Passive IRS system channel estimation method and system based on random and fixed sampling

Abstract

The invention 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: carrying out two-layer sampling on a cascade channel to be estimated, and carrying out preliminary estimation on the sampled cascade channel to obtain a noise observation estimation result; obtaining first angle estimation values of the antennas at the two ends based on the noise observation estimation result; constructing a precoder and a combiner based on the first angle estimation value, and obtaining a second angle estimation value of the reflecting surface based on the precoder and the combiner; constructing a dictionary matrix based on the first angle estimation value and the second angle estimation value, and obtaining an overall gain of the channel based on the dictionary matrix; and based on the first angle estimation value, the second angle estimation value and the overall gain, obtaining an estimation value of the cascade channel matrix, and completing channel recovery. According to the invention, the complexity and overhead of channel estimation can be reduced under the condition of accurately estimating the channel state information.

Description

Technical Field

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

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

[0003] In practice, channel estimation in massive MIMO systems remains a significant challenge due to the influence of noise and multipath fading. Numerous researchers have proposed various solutions, such as utilizing low-rank matrix completion and the Root-MUSIC algorithm to achieve 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 of large-scale IRS deployments, a staged processing framework distinguishes between quasi-static BS-IRS channels and dynamic IRS-UE channels, updating estimates at differentiated time scales. However, all of these approaches suffer from high estimation complexity and excessive overhead in acquiring channel state information. Summary of the Invention

[0004] The present invention aims to address the deficiencies of the prior art and proposes a passive IRS system channel estimation method based on random and fixed sampling. The scheme is as follows: The passive IRS system channel estimation method based on random and fixed sampling includes the following steps:

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

[0006] S2. Obtaining first angle estimation values of the antennas at both ends based on the noise observation estimation result;

[0007] S3. Constructing a precoder and a combiner based on the first angle estimation value, and obtaining a second angle estimation value of a reflecting surface based on the precoder and the combiner;

[0008] S4. Constructing a dictionary matrix based on the first angle estimation value and the second angle estimation value, and obtaining an overall gain of the channel based on the dictionary matrix;

[0009] S5. Obtain an estimated value of the cascaded channel matrix based on the first angle estimation value, the second angle estimation value, and the overall gain, thereby completing channel recovery.

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

[0011] S1.1. Modeling the cascade channel to be estimated to obtain a cascade channel model;

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

[0013] Further preferably, the method for obtaining the cascade channel model includes:

[0014] Model the channel between the transmitter and the reflector to obtain H MR Channel model:

[0015]

[0016] Where N t and N I Respectively represent the number of transmitting antennas and reflector array elements; L MR Represents the total number of paths between the transmitter and the reflector; θ MR,l 、φ MR,l and γ MR,l They represent the arrival angle at the reflection surface of the lth path, the departure angle at the transmitting end, and the gain of the lth path respectively; a I (θ MR,l )and All are steering vectors; A I (θ MR ), and Γ MR denote the reflector array response matrix, transmitter array response matrix and diagonal path gain matrix respectively;

[0017] Model the channel between the reflecting surface and the receiving end and obtain H RB Channel model:

[0018]

[0019] Where N r Indicates the number of antennas at the receiving end; L RB Represents the total number of paths from the reflection surface to the receiving end; φ RB,l ,θ RB,l and γ RB,l They represent the departure angle at the reflection surface of the lth path, the arrival angle at the receiving end, and the gain of the lth path respectively; a RB (θ RB,l )and All are steering vectors; A RB (θ RB ), and Γ RB denote the receiving end 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 obtains the cascade channel model H:

[0021]

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

[0023] in,

[0024] Further preferably, the method of performing two-layer sampling on the cascade channel model to obtain the noise observation estimation result includes:

[0025] The sparse matrix is used to perform the first layer sampling on the cascade channel to obtain the submatrix U0:

[0026]

[0027] Where, and Represent the sparse matrix of reflection surface sampling and the sparse matrix of transmitting end sampling respectively;

[0028] Perform the second layer sampling on the submatrix U0 to obtain the noise observation estimation result:

[0029]

[0030] Where Ω represents the uniform sampling space sampling mode, A Ω represents the corresponding sampling operator; N represents additive Gaussian white noise,

[0031] More preferably,

[0032] The low-rank matrix recovery method is used to estimate the submatrix U0 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] The Frobenius norm representation of the nuclear norm is used to recover the re-expressed estimation result:

[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] Where U0 = UV H ;

[0042] Get the estimated result after recovery

[0043] Further preferably, the first angle estimation value includes: the arrival angle of the receiving end and the departure angle of the transmitter

[0044] Methods for obtaining the arrival angle at the receiving end include:

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

[0046]

[0047] The eigenvalue decomposition scheme of root-MUSIC is used to recover the arrival angle of the receiving end based on the covariance matrix.

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

[0049] The precoder P and combiner W are constructed based on the first angle estimate:

[0050]

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

[0052]

[0053] Where H d Indicates a valid channel; is the training symbol; n d,l represents the noise during the l-th channel usage in step d;

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

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

[0056]

[0057] Where, Indicates gain.

[0058] The present invention also provides a passive IRS system channel estimation 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 cascade channel to be estimated, and perform preliminary estimation on the sampled cascade channel to obtain a noise observation estimation result;

[0060] The first angle estimation module is used to obtain first angle estimation values of the antennas at both ends based on the noise observation estimation result;

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

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

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

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] The present invention uses random and fixed sampling methods, and the path gain γ MR and γ RB obey At the same time, the departure angle and arrival angle are uniformly distributed within [30°, 150°]. Compared with traditional methods, accurate channel state information recovery is performed using a small amount of channel information, reducing the channel estimation complexity and overhead. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] 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.

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

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

[0069] Figure 3 This is a simulation diagram of the NMSE performance of passive channel estimation under different signal-to-noise ratio conditions in an embodiment of the present invention. DETAILED DESCRIPTION

[0070] 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.

[0071] 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.

[0072] Example 1:

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

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

[0075] Specifically, S1 includes the following steps:

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

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

[0078]

[0079] Where N t and N I Respectively represent the number of transmitting antennas and reflector array elements; L MR Represents the total number of paths between the transmitter and the reflector; θ MR,l 、φ MR,l and γ MR,l They represent the arrival angle at the reflecting surface, the departure angle at the transmitting end, and the gain of the lth path respectively; a I (θ MR,l )and All are steering vectors; A I (θ MR ), and Γ MR represent the reflector array response matrix, transmitter array response matrix, and diagonal path gain matrix, respectively.

[0080]

[0081] Where k represents the carrier wavelength; is the antenna spacing; angle θ MR,l Obey the uniform distribution of [0, π].

[0082] Similarly, the channel between the reflecting surface and the receiving end is modeled to obtain H RB Channel model:

[0083]

[0084] Where N r Indicates the number of antennas at the receiving end; L RB Represents the total number of paths from the reflection surface to the receiving end; φ RB,l ,θ RB,l and γ RB,l They represent the departure angle at the reflecting surface, the arrival angle at the receiving end, and the gain of the lth path respectively; a RB (θ RB,l )and All are steering vectors; A RB (θ RB ), and Γ RB represent the receiving end array response matrix, the reflecting surface array response matrix and the diagonal path gain matrix respectively.

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

[0086]

[0087] Where Ω = diag(ω), ω contains the phase shift information of the reflector element and is expressed as follows:

[0088]

[0089] Where, β i and ζ i Represent the reflection coefficient and phase shift of the i-th reflection surface element respectively. i =1 means the i-th element is turned on, β i =0 means that the i-th element is closed.

[0090] According to the formula vec(Ediag(f)G)=(G T ◇E)f can be obtained:

[0091]

[0092] Where, is the cascade channel, and ◇ represents the Khatri-Rao product.

[0093] By the identity and and The cascaded channel can be modeled as:

[0094]

[0095] In the formula, superscript T indicates transposition; superscript * indicates conjugation; represents the Kronecker product; ◇ represents the Khatri-Rao product; Indicates H MR Channel and H RB The complex of the channel path gain; Γ represents the diagonal path gain matrix; ψ I Represents the composite angle of the reflecting surface.

[0096] in,

[0097] Among them, ψ I,i,j =cos -1 (cos(φ RB,j )-cos(θ MR,i )) is 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 cascade channel model to obtain a noise observation estimation result.

[0099] First, a sparse matrix is used to sample the first layer of the cascade channel to obtain the submatrix U0:

[0100]

[0101] Where, and They represent the sparse matrix of reflection surface sampling and the sparse matrix of transmitting end sampling respectively.

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

[0103]

[0104] Among them, N s ≤Q, it can be clearly seen that the aperture of the subarray is reduced and restricted according to the number of selected antennas.

[0105] When using GNS, a GNS sampler and Get the fixed sampling matrix:

[0106]

[0107] in, Γ(Q)=1+Q-Θ 2 (Q), the total number of antennas selected is N s =Γ(Q)+Θ(Q)-1. When the sizes of the selected sub-arrays are the same, the array using the GNS sampling mode usually has a larger array aperture than the array using the UBS sampling mode, which means higher spatial resolution.

[0108] Perform the second-level sampling on the submatrix U0 to obtain the noise observation estimation result:

[0109]

[0110] Where Ω represents the uniform sampling space sampling mode, A Ω represents the corresponding sampling operator; N represents additive Gaussian white noise,

[0111] S2. Obtain first angle estimation values of the antennas at both ends based on the noise observation estimation result.

[0112] Using IMC from Estimated θ RB and φ RB .in, represents the noise pattern of U0.

[0113] First, the low-rank matrix recovery method is used to estimate the submatrix U0 and the estimated result is:

[0114]

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

[0116] And the estimation results are re-expressed using the nuclear norm regularization method:

[0117]

[0118] Where μ>0 represents the regularization parameter; ||·|| * represents the nuclear norm.

[0119] Using the Frobenius norm representation of the nuclear norm, let U0 = UV H , restore the re-expressed estimation result and obtain the restored estimation result

[0120]

[0121] Where U represents the left factor matrix of low-rank matrix decomposition; V represents the right factor matrix of low-rank matrix decomposition;

[0122] In this embodiment, the first angle estimation value includes: the arrival angle of the receiving end and the departure angle of the transmitter Methods for obtaining the arrival angle at the receiving end include:

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

[0124]

[0125] The root-MUSIC eigenvalue decomposition method is used to recover the arrival angle of the receiving end based on the covariance matrix.

[0126] Using the above steps, we can get The covariance matrix of the transmitter is then used to recover the departure angle of the transmitter using the eigenvalue decomposition method of root-MUSIC.

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

[0128] Among them, the precoder P and combiner W are expressed as:

[0129]

[0130] Based on the obtained precoder and combiner, the received signal is obtained. Assume that the reflection plane angle training includes a total of D steps, and each step uses L MR channels; at each step, the precoder P and combiner W and the phase shift Ω of the reflection surface d Keep it fixed. The effective channel is H d =H RB Ω d H MR .

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

[0132]

[0133] Where, is the training symbol; n d,l represents the noise during the lth channel usage in step d.

[0134] Also assume and It can be obtained that at step d, the observation value of the receiver is equivalent to:

[0135]

[0136] Vectorizing the observations yields:

[0137]

[0138] Where n' d represents the vectorization of the noise observations in step d.

[0139] in,

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

[0141] In D training steps, the reflector is used with a variable phase shift Ω d , thus obtaining the overall observation value:

[0142]

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

[0144] In order to reduce the training cost, Set as:

[0145]

[0146] Where, is a DFT matrix, and 0 represents an all-zero matrix.

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

[0148] Applying the LS estimator yields:

[0149]

[0150] Where, The matrix corresponding to the sub-array of D open elements on the reflective surface element is,

[0151] A second angle estimation value of the reflecting surface is obtained based on the received signal

[0152] According to the above formula, we can get the angle information The covariance matrix of :

[0153]

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

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

[0156] Use LS to fit the received training signal to the model, the expression is as follows:

[0157]

[0158] in,

[0159] The OMP algorithm is used to estimate the overall gain of the channel, which is expressed as follows:

[0160]

[0161] S5. Obtain an estimated value of the cascade channel matrix based on the first angle estimation value, the second angle estimation value, and the overall gain, thereby completing channel recovery.

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

[0163]

[0164] Where, Indicates gain.

[0165] Example 2:

[0166] This embodiment provides a passive IRS system channel estimation system based on random and fixed sampling, which is used 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 cascade channel to be estimated, and to perform preliminary estimation on the sampled cascade channel to obtain the noise observation estimation result.

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

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

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

[0171] The recovery module is used to obtain an estimated value of the cascade channel matrix based on the first angle estimation value, the second angle estimation value and the overall gain, so as to complete channel recovery.

[0172] Example 3:

[0173] This embodiment describes in detail the proposed passive IRS system channel estimation method based on random and fixed sampling in conjunction with specific application examples. Figure 2 As shown, the channel estimation system model consists of N t 、N I and N r The system 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 N r =Nt =64, reflector array element N I =128, Table 1 gives the general parameter settings, and channel estimation is performed according to 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 number 22 <![CDATA[Number of paths from the transmitting end 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 a passive channel system based on random and fixed sampling is equipped with a receiving end and a transmitting end with 64 antennas, and a reflecting surface with 128 antennas. There are two paths from the transmitting end to the reflecting surface and from the reflecting surface to the receiving end. The channel between the transmitting end and the reflecting surface is modeled to obtain H MR Channel model:

[0178]

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

[0180] in,

[0181]

[0182] Where k represents the carrier wavelength; is the antenna spacing; angle θ MR,l Obey the uniform distribution of [0, π].

[0183] Similarly, we can get H between the reflecting surface and the receiving end. RB Channel model:

[0184]

[0185] Where, φ RB,l ,θ RB,l and γ RB,l They represent the departure angle at the reflecting surface, the arrival angle at the receiving end, and the gain of the lth path respectively; a RB (θ RB,l )and All are steering vectors; A RB (θ RB ), and Γ RB represent the receiving end array response matrix, the reflecting surface array response matrix and the diagonal path gain matrix respectively.

[0186] According to the above obtained H MR Channel model and H RB Channel model, the cascade channel model H between the transmitter and the receiver is obtained:

[0187]

[0188] Where Ω = diag(ω), ω represents the phase shift information of the emission surface element, which can be expressed as:

[0189]

[0190] Based on H MR Channel model and H RB The channel model obtains the cascade channel model H:

[0191]

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

[0193] in,

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

[0195] The sparse matrix is used to sample the first layer of the cascade channel to obtain the submatrix U0:

[0196]

[0197] Where, and They represent the sparse matrix of reflection surface sampling and the sparse matrix of transmitting end sampling respectively.

[0198] 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 matrix of fixed sampling 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 Get the fixed sampling matrix:

[0202]

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

[0204] Perform the second-level sampling on the submatrix U0 to obtain the noise observation estimation result:

[0205]

[0206] Where Ω represents the uniform sampling space sampling mode, A Ω represents the corresponding sampling operator; N represents additive Gaussian white noise,

[0207] Using IMC from Estimated θ RB and φ MR .in, represents the noise pattern of U0.

[0208] First, the low-rank matrix recovery method is used to estimate the submatrix U0 and the estimated result is:

[0209]

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

[0211] And the estimation results are re-expressed using the nuclear norm regularization method:

[0212]

[0213] Where μ>0 represents the regularization parameter; ||.||* represents the nuclear norm.

[0214] Using the Frobenius norm representation of the nuclear norm, let U0 = UV H , restore the re-expressed estimation result and obtain the restored estimation result

[0215]

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

[0217] In this embodiment, the first angle estimation value includes: the arrival angle of the receiving end and the departure angle of the transmitter Methods for obtaining the arrival angle at the receiving end include:

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

[0219]

[0220] The root-MUSIC eigenvalue decomposition method is used to recover the arrival angle of the receiving end based on the covariance matrix.

[0221] Using the above steps, we can get The covariance matrix of the transmitter is then used to recover the departure angle of the transmitter using the eigenvalue decomposition method of root-MUSIC.

[0222] A precoder and a combiner are constructed based on the first angle estimate to achieve beamforming gain, and a second angle estimate of the reflecting surface is obtained based on the precoder and the combiner.

[0223] Among them, the precoder P and combiner W are expressed as:

[0224]

[0225] Based on the obtained precoder and combiner, the received signal is obtained. Assume that the reflector angle training consists of 128 steps in total, and each step uses 2 channels; in each step, the precoder P and combiner W and the phase shift Ω of the reflector are d Keep it fixed. The effective channel is H d =H RB Ω d H MR .

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

[0227]

[0228] Where, is the training symbol; n d,l represents the noise in the lth channel usage in the dth step.

[0229] Also assume and It can be obtained that at step d, the observation value of the receiver is equivalent to:

[0230]

[0231] Vectorizing the observations yields:

[0232]

[0233] Where n' d represents the vectorization of the noise observations in step d.

[0234] in,

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

[0236] In D training steps, the reflector is used with a variable phase shift Ω d , thus obtaining the overall observation value:

[0237]

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

[0239] In order to reduce the training cost, Set as:

[0240]

[0241] Where, is a DFT matrix, and 0 represents an all-zero matrix.

[0242] This is equivalent to not turning off reflector elements during reflector angle training and sampling 128 reflector elements.

[0243] Applying the LS estimator yields:

[0244]

[0245] Where, The matrix corresponding to the sub-array of D open elements on the reflective surface element is,

[0246]

[0247] A second angle estimation value of the reflecting surface is obtained based on the received signal

[0248] According to the above formula, we can get the angle information The covariance matrix of :

[0249]

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

[0251] Use LS to fit the received training signal to the model, the expression is as follows:

[0252]

[0253] in,

[0254] The OMP algorithm is used to estimate the overall gain of the channel, which is expressed as follows:

[0255]

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

[0257]

[0258] Where, Indicates gain.

[0259] like Figure 3 As shown in Figure 2, the NMSE performance of passive channel estimation under different PNR conditions is compared.

[0260] in,

[0261] The 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 demonstrates that sampling in a passive IRS system can significantly reduce training overhead and estimation complexity.

[0262] 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 passive IRS system channel estimation method based on random and fixed sampling, characterized in that: The following steps are involved: S1. Perform two-layer sampling on the cascade channel to be estimated, and make a preliminary estimate of the sampled cascade channel to obtain the noise observation estimation result; S2. Obtaining first angle estimation values of the antennas at both ends based on the noise observation estimation result; S3. Constructing a precoder and a combiner based on the first angle estimation value, and obtaining a second angle estimation value of a reflecting surface based on the precoder and the combiner; S4. Constructing a dictionary matrix based on the first angle estimation value and the second angle estimation value, and obtaining an overall gain of the channel based on the dictionary matrix; S5. Based on the first angle estimation value, the second angle estimation value and the overall gain, obtain an estimation value of the cascaded channel matrix to complete channel recovery.

2. The passive IRS system channel estimation method based on random and fixed sampling according to claim 1, characterized in that: S1 includes the following steps: S1.

1. Modeling the cascade channel to be estimated to obtain a cascade channel model; S1.

2. Perform two-layer sampling on the cascade channel model to obtain the noise observation estimation result.

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 cascade channel model includes: Model the channel between the transmitter and the reflector to obtain H MR Channel model: Where N t and N I Respectively represent the number of transmitting antennas and reflector array elements; L MR Represents the total number of paths between the transmitter and the reflector; θ MR,l 、φ MR,l and γ MR,l They represent the arrival angle at the reflection surface of the lth path, the departure angle at the transmitting end, and the gain of the lth path respectively; a I (θ MR,l )and All are steering vectors; A I (θ MR ), and Γ MR denote the reflector array response matrix, transmitter array response matrix and diagonal path gain matrix respectively; Model the channel between the reflecting surface and the receiving end and obtain H RB Channel model: Where N r Indicates the number of antennas at the receiving end; L RB Represents the total number of paths from the reflection surface to the receiving end; φ RB,l ,θ RB,l and γ RB,l They represent the departure angle at the reflection surface of the lth path, the arrival angle at the receiving end, and the gain of the lth path respectively; a RB (θ RB,l )and All are steering vectors; A RB (θ RB ), and Γ RB denote the receiving end 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 obtains the cascade channel model H: In the formula, superscript T indicates transposition; superscript * indicates conjugation; represents the Kronecker product; ◇ represents the Khatri-Rao product; Indicates H MR Channel and H RB The complex of the channel path gain; Γ represents the diagonal path gain matrix; ψ I Represents 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 of performing two-layer sampling on the cascade channel model to obtain the noise observation estimation result includes: The sparse matrix is used to perform the first layer sampling on the cascade channel to obtain the submatrix U0: Where, and Represent the sparse matrix of reflection surface sampling and the sparse matrix of transmitting end sampling respectively; Perform the second layer sampling on the submatrix U0 to obtain the noise observation estimation result: Where Ω represents the uniform sampling space sampling mode, A Ω represents the corresponding sampling operator; N represents additive Gaussian white noise, 5. The passive IRS system channel estimation method based on random and fixed sampling according to claim 4, characterized in that: The low-rank matrix recovery method is used to estimate the submatrix U0 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; The Frobenius norm representation of the nuclear norm is used to recover the re-expressed estimation result: Where U represents the left factor matrix of low-rank matrix decomposition; V represents the right factor matrix of low-rank matrix decomposition; Where U0 = UV H ; Get the estimated result after recovery 6. The passive IRS system channel estimation method based on random and fixed sampling according to claim 5, characterized in that: The first angle estimation value includes: the arrival angle of the receiving end and the departure angle of the transmitter Methods for obtaining the arrival angle at the receiving end include: Based on the estimation results, the covariance matrix of the arrival angle at the receiving end is obtained: The eigenvalue decomposition scheme of root-MUSIC is used to recover the arrival angle of the receiving end 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: The precoder P and combiner W are constructed based on the first angle estimate: A received signal is obtained based on the precoder and the combiner: Where H d Indicates a valid channel; is the training symbol; n d,l For noise; A second angle estimation value 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 value of the cascaded channel matrix includes: Where, Indicates gain.

9. A passive 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 8, characterized in that: include: 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 cascade channel to be estimated, and perform preliminary estimation on the sampled cascade channel to obtain a noise observation estimation result; The first angle estimation module is used to obtain first angle estimation values of the antennas at both ends based on the noise observation estimation result; The second angle estimation module is used to construct a precoder and a combiner based on the first angle estimation value, and obtain a second angle estimation value of the reflecting surface based on the precoder and the combiner; The calculation module is used to construct a dictionary matrix based on the first angle estimation value and the second angle estimation value, and obtain an overall gain of the channel based on the dictionary matrix; The recovery module is used to obtain an estimated value of the cascade channel matrix based on the first angle estimation value, the second angle estimation value and the overall gain, thereby completing channel recovery.

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