, U0 = UV H ;

[0042] The estimated result after restoration is obtained.

[0043] More preferably, the first angle estimate includes: the angle of arrival of the receiver. and the departure angle of the launcher

[0044] Methods for obtaining the angle of arrival at the receiver include:

[0045] Based on the estimation results, the covariance matrix of the angle of arrival at the receiver is obtained:

[0046]

[0047] Using the root-mUSIC eigenvalue decomposition scheme, the angle of arrival at the receiver is recovered based on the covariance matrix.

[0048] More preferably, S3 includes the following steps:

[0049] Construct a preencoder P and a combiner W based on the first angle estimate:

[0050]

[0051] The received signal is obtained based on the precoder and the combiner:

[0052]

[0053] In the formula, H d Indicates a valid channel; For training symbols; n d,l This represents the noise during the l-th channel usage in step d;

[0054] A second angle estimate of the reflecting surface is obtained based on the received signal.

[0055] More preferably, the estimated value of the cascaded channel matrix includes:

[0056]

[0057] In the formula, Indicates gain.

[0058] The present invention also provides a channel estimation system for a passive IRS system based on random and fixed sampling, comprising: a sampling module, a first angle estimation module, a second angle estimation module, a calculation module, and a recovery module;

[0059] The sampling module is used to perform two-layer sampling on the cascaded channel to be estimated, and to perform a preliminary estimation on the sampled cascaded channel to obtain the noise observation estimation result;

[0060] The first angle estimation module is used to obtain the first angle estimate of the two antennas based on the noise observation estimation result;

[0061] The second angle estimation module is used to construct a pre-encoder and a combiner based on the first angle estimation value, and to obtain a second angle estimation value of the reflecting surface based on the pre-encoder and the combiner;

[0062] The calculation module is used to construct a dictionary matrix based on the first angle estimate and the second angle estimate, and to obtain the overall channel gain based on the dictionary matrix;

[0063] The recovery module is used to obtain an estimate of the cascaded channel matrix based on the first angle estimate, the second angle estimate, and the overall gain, thereby completing channel recovery.

[0064] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0065] This invention utilizes a method of random and fixed sampling, with path gain γ MR and γ RB obey Meanwhile, both the departure angle and the arrival angle are uniformly distributed within [30°, 150°]. Compared with traditional methods, accurate channel state information recovery is achieved using a small amount of channel information, reducing the complexity and overhead of channel estimation. Attached Figure Description

[0066] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are 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.

[0067] Figure 1 This is a schematic diagram of the channel estimation method for a passive IRS system based on random and fixed sampling according to an embodiment of the present invention;

[0068] Figure 2 This is a system model diagram of a passive IRS system based on random and fixed sampling, according to an embodiment of the present invention.

[0069] Figure 3 The figure shows the NMSE performance simulation of passive channel estimation under different signal-to-noise ratio conditions in this embodiment of the invention. Detailed Implementation

[0070] 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.

[0071] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] Example 1:

[0073] like Figure 1 As shown, this embodiment provides a channel estimation method for a passive IRS system based on random and fixed sampling, including the following steps:

[0074] S1. Perform two-layer sampling on the cascaded channel to be estimated, and make a preliminary estimate on the sampled cascaded channel to obtain the noise observation estimation result.

[0075] Specifically, S1 includes the following steps:

[0076] S11. Model the cascaded channel to be estimated to obtain the cascaded channel model.

[0077] First, the channel between the transmitter and the reflector is modeled to obtain H. MR Channel model:

[0078]

[0079] In the formula, N t and N I These represent the number of transmitting antennas and the reflector array elements, respectively; L MR θ represents the total number of paths from the transmitter to the reflector. MR,l φ MR,l and γ MR,l These represent the angle of arrival at the reflecting surface, the angle of departure at the transmitting end, and the gain of the l-th path, respectively; a I (θ MR,l )and All are steering vectors; A I (θ MR ), and Γ MR These represent the reflector array response matrix, the transmitter array response matrix, and the diagonal path gain matrix, respectively.

[0080]

[0081] In the formula, k represents the carrier wavelength; Antenna spacing; angle θ MR,l It follows a uniform distribution in the range [0, π].

[0082] Similarly, by modeling the channel between the reflector and the receiver, we obtain H. RB Channel model:

[0083]

[0084] In the formula, N r Indicates the number of antennas at the receiving end; L RB φ represents the total number of paths between the reflector and the receiver. RB,l θ RB,l and γ RB,l These represent the departure angle at the reflecting surface, the arrival angle at the receiving end, and the gain of the l-th path, respectively; a RB (θ RB,l )and All are steering vectors; A RB (θ RB ), and Γ RB These represent the receiver array response matrix, the reflector array response matrix, and the diagonal path gain matrix, respectively.

[0085] Based on formulas (1) and (2), the cascaded channel model H between the transmitter and receiver is obtained:

[0086]

[0087] In the formula, Ω = diag(ω), where ω contains the phase shift information of the reflecting surface elements, as shown below:

[0088]

[0089] In the formula, β i and ζ i Let β represent the reflection coefficient and phase shift of the i-th reflecting surface element, respectively. i =1 indicates that the i-th element is turned on, β i =0 indicates that the i-th element is turned off.

[0090] From the formula vec(Ediag(f)G)=(G T ◇E)f yields:

[0091]

[0092] In the formula, It is a cascaded channel, and ◇ represents the Khatri-Rao product.

[0093] By identities and and Cascaded channels can be modeled as:

[0094]

[0095] In the formula, the superscript T indicates transpose; the superscript * indicates conjugate; The ◇ symbol represents the Kronecker product; the ◇ symbol represents the Khatri-Rao product. H represents MR Channel and H RB The composite of channel path gains; Γ represents the diagonal path gain matrix; ψ I This indicates the composite angle of the reflecting surface.

[0096] in,

[0097] Where, ψ I,i,j =cos -1 (cos(φ RB,j )-cos(θ MR,i )) represents the effective angular difference between the i-th arrival angle and the j-th departure angle in the reflecting surface.

[0098] S12. Perform two-layer sampling on the cascaded channel model to obtain the noise observation estimation results.

[0099] First, a sparse matrix is ​​used to perform the first layer of sampling on the cascaded channel, resulting in a submatrix U0:

[0100]

[0101] In the formula, and These represent the sparse matrix of the reflector sampling and the sparse matrix of the transmitter sampling, respectively.

[0102] When using UBS, the subarray antennas range from the first antenna of the original array of size Q to the Nth antenna. s The antennas are selected uniformly. The matrix for fixed sampling is constructed as follows:

[0103]

[0104] Where, N s With a value ≤Q, it is clear that the aperture of the subarray is reduced and limited depending on the number of antennas selected.

[0105] When using GNS, a GNS sampler and The matrix obtained by fixed sampling is:

[0106]

[0107] in, Γ(Q)=1+Q-Θ 2 (Q), the overall selected antenna is N. s =Γ(Q)+Θ(Q)-1. When the selected subarrays are the same size, arrays using the GNS sampling mode typically have a larger array aperture than arrays using the UBS sampling mode, which means higher spatial resolution.

[0108] Perform a second layer of sampling on submatrix U0 to obtain the noise observation estimation results:

[0109]

[0110] In the formula, Ω represents the uniform sampling spatial sampling mode, and A Ω Indicates the corresponding sampling operator; N represents additive white Gaussian noise.

[0111] S2. Based on the noise observation estimation results, the first angle estimate of the antennas at both ends is obtained.

[0112] Using IMC from Estimating θ RB and φ RB .in, This indicates the noise mode of U0.

[0113] First, the submatrix U0 is estimated using the low-rank matrix recovery method, and the estimation result is obtained:

[0114]

[0115] In the formula, ||·|| F Denotes the Frobenius norm; δ 2 Indicates tolerance.

[0116] The estimation results are then re-presented using nuclear norm regularization.

[0117]

[0118] In the formula, μ>0 represents the regularization parameter; ||·|| * This represents the nuclear norm.

[0119] Using the Frobenius norm of the nuclear norm, let U0 = UV H The reconstructed estimation result is then restored to obtain the restored estimation result.

[0120]

[0121] In the formula, U represents the left factor matrix of the low-rank matrix decomposition; V represents the right factor matrix of the low-rank matrix decomposition.

[0122] In this embodiment, the first angle estimate includes: the angle of arrival of the receiver. and the departure angle of the launcher Methods for obtaining the angle of arrival at the receiver include:

[0123] Based on the estimation results, the covariance matrix of the angle of arrival at the receiver is obtained:

[0124]

[0125] The angle of arrival at the receiver is recovered using the root-music eigenvalue decomposition method based on the covariance matrix.

[0126] Following the steps described above, we first obtain... The covariance matrix is ​​then used, and the eigenvalue decomposition method of root-MUSIC is applied to recover the departure angle of the transmitter.

[0127] S3. Construct a pre-encoder and combiner based on the first angle estimate to achieve beamforming gain. Then, obtain the second angle estimate of the reflecting surface based on the pre-encoder and combiner.

[0128] The preencoder P and combiner W are represented as follows:

[0129]

[0130] Based on the obtained preencoder and combiner, the received signal is obtained. Assuming the reflector angle training comprises a total of D steps, with each step using L... MR One channel; in each step, the precoder P and the combiner W, as well as the phase shift Ω of the reflector. d Keep it fixed. This yields an effective channel H. d =H RB Ω d H MR .

[0131] During the l-th channel usage in step d, the received signal is represented as:

[0132]

[0133] In the formula, For training symbols; n d,l This represents the noise during the l-th channel usage in step d.

[0134] Simultaneously assume and Therefore, at step d, the receiver's observation is equivalent to:

[0135]

[0136] Vectorizing the observations yields:

[0137]

[0138] In the formula, n' d This represents the vectorization of the noise observations in step d.

[0139] in,

[0140] In an ideal scenario, if the number of antennas is infinite, the external angle estimation is perfect, and the transceiver phase shifter resolution is infinite, Ψ is an identity matrix. However, in practical systems, Ψ is neither an identity matrix nor a diagonal matrix. Therefore, Z is used for joint estimation of the reflector angle to improve performance.

[0141] In the D training steps, the reflector uses a variable phase shift Ω. d Thus, the overall observation values ​​are obtained:

[0142]

[0143] in, N' represents the noise of the overall observations;

[0144] To reduce training costs, Set as:

[0145]

[0146] In the formula, It is a DFT matrix, where 0 represents a matrix of all zeros.

[0147] This is equivalent to turning off N during reflector angle training. I -D reflective surface elements, only D reflective surface elements are sampled.

[0148] Applying the LS estimator yields:

[0149]

[0150] In the formula, The matrix that corresponds to the subarray with D open elements on the reflective surface is conceived as follows:

[0151] The second angle estimate of the reflecting surface is obtained based on the received signal.

[0152] The above formula yields information including angle. Covariance matrix:

[0153]

[0154] Then, the root-MUSIC algorithm is used to generate the estimated angle of the reflecting surface.

[0155] S4. Construct a dictionary matrix Φ based on the first angle estimate and the second angle estimate, and obtain the overall channel gain based on the dictionary matrix.

[0156] The received training signal is fitted to the model using LS, as shown in the following expression:

[0157]

[0158] in,

[0159] The overall channel gain is estimated using the OMP algorithm, as shown in the following expression:

[0160]

[0161] S5. Based on the first angle estimate, the second angle estimate, and the overall gain, obtain the estimated value of the cascaded channel matrix to complete channel recovery.

[0162] The estimated values ​​of the cascaded channel matrix include:

[0163]

[0164] In the formula, Indicates gain.

[0165] Example 2:

[0166] This embodiment provides a passive IRS system channel estimation system based on random and fixed sampling to implement the above method, including: a sampling module, a first angle estimation module, a second angle estimation module, a calculation module, and a recovery module.

[0167] The sampling module is used to perform two-layer sampling on the cascaded channel to be estimated, and to perform a preliminary estimation on the sampled cascaded channel to obtain the noise observation estimation result.

[0168] The first angle estimation module is used to obtain the first angle estimate of the antennas at both ends based on the noise observation estimation results.

[0169] The second angle estimation module is used to construct a pre-encoder and a combiner based on the first angle estimate, and to obtain the second angle estimate of the reflecting surface based on the pre-encoder and the combiner.

[0170] The calculation module is used to construct a dictionary matrix based on the first angle estimate and the second angle estimate, and to obtain the overall channel gain based on the dictionary matrix.

[0171] The recovery module is used to obtain the estimated value of the cascaded channel matrix based on the first angle estimate, the second angle estimate, and the overall gain, and to complete the channel recovery.

[0172] Example 3:

[0173] This embodiment provides a detailed explanation of the proposed passive IRS system channel estimation method based on random and fixed sampling, using specific application examples. For instance... Figure 2 As shown, the channel estimation system model consists of N t N I and N r An antenna consists of a transmitter, a smart reflector, and a receiver. Assuming the direct path between the transmitter and receiver is blocked, a smart reflector is needed to assist in the transmission from the transmitter to the receiver.

[0174] Let L MR =L RB =2, the number of transmitting antennas and the number of receiving antennas Nr =N t =64, reflective surface array element N I =128. Table 1 shows the general parameter settings. Channel estimation is performed based on the parameters in Table 1.

[0175] Table 1

[0176] parameter Value <![CDATA[Reflective surface array element N I > 128 <![CDATA[Number of receiving antennas N r > 64 <![CDATA[Number of transmitting antennas N t > 64 Second layer sampling ratio 50％ UBS sampling number 22 GNS sampling numbers 22 <![CDATA[Number of paths from the transmitter to the reflecting surface L MR > 2 <![CDATA[Number of paths L from the reflecting surface to the receiving end RB > 2 Signal-to-noise ratio -10，-5，0，5，10

[0177] In this embodiment, it is assumed that in a passive channel system based on random and fixed sampling, there is a receiver and transmitter equipped with 64 antennas, and a reflector with 128 antennas. There are two paths each from the transmitter to the reflector and from the reflector to the receiver. Therefore, the channel between the transmitter and the reflector is modeled to obtain H. MR Channel model:

[0178]

[0179] In the formula, θ MR,l φ MR,l and γ MR,l These represent the angle of arrival at the reflecting surface, the angle of departure at the transmitting end, and the gain of the l-th path, respectively; a I (θ MR,l )and All are steering vectors; A I (θ MR ), and Γ MR These represent the reflector array response matrix, the transmitter array response matrix, and the diagonal path gain matrix, respectively.

[0180] in,

[0181]

[0182] In the formula, k represents the carrier wavelength; Antenna spacing; angle θ MR,l It follows a uniform distribution in the range [0, π].

[0183] Similarly, the H between the reflecting surface and the receiving end is obtained. RB Channel model:

[0184]

[0185] In the formula, φ RB,l θ RB,l and γ RB,l These represent the departure angle at the reflecting surface, the arrival angle at the receiving end, and the gain of the l-th path, respectively; a RB (θ RB,l )and All are steering vectors; A RB (θRB ), and Γ RB These represent the receiver array response matrix, the reflector array response matrix, and the diagonal path gain matrix, respectively.

[0186] Based on the H obtained above MR Channel model and H RB Channel model, obtaining the cascaded channel model H between the transmitter and receiver:

[0187]

[0188] Where Ω = diag(ω), ω represents the phase shift information containing the emitter element, expressed as:

[0189]

[0190] Based on H MR Channel model and H RB The channel model yields the cascaded channel model H:

[0191]

[0192] In the formula, the superscript T indicates transpose; the superscript * indicates conjugate; The ◇ symbol represents the Kronecke product; the ◇ symbol represents the Khatri-Rao product. H represents MR Channel and H RB The composite of channel path gains; Γ represents the diagonal path gain matrix; ψ I Indicates the composite angle of the reflecting surface; A TR This represents the combined array response matrix.

[0193] in,

[0194] Where, ψ I,i,j =cos -1 (cos(φ RB,j )-cos(θ MR,i )) represents the effective angular difference between the i-th AoA and the j-th AoD in the reflecting surface.

[0195] The first layer of sampling of the cascaded channel is performed using a sparse matrix, resulting in submatrix U0:

[0196]

[0197] In the formula, and These represent the sparse matrix of the reflector sampling and the sparse matrix of the transmitter sampling, respectively.

[0198] When using UBS, the subarray antennas are uniformly selected from the first antenna to the 22nd antenna of the original array, which is 64 in size. The fixed-sampling matrix is ​​constructed as follows:

[0199]

[0200] Among them, 22≤64, it can be clearly seen that the aperture of the subarray is reduced and limited according to the number of selected antennas.

[0201] When using GNS, a GNS sampler and The matrix obtained by fixed sampling is:

[0202]

[0203] Where Θ(64)=7, Γ(64)=16, and the total number of antennas selected is 22. When the selected subarrays are the same size, arrays using GNS sampling mode usually have a larger array aperture than arrays using UBS sampling mode, which means higher spatial resolution.

[0204] Perform a second layer of sampling on submatrix U0 to obtain the noise observation estimation results:

[0205]

[0206] In the formula, Ω represents the uniform sampling spatial sampling mode, and A Ω Indicates the corresponding sampling operator; N represents additive white Gaussian noise.

[0207] Using IMC from Estimating θ RB and φ MR .in, This indicates the noise mode of U0.

[0208] First, the submatrix U0 is estimated using the low-rank matrix recovery method, and the estimation result is obtained:

[0209]

[0210] In the formula, ||.|| F Denotes the Frobenius norm; δ 2 Indicates tolerance.

[0211] The estimation results are then re-presented using nuclear norm regularization.

[0212]

[0213] In the formula, μ>0 represents the regularization parameter; ||.|| * This represents the nuclear norm.

[0214] Using the Frobenius norm of the nuclear norm, let U0 = UV H The reconstructed estimation result is then restored to obtain the restored estimation result.

[0215]

[0216] In the formula, U represents the left factor matrix of the low-rank matrix decomposition; V represents the right factor matrix of the low-rank matrix decomposition.

[0217] In this embodiment, the first angle estimate includes: the angle of arrival of the receiver. and the departure angle of the launcher Methods for obtaining the angle of arrival at the receiver include:

[0218] Based on the estimation results, the covariance matrix of the angle of arrival at the receiver is obtained:

[0219]

[0220] The angle of arrival at the receiver is recovered using the root-music eigenvalue decomposition method based on the covariance matrix.

[0221] Following the steps described above, we first obtain... The covariance matrix is ​​then used, and the eigenvalue decomposition method of root-MUSIC is applied to recover the departure angle of the transmitter.

[0222] A pre-encoder and combiner are constructed based on the first angle estimate to achieve beamforming gain. A second angle estimate of the reflecting surface is then obtained based on the pre-encoder and combiner.

[0223] The preencoder P and combiner W are represented as follows:

[0224]

[0225] The received signal is obtained based on the precoder and combiner. Assuming the reflector angle training comprises 128 steps, with each step using two channels; in each step, the precoder P, combiner W, and reflector phase shift Ω are used. d Keep it fixed. This yields an effective channel H. d =H RB Ω d H MR .

[0226] During the l-th channel usage in step d, the received signal is represented as:

[0227]

[0228] In the formula, For training symbols; n d,l This represents the noise during the l-th channel usage at step d.

[0229] Simultaneously assume and Therefore, at step d, the receiver's observation is equivalent to:

[0230]

[0231] Vectorizing the observations yields:

[0232]

[0233] In the formula, n' d This represents the vectorization of the noise observations in step d.

[0234] in,

[0235] In an ideal scenario, if the number of antennas is infinite, the external angle estimation is perfect, and the transceiver phase shifter resolution is infinite, Ψ is an identity matrix. However, in practical systems, Ψ is neither an identity matrix nor a diagonal matrix. Therefore, Z is used for joint estimation of the reflector angle to improve performance.

[0236] In the D training steps, the reflector uses a variable phase shift Ω. d Thus, the overall observation values ​​are obtained:

[0237]

[0238] in, N' represents the noise of the overall observations.

[0239] To reduce training costs, Set as:

[0240]

[0241] In the formula, It is a DFT matrix, where 0 represents a matrix of all zeros.

[0242] This is equivalent to sampling 128 reflective elements without turning off the reflective elements during reflective surface angle training.

[0243] Applying the LS estimator yields:

[0244]

[0245] In the formula, The matrix that corresponds to the subarray with D open elements on the reflective surface is conceived as follows:

[0246]

[0247] The second angle estimate of the reflecting surface is obtained based on the received signal.

[0248] The above formula yields information including angle. Covariance matrix:

[0249]

[0250] Then, the root-MUSIC algorithm is used to generate the estimated angle of the reflecting surface.

[0251] The received training signal is fitted to the model using LS, as shown in the following expression:

[0252]

[0253] in,

[0254] The overall channel gain is estimated using the OMP algorithm, as shown in the following expression:

[0255]

[0256] The estimated values ​​of the cascaded channel matrix include:

[0257]

[0258] In the formula, Indicates gain.

[0259] like Figure 3 As shown, the NMSE performance of passive channel estimation under different conduction-to-noise ratio (PNR) conditions is compared.

[0260] in,

[0261] Simulation results show that the channel estimation accuracy is highest when there is no sampling condition. Furthermore, the GNS sampling mode also demonstrates advantages in passive channel estimation, with higher accuracy than the UBS sampling mode. This also shows that sampling in a passive IRS system can significantly reduce training overhead and estimation complexity.

[0262] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A channel estimation method for a passive IRS system based on random and fixed sampling, characterized in that, Includes the following steps: S1. Perform two-layer sampling on the cascaded channel to be estimated, and make a preliminary estimate on the sampled cascaded channel to obtain the noise observation estimation result; S2. Based on the noise observation estimation results, obtain the first angle estimate of the antennas at both ends; S3. Construct a pre-encoder and a combiner based on the first angle estimate, and obtain a second angle estimate of the reflecting surface based on the pre-encoder and the combiner; S4. Construct a dictionary matrix based on the first angle estimate and the second angle estimate, and obtain the overall channel gain based on the dictionary matrix; S5. Based on the first angle estimate, the second angle estimate, and the overall gain, obtain the estimated value of the cascaded channel matrix to complete channel recovery.

2. The channel estimation method for a passive IRS system based on random and fixed sampling according to claim 1, characterized in that, S1 includes the following steps: S1.1 Model the cascaded channel to be estimated to obtain the cascaded channel model; S1.2 Perform two-layer sampling on the cascaded channel model to obtain the noise observation estimation results.

3. The passive IRS system channel estimation method based on random and fixed sampling according to claim 2, characterized in that, The method for obtaining the cascaded channel model includes: Modeling the channel between the transmitter and the reflector, we obtain H. MR Channel model: In the formula, N t and N I These represent the number of transmitting antennas and the reflector array elements, respectively; L MR θ represents the total number of paths from the transmitter to the reflector. MR,l φ MR,l and γ MR,l Let a represent the angle of arrival at the reflector of the l-th path, the angle of departure at the transmitter, and the gain of the l-th path, respectively; I (θ MR,l )and All are steering vectors; A I (θ MR ), and Γ MR These represent the reflector array response matrix, the transmitter array response matrix, and the diagonal path gain matrix, respectively. Modeling the channel between the reflector and the receiver yields H. RB Channel model: In the formula, N r Indicates the number of antennas at the receiving end; L RB φ represents the total number of paths between the reflector and the receiver. RB,l θ RB,l and γ RB,l Let a represent the departure angle at the reflector of the l-th path, the arrival angle at the receiver, and the gain of the l-th path, respectively; RB (θ RB,l )and All are steering vectors; A RB (θ RB ), and Γ RB These represent the receiver array response matrix, the reflector array response matrix, and the diagonal path gain matrix, respectively. Based on the H MR Channel model and H RB The channel model yields the cascaded channel model H: In the formula, the superscript T indicates transpose; the superscript * indicates conjugate; The ◇ symbol represents the Kronecker product; the ◇ symbol represents the Khatri-Rao product. H represents MR Channel and H RB The composite of channel path gains; Γ represents the diagonal path gain matrix; ψ I Indicates the composite angle of the reflecting surface; A TR Represents the combined array response matrix; in, 4. The passive IRS system channel estimation method based on random and fixed sampling according to claim 3, characterized in that, The method for obtaining the noise observation estimation result by performing two-layer sampling on the cascaded channel model includes: The cascaded channel is sampled using a sparse matrix to obtain the first layer of submatrix U0: In the formula, and These represent the sparse matrix of the reflector sampling and the sparse matrix of the transmitter sampling, respectively. The submatrix U0 is sampled in a second layer to obtain the noise observation estimation result: In the formula, Ω represents the uniform sampling spatial sampling mode, and A Ω Indicates the corresponding sampling operator; N represents additive white Gaussian noise.

5. The passive IRS system channel estimation method based on random and fixed sampling according to claim 4, characterized in that, The submatrix U0 is estimated using the low-rank matrix recovery method, and the estimation result is obtained as follows: In the formula, ||·|| F Denotes the Frobenius norm; δ 2 Indicates tolerance; The estimation results are then re-represented using the nuclear norm regularization method: In the formula, μ>0 represents the regularization parameter; ||.|| * Represents the nuclear norm; The estimated result is recovered by using the Frobenius norm representation of the nuclear norm: In the formula, U represents the left factor matrix of the low-rank matrix decomposition; V represents the right factor matrix of the low-rank matrix decomposition. Where, U0 = UV H ; The estimated result after restoration is obtained.

6. The passive IRS system channel estimation method based on random and fixed sampling according to claim 5, characterized in that, The first angle estimate includes: the angle of arrival of the receiver. and the departure angle of the launcher Methods for obtaining the angle of arrival at the receiver include: Based on the estimation results, the covariance matrix of the angle of arrival at the receiver is obtained: Using the root-mUSIC eigenvalue decomposition scheme, the angle of arrival at the receiver is recovered based on the covariance matrix.

7. The passive IRS system channel estimation method based on random and fixed sampling according to claim 6, characterized in that, S3 includes the following steps: Construct a preencoder P and a combiner W based on the first angle estimate: The received signal is obtained based on the precoder and the combiner: In the formula, H d Indicates a valid channel; For training symbols; n d,l For noise; A second angle estimate of the reflecting surface is obtained based on the received signal.

8. The passive IRS system channel estimation method based on random and fixed sampling according to claim 7, characterized in that, The estimated values ​​of the cascaded channel matrix include: In the formula, Indicates gain.

9. A channel estimation system for a passive IRS system based on random and fixed sampling, said system being used to implement the method as described in any one of claims 1-8, characterized in that, include: The system includes a sampling module, a first angle estimation module, a second angle estimation module, a calculation module, and a recovery module. The sampling module is used to perform two-layer sampling on the cascaded channel to be estimated, and to perform a preliminary estimation on the sampled cascaded channel to obtain the noise observation estimation result; The first angle estimation module is used to obtain the first angle estimate of the two antennas based on the noise observation estimation result; The second angle estimation module is used to construct a pre-encoder and a combiner based on the first angle estimation value, and to obtain a second angle estimation value of the reflecting surface based on the pre-encoder and the combiner; The calculation module is used to construct a dictionary matrix based on the first angle estimate and the second angle estimate, and to obtain the overall channel gain based on the dictionary matrix; The recovery module is used to obtain an estimate of the cascaded channel matrix based on the first angle estimate, the second angle estimate, and the overall gain, thereby completing channel recovery.

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