A RIS-assisted channel estimation method for NOMP-based millimeter-wave MIMO systems

Abstract

This invention relates to a NOMP-based RIS-assisted millimeter-wave MIMO system channel estimation method, belonging to the category of channel estimation methods. Taking the downlink of a RIS-assisted millimeter-wave MIMO system as an example, the channel model of the base station (BS)-RIS and the RIS-mobile station (MS) is represented as a concatenated channel model in Khatri-Rao product form. One-dimensional NOMP, two-dimensional NOMP, and least squares (LS) algorithms are used to estimate multiple parameters in the concatenated channel, thereby achieving channel estimation. The advantages are that the proposed RIS-assisted millimeter-wave MIMO system channel estimation method estimates channel parameters with lower pilot overhead, providing effective CSI for RIS-assisted systems; applying the NOMP method to RIS-assisted millimeter-wave MIMO channel estimation can solve the grid mismatch problem existing in traditional compressed sensing algorithms, improve the accuracy of joint parameter estimation, and thus improve the channel estimation accuracy.

Description

Technical Field

[0001] This invention relates to a channel estimation method, particularly to the field of channel estimation for millimeter-wave multiple-input multiple-output (MIMO) systems assisted by reconfigurable smart reflectors (RIS), and specifically to channel estimation for RIS-assisted millimeter-wave MIMO systems based on Newton's orthogonal matching pursuit (NOMP). Background Technology

[0002] While fifth-generation (5G) wireless networks are still being deployed globally, academia and industry have been keenly focused on future generations beyond 5G, such as sixth-generation (6G) wireless networks. Compared to 5G, 6G demands higher data transmission rates and energy efficiency, better global coverage and connectivity, and extremely high reliability and low latency. To meet these requirements, disruptive innovative technologies must be developed to achieve sustainable capacity growth in future wireless networks with low cost, low complexity, and low energy consumption, thus realizing sustainable green communication networks. In recent years, a novel technology has attracted widespread attention in the field of wireless communication—Reconfigurable Smart Reflectors (RIS). Research indicates that millimeter-wave and Asia-Pacific Hertz (APH) communications are poised to be among the biggest beneficiaries of emerging RIS technologies. RIS can compensate for the inherently high path loss and congestion in the millimeter-wave and APH bands, thereby improving communication performance in these bands.

[0003] To design reliable beams and achieve high beamforming gain, obtaining accurate Channel State Information (CSI) is crucial. Channel estimation in RIS-assisted millimeter-wave MIMO systems faces several challenges: firstly, compared to systems without RIS, RIS typically consists of hundreds of elements, leading to a sharp increase in channel coefficients; secondly, the low-cost reflective elements of RIS lack any radio frequency processing capabilities, preventing them from transmitting, receiving, or processing pilot signals for channel estimation. To address the channel estimation problem in RIS-assisted millimeter-wave MIMO systems, some traditional channel estimation methods, such as the least squares (LS) method, have been proposed; however, these methods incur significant pilot overhead. To reduce pilot overhead, the most common approach is to leverage the inherent sparsity of millimeter-wave channels by designing compressed sensing-based channel estimation methods. However, traditional compressed sensing methods, such as the Orthogonal Matching Pursuit (OMP) algorithm, construct an overcomplete atom library based on grid partitioning, then select the atom closest to the observed signal from the existing overcomplete atom library to construct a sparse approximation, replacing the observed signal with the residual, and continuing to select the atom that best matches the signal. After a certain number of iterations, the observed signal is linearly represented using a certain number of atoms from the atomic library. The drawback of this method is that it cannot achieve fine-grained meshing, ignores the mesh mismatch problem, and cannot obtain satisfactory estimation accuracy.

[0004] In recent years, a new off-grid parameter estimation method has emerged in the field of compressed sensing—the Newton Orthogonal Matching Pursuit (NOMP) algorithm. Based on the OMP algorithm, it further refines the grid by using the concept of Newton's gradient to improve parameter estimation accuracy. The algorithm mainly includes four steps: greedy search, single-step refinement, iterative refinement, and gain update. This algorithm has relatively low computational complexity. Currently, there is no method using the NOMP algorithm for channel estimation in RIS-assisted millimeter-wave MIMO systems. Summary of the Invention

[0005] This invention provides a RIS-assisted channel estimation method for millimeter-wave MIMO systems based on NOMP, which effectively reduces pilot overhead and improves channel estimation accuracy by addressing the shortcomings of traditional channel estimation algorithms.

[0006] The technical solution adopted by this invention includes the following steps:

[0007] Step 1: Construct the channel model and received signal model of the millimeter-wave multiple-input multiple-output (MIMO) system assisted by a reconfigurable smart reflector (RIS).

[0008] Step 2: Process the received signal of the mobile station MS within the coherence time to obtain a received signal model with cascaded channel form, and transform the cascaded channel estimation problem into a channel parameter estimation problem.

[0009] Step 3: Estimate multiple channel parameters in the cascaded channel using the two-dimensional Newton-Orthogonal Matching Pursuit (NOMP) algorithm, the one-dimensional NOMP algorithm, and the least squares (LS) algorithm, respectively. These parameters include the departure angle (AOD) of the base station BS-RIS, i.e., θ. BR The angle of arrival (AOA) of RIS-MS, i.e., φ RM Path gain product Angular difference between arrival and departure from RIS

[0010] Step 4: Utilize the estimated channel parameters Complete the cascaded channel H eff The estimate.

[0011] Step one of the present invention specifically includes:

[0012] Taking the downlink of a RIS-assisted millimeter-wave MIMO system as an example, channel models for BS-RIS and RIS-MS are constructed respectively. The BS is equipped with N B One antenna, MS equipped with N M One antenna, RIS equipped with N REach reflecting element can independently control its reflection coefficient. Assuming that the BS, MS, and RIS all use uniform linear arrays (ULAs), the signals transmitted at the BS are narrowband signals, and signal propagation satisfies the far-field condition. The direct channel between the BS and MS is blocked. The classic Saleh-Valenzuela channel model is used to represent the channels between the BS and RIS. and the channel between RIS-MS Right now:

[0013]

[0014] Among them, [θ BR ] l This represents the departure angle (AOD) of the l-th path of BS-RIS, [φ BR ] l This represents the angle of arrival (AOA) of the l-th path in BS-RIS. Let represent the channel gain of the l-th path in BS-RIS, and The emission direction matrix of BS-RIS is then expressed as: The receiver direction matrix of BS-RIS is represented as follows: L BR Represents the total number of paths in BS-RIS. Where d represents the element spacing and λ represents the wavelength; similarly, H RM It can be represented as:

[0015]

[0016] Among them, [θ RM ] l Denotes the departure angle AOD of the l-th path of RIS-MS, [φ RM ] l L represents the angle of arrival (AOA) of the l-th path of RIS-MS. RM Represents the total number of RIS-MS paths. Let the channel gain of the l-th path of RIS-MS be represented by... The RIS-assisted millimeter-wave MIMO channel satisfies the following channel characteristics: A block fading channel is divided into K blocks within a channel coherence time Ts, and each block contains T time slots, then Ts = KT, and satisfies the following structured time-domain protocol: 1) The RIS phase shift vector is constant in the T time slots of the k-th block, but it changes with block k, s[k,t] = s[k], t = 1,…,T; 2) The pilot signal {x[1],…,x[T]} is repeated in the k blocks, that is, x[k,t] = x[t], k = 1,…,K, so the total signal received in the T time slots of the k-th block can be expressed as Where y[k,t]=H RM diag(s[t])H BR x[t]+n[t], It is the orthogonal pilot signal vector transmitted by the base station at time t. σ 2 It is noise power, and the RIS control matrix can be represented as: Where β n and n n Let n represent the reflection coefficient and phase shift of the nth antenna, respectively. n ∈[0,2π],β n ∈{0,1}, where 0 and 1 represent the failure and activation of the RIS array element, respectively.

[0017] Step two of this invention specifically includes:

[0018] Multiply the received signals in the T time slots of each block k by the same pilot signal X = [x[1],…,x[T]]. The pilot signals satisfy orthogonality, i.e., X H X = I, and by vectorizing the signal obtained in each block k, the received signal within the coherent time can be obtained as follows:

[0019]

[0020] in, This represents the processed received signal in each block. The control matrix of the RIS for K blocks, after processing, has its column dimensions dependent only on the number of blocks K. K is called the required pilot overhead. The cascaded channel to be estimated can be expressed as... in If it is a Khatri-Rao matrix product, then the cascaded channel H eff Expressed using channel parameters:

[0021]

[0022] in, It is the Kronecker matrix product, for simplification Define a variable satisfy but It is a diagonal matrix with diagonal elements as follows: Therefore, the cascaded channel can be simplified to... The cascaded channel estimation problem can then be transformed into channel parameter estimation. Estimation problem.

[0023] Step three of this invention includes three processes: two-dimensional NOMP algorithm estimation (θ)BR ,φ RM One-dimensional NOMP algorithm estimation Least squares algorithm estimation in:

[0024] (1) Two-dimensional NOMP algorithm estimation (θ) BR ,φ RM The received signal can be represented as:

[0025] Y = AX + N

[0026] in, It is (N) B N M ×L BR L RM A 3D steering vector matrix, where N is the matrix composed of the noise sums of K blocks. Obviously, for estimating θ BR and φ RM This is a two-dimensional angle estimation problem, therefore the two-dimensional NOMP algorithm is used for two-dimensional angle estimation, after L = L BR L RM In the next iteration, the AOD estimate θ of BS-RIS is obtained. BR The estimated value of AOA φ by RIS-MS RM ;

[0027] The two-dimensional NOMP algorithm flow is as follows:

[0028] 1) Greedy search: Divide the two-dimensional angle into a grid and use the idea of ​​sparse reconstruction to form a set of possible grid locations for the two-dimensional angle. Assumption The parameters were estimated in previous iterations. The residual after i iterations is:

[0029]

[0030] Among them, the initial residual

[0031] A rough estimate of a grid point is obtained by maximizing the generalized likelihood ratio test (GLRT) function:

[0032]

[0033] in At the same time, record the sequence number C = {[c1,...,c...} of each column in the discrete grid where the parameter falls. i ], i<=L BR L RM This allows us to obtain a rough estimate of the angle parameters. At the same time, a corresponding gain can also be obtained:

[0034]

[0035] in

[0036] 2) Single refinement: For the coarse channel parameter estimates obtained from the greedy search, further refinement using the Newton gradient method is needed. When estimating the angle, the objective function is to minimize... This is equivalent to maximizing the following function:

[0037]

[0038] but and The Newtonian refinement process can be expressed as:

[0039]

[0040] in,

[0041] The corresponding first-order partial derivative is:

[0042]

[0043]

[0044] The corresponding second-order partial derivative is:

[0045]

[0046] x2 can represent θ BR Or φ RM After refining (θ) BR φ RM After that, the gain x also needs to be updated. i :

[0047]

[0048] The total number of iterations is R. s Second-rate;

[0049] 3) Iterative refinement: Iterative refinement is a single refinement of each detected parameter across all parameters. This process provides feedback on the local refinement of previously detected parameters, resulting in a more accurate estimate. After the single refinement process in the previous step, the estimated parameter set becomes: When refining the k-th objective Treated as a new observation, and then applied to this target. Perform a single refinement step to make corrections and update x.k The total number of iterations is R. c ;

[0050] 4) Gain update, based on the new estimated parameter values. These parameter values ​​are obtained after single refinement and iterative refinement, and the corresponding gain vector is updated using the least squares method. in The number of iterations i = i + 1;

[0051] Repeat the above four steps of the two-dimensional NOMP algorithm, after i = L BR L RM After the iteration, the estimated AOD of BS-RIS and AOA of RIS-MS are expressed as: For repeatedly estimated angles, the sequence number C = {[c1,...,c...} recorded during the greedy search process is... i ], i<=L BR L RM Sort the results according to the order of C. Estimate the value, then calculate the mean.

[0052]

[0053]

[0054] This allows for the generation of non-repeating angle parameter estimates. and

[0055] (2) The one-dimensional NOMP algorithm is used to estimate the angle of arrival (AOA) of BS-RIS (i.e., φ). BR The launch angle AOD (i.e., θ) of RIS-MS RM The angle difference between ) The observation matrix is ​​still the received signal, except that the received signal needs to be transposed using its conjugate:

[0056]

[0057] Therefore, the received signal can be written as: Ψ = S H The perceptron matrix Ψ is used in the Newton gradient refinement process. During differentiation, the perceptron matrix Ψ can be considered a constant. The steps of the one-dimensional NOMP algorithm are consistent with those of the two-dimensional NOMP algorithm, including greedy search, single-step refinement, iterative refinement, and gain update. After i = L... BR L RM In the next iteration, the estimate is...

[0058] (3) Estimating channel gain using the least squares method Based on the received signal Y and the previously estimated angle Estimate channel gain:

[0059]

[0060] Each diagonal element is The parameters can then be estimated.

[0061] In step four of this invention, the estimated channel parameters are used Complete the cascaded channel H eff The estimated channel parameters are then substituted into the cascaded channel from step two to obtain the estimated values ​​for the cascaded channel:

[0062]

[0063] This invention takes the downlink of a RIS-assisted millimeter-wave MIMO system as an example. First, it simplifies the classic Saleh-Valenzuela channel model, representing the base station (BS)-RIS channel model and the RIS-mobile station (MS) channel model as cascaded channel models in Khatri-Rao product form. Then, it transforms the cascaded channel estimation problem into a joint channel parameter estimation problem, employing one-dimensional NOMP, two-dimensional NOMP, and least squares (LS) algorithms to estimate multiple parameters in the cascaded channel, thereby achieving channel estimation.

[0064] The advantages of this invention are: (1) The proposed RIS-assisted millimeter-wave MIMO system channel estimation method estimates the channel parameters with low pilot overhead, providing effective CSI for RIS-assisted systems; (2) Applying the NOMP method to RIS-assisted millimeter-wave MIMO channel estimation can solve the grid mismatch problem existing in traditional compressed sensing algorithms, improve the accuracy of joint parameter estimation, and thus improve the channel estimation accuracy. Attached Figure Description

[0065] Figure 1 This is a model diagram of the RIS-assisted millimeter-wave MIMO system used in this invention;

[0066] Figure 2 This is a structured time-domain protocol diagram of the RIS-assisted millimeter-wave MIMO system used in this invention;

[0067] Figure 3 This is a flowchart of the present invention;

[0068] Figure 4 The channel parameters (θ) are obtained using the method proposed in this invention.BR ,φ RM A graph showing the root mean square error (RMSE) between the estimated and true values ​​as a function of signal-to-noise ratio (SNR) and K (i.e., pilot number);

[0069] Figure 5 The channel parameters are obtained using the method proposed in this invention. A comparison chart of the changes in RMSE between estimated and actual values ​​as a function of SNR and K;

[0070] Figure 6 This is a comparison chart showing the normalized mean square error (NMSE) between the channel estimated using the method of this invention and other channel estimation methods and the actual channel as a function of SNR. Detailed Implementation

[0071] Step 1: Construct a RIS-assisted channel model and received signal model for a millimeter-wave MIMO system;

[0072] Taking the downlink of a RIS-assisted millimeter-wave MIMO system as an example, the model of a RIS-assisted millimeter-wave MIMO system is as follows: Figure 1 As shown, both BS-RIS and RIS-MS exhibit multipath propagation, and the direct path of BS-MS is blocked. BS is equipped with N B One antenna, MS equipped with N M One antenna, RIS equipped with N R Each reflector element can independently control its reflection coefficient. Assuming the BS, MS, and RIS all use uniform linear arrays (ULA), the signals emitted at the BS side are narrowband signals, and signal propagation satisfies the far-field condition. The number of paths between the BS and RIS is L. BR The number of paths in RSI-MS is L. RM The classic Saleh-Valenzuela channel model is used to represent the channels between BS and RIS. and the channel between RIS-MS Right now:

[0073]

[0074] Among them, [θ BR ] l This represents the departure angle (AOD) of the l-th path of BS-RIS, [φ BR ] l This represents the angle of arrival (AOA) of the l-th path in BS-RIS. Let represent the channel gain of the l-th path in BS-RIS, and The emission direction matrix of BS-RIS is then expressed as: The receiver direction matrix of BS-RIS is represented as follows: L BR Represents the total number of paths in BS-RIS. d represents the element spacing, λ represents the wavelength, and similarly H RM It can be represented as:

[0075]

[0076] Among them, [θ RM ] l This represents the departure angle (AOD) of the l-th path in RIS-MS, [φ RM ] l L represents the angle of arrival (AOA) of the l-th path in RIS-MS. RM Represents the total number of RIS-MS paths. Let the channel gain of the l-th path of RIS-MS be represented by...

[0077] Figure 2 This represents a structured time-domain protocol. It satisfies the following channel characteristics: A block fading channel is divided into K blocks within a channel coherence time Ts, each block containing T time slots, then Ts = KT, and satisfies the following structured time-domain protocol: 1) The RIS phase shift vector is constant in the T time slots of the k-th block, but changes with block k, s[k,t] = s[k], t = 1,…,T; 2) The pilot signal {x[1],…,x[T]} repeats in the k blocks, i.e., x[k,t] = x[t], k = 1,…,K. Therefore, the total signal received in the T time slots of the k-th block can be expressed as… Where y[k,t]=H RM diag(s[t])H BR x[t]+n[t], It is the orthogonal pilot signal vector transmitted by the base station at time t. σ 2 This is noise power. The RIS control matrix can be represented as... Where β n and n n Let n represent the reflection coefficient and phase shift of the nth antenna, respectively. n ∈[0,2π],β n ∈{0,1}, where 0 and 1 represent the failure and activation of the RIS element, respectively. In practical applications, to further reduce hardware costs and design complexity, RIS typically only satisfy phase shift control or amplitude control, and in practice, the amplitude of the RIS is often fixed. Therefore, in this invention, the amplitude control of the RIS is β=1.

[0078] Step 2: Process the MS received signal within the coherence time to obtain a received signal model with a cascaded channel form. First, multiply the received signal in each block k within T time slots by the same pilot signal X = [x[1],…,x[T]]. The pilot signals satisfy orthogonality, i.e., X H Given X = I, and vectorizing the signal obtained from each block k, we can obtain:

[0079]

[0080] in, This represents the processed received signal in each block. Let Y represent the control matrix of the RIS for K blocks. After processing, the column dimensions of Y depend only on the number of blocks K, which is called the required pilot overhead. The cascaded channel to be estimated can be expressed as... in It is the Khatri-Rao matrix product, and the cascaded channel H eff Expressed using channel parameters:

[0081]

[0082] in, It is the Kronecker matrix product. To simplify... Define a variable satisfy but It is a diagonal matrix, and its diagonal elements are Therefore, the cascaded channel can be simplified to... The cascaded channel estimation problem is then transformed into the channel parameter θ BR φ RM , and parameters The estimation problem.

[0083] Step 3: Estimate the parameters in the concatenated channel using the two-dimensional NOMP algorithm, the one-dimensional NOMP algorithm, and the LS algorithm, respectively. in:

[0084] (1) Two-dimensional NOMP algorithm estimation (θ) BR ,φ RM The received signal can be represented as:

[0085] Y = AX + N

[0086] in, It is (N) B N M ×L BR L RMA 3D steering vector matrix, where N is the matrix composed of the noise sums of K blocks. Obviously, for estimating θ BR and φ RM This is a two-dimensional angle estimation problem, therefore the two-dimensional NOMP algorithm is used for two-dimensional angle estimation, after L = L BR L RM In the next iteration, the AOD estimate θ of BS-RIS is obtained. BR The estimated value of AOA φ by RIS-MS RM .

[0087] The two-dimensional NOMP algorithm flow is as follows:

[0088] 1) Greedy Search. The two-dimensional angle is divided into a mesh, and the idea of ​​sparse reconstruction is used to form a set of possible mesh locations for the two-dimensional angle. Assumption The parameters were estimated in previous iterations. The residual after i iterations is:

[0089]

[0090] Among them, the initial residual

[0091] A rough estimate of a grid point is obtained by maximizing the generalized likelihood ratio test (GLRT) function:

[0092]

[0093] in At the same time, record the sequence number C = {[c1,...,c...} of each column in the discrete grid where the parameter falls. i ], i<=L BR L RM Based on C, a rough estimate of the angle parameters can be obtained. At the same time, a corresponding gain can also be obtained:

[0094]

[0095] in

[0096] 2) Single refinement: For the coarse channel parameter estimates obtained from the greedy search, further refinement using the Newton gradient method is needed. When estimating the angle, the objective function is to minimize... This is equivalent to maximizing the following function:

[0097]

[0098] but and The Newtonian refinement process can be expressed as:

[0099]

[0100] in,

[0101] The corresponding first-order partial derivative is:

[0102]

[0103]

[0104] The corresponding second-order partial derivative is:

[0105]

[0106] x2 can represent θ BR Or φ RM After refining (θ) BR φ RM After that, the gain x also needs to be updated. i

[0107]

[0108] And repeat step five R s Second-rate;

[0109] 3) Iterative refinement: Iterative refinement is a single refinement of each detected parameter across all parameters. This process provides feedback on the local refinement of previously detected parameters, resulting in a more accurate estimate. After the single refinement process in the previous step, the estimated parameter set becomes: When refining the k-th objective Treated as a new observation, and then applied to this target. Perform a single refinement step to make corrections and update x. k The total number of iterations is R. c ;

[0110] 4) Gain update, based on the new estimated parameter values. These parameter values ​​are obtained after single refinement and iterative refinement, and the corresponding gain vector is updated using the least squares method. in The number of iterations i = i + 1;

[0111] Repeat the above four steps of the two-dimensional NOMP algorithm, after i = L BR L RMAfter the iteration, the estimated AOD of BS-RIS and AOA of RIS-MS are expressed as: In reality, the BS-RIS's launch angle AOD (i.e., θ) BR Only L BR Similarly, the angle of arrival (AOA) of RIS-MS (i.e., φ) RM Only L RM There are 1, so there are overlapping estimated angles. Theoretically, these overlapping estimated angles are all the same, and these duplicate values ​​can be easily discarded. However, in practice, due to the estimation error, it is difficult to determine which estimated values ​​are theoretically the same. Therefore, we can use the sequence number C = {[c1,...,c...} recorded by the greedy search to find the grid where the estimated values ​​fall. i ], i<=L BR L RM First, sort C, then arrange (θ) in this order. BR ,φ RM The estimated value of ) for adjacent L RM Or L BR The estimated value is considered the same theoretically possible value, and the mean is used instead:

[0112]

[0113]

[0114] This allows for the generation of non-repeating angle parameter estimates. and

[0115] Furthermore, the one-dimensional NOMP algorithm is used to estimate the angle of arrival (AOA) of BS-RIS (i.e., φ). BR The launch angle AOD (i.e., θ) of RIS-MS RM The angle difference between ) The observation matrix is ​​still the received signal, except that the received signal needs to be transposed using its conjugate, i.e.:

[0116]

[0117] Therefore, the received signal can be written as Where Ψ = S H The perceptual matrix Ψ is used for Newton gradient refinement. During the derivative process, the perceptual matrix Ψ can be considered a constant. This is a one-dimensional angle estimation problem, therefore a one-dimensional NOMP algorithm is used to solve it. The steps of the one-dimensional NOMP algorithm are similar to those of the two-dimensional NOMP algorithm, including greedy search, single-step refinement, iterative refinement, and gain update. All parameters are useful and have no duplicate values.

[0118] The one-dimensional NOMP algorithm process is as follows:

[0119] 1) Greedy Search: Constructing a one-dimensional angular sparse domain A rough estimate of a grid point is obtained by maximizing the generalized likelihood ratio test (GLRT) function: in At the same time, a corresponding gain can also be obtained:

[0120] 2) Single-step refinement: Further refinement is performed using the Newton gradient method, and the least squares method is used to minimize the result. To estimate the parameters, which is equivalent to maximizing Then the corrected for: The corresponding first-order partial derivative is: The second-order partial derivative is: The number of refinements in a single loop is R. s ;

[0121] 3) Iterative Refinement: After the single refinement process in the previous step, the estimated parameter set becomes: When refining the k-th objective Treated as a new observation, and then applied to this target. Perform a single refinement step to make corrections and update x. k The total number of iterations is R. c ;

[0122] 4) Gain update: This requires updating the gain based on the new estimated parameter values. These estimates are obtained after single refinement and cyclic refinement, and the corresponding gains are updated using the LS algorithm. in The number of iterations i = i + 1;

[0123] Repeat the process four times until i = L BR L RM Estimate

[0124] After the preceding process, only the channel gain of the RIS millimeter-wave MIMO channel has not yet been estimated. Therefore, the LS method is used to solve for the gain:

[0125]

[0126] Step 4: Utilize the estimated channel parameters Complete the cascaded channel H eff The estimated channel parameters are then substituted into the cascaded channel from step two to obtain the estimated values ​​for the cascaded channel:

[0127]

[0128] The following examples demonstrate the effectiveness of this invention through MATLAB simulation experiments.

[0129] The simulation parameters are set as follows: assuming the element spacing d = λ / 2, N B =16, N M =16, N R =64, L BR =2,L RM =2,θ BR =[20.5 30.5], φ RM = [-40.6 -20.6], θ RM =[40 50], φ BR =[10 20], Path loss of BS-RIS d BR =10m represents the distance between BS and RIS, and the path loss between RIS and MS. d RM =100m represents the distance between RIS and MS. The RIS control matrix is ​​generated by the Discrete Fourier Transform (DFT) codebook.

[0130] Figure 4 The channel parameters (θ) obtained using the method proposed in this invention BR ,φ RM The graph shows the root mean square error (RMSE) between the estimated and true values ​​as a function of signal-to-noise ratio (SNR) and K. Pilot overhead numbers K = 40, K = 60, and the overcomplete atomic library is set to θ. BR ∈[-π / 2,π / 2], search interval is 2°, φ RM ∈[-π / 2,π / 2], search interval is 1°, single-step refinement of R s =5, refine R in a loop c =5, a total of 100 Monte Carlo experiments were conducted. From Figure 4 It can be seen that the RMSE between the estimated value and the true value decreases with SNR. Since (θ) BR ,φ RM The true value of the parameter does not fall on the grid, resulting in low estimation accuracy using traditional OMP-based methods. In contrast, the method used in this invention provides high parameter estimation accuracy. Furthermore, the estimation performance improves as the number of pilot overheads increases.

[0131] Figure 5 The channel parameters are estimated using the method proposed in this invention. Comparison of RMSE with SNR and K between actual values; pilot overhead numbers K=40, K=60, overcomplete atomic library The search interval is 1°, and R is refined in a single step. s =5, refine R in a loop c =5. From Figure 5 It can be seen that, The RMSE between the estimated and true values ​​decreases with increasing SNR. Compared to OMP-based methods, the method used in this invention provides higher parameter estimation accuracy, and its estimation performance improves with increasing pilot overhead.

[0132] Figure 6 This is a comparison chart showing the normalized mean square error (NMSE) of the channel estimated using the method of this invention and other channel estimation methods, versus the actual channel, as a function of SNR. The pilot overhead number K = 60, and the Oracle-LS method with known angles is used as the theoretical lower bound. From... Figure 6 It can be seen that the NMSE of the RIS-assisted millimeter-wave channel estimation method based on NOMP is closer to the theoretical lower bound than that of the OMP-based and LS-based methods. Furthermore, it was found that because the true values ​​of the channel parameters do not fall on the grid, the performance of the OMP method is even worse than that of LS, while the NOMP algorithm based on off-grid parameters of this invention has higher channel parameter estimation accuracy and requires less pilot overhead than the LS method.

[0133] The simulation results show that the proposed method can achieve channel estimation for RIS-assisted millimeter-wave MIMO systems with low pilot overhead, and reduces the impact of grid mismatch in traditional compressed sensing methods, thus greatly improving the accuracy of channel estimation.

Claims

1. A method for channel estimation of a NOMP-based RIS-assisted millimeter wave MIMO system, characterized in that, Includes the following steps: Step 1: Construct the channel model and received signal model of the millimeter-wave multiple-input multiple-output (MIMO) system assisted by a reconfigurable smart reflector (RIS). Step 2: Process the received signal of the mobile station MS within the coherence time to obtain a received signal model with cascaded channel form, and transform the cascaded channel estimation problem into a channel parameter estimation problem. Step three, respectively using two-dimensional Newton orthogonal matching pursuit NOMP algorithm, one-dimensional NOMP algorithm and least square LS algorithm to estimate multiple channel parameters in cascade channel, including: the angle of departure AOD of base station BS-RIS, that is , the angle of arrival AOA of RIS-MS, that is , the product of path gain , the angle difference between arrival and departure of RIS , as follows: (1) Two-dimensional NOMP algorithm estimation The received signal is represented as: ； in, It is The dimensional guiding vector matrix, yes The noise of each block and the matrix formed by it. ,go through In the next iteration, the AOD estimate of BS-RIS is obtained. The estimated AOA values ​​of RIS-MS The emission direction matrix of BS-RIS is represented as follows: , Represents the total number of paths in BS-RIS. Represents the total number of RIS-MS paths; (2) The one-dimensional NOMP algorithm is used to estimate the angle of arrival (AOA) of BS-RIS. AOD of RIS-MS The angle difference between The observation matrix is ​​still the received signal; the received signal is then transposed using its conjugate: ； The received signal is written as: , It is the perceptron matrix, which is used during the Newton gradient refinement process. In the differentiation process, it is treated as a constant. The steps of the one-dimensional NOMP algorithm are consistent with those of the two-dimensional NOMP algorithm, including greedy search, single-step refinement, iterative refinement, and gain update. In the next iteration, the estimate is... ; (3) Estimating channel gain using the least squares method According to the received signal and the previously estimated angle , , Estimate channel gain: ； Each diagonal element is Estimate the parameters ; Step 4: Utilize the estimated channel parameters Complete the cascaded channel The estimate.

2. The channel estimation method for a NOMP-based RIS-assisted millimeter-wave MIMO system according to claim 1, characterized in that, Step one specifically includes: Taking the downlink of a RIS-assisted millimeter-wave MIMO system as an example, channel models for BS-RIS and RIS-MS are constructed respectively. The BS is equipped with One antenna, MS equipped with One antenna, RIS equipped with Each reflecting element can independently control its reflection coefficient. Assuming that the BS, MS, and RIS all use uniform linear arrays (ULAs), the signals transmitted at the BS are narrowband signals, and signal propagation satisfies the far-field condition. The direct channel between the BS and MS is blocked. The classic Saleh-Valenzuela channel model is used to represent the channels between the BS and RIS. and the channel between RIS-MS ,Right now: ； in, This indicates the first BS-RIS The starting angle (AOD) of the path. This indicates the first BS-RIS There is a path to reach angle AOA. This indicates the first BS-RIS The channel gain of each path, and Then the emission direction matrix of BS-RIS is expressed as The receiver direction matrix of BS-RIS is represented as follows: , Represents the total number of paths in BS-RIS. , , Indicates the spacing between array elements. Representing wavelength, similarly It can be represented as: ； in, Representing the first RIS-MS The starting angle (AOD) of the path. Representing the first RIS-MS The angle of arrival (AOA) of the path. Represents the total number of RIS-MS paths. The first RIS-MS The channel gain of each path, then RIS-assisted millimeter-wave MIMO channels satisfy the following channel characteristics: a block fading channel within one channel coherence time. Internally divided into Each block contains [number] blocks. Each time slot, then And satisfy the following structured time-domain protocol: 1) The RIS phase shift vector in the 1st... Each block It is constant within each time slot, but it will change with the block. And change, ;2) Pilot signal exist Repeated on each block, that is, Therefore, the first Each block The total signal received within each time slot can be represented as: ,in , Is The orthogonal pilot signal vector transmitted by the base station at any given time. , It is noise power, and the RIS control matrix can be represented as: ,in and They represent the first The reflection coefficient and phase shift of each antenna, where , 0 and 1 represent the failure and activation of the RIS array element, respectively.

3. The channel estimation method for a NOMP-based RIS-assisted millimeter-wave MIMO system according to claim 2, characterized in that, Step two specifically includes: Each block of The signal received in each time slot is multiplied by the same pilot signal. The pilot signals satisfy orthogonality, that is and each block Vectorizing the signal obtained in the process, we can obtain the received signal within the coherence time as follows: ； in, This represents the processed received signal in each block. express The control matrix of each block of the RIS is processed. The column dimension depends only on the number of blocks. related, This is called the required pilot overhead, and the cascaded channel to be estimated is expressed as... ,in If it is a Khatri-Rao matrix product, then the cascaded channel Expressed using channel parameters: ； in, It is the Kronecker matrix product, for simplification Define a variable satisfy ,but , It is a diagonal matrix with diagonal elements as follows: , , Therefore, the cascaded channel can be simplified to Therefore, the cascaded channel estimation problem can be transformed into channel parameter estimation. Estimation problem.

4. The channel estimation method for a NOMP-based RIS-assisted millimeter-wave MIMO system according to claim 1, characterized in that... The flow of the two-dimensional NOMP algorithm in step three is as follows: 1) Greedy search: Divide the two-dimensional angle into a grid and use the idea of ​​sparse reconstruction to form a set of two-dimensional angles existing at the grid positions. Assuming The parameters were estimated in previous iterations. At the same time, The residual after the next iteration is: ； Among them, the initial residual , A rough estimate of a grid point is obtained by maximizing the generalized likelihood ratio test GLRT function: ； in At the same time, record the sequence number of each column in the discrete grid where the parameter falls. This allows us to obtain a rough estimate of the angle parameters. At the same time, a corresponding gain can also be obtained: ； in ; 2) Single refinement: For the coarse channel parameter estimates obtained from the greedy search, further refinement using the Newton gradient method is needed. When estimating the angle, the objective function is to minimize... This is equivalent to maximizing the following function: ； but and The Newtonian refinement process can be expressed as: ； in, , ; The corresponding first-order partial derivative is: ； ； The corresponding second-order partial derivative is: ,here and Can represent or After refining ( , After that, the gain also needs to be updated. : ； The total number of loops is Second-rate; 3) Iterative refinement: Iterative refinement is a single refinement of each detected parameter across all parameters. This process provides feedback on the local refinement of previously detected parameters, resulting in a more accurate estimate. After the single refinement process in the previous step, the estimated parameter set becomes: When the details are refined When there is a target, Treated as a new observation, and then applied to this target. Make corrections and updates by performing a single, detailed step. The total number of iterations is ; 4) Gain update, based on the new estimated parameter values. These parameter values ​​are the result of single refinement and iterative refinement, and the corresponding gain vector is updated using the least squares method. : ,in , Number of iterations ; Repeat the above four steps of the two-dimensional NOMP algorithm, after... After the iteration, the estimated AOD of BS-RIS and AOA of RIS-MS are expressed as: For repeatedly estimated angles, the sequence number recorded during the greedy search process. Sort according to Arranged in order Estimate the value, then calculate the mean: ； ； This allows for the generation of non-repeating angle parameter estimates. and .

5. The channel estimation method for a NOMP-based RIS-assisted millimeter-wave MIMO system according to claim 1, characterized in that, In step four, the estimated channel parameters are substituted into the cascaded channel from step two to obtain the estimated value of the cascaded channel: 。

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